Pressure Vessel Research Council 02 LA-UR-04-8692.pdf · HMX Cyclotetramethylene-tetranitramine (high-explosive) HSLA High-strength low-alloy HSST Heavy Section Steel Technology program

Pressure Vessel Research Council

Fracture-Safe and Fatigue Design Criteria for Detonation-Induced Pressure Loading in Containment Vessels

Edward A. Rodriguez, LANL Thomas A. Duffey, Consultant

15 June 2004

LA-UR-04-8692

Report Submitted to:

Committee on Dynamic Analysis and Testing

Pressure Vessel Research Council

Pressure Vessel Research Council LA-UR-04-8692

Los Alamos National Laboratory ii

EXECUTIVE SUMMARY

The DynEx Project at Los Alamos National Laboratory (LANL) has the overall responsibility for design, analysis, manufacture, and implementation of new high-strength low-alloy (HSLA) steel spherical vessels to confine explosion products and debris from detonations of high-explosive assembly experiments. The high yield and ultimate strength material, HSLA-100, was chosen for the next generation vessel designs because of its superior strength, high ductility, high fracture toughness capacity, and design for avoidance of the requirement of post-weld heat treatment. In comparison with the past generation A516 and A537 carbon steel spherical vessels, HSLA-100 greatly exceeds their strength and fracture toughness. This report provides the technical basis and justification for a fracture-safe and fatigue crack-growth adequacy design of HSLA-100 steel containment vessels. Although this report specifically addresses the LANL containment vessel design, the methodology and criteria applied herein may be extended to other vessel geometries (i.e., cylinders, ellipsoidal or torispherical shells, cones, etc) and more complex vessel systems (i.e., cylinder-to-cylinder intersections, etc). Lastly, because the explosion products and debris from these experiments produce hazardous materials, the criteria described in this paper are for a single-use application of a high-explosive (HE) detonation-induced loading event. The reconstitution of these vessels for further use, i.e., multiple HE events, becomes prohibitive from a financial standpoint. As such, the containment design must incorporate full advantage of the material’s ductility and fracture toughness. The technical approach utilized herein is that of Fracture Safe Design, which was developed by the Naval Research Laboratory in the 1970’s and is based upon the Dynamic Tear Test Energy (DTTE), an ASTM-approved procedure (ASTM E 604). This work was published as WRC Bulletin 186. However, the Fracture Safe Design approach is further supplemented by other data (i.e., Charpy, J-R) and advanced fracture mechanics procedures presented in the Appendices. Issues arose during investigation of fracture analysis of flaws for impulsively-driven structural response of structures. Although there is a wealth of information available for elastic, elastic-plastic, and fully plastic stress intensity factor solutions for statically pressurized systems, there is virtually no information on impulsively loaded structures, nor available guidance on treatment of these loads in a fracture assessment. Furthermore, stress intensity factor solutions for pressurized (i.e., load-controlled) systems are based on the predominance of a “primary” stress coupled with knowledge of the limit load of the flawed structure. For impulsive events, such as the LANL vessel response, primary stresses are developed from the quasi-static residual gas pressure resulting from the HE detonation gas product expansion/collapse phase, and are shown to be relatively quite low. Predominant vessel response is higher-order, localized, through-thickness bending, which is a deformation-


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controlled phenomenon. These stresses are, in effect, secondary stresses and must be treated as such. It is therefore deemed inappropriate to use the existing broad classes of stress intensity factor solutions, which are load-controlled, for impulse-driven structural response, where the solution scheme revolves around determining a load-controlled limit-load of the structure, or, of a flawed structure. Thus, the only currently available alternative is to perform a high-fidelity 3D finite element analysis (FEA) of the structure containing a flaw and resolve the dynamic state-of-stress with an explicit FEA code. At specific time intervals during the dynamic analysis, and where high stress/strain occurs at or near the flaw location, the dynamic analysis would be terminated and the resulting stress/strain history saved. A subsequent J-integral analysis, solved with an implicit FEA code, would then be required, including embedding the initial dynamic state-of-stress from the explicit solution as an initial condition. The resulting J-integral solution would only be representative of that specific time during the dynamic transient. If there are several potential time-points during the dynamic transient where high strains occur in the flaw region, these would require evaluation on a case by case basis. It should be noted that this type of effort, while resulting in a best-possible technical solution, would in the end be quite time consuming, and in some cases, financially prohibitive. This would be especially true for complex structures undergoing single or multiple impact or impulse events. As such, the authors recommend an assessment be initiated to address the feasibility of developing future fracture-prevention design guidance for impact and/or impulsively-driven structural response of flawed structures. This (future) design guidance is viewed in the same vein as that embodied in API-579. The assessment would entail a MPC/PVRC sponsorship of (1) a critical review of existing methods for impact or impulse-controlled fracture-prevention design, (2) whether current methods such as those employed in API-579 for static loading are applicable, with some modification, for impulse loadings, (3) development of a simplified theoretical treatment for flaw evaluation in the impulsive regime, and (4) performance of several detailed 3D FEA analyses in an impulse-regime for comparison with theory and to assist in developing future guidance.


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ACRONYMS AND SYMBOLS

AWS American Welding Society ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials B&PVC Boiler and Pressure Vessel Code (ASME) CAT Crack-arrest Temperature CVP Containment Vessel Program CVN Charpy V-Notch impact energy, (ft-lb) DACS Dual-Axis Confinement System DARHT Dual-Axis Radiographic Hydrodynamic Test Facility DOE Department of Energy DNFSB Defense Nuclear Facilities Safety Board DTTE Dynamic Tear Test Energy, (ft-lb) DTRC David Taylor Research Center EPFM Elastic-Plastic Fracture Mechanics FAD Fracture Analysis Diagram and Failure Assessment Diagram FTE Fracture-Transition-Elastic; Highest possible temperature for unstable

fracture propagation through elastic stress field FTP Fracture-Transition-Plastic; Temperature where fully ductile tearing occurs. GY General yield criterion; upper-shelf behavior. HAZ Heat-Affected Zone HE High-explosive HMX Cyclotetramethylene-tetranitramine (high-explosive) HSLA High-strength low-alloy HSST Heavy Section Steel Technology program ID Inside diameter L Lower limit of elastic-plastic region in DTTE curve LBB Leak-Before-Break criterion LEFM Linear-Elastic Fracture Mechanics LLNL Lawrence Livermore National Laboratory LST Lowest Service Temperature MINS Mare Island Naval Shipyard MOT Minimum Operating Temperature NDE Non-Destructive Examination NDT Nil-Ductility Transition NRC Nuclear Regulatory Commission NRL Naval Research Laboratory NSWCC Naval Surface Warfare Center - Carderock ORNL Oak Ridge National Laboratory PBX Plastic-bonded explosive PCCV Pre-cracked Charpy V-Notch impact energy, (ft-lb)


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PHERMEX Pulsed High-Energy Radiographic Machine Emitting X-rays PWHT Post-weld heat treatment SCF Stress concentration factor SIF Stress intensity factor SNL Sandia National Laboratories TNT 2,4,6 trinitrotoluene (high-explosive) UT Ultrasonic Testing YC Yield criterion, upper-limit of elastic-plastic region in DTTE curve Mathematical and Greek Symbols a Half-crack length, (in) a Major axis of ellipse, (in)

crita Critical crack size, (in) a2 Crack-length, (in)

b Minor axis of ellipse B Specimen thickness, (in) c2 Width of flaw, (in) iD Inner diameter, (in)

oD Outer diameter, (in) E Modulus of elasticity, (psi)

1h Influence function for J-integral

IcJ Critical elastic-plastic J-Integral crack driving force, (in-lb/in2)

IdJ Dynamic elastic-plastic J-integral crack driving force, (in-lb/in2)

elJ Elastic crack driving force J-integral, (in-lb/in2)

plJ Fully plastic crack driving force J-integral, (in-lb/in2)

TotJ Total crack driving force, (in-lb/in2)

IcK Plane-strain fracture toughness, (ksi-in1/2)

IdK Plane-strain fracture toughness under dynamic conditions, (ksi-in1/2)

IRK Reference plane-strain fracture toughness curve (ASME designation)

TK Stress concentration factor

oK Power-law coefficient K∆ Stress intensity factor range, (ksi-in1/2)

m Number of vessel tests performed m Ramberg-Osgood strain hardening exponent N Number of vessel vibration cycles n Power-law strain hardening exponent n Paris-Law exponent P Load

oP Limit load


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T Temperature, (oF, oC, or K) tT , Plate thickness, (in)

meltT Melt temperature (Johnson-Cook model)

refT Reference temperature (Johnson-Cook model)

shiftT∆ Shift in temperature from static to dynamic loading

NDTRT Referenced temperature to the nil-ductility transition temperature W Plate thickness α Ramberg-Osgood coefficient β Irwin factor for plane-stress determination δ Logarithmic decrement σ Nominal stress, (ksi)

yσ Yield strength, (ksi)

ysσ Static yield strength, (ksi)

ydσ Dynamic yield strength, (ksi)

yoσ Yield stress (@0.2% offset), (ksi)

oσ Power-law coefficient σ∆ Stress range, (ksi)

oε Yield strain (0.2%)

pε Plastic strain φ Reduction factor for contained plasticity Φ Factor for secondary stress intensity factor ν Poisson’s ratio


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TABLE OF CONTENTS Page No. EXECUTIVE SUMMARY ii ACRONYMS AND SYMBOLS iv

ABSTRACT 1

1.0 INTRODUCTION 2

2.0 HISTORY OF VESSEL DESIGN AT LANL 7

3.0 FRACTURE SAFE DESIGN CRITERIA 9

3.1 Underlying philosophy 3.2 Steps in Establishing Vessel MOT 3.3 Development of MOT for HSLA-100 Vessels 3.4 Summary of MOT Results

4.0 DETONATION-INDUCED LOADS 22

4.1 Dynamic Pressure Loading 4.2 Structural Response 4.3 Stress Classification

5.0 CRITICAL CRACK SIZE 29

5.1 Elastic-Plastic Fracture Mechanics 5.2 Nozzle Forging 5.3 Vessel Shell 5.4 Welds and HAZ

6.0 FATIGUE CRACK PROPAGATION 35

7.0 ASME CODE GUIDELINES FOR NON-DUCTILE FAILURE 48

8.0 CONCLUSIONS 51

9.0 RECOMMENDATIONS 52

ACKNOWLEDGEMENTS 53 REFERENCES 54


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TABLE OF CONTENTS (CONT’D)

APPENDICES Page No. A. David Taylor Research Center Data for HSLA-100 60

A.1 Mechanical Properties A.2 Impact and Fracture Properties A.3 NDT Test Results

B. LANL HSLA-100 Material Certification 71

B.1 Mechanical Properties B.2 Impact and Fracture Properties

C. Pressure Vessel Steel Comparison 77

C.1 Chemistry C.2 Mechanical Properties Comparison C.3 Impact and Fracture Properties C.4 ASME Code Comparison

D. Welds and Welding 84

D.1 Weld Development for Production welds D.2 “As-Built” Vessel Weld Mechanical Properties D.3 “As-Built” Impact and Fracture Properties D.4 Dynamic Fracture Toughness of Under-matched Welds D.5 Post-Weld Heat Treatment D.6 Residual Weld Stresses

E. IcK Correlation with CVN 96

E.1 Upper-Shelf Correlation E.2 Transition Temperature Correlation

F. Critical Flaw Sizes 100

F.1 Vessel Shell F.2 Nozzle Forging F.3 Welds/HAZ


Los Alamos National Laboratory 1

Fracture-Safe and Fatigue Design Criteria for Detonation-Induced Pressure Loading in Containment Vessels

Edward A. Rodriguez and Thomas A. Duffey

15 June 2004

ABSTRACT The DynEx Project at Los Alamos National Laboratory (LANL) has the overall responsibility for design, analysis, manufacture, and implementation of new high-strength low-alloy (HSLA) steel spherical vessels to confine explosion products and debris from detonations of high-explosives (HE) experiments. Over the past 30 years, LANL, under the auspices of the US Department of Energy (DOE), National Nuclear Security Administration (NNSA), has been conducting confined HE experiments utilizing large, spherical, steel pressure vessels. Design of these spherical vessels was originally accomplished by maintaining that the vessel’s kinetic energy, developed from the detonation impulse loading, be equilibrated by the elastic strain energy inherent in the vessel. Past designs have utilized common pressure vessel steels used in the commercial nuclear industry. Current designs have evolved to utilizing high-strength low-alloy (HSLA) steels commonly used by the US Navy in surface vessel and submarine applications. This document provides the technical basis for the fracture prevention and fatigue adequacy design criteria used for the DynEx Project containment vessels, information on HSLA-100 material test data performed at David Taylor Research Center (DTRC) and LANL, and detailed calculations leading to the critical flaw sizes above which brittle fracture is postulated. Although this report specifically addresses the LANL containment vessel, the methodology and criteria applied herein may be extended to other vessel geometries (i.e., cylinders, ellipsoidal or torispherical shells, cones, etc.) and more complex vessel systems (i.e., cylinder-to-cylinder intersections, etc) subjected to high-explosive (i.e., impulsive) loading.



1.0 INTRODUCTION For the past 30 years, Los Alamos National Laboratory (LANL) has been conducting confined experiments involving detonation of high explosives (HE) in support of its experimental programs. The spherical containment vessels have been constructed from medium-strength steels with nominally 1-in. and, later in the 1970s, 2-inch wall thickness. Current designs, which are based upon US Navy approved design and material testing experience, implement high-strength low-alloy (HSLA) steel with a nominally 2-in. wall thickness. The HSLA-100 material is extensively used by the US Navy for aircraft carrier decking and armor plating, and other military vessels. The material has been proposed for nuclear submarine hulls but has not yet been implemented. Importantly, the manufacture of HSLA-100 containment vessels represents a major step forward in ensuring safety through use of higher strength, greater ductility, and higher fracture toughness material. Another attractive feature is that significant weld preheat and post-weld heat treatment (PWHT) are not required. For the past several decades, the Containment Vessel Program (CVP) design for spherical vessels has included several types of pressure vessel steels commonly used in the commercial nuclear industry, namely, A516 and A537 carbon steels. While these steels have proven adequate for the containment of explosion products, the need was identified for higher-strength materials with higher fracture toughness at lower temperatures, allowing for lower minimum operating temperature (MOT). The technical approach utilized herein is that of Fracture Safe Design, which was developed by the Naval Research Laboratory in the 1970’s and published extensively in seven WRC Bulletins including Bulletin 186 [1], which is the basis upon the Dynamic Tear Test Energy (DTTE), an ASTM-approved procedure (ASTM E 604) [2]. This procedure is the preferred approach for the US Navy Laboratories in testing and designing for submarine hulls and other combatant applications. Although this approach is used as a primary basis for containment vessel design for high-explosive loading, it is supplemented by conventional test methods (i.e., Charpy V-Notch, IcK , J-R curve, etc.) coupled with current analytical and numerical methods for failure prevention. Emphasis herein is the technical basis for assurance that HSLA-100 steel containment vessels adhere to a Fracture Safe Design. Fracture Safe Design is a technical design and analysis philosophy for component or vessel design that incorporates full knowledge of the actual material characteristics, including mechanical and impact properties, fracture resistance or fracture toughness, and transition temperature conditions. Fracture Safe Design applies these data to maintain the operation of the vessel in a temperature regime away from a brittle state. Specifically, this report focuses on information concerning the avoidance of catastrophic fracture, and the assurance of operation well above the brittle-to-ductile transition by specification of the MOT required for assuring a safe design.



This report details the following technical aspects of LANL’s approach to assure containment vessel structural integrity from a Fracture Safe Design perspective:

• Historical perspective for LANL vessel design; and • LANL containment vessel design criteria for avoidance of brittle fracture.

While the Fracture Safe Design principles are outlined and applied in the body of this report, the bulk of technical information and design for brittle fracture avoidance is contained in Section 5 of this report and in Appendix E and F. The appendices reflect the body of knowledge relative to fracture properties of HSLA-100, fracture mechanics analysis for determination of critical flaw sizes, and a comparison between HSLA-100 and other pressure vessel steels used in the past for the CVP. The topics addressed in the appendices are

• David Taylor Research Center’s (DTRC ) HSLA-100 material certification, • LANL’s HSLA-100 vessel material certification, • Comparison of typical pressure vessel steels, • Weld toughness and welding, • IcK correlation with Charpy V-Notch (CVN), and • Critical flaw size evaluation.

These topics taken collectively constitute the basis for LANL’s approach for a fracture safe design in assuring structural integrity of HSLA-100 containment vessels. Design Criteria The design of the HSLA-100 containment vessels follows guidance provided in the LANL DynEx Vessel Construction Standard [3]. That document provides the framework for activities associated with design, fabrication, manufacturing, inspection, and Vessel Qualification of Safety Class vessels, that will ultimately assure the vessels meet the requirements of operational safety. Three potential failure modes have been identified with HE detonation-induced impulsive loading of HSLA-100 vessels: (1) ductile failure, (2) brittle fracture, and (3) fatigue failure. These vessels, however, are designed primarily as single-use vessels. The design methodology must, of course, be consistent with operational intent. Multiple-use pressure vessels must have different design criteria than single-use vessels. The multiple-use pressure vessels must, in effect, be designed with similar rules as those in Section III or VIII of the ASME Boiler & Pressure Vessel Code, hereafter referred to as the ASME Code. That is, it becomes imperative to the designer to maintain a purely elastic membrane response of the structural system. On the other hand, Environment, Safety, and Health (ESH) issues, such as waste-stream isolation, and clean-up costs associated with HE detonations within vessels, may be prohibitively expensive because of hazardous materials present in the waste stream. In this scenario, the pressure vessel design is driven to a “single-use” mode, dictating that a more cost-effective design be developed.



The designer must start with a rational ductile failure design criterion that utilizes the plastic reserve capacity of the material in providing structural margin, then progresses to a fatigue and fracture criteria that enhances the single-use mode. Ductile Failure - LANL has established a criterion for vessel design for impulsive HE-detonation loading, which requires no through-thickness yielding anywhere in the vessel. Through-thickness membrane stresses are maintained at, or below, the yield strength of the vessel material, including within the regions of high-strain concentrations such as the shell-to-nozzle discontinuity. A ductile failure limit, based on the material’s strain-hardening exponent parameter, is stipulated at the onset of instability (i.e., necking in a uni-axial specimen), not the true strain at failure. A description of ductile failure design criteria has been developed for containment vessel design by Duffey et al. [4,5]. Catastrophic Failure - To prevent brittle fracture of the containment vessel, LANL requires that Dynamic Tear Test Energy (DTTE) for representative vessel material be at least 750 ft-lb at a temperature of -60°F. This limit was specified for the thickest plate expected (i.e., ~4-in. thick). The DTTE methodology was developed by the Naval Research Laboratory (NRL) for prevention of non-ductile fracture for US Navy submarine hull and surface vessel applications [6-10]. The DTTE criterion assures crack arrest within the material from a postulated through-thickness flaw of length equal to twice the wall thickness. This is considered in the fracture safe design methodology, as a leak-before-break (LBB) criterion. This methodology is conservative and consistent with that recommended in the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (B&PVC), Section III [11] for assuring fracture toughness of pressure vessel steel. A comparison of DTTE and ASME Code rules is provided in this report. The limiting component, from a fracture toughness perspective, is used to obtain the MOT for the containment vessel. The focus of this report is on the criteria for prevention of brittle fracture and fatigue. Fatigue – For single-use vessels under detonation loading, classical fatigue failure will not be a predominant failure mode. However, fatigue crack growth resulting from vibrational cycles, during the vessel response to the detonation-induced loading, could potentially cause some stable crack growth. The high-explosive (HE) event will induce vibrations in the structurally-damped vessel of the order of 100 cycles. Section 6 of this report provides the necessary information for vessel design to prevent fatigue crack growth failures. Although the primary emphasis of this report is on single-use vessels, fatigue crack-growth methodologies are developed in Section 6 for instances in which multiple testing is suitable.



Dynamic Impulsive Loading Containment vessels are subjected to dynamic, high-impulse, and short-lived pressure pulse loads. Much analytical work has recently been performed [12-14] for HSLA-100 containment vessel design, and is a topic of a current WRC Bulletin [4]. Peak stresses have been shown to be highly localized and manifest in the shell from predominantly higher-order bending modes, which occur during the “ringing” after the initial blast loading. The maximum principal stress tensor anywhere in the vessel changes direction and location with time throughout the transient. Section 4 of this report provides a synopsis of dynamic-impulsive loading and stress calssification. Vessel Description Although this report focuses on the LANL designed spherical containment vessels, the same principles may be applied to other vessel geometries, or more complex vessel systems. The HSLA-100 steel vessel design for the single-axis vessels incorporates three nozzle ports as shown in Figure 1.1. Inside diameter (ID) is nominally 6 ft, with 2-in. nominal wall thickness. There are two diametrically opposed 16-in. diameter nozzles and one 22-in. diameter nozzle. Due to fabrication constraints, the vessel wall thickness exceeds 2 in. with a maximum of ~2.5 in. in some regions. Figure 1.2 shows the next generation design dual-axis containment systems incorporating two radiographic entry ports and two exit ports.

Figure 1.1 –Single-axis containment and safety vessels.



Figure 1.2 – Dual-Axis containment and safety vessels.



2.0 HISTORY OF LANL VESSEL DESIGN The following is a historical perspective of the CVP at LANL starting in 1966 and extending until early 2000. Much of the history resides in separate LANL documents, although a synopsis is contained in one LANL memorandum [15]. Table 2.1 provides a brief view of containment vessel design development.

Table 2.1 - Historical Timeline for LANL CVP [15] Date Milestone or Program

Action Plan Particular Issues or Highlights

1966 Conceptual idea - Doug Venable

• All HE energy is required to be stored elastically in vessel shell

1966 Instrumented old LASL vessel and tested

• Decision made to proceed with new concept

1966 New vessels designed and fabricated

• A516-70, 3-ft ID by 1-in. wall • Designed for 6-lb TNT equivalent based

on onset of plastic deformation • CVN considerations

1966 Tests on new vessels started

• Discovered that PWHT degraded performance by ~12% at hydrotest stage

1969 Larger vessel designed and fabricated

• A516-70 6-ft ID by 1-in. wall • 25-lb TNT equivalent rating

1969 12’ I.D. safety vessel designed and fabricated

• Hold gasses in event of leak only

1971 DOE/ALO safety study on containment operations at PHERMEX

• SNL-A critique of LANL operations and design leads to LANL contracting NRL consultations (Pellini, Puzak, Lange)

1971 FAD (Fracture Analysis Diagram)

• Fracture safe design • Controversy on PWHT

1973 New design and fabrication

• 6-ft ID by 1-in. wall thickness • A 537 class 2 shell • A 537 – LF2 nozzle forgings • ~25-lb TNT equivalent rating (i.e.,

capable of 40 lb at increased yield strength)

1973 Computer modeling of vessel response

• Numerical FEA model of vessel response showed vibrational modes not previously understood.

1975 Containment vessel “cookbook” published

• State-of-the-art at LANL • NRL Fracture Assessment Diagrams

(FAD) based analysis • crack-arrest temperature (CAT) curve

utilized for “unconditional crack arrest” • DTTE utilized



Table 2.1 - Historical Timeline for LANL CVP [15] (cont.) Date Milestone or Program

Action Plan Particular Issues or Highlights

1977 &

1978

New containment vessel designed

• 6-ft ID by 2-in. wall thickness to lower response frequency

• New nozzle material • American Society for Testing and

Materials (ASTM) A707-L5, Class 4 forging for increased yield strength

1978 Study of safety vessel ability to contain all HE products after worst case failure of inner vessel

• Bounding safety case scenario of containment vessel failure.

• Secondary containment approved for design.

1977 &

1978

Same HE limit with no credit for increased wall thickness

• Incorporated “Assured Crack Arrest” for LBB flaw design.

1979 &

1980

30 new containment vessels fabricated

• Later testing revealed that PWHT significantly lowered toughness. New MOT increased to +90 °F

1979 NRL consultants hired to make new material recommendations

• NRL recommended HY-80 and ASTM-A710, which later became HSLA-100.

1980 New vessel certification proposal adopted

• Assured crack arrest criterion used for a LBB flaw.

1985 Review paper on charge rating system utilized

• Approved

1988 Review paper on shock-wave mitigation activities at LANL

• Approved by DOE

1989 Review paper on fracture safe design used at LANL

• Approved by LANL and DOE

1990 HSLA-100 recommended for DARHT vessels

• LANL uses at the Nevada Test Site (NTS) for down-hole experiments

• Low MOT • Ease of welding (i.e., no PWHT) • Low, or no, preheat

1991 Decision to develop 2- 6-ft ID by 2-in. wall HSLA-100 vessels for containment program

• 22-in. ID nozzle (north pole) • 16-in. ID nozzles (equator) • Vessels #6-2-3-1 and #6-2-3-2



Table 2.1 - Historical Timeline for LANL CVP [15] (cont.)

Date Milestone or Program Action Plan

Particular Issues or Highlights

1992 Parts/materials ordered • Lukens Steel 1994 HSLA-100 vessel

fabrication begun • Ranor Corporation

1999 Test series on HSLA-100 vessel

• Four tests conducted in single-axis vessel #6-2-3-1.

2000 Pressure Vessel Research Council

• LANL began interactions with PVRC for potential ASME Code Case or Code modification adoption.

2001 ASME Executive Committee

• LANL approached ASME with request for Code adoption of detonation-induced pressure vessel design criteria.

2002 IdJ Testing or J-R Curve

determination • LANL pursuing high strain-rate J-R

curve assessment of HSLA-100 plate, forging, and weld metal.

2002 Dual-Axis Containment Vessel Design

• New vessel design to DTTE and J-R curve data.

3.0 FRACTURE-SAFE DESIGN CRITERIA This section describes and applies the Fracture Safe Design philosophy for the DynEx Project vessel design. This philosophy was developed by NRL [1,6-10] and used extensively and successfully [6] for US Navy applications involving design of submarine hull and armor plate decking for aircraft carriers. The Fracture Safe Design criterion has been adopted by DynEx Project in assuring that a flaw will arrest, given the material minimum operating temperature (MOT) is within the appropriate elastic-plastic range of the toughness curve. This design methodology has been used on a qualitative basis for the design of containment vessels at LANL since 1981. Note that ductile tearing initiation for the nominal vessel design is investigated by Duffey et al. [4]. LANL has implemented this criterion in the design of containment vessels and draws upon much of the earlier work on material properties testing of HSLA-100 for US Navy applications. These data are contained in several reports from DTRC [16-19] and detailed in Appendix A of this report. The DTRC documentation provides the material qualification of HSLA-100 for use in shipboard applications. The DTRC work culminated in the development of a Military Standard, MIL-S-24645A [20]. The development of the HSLA-100 military specification was based upon the HY-100 steel specification [21], which is also used extensively in US Navy applications. The LANL “as-built” mechanical and toughness properties, and evaluation for HSLA-100 single-axis vessels, are contained in Appendix B.



Appendix C of this report provides a comparison of pressure vessel steels commonly used in industry, and also used in past LANL containment tests, with HSLA-100. Appendix D provides “as-built” mechanical and toughness property documentation for the LANL vessel’s weld and heat-affected zone (HAZ), drawing from the US Navy laboratory archival information including J-R curve data. Appendix E provides the fracture mechanics plane-strain fracture toughness ( IcK ) correlation with CVN, for comparison with DTRC values. Lastly, although LANL incorporates the Fracture Safe Design methodology, supplemental design work is accomplished with classical fracture mechanics solutions using both linear elastic fracture mechanics (LEFM) [22-24] and elastic-plastic fracture mechanics (EPFM) [22-24]. Furthermore, analytical procedures contained in API 579 [25] are used where appropriate. Procedures for assessing critical flaw sizes are presented in Section 5 of this report with analytical results contained in Appendix F. 3.1 Underlying Philosophy The DTTE requirement for assured fracture arrest of a design flaw, i.e., the through thickness LBB crack, is a function of the stress, material thickness, and material temperature. The determination of the temperature, at which the required DTTE is achieved, is made for all components of the as-built vessels, including the weld HAZ. The component having the highest value of MOT is the limiting component, which sets the overall vessel system MOT. Sections 3.1 through 3.4 describe implementation. An essential ingredient to the Fracture Safe Design philosophy is the DTTE approach. The method was developed by NRL in the early 1970s in response to development of other fracture test methods, and as a result of structural failures in equipment that supposedly had “adequate” upper-shelf Charpy V-Notch (CVN) energies. The shortcomings of the CVN test were recognized to be the following:

• Notch does not represent a true sharp flaw, • Specimen is too thin (i.e., 0.394-in. by 0.394-in.), • Plane stress effect is predominant, and • No temperature shift applied for thicker parts.

NRL subsequently instituted a criterion to provide a lower limit to fracture energy values, above which the material would arrest a crack. NRL recommended a DTTE of 450 ft-lb at -40°F as being the required toughness to maintain crack arrest for all US Navy ship plate above 5/8-in. thickness. The Fracture Safe Design philosophy was applied to LANL vessels under the guidance of Lange from NRL [26]. The philosophy is documented in detail by Neal [27]. The following description of the procedure for containment vessels is primarily summarized from the work by Neal.



The underlying principle is that vessel use is restricted to a temperature regime that ensures all materials are sufficiently ductile so any cracks will arrest. A key factor is that unlike standard engineering structures that might in the worst case be stressed to only 0.4 of the yield strength, these vessels may operate at stresses on the order of the yield strength, depending upon the quantity of high-explosive charge to be contained. In the following, the philosophy and basic steps for determining an appropriate MOT are described for the different vessel components and the relative operating (HE charge) level.

The approach to safe operation of a vessel is based on a leak-before-break (LBB) concept. The LBB concept is key to the design process because leaking gases can be easily held in a surrounding container in the unlikely event of a leak in the containment vessel. If, however, the inner vessel were to completely fracture in a brittle manner then the resulting vessel fragments would be accelerated by the high pressure of the explosive products and would be difficult to stop by the surrounding vessel. Therefore, if the vessel begins to tear it is important that the material be sufficiently ductile to stop propagation of a crack. A criterion for arresting tears negates the need for exhaustive vessel inspection for most minor starting cracks. The essence of such a criterion is based on the dynamic tear test, whose use has been described extensively with regard to fracture safe design [1,6-10]. The standard size dynamic tear specimen is 5/8-inch thick. It is possible to test specimens of the same thickness as the actual structural members, but because such tests are expensive and because it has been possible to relate the results for thicker sections to the results for the standard 5/8-inch specimens, the larger tests are not commonly done. Consequently, when considering the use of thicker sections, a temperature correction must be added to properly establish the MOT of the vessel. It has been shown that the different regimes of fracture can be identified by reference to a parameter β given by [6] BK YDID /)/( 2σβ = (3.1) where =B Specimen thickness, and

=ydIdK σ/ Ratio of the dynamic stress-intensity factor to the dynamic yield stress.

This relationship is plotted in Figure 3.1. The “beta” factor is based upon Irwin’s [22-24,28-31] theory for plane-stress behavior, such that crack arrest is assured. The appearance of ydIdK σ/ as a parameter suggests that in order to maintain a given level of structural performance, fracture resistance must be increased as yield strength increases [32]. As stated by Pellini and Loss [33], ydIdK σ/ is a measure of the amount of plasticity that must develop in the proximity of a flaw for fracture to occur.



Referring to Fig. 3.1, the value of 4.0=β corresponds to the “plane-strain limit” (L). This is basically the point in the dynamic tear test regime where the break first begins to exhibit some ductility (if the material is 5/8 in. thick, 4.0=β corresponds to the toughness at the NDT Temperature). The next reference point is 9.0=β , which corresponds to the “yield criterion” (YC). This point is also referred to as the Fracture-Transition-Elastic (FTE) temperature. Pellini and Loss have calibrated this location, which translates to a common ASME guideline, FTE = NDT + 60o [33]. It occurs at one-half the energy of the upper shelf in a 5/8 in. DT Curve. At this point approximately half the break in the dynamic test is associated with tearing in a ductile manner. This is the value at which the criterion for typical structural design is usually set, where conventional engineering practice limits stresses to less than yσ4.0 . Under the YC criterion a flaw in a tensile-loaded member at half the yield stress can grow until it penetrates the section before it becomes critical, i.e., the condition of “leak-before-break” at yσ5.0 . Finally, beyond the value of 6.1=β defines the region of “general yield” (GY), or commonly termed the fracture-transition-plastic (FTP). This GY condition, which specifies leak-before-break in the plastic regime (i.e., at yσ0.1 ) is of special interest here with regard to maximum-size charges in vessels. For this condition, leak-before-break is assured at all elastic stress levels. The fracture-transition-plastic (FTP) temperature is located mid-way between the FTE and the upper-shelf. Pellini and Loss[33] have calibrated this location as FTP = NDT + 120o, which represents attainment of fully plastic fracture.

0

0.4

0.8

1.2

1.6

2

0 0.5 1 1.5 2 2.5 3

Elastic-Plastic Region for Assured Crack Arrest

B=1.0B=2.0B=3.0B=4.0

Toughness-Yield Ratio

β Leak-Before-Break@ 0.5 Sy

Leak-Before-Break@ 1.0 Sy

Elastic-Plastic

Figure 3.1 - Beta factor for assured crack arrest [26].



0

0.4

0.8

1.2

1.6

2

0 0.6 1.2 1.8 2.4 3

B=2.5B=5.0

Toughness-Yield Ratio

Elastic-Plastic Region for Assured Crack Arrest

β



Figure 3.2 - Beta factor for assured crack arrest for 2.5 and 5.0 inch thick sections. [26].

To apply the criterion for crack arrest, it is necessary to first fix the appropriate value for β . For the range in vessel sizes considered in this report and for response in the elastic range, it has been shown that the stress and strain are directly proportional to the high-explosive charge mass [27]. The maximum membrane stress that can be expected in the shell can be written σ = m(σ y /my ) (3.2) where m is the size of the actual charge, and ym is the size of the maximum design charge for the vessel, corresponding to a maximum stress at the yield stress, yσ . The value of β can be linearly extrapolated between the YC criterion and the GY criterion according to β = 0.9 ymm 4.0< (3.3) β = (0.26 + 0.7m /my )/0.6 yy mmm <<4.0



The use of the above relationship allows the criterion for the shell to be tailored to the actual mass of the charge. For vessels driven to the yield stress, i.e., ymm = , the above criteria assure operation at the GY condition, 6.1=β , corresponding to leak before break under the condition of general yield. For vessels driven to stress levels typically experienced by conventional structures, however, i.e., ymm 4.0< , then a corresponding value of 9.0=β would be used. Nozzle forgings are normal structural members that are generally designed to be much thicker than the shell. In the dynamic case, nozzles are not subjected to the magnitude of strain seen in shell material, and therefore are limited to stresses below yσ5.0 . Nozzles are thus assumed to operate at the YC level, i.e., 9.0=β . The component with the highest minimum operating temperature, be it shell, weld, heat-affected zone (HAZ), or nozzle, governs the minimum operating temperature for the vessel. Equation (3.3) accounts for the fact that the toughness requirements for a high-explosive containment vessel that must be capable of undergoing plastic deformation or high elastic stresses are more severe than for conventionally loaded structures subjected to elastic stresses at but a fraction of yield [32]. 3.2 Steps in Establishing Vessel MOT Step 1: Choose the appropriate value of the parameter β for the component of interest (i.e., shell, nozzle, weld), using guidance given above. Step 2: Determine the maximum thickness, B , of the structural section being considered. Step 3: Determine the appropriate value of the ratio ydIdK σ/ from Eqn. (3.1),

BK

Yd

Id βσ

= (3.4)

The above ratio governs the crack-propagation situation for dynamic loads. For clarity, the relationship between β , B , and ydIdK σ/ is plotted in Figure 3.1 for a range of thicknesses from 1-inch to 4-inch, and Figure 3.2 for two thicknesses corresponding to vessel shell and nozzle. Step 4: Refer to Figure 3.3. Through a series of measurements on various steels with static yield strengths of 40–100 ksi, it has been determined that the dynamic yield strength, corresponding to the strain-rates in a dynamic tear test, may reach 30 ksi higher than the static one [4,34] for certain materials. For quenched and tempered steels, this dynamic yield strength increase could be 5-15 ksi.



Figure 3.3 - Required DTTE as a function of dynamic yield strength [26,27]. The dynamic yield strength is shown on the lower abscissa of the figure. The choice of the ratio ydIdK σ/ and dynamic yield strength determines the equivalent 5/8-inch dynamic tear energy required to satisfy the crack-arrest criterion. The energy required is determined from Figure 3.3. Goode, Huber, and Judy [35], and Judy, Goode, and Freed [36] have provided correlations of IcK with DT for titanium [35] and aluminum [36] plus a number of shipbuilding steels, including A533 pressure vessel steel. Judy, et al. [36], however, determined that DTKIc − correlation is not linear over its entire range, especially in the lower values of IcK . Yet, over the range of interest, the correlations are linear.



Figure 3.4 is a parametric format representation, similar to Figure 3.3, for dynamic yield strength as a function of dynamic tear energy. The figure depicts a wider range of fracture toughness-to-dynamic yield strength ratios. Figure 3.4 curves were analytically derived from Figure 3.3 data using simple power-law representations, with an extension of the upper-bound DTTE to 1000 ft-lb. This derivation was accomplished as a design aid because Figure 3.3 does not extend to higher DTTE values exhibited by HSLA-100, namely 750 ft-lb and above.

50

100

150

200 300 400 500 600 700 800 900 1000

Dynamic Yield Strength as a Function of Dynamic Tear Energy

1.41.61.82.02.22.42.6

Dyn

amic

Yie

ld S

tren

gth,

(ks

i)

Dynamic Tear Energy, (ft-lb)

1.4 1.61.8 2.0 2.2 2.4

2.6

Figure 3.4 - Required DTTE as a function of dynamic yield strength. Step 5: The next item needed is the curve for 5/8-inch tear energy as a function of temperature for the material comprising the component of interest. This curve is determined from the dynamic tear test using a 5/8 in. thick specimen. A typical DTTE curve is shown in Figure 3.5. The standard form is similar to a typical toughness curve (i.e., CVN, K, etc.) with an upper-shelf at high temperatures, a elastic-plastic transition region in the middle, and a lower-shelf at lower temperatures. The lower-shelf will not usually go to zero in the range of the data, because some energy is required for the tear even at the nil-ductility transition temperature. The temperature corresponding to the energy found from Figures 3.3 and 3.4 is determined from Figure 3.5.



Figure 3.5 Typical DTTE-Temperature Curve [27]

Step 6: The next step is to determine the temperature correction for thickness, so that results can be extended to the actual vessel thickness, B . This correction is added to the temperature determined from the tear energy curve. The final result is the minimum operating temperature for that material. Now that the required DTTE is determined from Figures 3.3 or 3.4, the relevant DTTE-temperature curve for the material (see notional Figure 3.5) is used to determine the MOT, based upon a 5/8-in. sample thickness. Figure 3.6 is then utilized to correct for the actual structural thickness. The figure shows that, using midrange values, an additional 40°F temperature difference is required to satisfy the condition of going from a specimen thickness of 5/8-in. to the actual part (shell wall) of 2.50-in. shell thickness. As shown in Figure 3.6, thicker parts imply higher constraint, resulting in the fracture toughness curve to displace upward in temperature for a given DTTE. Figure 3.7 shows actual DTTE data for the LANL vessel’s 16-in. diameter nozzle, using the required 5/8-in thick specimen. The LANL specification required a DTTE of 750 ft-lb at -40°F for the 5/8-in. thick specimen, as stipulated in the vessel purchase order. This was achieved (See Appendix B), and the resulting temperature shift for the actual nozzle component (5-in. thick nozzle) was displaced by 70°F.



Figure 3.6 - Temperature correction for thickness [26,27].

3.3 DTTE and MOT Requirements The DynEx single-axis containment vessel design stipulates a 2.0-inch shell thickness. However, many regions of the shell are between 2- and 2.50-in. thick, with a mean of 2.375-in. thick. For determining the MOT, the 2.50-in. thickness is used, thus conservatively achieving a slightly higher MOT than using a smaller plate thickness. The dual-axis vessels are designed for 2.50-in thick shell and machined to a finished thickness of 2.5 inch throughout. Vessel Shell Requirement The vessel shell design assumes stresses at yσ0.1 for meeting the LBB criterion. This is equivalent to ymm = , so that from Eqn. (3.3), 6.1=β . Using a shell thickness of

5.2=B in Eqn. (3.4), results in a fracture-toughness to dynamic yield strength ratio of 0.2/ =ydIdK σ . Entering Figure 3.3, or similarly Figure 3.4 with this ratio, with a

dynamic yield strength of 105 ksi, the required DTTE is determined. The required DTTE is shown in Table 3.1.



Appendix A shows J-R curve and IcJ data with a lower-bound in-psi 2177=IcJ . With this data, the “as-built” toughness-to-yield strength ratio is 524.2/ =ydIdK σ . Also, the DTTE requirement is met for -40oF as shown in Appendix B. Lastly, Table 3.2 shows the “as-built” data. Nozzle Forging Requirement The nozzle design assumes stresses are not to exceed yσ5.0 for meeting the LBB criterion. For 9.0=β (See Fig. 3.1 or 3.2) and 0.5=B in., Eqn. (3.4) provides a fracture toughness to dynamic yield strength ratio of 12.2/ =ydIdK σ . Table 3.1 shows the required DTTE for nozzle forging. Forging data is similar to the shell plating with IcJ lower-bound value from Appendix A, thus the “as-built” toughness to yield strength ratio is 524.2/ =ydIdK σ . Table 3.2 shows the “as-built” results for nozzle forging. The DTTE requirements are not met for -70oF operation as shown in Appendix B “as-built” data. However, Figure 3.7 shows that at FTE, a -40oF operation is met with a DTTE of 750 ft-lb.

200

400

600

800

1000

1200

1400

1600

1800

-150 -100 -50 0 50 100 150

LANL HSLA-100 Nozzle DTE

5/8" Specimen

DT,

(ft-

lb)

Noz

zle

Temperature, (°F)

16" Diam Nozzle

Nozzle Thickness = 5"

70oF

∆T Shift for 5" Nozzle = 70oF

Figure 3.7 - DTTE for CV nozzle material.



Weld Requirements Girth welds and shell-to-nozzle welds are conservatively assumed to be 2.50-in. nominally for the MOT calculations. Referring to Figure 3.4, enter the curve with a toughness-to-yield ratio of 0.2/ =ydIdK σ , and a dynamic yield strength of

ksiyd 95=σ , which is indicative of under-matched welds. The required DTTE is shown in Table 3.1. However, referring to Appendix D of this report, weld toughness has been determined for both static, IcJ , and dynamic, IdJ ,conditions. The average IcJ is shown as 2185 psi-in, and the lower-bound value critical toughness is taken as 1800 psi-in, based on dynamic conditions. Using this lower-bound value, the “as-built” 521.2/ =ydIdK σ . Based on results shown in Appendix D, Table D.5 for “as-built” properties, weld DTTE is met for all specimens at -40oF. See Table 3.2 for “as-built” results. Shell/Nozzle Weld HAZ Requirements Weld HAZ is assumed at 2.50-in. nominally for the MOT calculations. Referring to Figure 3.4 and entering the curve with a toughness-to-yield ratio of 0.2/ =ydIdK σ , and a dynamic yield strength of ksiyd 105=σ , the required DTTE is shown in Table 3.1. Referring to Appendix D, Table D.6, weld HAZ toughness has been determined for both static, IcJ , and dynamic, IdJ ,conditions. The average IcJ is shown as 2351 psi-in, and the lower-bound value critical toughness at onset of slow, stable crack extension is taken as 2057 psi-in, based on dynamic conditions. Thus, “as-built” toughness-to-yield ratio is

845.2/ =ydIdK σ .

Table 3.1 Required Toughness-to-Yield Ratio and DTTE’s to Meet Fracture Safe Design

Part Thickness

(in) Design Stress ydIdKB σβ /=

DTTE’s (ft-lb)

Shell 2.5 yσ0.1 2.0 450 Nozzle 5.0 yσ5.0 2.12 490 Weld 2.5 yσ0.1 2.0 400 HAZ 2.5 yσ0.1 2.0 450

The lower DTTE requirement for the weld is based on the 95 ksi dynamic yield strength, i.e., under-matched weld.



Table 3.2 – “As-Built” Toughness-to-Yield Ratios and DTTE’s

Part Thickness

(in) ydσ ydIdK σ/ DTTE* (ft-lb)

Temp (oF)

Shell 2.5 105 2.524 601 -40 Nozzle 5.0 105 2.524 750 -40 Weld 2.5 90 2.845 481 -40 HAZ 2.5 105 2.524 929 -40

(1) Lower-bound values of all test specimen shown. (2) ydIdK σ/ ratios and DTTE’s are determined from actual material

properties found in Appendix A, B, and D. 3.4 Summary of MOT Results Table 3.3 below shows the minimum operating temperature for the separate components with the temperature shift for correction from 5/8-inch specimen to actual thickness of part. Again,. the shiftT∆ is applied using Figure 3.6 for the appropriate thickness.

Table 3.3 – shiftT∆ and Minimum Operating Temperature

Part Thickness

(in) Temp (oF)

ShiftT∆ (oF)

MOT (oF)

Shell 2.5 -40 40 0 Nozzle 5.0 -40 70 +30 Weld 2.5 -40 40 0 HAZ 2.5 -40 40 0

The MOT for the vessel system is the highest MOT achieved for any of the components. That is, +30°F is the required MOT for the complete vessel system. CVN energies for HSLA-100 steel shell, nozzle forging, and welds at the MOT are well above the 15 ft-lb minimum required by Section VIII, Division 1, of the ASME Code. Appendix A and B show that the minimum CVN energy, over a wide range of plate thicknesses for HSLA-100, at the MOT of +300 F is approximately 115 ft-lbs, which exceeds the 15 ft-lb minimum required by the Code by nearly an order of magnitude.



4.0 DETONATION-INDUCED IMPULSE LOADS Duffey, et al. [4] in WRC Bulletin 477, provides a wealth of information on impulsive loading in a containment vessel resulting from a high-explosive detonation event. The document provides a technical basis for the loading characteristic (i.e., dynamic pressure history) developed under this type of transient, while focusing on the vessel’s structural response. Included in the first part of the Bulletin are simplified, yet robust, methods for assessing HE detonation loading history on a structure. The second part of WRC Bulletin 477 provides a methodology for development of a strain-based design criteria, which takes advantage of the plastic-reserve capacity of the structural material. Although the previous work by Duffey [4] contains the bulk of the information required as background material for fracture-prevention design, this section, nonetheless, provides a summary of the dynamic transient event, addresses structural response including stresses/strains developed, and finally attempts to classify these stresses accordingly for further fracture mechanics evaluation. This brief summary is an attempt to maintain, as much as possible, a stand-alone document. 4.1 Dynamic Pressure Loading The characteristic loading function of a high-explosive detonation in a containment vessel is shown in Figure 4.1 for a 40-lb HE charge. It depicts an immediate sharp peak-pressure of about 12,000 psi, generated about 250µs after detonation. This is followed by a long-term quasi-static residual pressure of about 1,740 psig.

0

2000

4000

6000

8000

1 104

1.2 104

0 0.001 0.002 0.003 0.004 0.005

40-lb HE Charge

Pressure

Pre

ssu

re, (

psi)

Time, (sec)

Figure 4.1 – Pressure-time history of detonation blast.



As emphasized by Duffey et al. [4], the peak pressure is irrelevant to the overall vessel response. The important function is the specific impulse, or the area under the pressure-time curve. The subsequent small pressure reverberations are generated as a result from the reaction-product gas expansion and collapse phase, immediately after the initial large peak pressure. Detailed 2D hydrodynamics of the detonation-phase coupled with 3D structural dynamics of the structure reveal that these small pressure reverberations do not add to, nor produce, significant structural effects. Therefore, the “driving energy” contributing to vessel response is merely the specific impulse to about 1ms (0.001 s) into the transient. 4.2 Structural Response Typical vessel response is shown in Figures 4.2 and 4.3, depicting a comparison between experiment and numerical prediction. Figure 4.2 shows the strain-time response at the south pole of a single-axis vessel design for 40-lb HE charge. This is a region of the vessel shell free-field, far away from geometric discontinuities, i.e., nozzles. Inspection of Figure 4.2 reveals that after an initial “breathing mode” response, strain growth ensues up to about 4-5 ms, with a follow-on damped response over for about 20-30 ms. The initial breathing mode response is seen clearly in Figure 4.3 and 4.4 to about 1-1.5 ms.

-0.005

0

0.005

0 0.01 0.02 0.03 0.04 0.05

Vessel Response for 40-lb High-Explosive Charge

NumericalTest Data

Stra

in, (

in/in

)

Time, (s)

Figure 4.2 – Strain response comparison, numerical and test data.



Figure 4.4 shows a plot of the inner and outer surface strains at the south pole location. Pure membrane strains are clearly seen in the first two pulses to about 1.5 ms. Through-thickness bending ensues immediately and continues throughout the remainder of the vessel response. Figure 4.5 shows a late-time (i.e., 4-8 ms) response, again depicting that localized bending is the significant mechanism. Strain linearization, at this location, reveals that the amount of primary membrane load is equal to the gas pressure remaining in the vessel post-detonation, while the bulk strain response is largely comprised of displacement-controlled, through-thickness bending. Table 4.1 shows typical results of “secondary” membrane and bending, and “primary” stress, which is merely the gas pressure.

-0.005

0

0.005

0 0.001 0.002 0.003 0.004 0.005

Vessel Response for 40-lb High-Explosive Charge

NumericalTest Data

Stra

in, (

in/in

)

Time, (s)

Figure 4.3 – Early-time transient strain-response comparison of

numerical and test data.



-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004

South-Pole Strain History

S6X (Outer)S18 (Inner)

Stra

in, (

in/in

)

Time, (s)

HE Load = 40-lb PBX-9501

Figure 4.4 – Through-thickness strain response

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.004 0.0045 0.005 0.0055 0.006 0.0065 0.007 0.0075 0.008

South-Pole Strain History

S6X (Outer)S18 (Inner)

Stra

in, (

in/in

)

Time, (s)


Figure 4.5 – Late-time through-thickness response.



TABLE 4.1 MEMBRANE AND BENDING STRESSES AT THE SOUTH POLE

Time (ms)

Stress* Component

Outer Surface

(ksi)

Inner Surface

(ksi)

Membrane Stress# (ksi)

Bending Stress# (ksi)

0.43 Merid. 56.92 61.30 59.11 +/- 2.19 SOUTH 0.43 Circum. 58.07 62.47 60.27 +/- 2.20 POLE 4.09 Merid. -103.35 69.52 -16.91 +/- 86.44 4.09 Circum. -106.45 97.85 -4.30 +/- 102.15 0.43 Merid. 56.38 60.67 58.53 +/- 2.14 EQUATOR 0.43 Circum. 56.55 60.65 58.60 +/- 2.05 4.25 Merid. 59.31 22.62 40.96 +/- 18.34 4.25 Circum. 54.76 -18.83 17.97 +/- 36.79

* These stress components are essentially aligned with principal stress directions. # Results presented neglect curvature effects, i.e., through-thickness stress variations

are assumed to be linear. Finite element simulations of the transient vessel in-plane stresses were examined at two specific vessel locations, at two key response times, to isolate the relative contributions of membrane and bending stresses. Results are shown in Table 4.1 for stresses at the south pole of the vessel and at a location along the equator of the vessel, equidistant between the two nozzle ports. The first four columns of data are based upon FE calculations. The last two columns showing membrane and bending stress are determined from the outer-surface and inner-surface stress columns, assuming a linear through-thickness distribution of stresses. In each case, the stress components were examined at the response time corresponding to the initial ‘membrane’ peak response (i.e., 0.43 ms) and at the time corresponding to the overall peak response that occurs as a result of late-time ‘strain growth.’ Examination of these tables reveals that, for both locations, the initial peak response occurs at the same time and at approximately the same peak stress in both principal directions. Moreover, it is seen that the response at this early point in time is almost exclusively of a membrane nature. Bending stresses indicated in Table 4.1 at 0.43 ms are due to curvature effects, i.e., because of the differing radii of inner and outer shell surfaces. In any case, bending stresses are slight at both locations for the first membrane peak. Later in time, with the buildup of strains due to the strain-growth phenomenon [4], Table 4.1 reveals the presence of considerable through-thickness bending. In fact, at the time selected, the stresses at the south pole are primarily bending. At the point selected on the equator, stresses contain significant bending. The relative bending and membrane stress contributions vary with time and this variation is related to the beating phenomenon described in [4], where membrane and bending modes of vibration interact. Finally, it is important to note that stresses indicated are mostly of a ‘secondary stress’ nature. Primary stresses (i.e., on the order of 13 ksi) due to the long-term quasi-static pressure



buildup in the vessel are, however, also present. These primary stresses are of a membrane nature and are included in Table 4.1.

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0

2000

4000

6000

8000

1 104

1.2 104

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004

South-Pole Response Superimposed with Pressure

S6X (Outer Surface)

S18 (Inner Surface)

Pressure, (psig)

Stra

in, (

in/in

)

Pressure, (psig)

Time, (s)

Figure 4.6 – Strain response and pressure transient combined.



As can be seen from Figure 4.6, the pressure peak has subsided just before the vessel response commences. The gas expansion and collapse phase continues to decay to some quasi-static residual level, equal to the amount of gas generated by the HE charge. The strain-equivalent to an “applied load” primary-membrane strain ( )

mPε is due to pressure. Figure 4.6 shows the gas pressure expansion-collapse reverberations, which if taken to steady-state at late-times (i.e., greater than 20-ms), results in a quasi-static residual pressure of 1740 psig. See for example, Figure 4.1, where the pressure pulses are slowly decaying to an asymptotic value. Primary-membrane strain corresponding to this pressure is 4.2E-4 in/in. Therefore, it should be emphasized that there are negligible primary-stresses (or primary strains) from “applied loads” during the response-period. This is evidenced by the pressure-time history shown in figure 4.6. For HSLA-100 containment vessel design, fatigue is not a concern because these vessels are subjected to a one-time loading event and subsequently discarded. Nonetheless, for the one-time application of load, the vessels respond harmonically to the impulsive event. Vessel loading-function and response to a detonation blast are shown in Figure 4.6. It is evident from the Figure 4.2 that strains increase after the initial “breathing mode” and subsequently decay. Thus, the peak stresses affecting fatigue are at the beginning of the transient, with a rapid decaying function. Residual stresses play a predominant role in fatigue life, but for typical impulsive loading events such as the containment vessel, fatigue and fatigue crack-growth are not a concern because of the relatively small number of vibration cycles and the damping effect, or decaying stress function. Section 6 of this report provides an analysis of fatigue crack growth, conservatively assuming a far-field “primary” stress is acting on the structure. 4.3 Stress Classification for Fracture Mechanics Classification of stresses for fracture mechanics assessments is necessary to mitigate further confusion in classification of stress intensity factors. That is, because the late-time through-thickness bending is classified as secondary stresses, this must carry onto the stress intensity classification as well. The only primary load ( )mP in the vessel is the late-time residual gas pressure. Through-thickness bending occurring late-time is purely secondary ( )bQ , and residual weld stresses are also considered secondary ( )RS

bQ . During the early-time breathing mode response, the stresses developed are uniform secondary membrane stresses mQ .



5.0 CRITICAL CRACK SIZE DETERMINATION This section provides background information on elastic-plastic fracture mechanics (EPFM) as used for determining critical flaw sizes and the potential for slow, stable, crack growth. Further, critical flaw sizes for the vessel shell, nozzle forgings, weld, and HAZ are summarized. A complete analysis of crack geometry cases being considered is presented in Appendix F. 5.1 Elastic-Plastic Fracture Mechanics Linear-elastic fracture mechanics is limited to small scale yielding [22-24, 37]. That is, yielding at the crack-tip is assumed small in comparison to the K-dominant region surrounding. Elastic-plastic fracture mechanics extends the theory where significant plasticity is occurs, with a potential slow stable crack growth, or tearing. A basic estimation scheme is used herein as presented by Ainsworth [37], Anderson [22], Kanninen and Popelar [23], and Scott et al. [38]. The total crack driving force is comprised of plelTot JJJ += (5.1)

where ( )E

KJel

221 ν−= for plane-strain conditions. (5.2)

For a material whose uniaxial stress-strain curve could be described by a Ramberg-Osgood approximation,

m

ooo⎟⎟⎠

⎞⎜⎜⎝

⎛+=

σσα

σσ

εε (5.3)

where =oσ Yield strength

=oε Yield strain (usually 0.2%)E

oσ=

=α Material constant =m Strain-hardening exponent and where the first term on the right hand side of the equation is the linear-elastic, while the second term is the plastic portion of the stress-strain curve. One should note that in most texts on EPFM, the Ramberg-Osgood (R-O) strain-hardening exponent is labeled as n , yet the authors are purposefully making this minor deviation and labeling the exponent m for a reason that will be explained later. Addressing the plastic portion of the R-O approximation,



m

oo⎟⎟⎠

⎞⎜⎜⎝

⎛=

σσα

εε (5.4)

Rearranging terms in the above equation and solving for the true stress,

mp

m

oo

11

1 εαε

σσ ⎟⎟⎠

⎞⎜⎜⎝

⎛= (5.5)

where =pε Plastic strain The total value of the crack driving force TotJ , at an applied load P is given by Kumar and Shih [39,40] as

( ) ( )1

1

22

,/1+

⎥⎦

⎤⎢⎣

⎡+−=

m

oooTot P

PmWabhE

KJ εασν (5.6)

Where the first term on the right-hand side of the equation is the elastic, and the second term is the plastic crack driving force under a given applied load normalized to a limit load. Here: aWb −= = Uncracked ligament =W Thickness of plate ( ) =mWah ,/1 Influence function =P Applied load =oP Limit load of flawed structure The influence functions ( )mWah ,/1 are derived from finite element solutions for specific geometry under fully plastic conditions. Further, the elastic portion of the crack driving force, elJ , is based on a modified or effective crack length effa , to account for the small scale yielding, and is designated by Kumar and Shih [39] as; yeff raa φ+= (5.7)

where ( )2/11

oPP+=φ (5.8)

2

111

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

+−=

oy

Kmmr

σβπ (5.9)



where =K Elastic stress intensity factor =P Applied load, (psi) =oP Limit load of flawed structure, (psi) oσ = Yield strength 2=β (for plane stress) 6=β (for plane strain) In calculations that follow, the implicit assumption is made that high triaxiality exists at the crack tip, and therefore a plane-strain condition will be conservatively used throughout. Because HSLA-100 obeys a power-law strain-hardening relationship, as shown in Appendix B, the true stress-strain behavior may be described as; n

pεσσ 0= (5.10) Herein, however, a slight modification is made in order to not confuse the yield stress oσ from the Ramberg-Osgood approximation, with the material constant oσ in the power-law. As such, the power-law is now re-defined as; n

poK εσ = (5.11) where =oK Material constant It is evident by inspection of Eq. (5.5) and (5.11), that the power-law strain-hardening

exponent is equal to the inverse of the Ramberg-Osgood exponent, that is, m

n 1= .

Furthermore, the term oK in Eq. (5.11) can be set equal to m

oo

1

1⎟⎟⎠

⎞⎜⎜⎝

⎛αε

σ in Eq. (5.5), such

that;

m

oooK

1

1⎟⎟⎠

⎞⎜⎜⎝

⎛=

αεσ or (5.12)

n

oooK ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

αεσ 1 (5.13)

The only unknown in the above equation is α . In Appendix B, it was shown that the HSLA-100 shell and forging material was characterized by the following power-law; 1375.0185 pεσ = (5.14)



Therefore, because 185=oK , solving for α is a trivial exercise.

n

o

o

o

K1

1−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

σεα (5.15)

where ksi 100o =σ 002.0=oε 1375.0=n 273.7=m The resulting Ramberg-Osgood parameter is, 70.5=α ; where the effective crack length,

effa , and the fully plastic crack driving force, plJ , can now be computed for a given applied load, P , and a normalizing limit load, oP of a flawed structure. The same procedure, as shown above, is employed in determining the elastic-plastic weld metal Ramberg-Osgood characteristic. Two problems immediately arise when this stipulation is made for a dynamic transient, i.e., impulse-driven, detonation event; (1) actual “applied loads” during the response-phase are negligible (See Section 4.0), and (2) the “limit load” of the structure is not based on simple static pressure collapse conditions. Miller [41] and Ainsworth [37] describe limit loads of structures, Anderson [22], API 579 [25], and Anderson et al. [42] provide reference stress solutions for flawed structures, yet all are consistent with a statically pressurized system, where “primary” stresses due to applied loads are predominant. Limit loads of flawed, pressurized structures are abundant, yet as Kumar, German, and Shih [39] explain;

The instability point in the ductile fracture process is highly dependent on the loading system. For a load-controlled system in which the load is monotonically increasing, the attainment of the maximum load carrying capability of the cracked structure represents the onset of unstable crack propagation, since any further applied load increment will result in rapid crack propagation. For a displacement-controlled situation, instability need not develop upon attainment of the maximum load capacity of the flawed structure. Instability may occur at some point beyond maximum load or not develop at all.

The latter statement by Kumar, German, and Shih is at the crux of the issue herein, i.e., the response of an impulsively-driven structure is considered a deformation-controlled effect. The limit load of the structure is therefore at a point well-beyond that for load-controlled conditions, or may not develop at all. Two final comments on the limit load; (1) the limit load of a structure purely subjected to secondary stresses is extremely difficult to achieve analytically, and (2) the limit load of a flawed structure can only be obtained by highly detailed 2D or 3D finite element analysis. Lastly, in some complex



geometric and loading situations, even a numerical assessment of the limit conditions might not be easily attained, as in the case of a spherical vessel. As described in Section 4, the “primary” membrane stresses in the 6-ft diameter, 2.5-inch wall thickness, containment vessel (i.e., post-detonation) are about 12-14% yσ for a 40-lb HE charge. The internal pressure associated with this primary membrane stress is indicative of gas formation and expansion from the HE detonation. The major stress contributions throughout the transient are, however, through-thickness deformation-controlled, “secondary” stresses, which develop at late-time (i.e., > 2-ms), and secondary membrane during the initial breathing mode (i.e., ~ 0.4 ms). Both primary and secondary effects must be considered in the stress-intensity factor solution for fracture assessment. The method employed in API 579 [25] and described by Scott et al. [38] will be used, which states that the overall stress intensity factor is the sum of the primary plus secondary and residual stress intensity factors, SR

IPII KKK += (5.16)

where =P

IK Stress intensity factor for primary stress =SR

IK Stress intensity factor for secondary stress Yet, it is overly conservative to directly sum the stress intensity factors as per Equation 5.16. Thus, the secondary and residual stress contribution employs a plasticity correction factor Φ , which is a function of the primary loads, SR

IPII KKK Φ+= (5.17)

where ⎟⎟⎠

⎞⎜⎜⎝

⎛=Φ

y

RS

y

P

fσσ

σσ ,

A conservative approach is taken in quantifying the solutions covered in this report. Main parameters in the assessment included herein are:

(1) Primary stresses are 12% yσ , ( mP only, based on 40-lb HE), (2) Residual weld stresses are assumed at yσ0.1 , (See Appendices D and F), (3) Impulse-driven, late-time, through-thickness bending stresses are secondary

(See Section 4 and Appendix F), (4) Plasticity correction factor Φ based on ( ) 0.2/ =y

SR σσ , (5) Fully-plastic J solutions are based on:

a. surface flaw; tension loaded plates b. part-through-wall; edge-cracked plane-strain [39,40]



Refer to Appendix F for a complete description of solutions. Sections 5.2, 5.3, and 5.4 provide summaries of critical crack sizes for shell, nozzle forgings, weld, and HAZ respectively. Lastly, NDE techniques (e.g., RT, UT, MT, etc.) would detect a flaw of 1/16-in. to a high probability. However, for analytical purposes, the detectable flaw size is assumed here at 1/8-in. throughout. 5.2 Vessel Shell The critical crack size for the LANL vessel’s shell is determined by postulating several different possible flaw geometries and orientations in the shell. Appendix F provides the analytical evaluation of critical flaw size using the IcK for HSLA-100, as documented in Appendix E. The limiting critical flaw size for the vessel shell is a complete through-wall flaw described in Appendix E. It is noted that this critical flaw size is completely through-wall and three times larger than the nominal vessel wall thickness. NDE techniques are capable of detecting flaws much smaller than this value. See Appendix F, Section F.2, for the complete evaluation. The critical flaw size and margin of safety are Surface Flaw inchacrit 0.1= Through-wall Flaw inchacrit 5.3= The minimum factor of safety based on a detectable 1/8-inch flaw size is, FS = 8.0 5.3 Nozzle Forging The critical flaw size for the containment vessel’s nozzles is determined by postulating several different possible flaw geometries and orientations within the nozzle. Appendix F provides the analytical evaluation of critical flaw size using the IcK and IdJ for HSLA-100, as documented in Appendices A and E. The limiting critical flaw size and geometry for the nozzle is described in Appendix F. Nozzle Corner Flaw inchacrit 4> Longitudinal Surface Flaw inchacrit 0.1= Thus the factor of safety on a detectable flaw is, FS = 8.0 5.4 Weld and HAZ Weld and HAZ data from NSWC [43,44] and DREA [45,46] is reported in Appendix D for the same weld consumable used for the LANL vessels. This provides assurance that weld toughness will be consistent. The evaluation criteria for critical flaw size is presented in Appendix F. The limiting critical flaw size for weld is

inchacrit 75.0= Thus the factor of safety on a detectable flaw is, FS = 6.0



6.0 FATIGUE CRACK PROPAGATION There appear to be two possible general approaches to the fatigue analysis and life prediction of the vessel. The first could be termed the S-N Curve approach (i.e., stress-cycles). In that case, vessel fatigue life is estimated using an S-N curve of the material, along with a method such as Miner’s rule for combining cycles at different amplitudes. A total number of N cycles (at decreasing amplitudes) occur due to vessel vibrations during each explosive test. If M tests are performed, the total number of cycles over the life of the vessel at each amplitude is then known. Using the S-N curve and Miner’s Rule, and incorporating a suitable factor of safety, results in a conservative life prediction for the vessel. The implication is that cracks nucleate and grow during the cyclic life of the material. A drawback is that with ultrasonic examination (UT) there is the possibility of an initial rogue crack present in the material just under the non-destructive evaluation (NDE) detectable depth, resulting in premature failure. A second drawback is that during NDE there could be a detected crack that meets the American Welding Society standard (AWS D1.1-92) acceptance criterion for the vessel (1/16 in. deep by 1.5 in. long). As the detected crack has effectively nucleated and grown to an extent before cycling of the vessel occurs, this would invalidate the S-N curve approach. An alternate fracture mechanics approach for the determination of remaining life of a containment vessel is to integrate HSLA steel material data for crack extension as a function of alternating stress. One advantage of this method is that a crack flaw depth can conservatively be assumed, either at the lower limit of the NDE crack detection technology to be applied for the vessel inspection, or at the maximum crack size specified in the AWS D.1.-92-based vessel acceptance criterion (as used here). An additional advantage is that such dNda / vs. K∆ data are readily available for HSLA 100 steel. Further, Linear Elastic Fracture Mechanics (LEFM) approach is inherently conservative, and we further assume that the vessel is being operated near the transition temperature region. Vessel operation is actually well above this region in the elastic-plastic portion of the fracture toughness curve. Thus, fatigue life is underpredicted. The purpose here is to develop and demonstrate a fatigue-crack-growth assessment method that incorporates the decaying nature of the peak stress response for containment vessels. Although API-579 may not be applicable to the present investigation primarily because of the nature of the impulsive pressure loading applied to the vessel, some guidance from API 579 is used as a starting point. Since the vessel structural response encompasses low-order and higher-order vibration modes, these can be considered cyclic events, and therefore need to be addressed. As such, a conservative evaluation is proposed herein, based upon DTRC fatigue crack propagation test data. Figures 6.1 depicts the loading history of the structure, and Figures 6.2 and 6.3 depict the short-term vibrational peak strain response for a 20-lb HE charge.



0

1000

2000

3000

4000

5000

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

20-lb PBX-9501 High-Explosive

Pressure, (psia)

Pres

sure

, (ps

ia)

Time, (s) Figure 6.1 - Pressure-time history for 20-lb HE charge.

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

-0.01 0 0.01 0.02 0.03 0.04 0.05

Strain Response Away from Nozzle for Single-Axis Vessel

Strain, (in/in)

Stra

in, (

in/in

)

Time, (s)


Figure 6.2 - Strain response away from nozzle for 20-lb test.



-0.002

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

0.002

-0.005 0 0.005 0.01 0.015 0.02 0.025

Strain Response at South-Pole of Single-Axis Vessel

Strain

Stra

in, (

in/in

)

Time, (s)


Figure 6.3 - Strain response @ south pole for 20-lb test.

The evaluation assumes the material behavior is within the range of purely LEFM, and thus the vessel is operating near the transition temperature region. This is a conservative assumption because the vessel operation will be well above the transition temperature region, and thus within the elastic-plastic or upper-shelf portion of the fracture toughness curve. From Figure 6.2, the peak strain developed in the vessel (south pole) is about 2.0E-3 in./in. This provides an upper-bound pseudo-elastic stress, at one single point in time, of

Eεσ =

ksi 58±=σ where E = 29E+3 ksi (for HSLA-100). The remaining damped strains decrease to about 1.0E-3 in./in. over 6 cycles, and subsequently to 0.5E-3 in./in. in another 6 cycles. Therefore, the following evaluation will assume a constant stress-range of ksi 120=∆σ for 100 cycles of response. But, only the crack-opening mode stress will be considered, that being half the stress range, or

ksi 60=∆σ . The crack-closing mode is assumed to not contribute to crack propagation. Figures 6.4 and 6.5 present the Paris Law ( dNda / ) test data performed at DTRC for 1-1/2-in. thick HSLA-100 plate material [17]. Figure 6.4 shows data for the longitudinal



direction (i.e., plate rolling direction), while Figure 6.5 shows data for the transverse (or weak) direction.

Figure 6.4 - HSLA-100 crack growth rate data ( dNda / ) for L-T specimen [17].

Figure 6.5 - HSLA-100 crack growth rate data ( dNda / ) for T-L specimen [17].



A conservative crack growth rate, employing the Paris Law equation [22-24], will be used to assess the crack growth at some specified number of cycles owing to the vibration response of the vessel,

( )nKCdNda ∆= 1 , (6.1)

where from Figure 6.4 we obtain the limiting flaw growth rate:

( ) 48.291056.1 KxdNda ∆= − , (6.2)

where 1C = Material coefficient (from log-log plot), K∆ = Stress intensity-factor range, and

dNda = Crack growth rate per cycle of applied load.

Assuming a conservative stress intensity factor, such as for an edge crack in an infinite medium, yields an upper-bound solution.

aCK πσ2= , (6.3) where 2C = Geometric constant. For a cyclic event, the stress intensity factor range is merely the range of stress intensity at the crack tip from the range of far-field applied stress.

aCK πσ∆=∆ 2 (6.4) Substituting the expression for K∆ into Equation (6.1),

( )naCC

dNda πσ∆= 21 (6.5)

( ) 2/2/21

nnnn aCCdNda πσ∆= (6.6)



which reduces to

( ) ( ) dNCCada nn

in

n2/

212/ πσ∫∫ ∆= (6.7)

Integrating the expression, the following solution for the incremental crack growth, through the 2-in. thick plate, as a function of the previous increment crack size is developed:

( ) ( )n

i

n

inn

i

j

i

nif NaCCnaa

−−

= ⎥⎥⎦

⎤

⎢⎢⎣

⎡∆⎟

⎠⎞

⎜⎝⎛ −+= Σ

22

22

2112/

211 σπ (6.8)

Now, a crack growth estimate is made of an initial 0.5-, 1.0-, and 1.5-in. deep (i.e., length of crack) surface flaw in a nominally 2-in. thick plate. The following values for the constants and parameters are used: 9569.11 −= EC 48.2=n 12.12 =C [24] ksi 60=∆ iσ ia = Various initial sizes iN = Number of cycles Solving the equation for the worst case initial possible flaw, with the worst case possible stress range throughout the transient, and exceeding the possible number of vibration cycles at this stress range, the final flaw size is determined. Table 6.1 presents the crack size after a number of vibration cycles at the exceedingly and conservative high levels of stress. Figure 6.6 presents the tabular data of Table 6.1 in graph format.

Table 6.1 Fatigue Crack Growth for Initial Flaws at Stress Range of 0.6Sy Number of

Cycles (N)

0.5” Initial Crack Size

(in.)


(in.)


(in.) 0 0.5 1.0 1.5 10 0.501 1.002 1.503 100 0.509 1.020 1.534 1000 0.595 1.230 1.885 2000 0.714 1.529 ----- 3000 0.864 1.924 ----- 4000 1.055 ------ ----- 5000 1.301 ------ ----- 10000 ------ ------ -----



For the one-time HE detonation impulse load, the vessel will respond throughout its different vibration modes. The above evaluation shows that under the assumption the vibration modes impose a gross through-thickness stress-range of yS6.0 , conservative initial flaw sizes would grow through the wall at greater than 2000 cycles. Since the actual, structurally damped, vessel response is approximately a total of 50-100 cycles[12,13,14], and the level of stress-range is typically much less than 60 ksi, there is no concern for fatigue crack growth. The actual operation of this vessel will be at 30°F, which implies elastic-plastic conditions, and therefore even higher fracture toughness than considered herein.

0.1

1

10

100

10 100 1000 104

Fatigue Crack Growth for HSLA-100 at Stress Range of 0.5Sy

0.125" Flaw0.25" Flaw1/2" Flaw1.0" Flaw1.5" Flaw1.75" Flaw

Cra

ck G

row

th, (

in)

Cycles

Figure 6.6 - Fatigue crack growth for certain flaw sizes. The conclusion drawn from the foregoing analysis is that there is no concern with fatigue crack growth in the LANL containment vessels. Now, let us take another view on fatigue crack growth. The design of containment vessels is based upon in-plane through-thickness stresses reaching, at most, the yield stress of the HSLA-100 material during the breathing mode response. However, late-time (i.e., 2-6 ms) stresses are predominantly through-thickness bending, which is considered “secondary.” Therefore, the peak stress at most reaches the



yield stress, oσ , i.e., the maximum stress range is or σσ = . The vibrational response of the vessel is extremely complex. However, due to various damping mechanisms, the vessel eventually ceases vibrating. Assuming viscous damping of the structural vibrations, and applying the logarithmic decrement [4,5] concept, the stress range, σr , is taken as the following:

δσσ nor e−= (6.9)

where δ is the logarithmic decrement and n represents number of cycles. Here a slight modification is used to eliminate confusion with the exponent as shown in Eqns. (6.7) and (6.8). Combining Eqns. (6.4) and (6.5) with (6.9) results in

dneCCada

o

mnmo

mma

am

f

∫∫∞

−= δσπ 2/212/

0

(6.10)

where the number of vibration cycles, N , has been replaced by ∞, at which point all vibrations have ceased for that particular explosive test. This is particularly convenient, as no assumption need be made as to the cycle number at which vibrations cease, nor at what cycle number the stress drops below the crack growth threshold. Use of an infinite number of vibration cycles for a given HE test is also conservative, as crack growth is assumed on every cycle, even for low cyclic stresses later in time. In reality, when the stress drops below the crack growth threshold, no further fatigue crack growth occurs. Performing the integration, and evaluating the limits of integration, results in the following expression for the final crack depth for a given containment vessel test (using the maximum rated charge) in terms of the initial crack depth, material, and geometric constants:

af = ao 1 + a0

m2

−1(1 −

m2

)C1C2

mπ m / 2σom

mδ

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

22− m

(6.11)

The initial crack size for the first test would be the maximum crack size permitted by the acceptance criterion. The same Equation applies for subsequent tests, where oa is equal to fa from the previous test. Therefore, the procedure is to evaluate Eqn. (6.11) as a recurrence relationship one test at a time, determining the new crack size and comparing it to the critical flaw size, in the following sequence: During vessel test No. 1, the initial crack size, oa , extends to 1a :



a1 = ao 1 + a0

m2

−1(1 −

m2

)C1C2

mπ m / 2σom

mδ

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

22 −m

(6.12)

During vessel test No. 2, the crack size following test No. 1 extends to, a2 :

a2 = a1 1 + a1

m2

−1(1 −

m2

)C1C2

mπ m / 2σom

mδ

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

22 −m

(6.13)

On the i+1st test, the crack size at the end of the ith test extends to 1+ia :

ai +1 = ai 1 + ai

m2

−1(1−

m2

)C1C2

mπ m / 2σ om

mδ

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

22− m

(6.14)

Crack growth during a given HE test is relatively small, permitting use of a constant value of the geometry parameter, 1C . This geometry parameter, which is typically a function of relative crack depth for a variety of crack geometries, is then updated, i.e., new values of 1C are used in Eqn. (6.13), (6.14), etc., as described below. The above recurrence process is repeated until the critical flaw size is reached, as determined individually for the various flaws in the containment vessel and the nozzle postulated in this study. Parameters required for evaluation of Eqn. (6.14) are presented next. Logarithmic Decrement (Delta) It is assumed that successive peak stresses monotonically decay in an exponential manner. The positive peak stresses are assumed of the form,

δσσ non e−= (6.15)

where n denotes the number of the oscillation cycle, and δ is the logarithmic decrement. A recent experiment was performed on an explosively loaded 6-ft. diameter vessel. Strain-time histories were recorded at various locations on the vessel. A typical surface strain-time history is shown in Figure 6.7. Equation (6.15) is also fitted to the positive peaks of the strain-time history in Figure 6.7. The fit results in a logarithmic decrement, δ , of 0.07.



-0.001

-0.0005

0

0.0005

0.001

0.0015

0 5 10 15 20 25

Time, ms

Figure 6.7 - Determination of logarithmic decrement from vessel strain-time test data. Constants C1 and m for Paris Law - Fatigue crack growth rate data are available from David Taylor Research Center (now called Naval Surface Warfare Center) for 1.5 in. thick HSLA-100 plate [17]. Figure 6.4 and 6.5 contains dNda / data and a Paris Law fit for the longitudinal (i.e., plate rolling) direction. Paris Law constants adopted for this study are therefore 9

1 1056.1 −= XC and 48.2=m .

Critical Crack Size, acr - The critical flaw size is determined by setting the stress-intensity-factor range to the critical stress intensity factor for the HSLA-100 material, IcK

2/12 )( crrIc aCK πσ= (6.16)

where as noted above, 2C shown in Figure 6.8 as solid black diamonds, is a function of crack depth and hence acr . The critical crack depth is then

2

2

1⎥⎦

⎤⎢⎣

⎡=

r

Iccr C

Ka

σπ (6.17)



STRESS INTENSITY FACTOR FIT

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

CRACK LENGTH TO THICKNESS RATIO, a/b

Figure 6.8 – Stress intensity factor fit to quadratic function.

A quadratic fit to the curve for the stress intensity constant is also shown in Figure 6.8 (i.e., solid black squares) and presented for values of 2C approaching an ba / ratio of 0.76 (corresponding to a value of 2C of 2.0). The form of 2C is taken from Barsom and Rolfe [24];

2

2 4.112.1 ⎟⎠⎞

⎜⎝⎛+=

baC (6.18)

This is considered a good fit below an a / b ratio of 0.7. Equation (6.18) is combined with Eqn. (6.17) resulting in the following transcendental equation for critical crack size:

2

2

4.112.1

1

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡+

=

ba

Ka

crr

Iccr

σπ

(6.19)

Equation (6.19) was solved iteratively for the critical crack depth, using actual lower-bound IcK test data for HSLA-100 [17], a very conservative far-field alternating stress equal to half the dynamic yield strength of the material, and the vessel thickness.



Based on inpsiJ Ic −= 2177 at 75oF, from Appendix A, the corresponding plane-strain

fracture toughness is, inksiKIc 265= . ksir 100=σ in. 5.2=b The resulting critical crack depth is 13.1=cra inch, which corresponds to a full circumferential crack slightly less than halfway through the thickness of the 2.5-in. vessel wall. An initial 1/16 in. partial through-wall crack was assumed, and the recurrence process of Equation 6.12 through 6.14 was continued until the critical flaw size was reached. Again, this initial crack size was selected for investigation because it is the maximum acceptable crack size for a new vessel per AWS D1.1-92. Resulting crack growth, up to the first 200 HE vessel tests, is shown in Figure 6.9, where it is seen that the crack size only increases to above 0.1 in., well below the critical flaw size. A total of 840 HE tests would be required for the crack to grow to its critical length of 1.13 in.

CRACK GROWTH AS A FUNCTION OF NUMBER OF

EXPLOSIVE TESTS

0

0.02

0.04

0.06

0.08

0.1

0.12

0 50 100 150 200 250

NUMBER OF TESTS

Figure 6.9 – Crack growth as a function of number of explosive tests.

The incremental number of tests that can be performed for a given flaw size using the above theory is shown in Figure 6.10. As can be seen in that figure, a flaw size of 0.6 in. would grow to the critical crack size in approximately 100 tests. However, the postulated flaw is an overly conservative model of fragment damage because of the localized damage inflicted by a fragment.



NUMBER OF VESSEL TESTS UP TO CRITICAL CRACK GROWTH IN VESSEL

0

100

200

300

400

500

600

0 0.2 0.4 0.6 0.8 1 1.2

INITIAL FLAW SIZE

Figure 6.10 – Number of remaining tests based on observed flaw size.

Results of four postulated flaws investigated are summarized in Table 6.2, where the critical crack depth is presented, followed by the number of HE tests that could be performed in the vessel with an initial, maximum acceptable flaw of 1/16" crack length. It is readily seen that the nozzle corner flaw permits the minimum number of HE tests, although the limit of 66 tests indicated in Table 6.2 is considered very conservative because of the high alternating stress value used. Applying a factor of safety of 3 on the number of tests, it is shown that the vessel is capable of withstanding in excess of 20 full HE tests before the postulated nozzle corner flaw would grow from the acceptable initial flaw length of 1/16" to the critical size.

TABLE 6.2 NUMBER OF HE TESTS FOR EACH POSTULATED FLAW

Postulated Flaw Location Critical Crack Size (in)

HE Tests to Critical Size

Full circumference internal part-throughwall flaw

Spherical Vessel

1.13 840 Tests

Finite length, semi-elliptical, internal circumferential part-throughwall flaw

Spherical Vessel

1.95 (2c/a=3) 1.52 (2c/a=6) 1.31 (2c/a=9) 1.17 (2c/a=12)

1796 Tests 1281 Tests 1104 Tests 1005 Tests

Full circumference internal part-throughwall flaw

Cylindrical Nozzle

1.44 926 Tests

Nozzle corner flaw Nozzle & Vessel Intersection

0.31 66 Tests



7.0 ASME CODE GUIDELINES FOR NON-DUCTILE FAILURE Appendix G of the ASME Code [11] provides design guidance for protection against non-ductile failures of nuclear pressure vessels. The guidance provided in Section III, Division 1, of the Code is similar to that in the non-nuclear Code, Section VIII, Division 2, and follows a very conservative approach for the materials of choice in nuclear pressure vessels.

20

40

60

80

100

120

140

160

-300 -200 -100 0 100 200

ASME Code: Reference Fracture Toughness Curve

KIR

Ref

ernc

e St

ress

Inte

nsity

Fac

tor K

IR (

ksi-

in1/

2 )

Temperature Relative to RTNDT, (°F) Figure 7.1 - ASME IRK toughness curve.

Specifically, the Code provides guidance for determination of critical flaw sizes using a parameter termed the “reference critical stress intensity factor” or IRK . This parameter is the lower-bound estimate of static, dynamic, and crack arrest critical IK values measured as a function of material. The IRK toughness values pertain to SA-533 Grade B Class 1, and SA-508-1, SA-508-2, and SA-508-3 steel. These steels have a maximum tensile yield strength of 50 ksi at room temperature. Furthermore, the guidance for determination of critical flaw size assumes the conditions for static internal pressure. Figure 7.1 presents the IRK curve from the ASME Code. The reference fracture toughness curve was empirically derived from the lower-bound of all test data, and is shown below: ( )[ ]1600145.0exp233.178.26 +−+= NDTIR RTTK , (7.1)



where KIR = Reference stress intensity factor, (ksi-in.1/2) , T = Temperature at which IRK is permitted, (°F) , and RTNDT = Reference nil-ductility temperature, (°F) . The Code points out that for material yield strengths greater than 50 ksi and less than 90 ksi, IcK testing must be accomplished and the resulting IK curve, or the critical stress intensity factor IcK , must be determined for the specific material. The Code provides no guidance for material yield strengths greater than 90 ksi. But, more importantly, the ASME Code reference fracture toughness curve depicts IcK values that are consistent with carbon steels, i.e, within the range of 40 ksi-in.1/2. As noted in Appendix E, the critical plane-strain stress intensity factor for HSLA-100 is in the range of 260 to 290 ksi-in.1/2. 7.1 ASME Code Comparison Here we describe linear elastic fracture mechanics (LEFM), as applied for Class 1 nuclear reactor pressure vessels and components in the ASME Code Section III, Appendix G, and in the ASME Code Section XI, Appendix A. Both Appendix G of Section III and Appendix A of Section XI require that the applied fracture mechanics stress intensity factor, called appl IK , must be shown to be less than the material fracture toughness, called

mat IK , with appropriate margin. EPFM procedures are prescribed in Appendix K of the ASME Code Section XI Division 1. The Appendix G approach can be described as a reference flaw procedure, since the flaw size against which the component must be evaluated is prescribed. In this case, the reference flaw is required to have a depth equal to 25% of the wall thickness, for vessels with a wall thickness less than 12 inches, with the depth limited to three inches for a wall thickness greater than 12 inches. The location of the flaw is assumed to be in the worst location in the component, relative to calculated stresses, and in the worst orientation, relative to the highest principal stress, for Mode 1 crack initiation. The calculated (applied) stress intensity, with a factor of safety of two applied to the membrane stress from internal pressure, is compared to an allowable material fracture toughness given by the lower bound to static, dynamic and crack arrest data-- IRK . Figure G-2210-1 from Appendix G, illustrates the lower-bound IRK curve, referenced to the nil-ductility transition temperature NDTT , that is used in lieu of mat IK in the Appendix G LEFM calculations. Also, Figure G-2214-1, illustrates the conservatism that can accrue to the applied stresses if those stresses are assumed to be equal to the yield strength of the material.



Appendix G can be applied directly to the DynEx containment vessel by assuming that the bounding IRK is conservative relative to the actual fracture toughness of the material, and by assuming that the membrane stress is equal to the minimum yield strength of the HSLA-100 material, 100 ksi. In addition, the pressure loads that cause this membrane stress are assumed to be expected (i.e., Level A) service loads. Using Equation 7.1, the bounding fracture toughness is used to estimate the fracture toughness at or near the MOT, with FRT o

NDT 210−= . The lower bound toughness at 0oF is; inksiK IR 290= , while the lower bound toughness at –30oF is inksiK IR 197= . These are reasonable values for upper shelf or near upper shelf fracture toughness values, as predicted by the upper-shelf CVN correlation in Appendix E. In comparison with the ASME Code, Section VIII, Division 1, Class D, for a vessel fabricated from a ferritic steel with a nominal wall thickness of 2.5 inches (the LANL vessel shell thickness), impact testing is required for a minimum design metal temperature of about 0oF, or less. For a wall thickness of 5 inches (the LANL nozzle thickness), impact testing is required for a minimum design metal temperature of 30oF, or less. Note the similarity of the temperature exemption limits of Figure 7.2 (Fig. UCS-66) to the MOT determinations in Section 4.0 of this report.

-80

-60

-40

-20

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6

Nominal Thickness, in.(Limited to 4 in. for Welded Construction)

Min

imum

Des

ign

Met

al T

empe

ratu

re, o F

D

C

B

A

Impact testing required

0.394

Figure 7.2 - Impact Test exemption curves, ASME Code Section VIII,

Division 1 (Fig. UCS-66)



For the LANL containment vessel shell with a 2.5-inch-thick wall, a ¼ thickness flaw and a grossly conservative membrane pressure stress of 100 ksi, MOT – TNDT must be a minimum of 140oF, or the MOT must be –25oF or higher. For the containment vessel nozzles with a 5-inch-thick wall, a ¼ thickness flaw, and a membrane pressure stress of 100 ksi, the minimum MOT is –17oF. Note that these calculated MOT values are more conservative than the values that would be obtained from Appendix R. Thus, use of the ASME Code reference toughness curves is appropriate and results in similar toughness values as determined in Appendix E. 8.0 CONCLUSIONS This report has addressed historical aspects of LANL’s Containment Vessel Program and the Fracture Safe Design and Fatigue Failure criteria adopted by the DynEx Project for HE detonation-induced pressure loading in HSLA-100 vessels. The Fracture Safe Design approach utilized herein was developed by NRL and reported in WRC Bulletin 186 [1], culminating in development of Dynamic Tear Test Energy (DTTE), an ASTM-approved procedure (ASTM E 604) [2]. Although LANL uses this approach as a design aid, the work is supplemented by other data (i.e., Charpy V-Notch, J-R curve, KIc, etc.) and advanced fracture mechanics procedures, as presented in Sections 5 and 6, and Appendix F herein. The response of impulsively loaded vessels is manifested predominantly in higher-order bending modes. The initial pressure pulse, i.e., breathing mode, applies a percentage of membrane load ( yσ4.0 for 40-lb HE), which is not large enough to drive potential flaws. Peak stresses, which develop from these high-order bending modes, are highly localized and are caused from the “ringing,” or vibration, of the vessel. Because the principal stress tensors are constantly changing orientation, and the location of peak principal stress is also constantly changing, any potential crack will arrest immediately because the crack driving force (stress) is not maintained. In supporting the conclusion reached herein, much information is detailed in Appendix A and Appendix B on fracture toughness characteristics of HSLA-100 using both DTRC and LANL “as-built” material data. A comparison of other pressure vessel steels to HSLA-100 is presented in Appendix C, showing the superiority of HSLA-100 in strength and ductility, as well as higher fracture toughness. Appendix D contains much of the weld and HAZ information on HSLA-100, from which conclusions are drawn as to its structural adequacy. The assured crack arrest criterion is consistent with the ASME Code methodology for prevention of non-ductile failures as discussed in ASME Code, Section III, Appendix G. Nonetheless, LANL is pursuing the pressure vessel industry’s more traditional methods including high strain-rate J-R Curve determination for subsequent vessel designs.



Critical flaw sizes determined for vessel shell, nozzles, and welds, and based upon LEFM and EPFM are conservatively about 8-times larger than those which NDE is able to detect. These critical flaw sizes are so large, in fact, that visual inspection alone is able to identify an unsatisfactory surface condition. These arguments notwithstanding, the possibility of a large embedded flaw does not imply catastrophic failure because vessel operating temperature assures upper-shelf behavior based on DTTE curves. As such, any surface or sub-surface flaw present in the vessel will arrest due to the inherent fracture toughness. For single-use vessels (i.e., single application of an explosive event), fatigue crack growth has been shown to be a rather small effect. It would require approximately 2000 cycles of yield stress amplitude to propagate a flaw through-thickness. For detonation-induced structural response, the number of vibrations cycles is about 50-100. Thus, there is no concern for vessel failure from fatigue crack growth. For multiple-use (i.e., multiple explosive experiments), fatigue crack growth can be determined based upon the logarithmic decrement of the decaying stress function. The log-decrement stress function is then applied to the Paris Law to calculate the number of cycles to reach the critical flaw size. Lastly, it should be recognized that several conservatisms are employed in the fracture mechanics assessment;

(1) Lower-bound toughness IdJ values (2) 100% σ residual weld stress

9.0 RECOMMENDATIONS As discussed in the Executive Summary and Section 5, it is recommended that MPC/PVRC develop design guidance to be included in API-579 for assessing flaws in a dynamic impulsive environment. Although it is recognized that current assessment methods for crack-like flaws is state-of-the-art, there are some pitfalls when dealing with highly impulsive loadings and the corresponding limit load assessment of the structure for secondary-type stresses.



ACKNOWLEDGEMENTS The authors are grateful to Dr. Robert Nickell in providing helpful comments and recommendations on this report. The authors also thank Jerry Bitner, Chairman of Committee on Dynamic Analysis and Testing of the Pressure Vessel Research Council, for his assistance and support on all aspects of this endeavor. The assistance of the following PVRC reviewers is gratefully acknowledged: Ted L. Anderson, David Osage, Martin Prager, Paul Bezler, Henry H. Hwang, Darrell R. Lee, John C. Minichiello, and Rudy Scavuzzo. Review comments from Alan Clayton (AWE) and Robert Forgan (AWE) are also gratefully acknowledged. Sincerest gratitude is extended to Ernie Czyryca at Naval Surface Warfare Center (NSWC) Carderock Division, for supplying all the HSLA-100 mechanical and impact data, and Dr. Stephen Graham at the United States Naval Academy, Annapolis, for supplying the weld toughness J-R curves.



REFERENCES (1) W. S Pellini, “Design Options for Selection of Fracture Control Procedures in the

Modernization of Codes, Rules, and Standards,” The Welding Research Council, WRC Bulletin 186, August 1973.

(2) ASTM Specification, ASTM E-604, “Standard Method for Dynamic Tear Testing

of Metallic Materials,” American Society for Testing and Materials, 2002. (3) Standard for Construction of HSLA-100 Confinement Systems, Los Alamos

National Laboratory, DynEx Vessel Project, Report No. DynEx-01-23, Rev. 1, June 2002.

(4) T. A. Duffey, E. A. Rodriguez, and C. Romero, “Design of Pressure Vessels for

High Strain Rate Loading: Dynamic Pressure and Failure Criteria,” Welding Research Council, WRC Bulletin 477, April 2002.

(5) R. E. Nickell, T. A Duffey, and E. A. Rodriguez, “Ductile Failure Criteria for

Design of HSLA-100 Steel Confinement Vessels,” ASME Pressure Vessel and Piping Conference, Cincinnati, OH, March 2002.

(6) W. S. Pellini, Guidelines for Fracture-Safe and Fatigue-Reliable Design of Steel

Structures, The Welding Institute, Abington Hall, Abington, England, 1986. (7) W. S. Pellini, Principles of Structural Integrity Technology, Naval Research

Laboratory, Report No. ADA 039-391, Office of Naval Research, 1976. (8) W. S. Pellini, “Criteria for Fracture Control Plans,” Naval Research Laboratory,

NRL Report 7406, May 1972. (9) E. A. Lange, “Dynamic Fracture Resistance Testing and Methods for Structural

Analysis,” Naval Research Laboratory, NRL Report 7979, April 1976. (10) J. R. Hawthorne and F. J. Loss, “Fracture Toughness Characterization of

Shipbuilding Steels,” Naval Research Laboratory, NRL Report 7701, July 1974. (11) ASME Boiler and Pressure Vessel Code, (2001 Edition), Section III, “Nuclear

Vessels,” Division 1, Appendix G, American Society of Mechanical Engineers, New York, NY, July 2001.

(12) R. L. Martineau, “HSLA-100 Test Series Structural Analysis and Experimental

Comparison for Vessel Certification,” Los Alamos National Laboratory, Report No. DX-5:99-013, May 1999.



(13) C. Romero and R. Thornton, “HSLA-100 Vessel Test Series for Vessel Certification,” Los Alamos National Laboratory, Report No. DX-5:99/CR-010, May 1999.

(14) R. R. Stevens and S. P. Rojas, “Containment Vessel Dynamic Analysis,” Los

Alamos National Laboratory, LA-13628-MS, August 1999. (15) N. L. Borch, “Historical Perspective of LANL Containment Vessel Program,”

Presentation to Blue Ribbon Panel, Los Alamos National Laboratory, October 1999. (16) R. E. Link and E. J. Czyryca, “Mechanical Property Characterization of HSLA-100

Steel Plate,” David Taylor Research Center, DTRC-SME-88/38, December 1988. (17) E. J. Czyryca, “HSLA-100 Steel Plate Production (2nd Production Heat),” David

Taylor Research Center, DTRC-SME-89/19, July 1989. (18) E. J. Czyryca, “Fracture Toughness of HSLA-100, HSLA-80, and ASTM A710

Steel Plate,” David Taylor Research Center, DTRC-SME-88/64, January 1990. (19) E. J. Czyryca, et al., “Development and Certification of HSLA-100 Steel for Naval

Ship Construction,” Naval Engineers Journal, May 1990. (20) Military Specification, MIL-S-24645A, “Steel Plate, Sheet, or Coil, Age-Hardened

Alloy, Structural, High Yield Strength (HSLA-80 and HSLA-100),” September 1984.

(21) Military Specification, MIL-S-16216K, “Steel Plate, Alloy, Structural, High Yield

Strength (HY-80 and HY-100),” June 1987. (22) T. L. Anderson, Fracture Mechanics: Fundamentals and Applications, CRC

Press, Boca Raton, Florida, 1991. (23) M. F. Kanninen and C. H. Popelar, Advanced Fracture Mechanics, Oxford

University Press, Oxford Engineering Science Series 15, New York, NY, 1985. (24) J. M. Barsom and S. T. Rolfe, Fracture and Fatigue Control in Structures:

Applications of Fracture Mechanics, 2nd Edition, Prentice-Hall Inc., 1987. (25) API Recommended Practice 579, “Fitness for Service,” American Petroleum

Institute, January 2000. (26) E. A. Lange, “Selection of Materials for the Containment of Explosions at Low

Temperatures,” NRL 6381-65N:EAL, Naval Research Laboratory Report, July 20, 1979.



(27) T.R. Neal, “Limitations and Minimum Operating Temperatures for Confinement Vessels,” M-4:GR-89-1, Los Alamos National Laboratory, Los Alamos, NM, February 10, 1989

(28) J. M. Barsom and S. T Rolfe, “Correlations Between IcK and Charpy V-Notch Test

Results in the Transition-Temperature Range,” Impact Testing of Metals ASTM STP 466, American Society for Testing and Materials, 1970.

(29) S. T. Rolfe and S. R. Novak, “Slow-Bend IcK Testing of Medium-Strength High

Toughness Steels,” Review of Developments in Plane Strain Fracture Toughness Testing, ASTM STP 463, American Society for Testing and Materials, 1970.

(30) G. R. Irwin, “Relation of Crack-Toughness Measurements to Practical

Applications,” ASME Paper No. 62-MET-15, Metals Engineering Conference, Cleveland, April 9-13, 1962.

(31) G. R. Irwin, J. M. Krafft, P. C. Paris, and A. A. Wells, “Basic Aspects of Crack

Growth and Fracture,” NRL Report 6598, Naval Research Laboratory, Washington, DC, 1967.

(32) W. O. Shabbits, “Dynamic Fracture Toughness Properties of Heavy Section A533

Grade B Class 1 Steel Plate,” WCAP-6723, Westinghouse Electric Corporation, Pittsburgh, December, 1970.

(33) W. S. Pellini, and F. J. Loss, “Integration of Metallurgical and Fracture Mechanics

Concepts of Transition Temperature Factors Relating to Fracture-Safe Design for Structural Steels,” The Welding Research Council, WRC Bulletin 141, June 1969.

(34) A.K. Shoemaker and S.T. Rolfe, “The Static and Dynamic Low-Temperature

Crack-Toughness Performance of Seven Structural Steels,” Engineering Fracture Mechanics 2, No. 4, p. 319, 1971.

(35) R. J. Goode, R. W. Judy, Jr., and R. W. Huber, “Procedures for Fracture Toughness

Characterization and Interpretations to Failure-Safe Design for structural Titanium Alloys,” The Welding Research Council, WRC Bulletin 134, October 1968.

(36) R. W. Judy, R. J. Goode, and C. N. Freed, “Fracture Toughness Characterization

Procedures and Interpretations to Fracture-Safe Design for Structural Aluminum Alloys, “ The Welding Research Council, WRC Bulletin 140, May 1969.

(37) R. A. Ainsworth, “The Assessment of Defects in Structures of Strain Hardening

Material,” Journal of Engineering Fracture Mechanics, Vol. 19, No. 4, pp. 633-642, Pergamon Press, 1984.



(38) P. M. Scott, T. L. Anderson, D. A. Osage, and G. M. Wilkowski, “Review of Existing Fitness for Service Criteria for Crack-Like Flaws,” Welding Research Council, WRC Bulletin 430, April 1998.

(39) V. Kumar, M. D. German, and C. F. Shih, “An Engineering Approach to Elastic

Plastic Fracture Analysis,” Electric Power Research Institute, EPRI NP-1931, July 1981.

(40) V. Kumar and C. F. Shih, “Fully Plastic Crack Solutions, Estimation Scheme and

Stability Analyses for the Compact Specimen,” American Society for Testing and Materials, ASTM-STP 700, pp. 406-438, 1979.

(41) A. G. Miller, “Review of Limit Loads of Structures Containing Defects,”

International Journal of Pressure Vessels and Piping, Volume 32, pp. 197-327, 1988.

(42) T. L. Anderson, G. Thorwald, D. Revelle, D. A. Osage, J. L. Janelle, and M. E.

Fuhry, “Development of Stress Intensity Factor Solutions for Surface and Embedded Cracks in API 579,” Welding Research Council, Bulletin No. 471, New York, May 2002.

(43) S. M. Graham, and M. D. McLaughlin, “Dynamic Fracture Toughness

Characterization of HY-100 Under-matched Welds,” Naval Surface Warfare Center, Carderock Division, NSWCCD-61-TR-2001/05, February 2000.

(44) S. M. Graham, “Dynamic Fracture Toughness Testing and Analysis of HY-100

Welds,” Fatigue and Fracture Mechanics, 32nd Volume, American Society for Testing and Materials, ASTM STP 1406, 2002.

(45) J. A. Gianetto, W. R. Tyson, and J. T. Bowker, “Weld Metal and Heat Affected

Zone Toughness of HY-100 and HSLA-100 Weldments,” Metals Technology Laboratories, for the Defence Research Establishment Atlantic, DREA CR/95/499, Ottawa, Ontario, Canada, January 1996.

(46) R. Yee, “Study of Undermatched Welds in HSLA-100,” Fleet Technology Limited,

for the Defence Research Establishment Atlantic, DREA CR 98/414, Kanata, Ontario, Canada, January 1998.

(47) ASTM Specification, ASTM E-208, “Standard Method for Conducting Drop

Weight Test to Determine Nil-Ductility Transition Temperature of Ferritic Steels,” American Society for Testing and Materials, 2000.

(48) N. R. Borch, “As-Built Mechanical Properties and Service Temperature

Certification for 6-2 HSLA-100 Containment Vessels,” Los Alamos National Laboratory, Internal Memorandum, DX-5:98-005, February 25, 1998.



(49) Shug-Rong Chen, “HSLA Experimental Data and Constitutive Modeling,” Los Alamos National Laboratory, Internal Memorandum to Christopher Romero, May 16, 1997.

(50) G. R. Johnson and W. H. Cook, “A Constitutive model and Data for Metals

Subjected to Large Strains, High Strain rates, and High Temperatures,” Proceedings of the 7th International Symposium on Ballistics, pp. 541-547, The Hague, The Netherlands, April 1983.

(51) ASM Structural Alloys Handbook, American Society for Metals, Metals Park,

Columbus, Ohio, 1994. (52) M. Q. Johnson, “Summary of Dual-Axis Confinement System (DACS) Component

Material Properties,” Los Alamos National Laboratory, Memorandum to T. A. Duffey, DX-5, January 29,2004.

(53) P. Dong and J. K. Hong, “Recommendations for Determining Residual Stresses in

Fitness-for-Service Assessments,” Welding Research Council, Bulletin No. 476, New York, November 2002.

(54) P. Dong, F. W. Brust, “Welding Residual Stresses and Effects on Fracture in

Pressure Vessel and Piping Components: A Millennium Review and Beyond,” Journal of Pressure Vessel Technology, American Society of Mechanical Engineers, Vol. 122, pp. 329-338, August 2000.

(55) H. Gao, H. Guo, J. M. Blackburn, and R. W. Hendricks, “Determination of Residual

Stresses by X-Ray Diffraction in HSLA-100 Steel Weldments,” Proceedings of the International Conference on Residual Stresses, Linkoping, Sweden, June 1997.

(56) H. Guo, H. Gao, and R. W. Hendricks, “Visualization of Triaxial Residual Stress

Tensors Near Welds in HSLA-100,” Proceedings of the International Conference on Residual Stresses, Linkoping, Sweden, June 1997.

(57) K. Wallin, “Correlation Between Static Initiation Toughness JcK and Crack Arrest

Toughness IaK 2024-T351 Alloy,” American Society for Testing and Materials, ASTM STP 1406, Vol. 32, pp. 17-34, 2002.

(58) ASME Boiler and Pressure Vessel Code, (2001 Edition), Section VIII, Division

3, “High Pressure Vessels,” American Society of Mechanical Engineers, New York, NY, July 2001.

(59) Yun-Jae Kim, D. Shim, J. Choi, and Young-Jin Kim, “Approximate J estimates for

Tension-Loaded Plates with Semi-Elliptical Surface Cracks,” Engineering Fracture Mechanics, Vol. 69, pp. 1447-1463, 2002.



(60) FractureGraphic User’s Manual, Verison 2.5, Structural Reliability Technology,

Boulder, Colorado, (2004). (61) C. Guozhong and H. Qichao, “Stress Intensity Factors of Nozzle Corner Cracks,”

Engineering Fracture Mechanics, Vol. 38, No. 1, pp. 27-35, (1991). (62) C. Guozhong and H. Qichao, “Approximate Stress-Intensity Factor Solutions for

Nozzle Corner Cracks,” International Journal of Pressure Vessel and Piping, Vol. 42, pp. 75-96, (1990).

(63) E. Ballard and D. Shunk, “Confinement Vessel: Blank, Radiographic and Top-

Cover Analysis,” Los Alamos National Laboratory, Report No. DV-CAL-0014, March 2004.

(64) D. Shunk, “Two Dimensional Dynamic Structural Analysis of Entrance Cover for

the Dual-Axis Confinement Vessel,” Los Alamos National Laboratory, Report No. DV-CAL-0051, November 2003.

(65) J. Decock, “Determination of Stress Concentration Factors and fatigue Assessment

of Flush and Extruded Nozzles in Welded Pressure Vessels,” 2nd International Conference on Pressure Vessel Technology, Part II, pp. 821-834 (1973).



APPENDICES



APPENDIX A

DAVID TAYLOR RESEARCH CENTER (DTRC) DATA FOR HSLA-100 DTRC performed the bulk of material testing [16-19] for the 1st and 2nd production heats on HSLA-100 qualification. Mare Island Naval Shipyard (MINS) conducted several tests that are reported in the DTRC documents. The testing ultimately led to certification of the material for US Navy applications in nuclear submarine hulls and other surface combatant vessel applications. Culmination of DTRC certification of HSLA-100 was the development of MIL-S-24645A [20], which imposes specific material chemistry control and impact tests for qualification. Similarity exists between MIL-S-24645A and the HY-80/HY-100 material specification MIL-S-16216K [21], specifically in the impact energy requirements. The list of technical reports from DTRC supports the breadth of information, range of plate material thickness tested, and their respective mechanical and impact properties. The important aspects are the mechanical, impact, and fracture toughness properties, as well as determination of the nil-ductility transition (NDT) temperature [16]. The mechanical properties are shown to exceed that of previous high-strength materials, such as HY-80 and HY-100. Most significant, however, is the higher fracture toughness of this material as compared to other steels, including pressure vessel steels currently used in the commercial nuclear industry. A comparison of this material with previous LANL vessel material and other pressure vessel steels is presented in Appendix C of this report. The purpose of this appendix is to provide a means of comparison between the mechanical and impact properties of HSLA-100, as determined from the DTRC qualification tests and those that have been documented for the LANL vessels. A comparison of the DTRC data with the LANL “as-built” mechanical and impact properties, shown in Appendix B of this report, provides assurance of the quality of the material and consistency of mechanical and impact properties. A.1 Mechanical Properties Typical mechanical properties for 1/4” through 3-1/2” thick plate material were obtained using uniaxial tension specimens. Table A.1 shows DTRC data for HSLA-100 for a subset of static tensile tests. As can be gleaned from the table, yield strength, ultimate tensile strength, and ductility parameters percent elongation and reduction of area (%e and %RA) have small variations.



Table A.1 - HSLA-100 Mechanical Properties (DTRC) [16,17] Thickness

(in.) Orientation 0.2% Yield

Strength (ksi)

Tensile Strength

(ksi)

Elong. (%)

Reduction in Area

(%) 3/4 T

L 109 110

121 121

29 29

77 76

1 T L

109 109

121 121

29 28

77 76

1-1/4 T L

116 117

124 123

25 25

74 74

2 T L

107 106

113 113

25 25

77 76

T - Transverse to rolling direction L - Longitudinal, or rolling direction

A.2 Impact and Fracture Properties Figures A.1 and A.2 present the CVN impact (absorbed) energy, while Figures A.3 and A.4 present DTTE for 1-1/4-in. and 2-in. thick plate HSLA-100 samples. Each figure depicts the size plate from which the specimens were fabricated. The DTTE approach was originally developed by NRL in the early 1970s in response to, and as a result of, structural failures that apparently had “adequate” upper-shelf CVN energies. The inadequacies of the CVN test were later recognized [6-10] to be the following:

• Radius notch instead of a sharp crack, • Lack of through-thickness constraint (i.e., relatively thin specimen), • Plane-stress effect, and • No temperature shift applied for thicker parts.

As a result, CVN energies used in this report are for confirmatory purposes only.



0

50

100

150

200

250

-200 -150 -100 -50 0 50 100

HSLA-100 CVN for 2" Thick Plate

T-L 1T-L 2T-L 3L-T 4L-T 5L-T 6

Cha

rpy

V-N

otch

, (ft-

lb)

Temperature, (°F)

• Austenitized @ 1660°F - WQ

• Aged @ 1180°F - WQ

Figure A.1 - CVN energy for 2-in. HSLA-100 plate [16,17].

0

50

100

150

200

-200 -150 -100 -50 0 50 100

HSLA-100 CVN Energy for 1-1/4" Thick Plate


Cha

rpy

V-N

otch

, (ft

-lb)

Temperature, (°F)


• Aged @ 1180°F - WQ

Lukens Steel

Figure A.2 - CVN energy for 1-1/4-in. HSLA-100 plate [16,17].



0

500

1000

1500

2000

-200 -150 -100 -50 0 50 100

HSLA-100 Dynamic Tear for 2" Thick Plate


Dyn

amic

Tea

r, (f

t-lb)

Temperature, (°F)


• Aged @ 1180°F - WQ 5/8" DT Specimen

Lukens Steel

Figure A.3 - DTTE for 2-in. HSLA-100 plate [16,17].

0

500

1000

1500

2000

-200 -150 -100 -50 0 50 100

HSLA-100 DT Energy for 1-1/4" Thick Plate


Dyn

amic

Tea

r, (f

t-lb

)

Temperature, (°F)


• Aged @ 1180°F - WQ

Lukens Steel

5/8" DT specimen

Figure A.4 - DTTE for 1-1/4-in. HSLA-100 plate [16,17].



The overall range of CVN impact energies from tests conducted at DTRC is shown in Figure A.5. The figure depicts upper-shelf CVN energies, even at temperatures between -90°F and -120°F. Therefore, one could assume, albeit incorrectly, that adequacy from a catastrophic fracture point of view would not be a concern by maintaining the material within the upper-shelf CVN energy temperature range. Thus, one could conceivably operate the vessel at -90°F to -120°F.

Figure A.5 - Range of CVN energy for all thickness HSLA-100 plate [16].



Figure A.6 - Range of DTTE for all thickness HSLA-100 plate [16]. To demonstrate why LANL cannot rely on the CVN approach, assume that a vessel is operated at -90°F because the material exhibited high upper-shelf CVN energy, as shown in Figure A.5. Now, using the -90°F as the entry point in Figure A.6, consider the associated dynamic tear test energy using the lower-bound DTTE curve. Clearly, the -90°F temperature would constitute a transition temperature for DTTE, such that brittle fracture would be possible. The use of the CVN energy in this case could lead to catastrophic fracture. It is therefore concluded for HSLA-100 that CVN energy, while applicable for manufacturer’s qualification of plate material, is unacceptable for design purposes and therefore unacceptable in setting the MOT for HSLA-100 material. This notion is expanded in detail in Appendix C. A.3 J-R Curve Results DTRC also performed J-R and CTOD toughness measurements [17,18], comparing several of the high-yield (HY) and high-strength low-alloy (HSLA) materials used in naval applications. J-R curve on plate material showed the average IcJ for HSLA-100 within the temperature range of 75oF to -160oF is approximately 2435 in-lb/in2 (i.e., IcK = 280 ksi-in1/2). These studies were conducted with fatigue pre-cracked, side-grooved compact tension (CT) specimen machined from 1-1/2 inch thick plate. Figure A.7 and A.8 show test data for (1) room temperature and (2) various temperatures, respectively.



Figure A.7 - Room temperature (75oF) toughness curve for 1-1/2 inch plate [17].

Figure A.8 – Range of J-R curve for 1-1/2 inch plate at75oF to -200oF [17].



The results of Figures A.7 and A.8 indicate no effect of orientation on fracture toughness behavior. IcJ values are also shown in the figures, indicating a lower-bound room temperature IcJ of 2177 psi-in. Furthermore, the J-R data of Figures A.7 and A.8 can be idealized by a power-law fit with the following parameters;

( ) 6864.037240 aJ ∆= Figure A.9 provides IcJ data (open circles) for 2-inch thick plate, showing consistent level above 2000 psi-in toughness. The notation IJ refers to a value of J near the onset of slow, stable tearing. The figure also shows those specimen (i.e., closed symbols) indicating the total value of J at cleavage fracture.

Figure A.9 – IcJ test data for 2-inch thick HSLA plate [18]. Figure A.10 depicts a J-R curve for 2-inch thick HSLA-100 plate at room temperature. At 0.1-inch crack extension, the 1-1/2 inch plate data shown in Figure A.7 results in a higher toughness value (7500 psi-in) than the 2-inch thick plate specimen (5500 psi-in) of Figure A.10.



Figure A.10 – J-R Curve for 2-inch thick HSLA-100 plate [18]. A.4 NDT Test Results Determination of the NDT temperature provides a designer and vessel operator with a temperature limit below which the material exhibits a purely brittle behavior. This is a condition to be avoided. As such, it is very important to determine NDT temperature. Above the NDT temperature, the material begins to exhibit a mixed-mode fracture behavior, which is predominantly cleavage with little ductile tearing. As the temperature increases, the mixed-mode behavior becomes more 50% cleavage and 50% ductile. DTRC used 3/4-in. thick plate stock from the 1st production heat [16] in administering drop-weight test (DWT) to determine the NDT temperature of HSLA-100. DWT’s were performed in accordance with ASTM Specification ASTM E-208 [47]. Results of the 3/4-in. plate DWT show NDT for HSLA-100 as

NDT = -210°F



For comparison with actual data, Figure A.11 shows CVN impact energy for 1-1/2-in. plate, well into the low-temperature region. This test was accomplished by DTRC to determine lower-shelf energies and transition temperatures. The figure reasonably depicts lower-shelf CVN energies of 20 to 30 ft-lb through the transition temperature range. Importantly, the figure also shows, albeit inconclusively, that the CVN transition temperature range is within the -210°F NDT measured with the DWT. This provides some assurance of the NDT temperature determined by DTRC. Figure A.12 presents the lower-shelf energies as well, but the transition temperature for the DTTE is much higher than the CVN energy. That is, the limit of plane-strain and transition to plane-stress effect is around -180°F for DTTE. Beyond this point, mixed-mode fracture takes effect where ductile tearing with some cleavage is predominant. Nearing the upper-shelf, the failure mode is purely ductile tearing. It is concluded from the foregoing that setting the MOT with DTTE data is reasonable, appropriate, and conservative for HSLA-100 material.

20

40

60

80

100

120

140

160

180

-400 -300 -200 -100 0 100

HSLA-100 CVN Energy for 1-1/2" Thick Plate

T-L 1T-L 2T-L 3T-L 4T-L 5T-L 6

Cha

rpy

V-N

otch

, (ft

-lb)

Temperature, (°F)

• Twice austenitized @ 1650°F - WQ

• Aged @ 1200°F - Initial heat treatment

• Aged again @ 1240°F - WQ

Luken Steel

Figure A.11 - CVN energy for 1-1/2-in. HSLA-100 plate [16,17].



0

500

1000

1500

-400 -300 -200 -100 0 100

HSLA-100 Dynamic Tear for 1-1/2" Thick Plate

T-L 1L-T 2

Dyn

amic

Tea

r, (f

t-lb)

Temperature, (°F)

Luken Steel

5/8" DT specimen

• Twice austenitized @ 1650°F - WQ

• Aged @ 1200°F - Initial heat treatment

• Aged again @ 1240°F - WQ

Figure A.12 - DTTE for 1-1/2-in. HSLA-100 plate [16,17].



APPENDIX B

LANL HSLA-100 MATERIAL CERTIFICATION

The certification of material in the first two HSLA-100 vessels was accomplished first by the vessel manufacturer and second by Material Sciences and Technology (MST) Division at LANL. Manufacturer’s information on the steel vessels is shown in Table B.1, encompassing all of the data for each specimen tested. The table also identifies the specimen location on the vessel geometry. This appendix, in conjunction with the DTRC data in Appendix A, provides assurance that mechanical and impact properties for HSLA-100 are consistent between the two testing laboratories.

B.1 Mechanical Properties Table B.1 presents the range of mechanical properties for the LANL vessels [48]. That is, these are typical mechanical properties determined under static, quasi-static, or impact conditions in accordance with the appropriate ASTM testing standards. Important to note is the lower static yield strength for the nozzle welds and nozzle-to-shell weld HAZ. The lower properties for the weld do not present a problem with regards to fracture toughness. As will be shown in Appendix D of this report, the dynamic yield strength and fracture toughness of the welds and HAZ appear equal to, or better than, the parent material near the nozzle region. Nevertheless, additional tensile testing for the “as-built” welds will be accomplished to determine the true stress-strain curve and dynamic yield strength. The condition that would be affected, by the lower static yield and ultimate strength of the welds, is the ductile failure mode of the vessel under static or quasi-static conditions. This would only be possible if the residual pressure remaining after detonation were near the burst pressure of the vessel. This failure mode is treated separately [4] for the LANL containment vessels. As previously mentioned, LANL’s MST Division also performed material testing of the specific HSLA-100 vessel plate material and as-built coupons. Low to medium strain-rate data were taken [49] with (1) an Instron test frame for low strain rate, and (2) an MTS test system for medium strain rate. The raw data, which included actual percent reduction in area (%RA) measurement as a function of applied load, were used to produce a true stress-strain curve in the form of a Johnson-Cook model, depicted graphically in Figure B.1.



Table B.1 - LANL Vessel As-Built Mechanical Properties [48] Vessel No. and Part

Yield Strength

(ksi)

Ultimate Tensile

Strength (ksi)

Elongation (%)

Reduction of Area (%)

Vessel 1 Head 1 102.10 113.10 25.0 74.0

Head 1a* 103.10 113.00 26.2 74.8 Head 1b* 103.20 112.30 ND 75.4

Head 2a 108.00 116.00 21.0 74.0 Head 2b 108.00 116.00 23.0 73.0 Head 2* 118.80 120.40 24.0 72.0

16 in. Nozzle 105.00 115.50 22.0 71.0 22 in. Nozzle 107.10 117.80 21.0 72.0 Girth Weld 1 89.90 98.40 23.5 71.6 Girth Weld 2 91.90 100.00 25.3 77.7

Average 90.00 99.20 24.4 74.7 Shell/Nozzle

Weld 1 95.00 100.00 25.0 74.0

Shell/Nozzle Weld 2

102.00 105.00 24.0 74.0

Average 98.50 102.50 24.5 74.0 Vessel 2

Head 3 102.10 113.10 25.0 74.0 Head 4 102.10 113.30 25.0 74.0

16 in. Nozzle 105.00 115.50 22.0 71.0 22 in. Nozzle 107.10 117.80 21.0 72.0 Girth Weld 1 91.40 98.40 24.0 75.7 Girth Weld 2 92.40 100.00 24.6 77.8

Average 91.90 99.20 24.3 76.8 * - Estimated values from manufacturer ND - Not determined



60

80

100

120

140

160

180

200

0 0.2 0.4 0.6 0.8 1 1.2

Johnson-Cook Constitutive Model

0.001 s-1

0.01 s-1

0.1 s-1

1.0 s-1

10 s--1

100 s-1

True

Stre

ss, (

ksi)

True Plastic Strain, (in/in)

Johnson-Cook Model

for: T = 298K

Figure B.1 - True stress-strain characteristic. The Johnson-Cook [50] model is

( )( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡

−−

−++=m

refmelt

refnp TT

TTCBA 1ln1 εεσ ,

where εp = Plastic strain, ε = Strain rate, (s-1), n = Strain-hardening exponent, m = Temperature exponent, CBA ,, = Material constants, and MPaA 175= MPaB 1375= 0085.0=C 6.0=m T = Test temperature, (298K), Tref = Reference temperature (200K), and Tmelt = Melt temperature, (1808K).



Conclusions drawn from the LANL strain-rate dependent tensile tests were

(1) Dynamic yield strength: ksiSyd 105= (2) Strain-hardening exponent: 1375.0=n (3) Small deviations are exhibited in stress-strain curves for strain-rates between

0.001s-1 and 100s-1. An important parameter obtained from this model is the strain-hardening exponent, n , which results in a value of 0.1375 for this material. The strain hardening exponent is crucial in determination of onset of instability for ductile failures [4] and, in a uniaxial test, the value of strain hardening exponent is numerically equal to the true strain at the onset of instability. The Johnson-Cook model is used for analysis of the vessel response under the dynamic blast wave for conditions of (1) room temperature and (2) strain rates within 10 s-1 to 100 s-1. These strain-rates are within the range of response for HE charges up to 60-lb. Thus, the model may be simplified to a power-law representation (with stress noted in ksi) for ease of computations;

npoεσσ =

where =oσ Material parameter; stress at plastic strain of unity, (ksi) =pε True plastic strain, (in/in) The resulting equation for HSLA-100 plate/shell/forging material within the strain-rate range of 10 s-1 to 100 s-1is;

1375.0185 pεσ = This information will be used in a subsequent Appendix to determine J-plastic for crack driving force. B.2 Impact and Fracture Properties Table B.2 presents the vessel manufacturer’s DTTE information for each sample taken from two sacrificial vessels [48]. Per requirements from LANL Construction Standard [3] and material purchase specification, a DTTE of 750 ft-lb at -60°F would satisfy the intent of assured crack arrest for the vessels. This requirement was derived from an original stipulation to cover requirements up to the thickest part, that being 4-in. thick plate. This information is used to determine the vessel shell and nozzle component MOT, and subsequently determine the limiting MOT for the complete vessel system.



Table B.2 - LANL Vessel Dynamic Tear Energy Data [48]

Part ID Sample ID Test Temperature (°F)

Dynamic Tear Test Energy (ft-lbs)

Head 1 1L1 1T1

-40.0 -40.0

1558 1670

Head 2 2L1 2T1

-40.0 -40.0

786 601

Head 3 3L1 3T1

-40.0 -40.0

1561 1514

Head 4 4L1 4T1

-40.0 -40.0

1528 1444

16 in. Nozzle 2844L-1 2844L-2

-70.0 -70.0

344 342

22 in. Nozzle 2844L-1 2844L-2

-70.0 -70.0

435 472

Vessel 1 Girth Weld VES1-1

VES1-2 -40.0 -40.0

686 481

Girth HAZ V1HAZ-1 V1HAZ-2

-40.0 -40.0

929 1663

Head 2 HAZ HAZ2-1 HAZ2-2

-15.0 -15.0

1447 1112

Nozzle Weld DTWT-1 DTWT-2 DTWT-3 DTWT-4

-40.0 -40.0 -20.0 -20.0

466 1118 1201 1174


VES2-2 -40.0 -40.0

513 507


-40.0 -40.0

1072 1181

Figure B.2 presents a complete DTTE curve from several nozzle specimens for LANL containment vessel material. These were actual “as-built” specimens. Five separate specimens were taken for the nozzle’s weld metal HAZ, which are also shown in Figure B.2. The FTE point for the 5/8-in. specimen is -30°F, and the lower-limit (L) of the elastic-plastic behavior is at -40°F. The fracture-transition-plastic (FTP) temperature is located mid-way between the FTE and the upper-shelf. Per Pellini and Loss [33], this location is roughly FTP = NDT + 120o, which represents attainment of fully plastic fracture. These two points at their respective stress levels are assured crack arrest conditions and are technically consistent with the NRL philosophy [6-10].



LANL containment vessel nozzle design is stipulated to not exceed the 0.5Sy limit, and therefore the DTTE required at the 0.5Sy limit is achieved at the lower limit of elastic-plastic behavior. As evident from the figure, the weld metal DTTE, at the specimen temperatures, is much higher than the parent material. This implies that the weld metal has a higher fracture toughness and should not be considered the “weak-link” in the design. Further details are provided in Appendix D for the weld and HAZ.

0

500

1000

1500

2000

-100 -50 0 50

Nozzle and Nozzle-to-Shell Weld HAZ Dynamic Tear Energy

NozzleWeld HAZ

Dyn

amic

Tea

r Ene

rgy,

(ft-l

b)

Temperature, (°F)

• 5/8" DT Specimen

FTE

FTE - Fracture transition elasticL

L - Lower limit of elastic-plastic

• 16" Diameter Nozzle

Figure B.2 - DTTE for nozzle and nozzle-to-shell weld HAZ [48].



APPENDIX C

PRESSURE VESSEL STEEL COMPARISON HSLA-100 is a low-carbon, copper precipitation strengthened, quenched and tempered steel meeting the requirements of HY-100. Chemistry is maintained with close tolerances, especially for the carbon content, which is from 0.04% to 0.06%. Hardenability is increased through addition of manganese, nickel, and molybdenum. The addition of nickel, while lowering the upper-shelf toughness, also lowers the transition temperature range, which becomes beneficial in low-temperature operation. C.1 Metallurgy Table C.1 presents data for several pressure vessel steels, including HSLA-100, that have been used at LANL over the past 3 decades for HE containment systems. As evident in the table, all other steels contain much higher carbon content, which limits their fracture toughness. Typically, for carbon-manganese steels such as A516 and A537, a small increase in carbon content results in a dramatic decrease in fracture toughness.

Table C.1 - Chemical Composition

Material

C (%)

Mn (%)

Ni

(%)

Cu (%)

Mo (%)

Cr

(%)

Cb (%)

HSLA-100 [20]

0.04 - 0.06

0.75 – 1.05

3.35 – 3.65

1.45 – 1.75

0.55 – 0.65

0.45 – 0.75

0.02 – 0.06

A516 [51]

0.30

0.80 – 1.25

0.25

0.35

0.08

0.08

Nil

A537 [51]

0.24

0.70 – 1.60

0.25

0.35

0.08

0.08

Nil

HY-80

[21]

0.13 – 0.18

0.10 – 0.40

2.50 - 3.00

0.25

0.35 – 0.60

1.40 - 1.80

Nil

HY-100

[21]

0.14 – 0.20

0.10 – 0.40

2.75 – 3.50

0.25

0.35 – 0.60

1.40 – 1.80

Nil

The conclusion that can be drawn from the foregoing table is that HSLA-100 has lower carbon content than all other pressure vessel steels, and therefore potentially lower NDT as well. This is an attractive feature as vessel operation with HSLA-100 can be performed at lower temperatures than other steels.



C.2 Mechanical Properties Comparison Table C.2 shows the range of mechanical properties for the different types of pressure vessel steels, including HSLA-100. Although it is clearly evident that HSLA-100 has much higher strength than previous vessels constructed at LANL, the most important parameter is “ductility.” The ductility of a material is its ability to plastically flow under stress. The parameters which affect ductility are the percent elongation (%Elong) and reduction of area (%RA), shown on the last two columns of Table C.2. Based on these parameters, HSLA-100 ductility is far higher than the HY-80/100 series, and somewhat comparable to carbon steel A537.

Table C.2 - Engineering Properties

Material Specificatio

n

Yield

Strength (ksi)

Tensile

Strength (ksi)

Elongation

(%)

Reduction

of Area (%)

HSLA-100

[20]

100

115

24

74

A516 [48]

38

70

21

54

A537 [48]

60

80

22

70

HY-80 [21]

80

95

20

50

HY-100

[21]

100

115

18

45

Figures C.1 and C.2 show a comparison of uniaxial engineering stress-strain and true stress-strain characteristics for HSLA-100 as compared with HY-80, HY-100, and A516 and A537 carbon steel for static conditions. These data were developed using a power-law representation to the point of uniform elongation (i.e., engineering ultimate strength) for the engineering stress-strain curves. The true stress-strain curves used a similar power-law representation to the point of true ultimate failure strain.



0

20

40

60

80

100

120

140

0 0.05 0.1 0.15 0.2 0.25

Pressure Vessel Steels: Engineering Stress Strain Data

HSLA-100A516A537HY-80HY-100

Stre

ss, (

ksi)

Strain, (in./in.)

HSLA-100 and HY-100

Note: Final strain measure isonset of necking based onuniaxial tensile specimen.

Figure C.1 - Engineering stress-strain curves, up to onset of necking.

0

20

40

60

80

100

120

140

160

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Pressure Vessel Steels Tensile Characteristic

HSLA-100A516A537HY-80HY-100

Tru

e St

ress

, (ks

i)

True Strain, (in./in.)

Power-Law Representation

Figure C.2 - True stress-strain curves.



A basis for comparison of the different materials is the total strain-energy to failure, using the true strain at failure, not the strain at onset of instability. Table C.3 depicts the total strain-energy to failure (or merely, the area under the true stress-strain curve). Importantly, the static tensile test curves depicted in Figures C.1 and C.2 for HSLA-100 are very conservative in terms of total strain energy. Thus, the total strain energy to failure presented in Table C.3 for HSLA-100 is a lower-bound estimate.

Table C.3 Total Strain Energy to Failure

Material

Strain Energy to Failure (in.-kips)

HSLA-100 156 A516 112 A537 119

HY-80 124 HY-100 146

C.3 Impact and Fracture Properties Figures C.3 and C.4 show a comparison of CVN absorbed energy for HSLA-100 as compared with HY-80, A516, and A537 carbon steel. It is evident that HSLA-100 has superior impact properties compared to other pressure vessel steels, including HY-80.

0

50

100

150

200

250

-200 -100 0 100 200 300

CVN Data Comparison

HSLA-100A516A537HY-80

Impa

ct E

nerg

y, (f

t-lb)

Temperature, (°F)

Ref: HSLA-100 (DTRC - E. Czyryca)Ref: A516/A537/HY-80 (Structural Alloy Hdbk.)

Figure C.3 - CVN data comparison [16,21,51].



20

30

40

50

60

70

80

90

100

-150 -100 -50 0 50 100 150 200

CVN Test for A516/A537

A516A537

Impa

ct E

nerg

y, (f

t-lbs

)

Temperature, (°F)

Containemnt vessel material used atLANL in the 1960's and 1970's

Figure C.4 - CVN data for A516 and A537 [51]. Important to note are the transition temperatures, as depicted by the CVN test, for both these steels. Steel A516 appears to have a transition temperature between +50°F and +70°F, and A537 between -50°F and -30°F. Ideally, one would want to operate these materials above the limit of plane-strain (i.e., the transition temperature) to achieve a mixed-mode or purely ductile failure. That entails assuring that A516 steel is operated above +70°F and A537 is operated above -30°F. The implication of using CVN energy is that it pertains not only to a specimen size (0.394-in. by 0.394-in.) but not the actual size of the part. In other words, the temperature at a given CVN energy is not corrected for thicker material part. Figure C.5 depicts complete DTTE curves for two steels, HSLA-100 and A537. The FTE point, being the mid-point between the upper and lower shelf DTTE [6-10], implies an operating temperature design point for “assured crack arrest.” Pellini and Loss provide a measure of this location at FTE = NDT + 60o [33]. HSLA-100 not only has a higher fracture toughness overall, but attains an operating temperature 80°F lower than A537. This implies that HSLA-100 may be operated at lower temperatures than A537 steel, which was one of the original attractive features of this material.



0

500

1000

1500

2000

-100 -50 0 50 100 150 200

HSLA-100 and A537 Steel Impact Properties

HSLA-100A537

Dyn

amic

Tea

r E

nerg

y, (f

t-lbs

)

Temperature, (F)

LANL DT test for nozzle material

FTE

FTE

Figure C.5 - DTTE data comparison. C.4 ASME Code Comparison The ASME Code [11] uses the CVN test as a basis for assessing a material’s adequacy for prevention of non-ductile failures, in conjunction with conservative estimates of IcK for analytical evaluation of potential critical flaws. The Code imposes the requirement that at (NDT + 60°F), the CVN energy for the given vessel material should be at or greater than 50 ft-lb. Given this guidance, the material is said to have good fracture toughness, and the material (e.g., a vessel) may be operated at a service temperature chosen from ASME Code guidance in Section III, Appendix G. In view that HSLA-100 has an NDT temperature of -210°F, the (NDT + 60°F) requirement from the Code would place the operating temperature at -150°F. In evaluating Figure C.6, the CVN energy for 2-in. HSLA-100 plate at -150°F is above 50 ft-lb. Therefore, according to the ASME Code, the vessel may be operated at this service temperature. The MOT for the LANL HSLA-100 vessels is based on use of a DTTE specimen. Figure C.7 shows that the lower-shelf DTT energy, for the 2-in. thick plate, is within the vicinity of -50°F to -30°F. As previously mentioned, the design point for the LANL vessels is the FTE location, which is midway between the upper and lower-shelf DTTE. As previously mentioned, the FTP is mid-way between the FTE and upper-shelf. Again, Pellini and Loss place FTP = NDT + 120o [33]. The temperature relative to FTE, for the 5/8-in. thick specimen taken from a 2-in. thick plate, is about 0°F.



0

50

100

150

200

250

-200 -150 -100 -50 0 50 100

HSLA-100 CVN for 2" Thick Plate


Cha

rpy

V-N

otch

, (ft-

lb)

Temperature, (°F)


• Aged @ 1180°F - WQ

Figure C.6 - CVN energy for 2-in. HSLA-100 plate [16,17].

0

500

1000

1500

2000

-200 -150 -100 -50 0 50 100

HSLA-100 Dynamic Tear for 2" Thick Plate


Dyn

amic

Tea

r, (f

t-lb)

Temperature, (°F)


• Aged @ 1180°F - WQ 5/8" DT Specimen

Lukens Steel

Figure C.7 - DTTE for 2-in. HSLA-100 plate [16,17].



APPENDIX D

WELDS AND WELDING HSLA-100 was developed as a replacement for HY-100 to reduce fabrication cost, but still meet, or exceed, the strength requirements of HY-100. More importantly, HSLA-100 is easily welded with little or no preheat, which is an attractive feature for large-scale components (i.e., submarine hulls) that could not easily be placed in a furnace. The significant factor, however, in cost savings for US Navy applications was the reduction or elimination of PWHT. Fusion welded marine structures are typically fabricated with welding consumables and procedures that produce welds with higher yield strengths than the base plates being joined (over-matching). This is done to prevent development of high strains in the weld metal, which typically has lower fracture toughness and more defects than base metal. Allowing the weld metal yield strength to be less than the parent metal (under-matching) can increase productivity, but more importantly, increase in weld toughness [43,44]. Welding of HSLA-100 and HY-100 steels is accomplished with the MIL-100S-1 welding consumables, which are known to produce under-matching welds [43,44]. Nonetheless, because there is no PWHT for HSLA-100, there are some definite benefits and drawbacks. The major benefit, as stated above, is the increase in toughness. Conversely, PWHT of HSLA-100 structures greatly reduces the weld fracture toughness. D.1 Weld Development for Production Welds For LANL’s Dual-Axis Confinement System (DACS) vessel, a double-V joint preparation has been used to join the hemispherical heads and nozzles-to-shell. Semi-automatic gas metal arc welding (GMAW) has been utilized to produce the internal weld while fully automatic submerged arc welding (SAW) was utilized to produce the external weld. Shielded metal arc welding (SMAW) procedures have been qualified in case a repair weld is required. Testing of welding consumables is conducted prior to purchase to ensure that the welding consumables would deposit welds with the expected properties over a wide range of welding conditions (i.e. fast and slow cooling rates). The primary concern for joining HSLA-100 is the ability of the welding consumables to deposit welds that do not significantly under-match the heads and forgings while possessing acceptable DTTE toughness and resistance to weld metal hydrogen assisted cracking. It has been found [52] that weld metal toughness is process-dependent and essentially independent of cooling rates for the range of weld metal cooling rates employed. Yield and tensile strength, conversely, is strongly dependent on weld metal cooling rate. Figure D.1 shows how cooling rate influences the tensile properties of the MIL-100S-1 welding consumables. As the time for cooling between 800 °C and 500 °C increases, weld metal



strength decreases. This cooling rate parameter, ∆t800-500, is a widely accepted method to characterize weld metal cooling rate. Production welding procedures are selected so that weld yield strength remains above 90 ksi and the risk of hydrogen assisted cracking is also minimized (this is influenced by interpass temperature, heat input, and diffusible hydrogen).

∆t800-500 (s)

0 10 20 30 40 50

YS o

r UTS

(ksi

)

70

80

90

100

110

120

Yield StrengthUTS

UTS (min)

YS (min)

Production SAW

Figure D.1 - Relationship between cooling rate and weld metal tensile properties

when using MIL-100S-1 welding consumables. A comparison of the static ( 10013.0 −= sstε ) and dynamic ( 110 −= sdyε ) strengths measured in all weld metal tensile specimens is shown in Table D.1. For the welds tested, the loading-rate results in a corresponding elevation of yield and ultimate tensile strengths from +6 to +10 ksi increase. Given the scatter in high strain-rate data, the use of static yield strength for design considerations seems appropriate. Relative to the heat-affected-zone (HAZ) testing results, all production qualified welds were produced with a single-bevel joint geometry to ensure that the DT notch sampled only heat affected zone rather than a combination of HAZ and weld metal. The weld metal and HAZ test results are shown in Tables D.2 and D.3. Review of this data with previous LANL data and the base metal toughness data indicates that the HAZ of the HSLA-100 material does not experience a drastic reduction in DTTE or CVN toughness when welded with the SMAW, GMAW, or SAW process and moderate heat input.



Table D.1 – Weld Static/Dynamic Yield Strengths [52] Weld Strain Rate

(s-1) Yield (ksi)

Ultimate (ksi)

SAW 1 1.5 101 113.3 SAW 2 9.4 99.1 112.1 SAW 3 8.4 99.7 113.3 Static 0.0018 90 106 GMAW 1 8.9 150.5 156.7 GMAW 2 10.3 100.2 111.5 GMAW 3 9.9 115.5 121.6 Static 0.0014 94 101 SMAW 1 7.1 108 124.8 SMAW 2 9.2 127 132.4 SMAW 3 9.4 127.2 129.9 Static 0.0013 112 122

Table D.2 – Weld HAZ Toughness [52]

HAZ Test Spec. (ft-lb)

GMAW (ft-lb)

SAW-0 (ft-lb)

SAW 1 (ft-lb)

SAW 2 (ft-lb)

SMAW (ft-lb)

CVN @ 0oF 60 144 117 164 No Data 87 CVN @ -60oF 35 107 80 114 No Data 56 DTT @ -20oF 450 1383 960 1054 No Data 755

Table D.3 – Weld HAZ Toughness [52]

HAZ Test Spec. (ft-lb)

GMAW (ft-lb)

SAW 1 (ft-lb)

SAW 2 (ft-lb)

SMAW (ft-lb)

CVN @ 0oF 60 171 238 262 184 CVN @ -60oF 35 131 240 217 167 DTT @ -20oF 450 775 1328 1941 817

D.2 “As-Built” Vessel Weld Mechanical Properties Table D.4 presents the actual as-built static tensile mechanical properties for LANL’s first two HSLA-100 vessels. Although the static yield strength is slightly lower than the LANL specification (i.e., 95 to 100 ksi), the dynamic yield strength of the welds and nozzle-to-shell weld HAZ are approximately 10-15 ksi higher than the static tensile test [24]. This increase in dynamic yield strength would match the parent material for both the shell and nozzles under HE-driven impulse conditions. The welds retain the excellent ductility that is also afforded by the parent metal. Further tensile testing of the “as-built” welds is being accomplished to accurately determine the strain-rate dependent yield strength and the actual true stress-strain curve. Although LANL has obtained limited data, additional testing is also on-going to determine true stress-strain characteristics and the strain-rate dependence of yield strength. These tests will confirm the increase of dynamic yield strength over the static strength.



Table D.4 - LANL Vessel As-Built Weld Mechanical Properties [48]

Vessel No. and Part

Yield Strength (ksi)

Ultimate Tensile Strength (ksi)

Elongation (%)

Reduction of Area (%)

Vessel 1 Girth Weld 1 89.90 98.40 23.5 71.6 Girth Weld 2 91.90 100.00 25.3 77.7

Average 90.00 99.20 24.4 74.7 Shell/Nozzle

Weld 195.00 100.00 25.0 74.0

Shell/Nozzle Weld 2

102.00 105.00 24.0 74.0

Average 98.50 102.50 24.5 74.0 Vessel 2

Girth Weld 1 91.40 98.40 24.0 75.7 Girth Weld 2 92.40 100.00 24.6 77.8

Average 91.90 99.20 24.3 76.8 The stress-strain curve for the weld metal also follows a power-law strain-hardening characteristic as shown in Figure D.2. Material tests accomplished for the LANL single-axis vessels [48], US Navy application by Graham [43,44], and Gianetto and Yee [45,46] at Defence Research Establishment Atlantic (DREA) in Canada, show good correlation for the MIL-100S-1 weld consumable. Weld true stress-strain characteristic compares favorably with test data obtained by DREA in Canada [45,46]. Below is the LANL single-axis vessel data, Average Girth Weld

psiSy 000,90= @ 0.2% plastic strain psiSu 200,99= 29.0=ν psiEE 629 += psiEG 615.11 +=

%4.24=EL (min) %7.74=RA (min) Average Nozzle-to-Shell Weld


%3.24=EL (min) %8.76=RA (min) Using minimum engineering values (i.e., Girth weld), the following true stress-true plastic strain curve represents the material up to a maximum plastic strain of 50%. The constitutive equation for HSLA-100 weld is the following, with 00302.0=yε at the proportional limit;



( ) 0617.03.125 pw εσ = (D.1a) The LANL dual-axis vessel “as-welded” data shows the following properties, and the true stress-strain curve can be characterized by a power-law;


%24=EL (min) %69=RA (min) where, 0752.0150 pw εσ = (D.1b) D.3 “As-Built” Impact and Fracture Properties Table D.5 presents DTTE data for the welds and HAZ for LANL’s first two HSLA-100 vessels. LANL decided to perform a complete DTTE for the weld material and nozzle-to-shell weld HAZ because of low suspect DTTEs. Figure D.3 shows actual DTTE data for the 16” diameter nozzle weld material and nozzle-to-shell weld HAZ. Five specimens were tested at different temperatures shown. The large thickness involved in welding tends to move the DTTE curve upward in temperature as shown in Figure D.3. Results of the testing show that the weld metal and nozzle-to-shell weld HAZ are as good, or better, than the nozzle base material in terms of DTTE. Figure D.4 presents both sets of data, nozzle base metal, and nozzle-to-shell weld HAZ.

80

100

120

140

160

180

0 0.1 0.2 0.3 0.4 0.5

Single-Axis Vessel Shell and Weld

ShellWeld

Tru

e St

ress

, (ks

i)

True Plastic Strain, (in/in)

Figure D.2 – HSLA-100 shell and weld metal strengths for Single-Axis vessels.



Table D.5 -

LANL Vessel Weld As-Built Dynamic Tear Energy Data [48] Part ID Sample ID Test

Temperature (°F)

Dynamic Tear Test Energy (ft-lbs)


VES1-2 -40.0 -40.0

686 481


-40.0 -40.0

929 1663

Head 2 HAZ HAZ2-1 HAZ2-2

-15.0 -15.0

1447 1112

Nozzle Weld DTWT-1 DTWT-2 DTWT-3 DTWT-4

-40.0 -40.0 -20.0 -20.0

466 1118 1201 1174


VES2-2 -40.0 -40.0

513 507


-40.0 -40.0

1072 1181

0

500

1000

1500

-150 -100 -50 0 50 100

LANL Nozzle-to-Shell Weld HAZ

5/8" HAZ Specimen

Dyn

amic

tear

Ene

rgy,

(ft-

lb)

Temperature, (°F)

HAZ Thickness = 2.5"

∆T Shift for 2.5' Forging = 30oF

Figure D.3 - Dynamic tear energy for 16-in. nozzle-to-shell HAZ [48].



0

500

1000

1500

2000

-100 -50 0 50

Nozzle and Nozzle-to-Shell HAZ Dynamic Tear Energy

NozzleWeld HAZ

Dyn

amic

Tea

r Ene

rgy,

(ft-l

b)

Temperature, (°F)

• 5/8" DT Specimen • LANL 16" Diameter nozzle

FTE - Fracture Transition Elastic

L - Lower limit of elastic-plastic

FTE

L

Figure D.4 - Dynamic tear energy 16-in. nozzle and nozzle-to-shell weld HAZ [48]. D.4 Dynamic Fracture Toughness of Under-matched Welds Graham [43,44] in the U.S., and Gianetto and Yee [45,46] in Canada have reported extensively on under-matched welds and HAZ for high strength applications including HY-100 and HSLA-100. The same weld consumable, MIL-100S-1 wire, was used in both these experimental programs. Graham [44] included both static and dynamic J-R curves for MIL-100S-1 in welded specimen for 2.0 inch thick plates. Although the LANL vessel design incorporates 2.5 inch thick steel, the results obtained by Graham are consistent with LANL results. Results of quasi-static fracture toughness tests by Graham [43] showed a IcJ value of over 1900 psi-in. Dynamic toughness IdJ values were slightly higher with an average value of 2350 psi-in and a lower-bound value of 2057 psi-in. Figures D.5 and D.6 show the J-R curves from quasi-static and dynamic tests, respectively. Table D.6 shows results for dynamic IdJ tests for HY-100 weld.



Figure D.5 – Weld metal J-R curve for quasi-static loading [43].

Table D.6 – Dynamic IdJ [43] Specimen Wao / Temp

(oF) IcJ

(psi-in) a∆

(in.) GOT-D02 0.578 140 2057 0.096 GOT-D04 0.587 100 2295 0.079 GOT-D05 0.586 90 2509 0.063 GOT-D06 0.587 100 2070 0.046 GOT-D07 0.540 100 3159 0.114 GOT-D08 0.585 100 2087 0.026 GOT-D10 0.571 100 2285 0.038

The preceding data shows that weld toughness ( )IcJ at onset of stable crack extension is comparable to the parent metal results shown in Appendix A. Toughness values of slow, stable, crack extension at 0.1-in. are also comparable to the parent metal. As an example, the HSLA-100, 2-inch thick J-R curve (Figure A.10) shows a toughness at 0.1-in. extension of 5500-6000 psi-in. The weld metal curve shows 5500-6500 psi-in.



Figure D.6 – Weld metal J-R curve for dynamic loading [43].

D.5 Post-Weld Heat Treatment Because HSLA-100 containment vessels do not require PWHT and very low (or no) preheat, some obvious benefits and shortcomings are realized. The benefits are the reduction in fabrication cost, time, and effort. However, residual stresses from the welding process are inevitably present and may be detrimental to structural integrity. Residual weld stresses are extremely difficult to predict, yet play a major role in reducing overall fatigue performance of a component. The rationale for PWHT is to relieve or reduce residual stresses in the welded regions. Dynamic tear energy of the nozzle-to-shell weld HAZ is somewhat better than the base metal itself, as shown in Figure D.4. Given this property and maintaining the material at the FTE or L limit, as shown in Figure D.4, any crack present in the weld will arrest. The above arguments notwithstanding, the vessel does respond harmonically to the HE-driven impulsive load, and the resulting vessel stresses are predominantly higher-order bending modes, which have been categorized as “secondary” stresses. As described in Section 6 of this report, the vibrational response does not pose a concern for fatigue crack propagation, even if the stress-field near the crack tip is at, or near, yS0.1 .



D.5 Residual Stresses For HSLA-100 containment vessel design, however, fatigue and fatigue crack growth is not a concern because these vessels are subjected to a one-time loading event and subsequently discarded. Nonetheless, for the one-time application of load, the vessels respond harmonically to the impulsive event, exhibiting a “ring-down” mode. Vessel loading-function and response to a detonation blast are shown in Section 4 of this report. It is evident from Figures 4.4 and 4.5 that strain growth is exhibited after the initial “breathing mode,” with a strain-decay, clearly visible in Figure 4.2. Thus, the peak stresses affecting fatigue are at the beginning of the transient, with a rapid decaying function. Because residual stresses play a predominant role in fatigue, for impulsive loading events in one-time application vessels, fatigue and fatigue crack growth are not a concern. Dong and Hong [53] provided recommendations for determining residual weld stresses in pressure vessels. Dong and Brust [54] compiled a state-of-the-art assessment in quantifying residual weld stresses for the pressure vessel community. Gao et al. [55,56] have investigated residual weld stresses specifically in HSLA-100 weldments by X-ray diffraction methods. Gao et al. used a 1-inch HSLA-100 plate, GMA welds produced with a MIL-120S-1 consumable wire, and a heat input of 36-43 kJ/in. The MIL-120S-1 weld wire is slightly stronger than the MIL-100S-1 used for the LANL vessels, yet results are representative of potential residual stresses in the LANL vessels. Furthermore, heat input for the MIL-100S-1 LANL vessel welds were in the range of 45-52 kJ/in. Welds for specimen RS1 and RS3 are produced with no edge constraint on the plates. Specimen RS2 weld is produced with edge constraints. Results from Gao et al. [55,56] reveal that maximum longitudinal tensile residual stresses on the surface of a 1-inch thick plate are ~30 ksi, 3-mm from the weld bead, then gradually decrease to a constant tensile value of about 4-7 ksi, as shown in Figure D.7. The maximum compressive stress are ~45 ksi transverse to the weld, gradually changing to tensile at 7-mm away from the weld edge line and reaches a constant value of 14-21 ksi. Figure D.8 shows results for the constrained plate specimen RS2, indicating qualitatively similar results as RS1. Figure D.9 shows results for specimen RS3, having a higher heat input than RS1. The results obtained by Gao et al. are validated by the “rule-of-thumb” residual stress computations described in API-579, Appendix E [25]. For the above noted plate thickness and heat input, residual stresses calculated per API-579 are of the order of 20 ksi on the outer surface and 50 ksi on the inner surface.



Figure D.7 – Residual stress; unconstrained plate, specimen RS1 [55].

Figure D.8 – Residual stress; constrained plate, specimen RS2 [55].

Figure D.9 – Residual stress; unconstrained plate, specimen RS3 [55].



The investigation developed the following conclusions: 1. Transverse residual stresses are always compressive on the surface

near the weld, and gradually become tensile as the distance from the weld increases. Longitudinal residual stress are usually tensile on the surface near the weld, and slowly decrease as the distance from the weld increases. The residual stress profiles of the o45=φ direction from the weld are always between the profiles of the longitudinal stress and transverse stress.

2. Specimens that are subjected to different welding heat input have similar distributions of residual stress on the surface, but the magnitudes of the stresses are different. Higher welding heat input generates smaller stresses.

3. Further from the weld bead, tensile residual stresses on the surface were observed in the rigid restrained weldment.

4. There is a subsurface tensile-longitudinal and compressive-transverse residual stresses near the weld in both the unrestrained and restrained conditions.

5. Residual stresses along different directions are compressive, or have a tendency of getting compressive on the subsurface further away from the weld under non-restrained condition. The longitudinal residual stress is compressive and the transverse residual stress is highly tensile on the subsurface further away from the weld under the restrained condition.

Although it has been argued that residual weld stresses pose no concern for a one-time application of a highly dynamic (impulsive) load in a containment vessel, and the level of residual stress in the LANL vessel welds is comparable to those shown above, the issue is nonetheless addressed herein and in Appendix F calculations for completeness.



APPENDIX E

IcK CORRELATION WITH CVN Introduction Notwithstanding the shortcoming of the CVN test, fracture mechanics experts have evaluated numerous CVN data, from all types of low-, medium-, and high-strength steels, to determine an empirical correlation with true fracture tests, e.g., IcK specimen data. The following correlation with CVN has been proposed [28,29,30] for upper-shelf temperature regions: E.1 Upper-Shelf Correlation The following correlation is specific for the CVN energy upper-shelf.

KIcσy

⎛

⎝ ⎜

⎞

⎠ ⎟

2

= 5CVNσ y

− 0.05⎛

⎝ ⎜

⎞

⎠ ⎟ ,

where σy = Yield strength (ksi), KIc = Plane-strain fracture toughness ( ksi in .), and CVN = Upper-shelf CVN energy (ft-lb). Although the above correlation is indexed to IcK , the actual data are taken from CVN impact tests. As such, the critical stress intensity factor is really a dynamic IcK or, more precisely, IdK . Also, the dynamic yield strength of the material must be used when the correlation is indexed with IdK . Thus, the upper-shelf equation becomes

KIdσ yd

⎛

⎝ ⎜

⎞

⎠ ⎟

2

= 5CVNσ yd

− 0.05⎛

⎝ ⎜

⎞

⎠ ⎟ (E.1)

The data in Table E.1, however, appear quite reasonable when compared to the DTRC data shown in Figures A.1, A.2, A.5, and A.7 of Appendix A. As such, for CVN to IdK the Rolfe-Novak upper-shelf correlation [29] is appropriate for temperatures of -60°F and above.



Although Table E.1 shows IdK values using the upper-shelf correlation, resulting in slightly higher IdK values typical of HSLA-100, these appear quite reasonable and within 5-10% of lower-bound toughness.

Table E.1 - CVN and IdK Upper-Shelf Correlation

Orient. (T/L)

Temp. (°F)

CVN (ft-lbs)

IdK (ksi•in.1/2)

T L

0 175 168

298 292

T L

-120 130 148

255 274

To calibrate the IcK obtained in Table E.1 for the HSLA-100 LANL vessel, data from DTRC (now NSWC) elastic-plastic fracture testing of HSLA-100 are presented. Elastic-plastic fracture mechanics (EPFM) testing is based on the J-integral approach and is typically used for materials that fail in an elastic-plastic or purely plastic (i.e., ductile) manner [22-24]. It characterizes the fracture toughness of materials by determining IcJ , an engineering estimate of toughness near the initiation of slow stable crack extension.

IcJ is a material property independent of specimen size or thickness, as long as certain minimum requirements on specimen size and thickness are met. Furthermore, EPFM is directly correlated with computational schemes in determining critical crack sizes. DTRC performed numerous elastic-plastic IcJ tests [17] for material qualification of HSLA-100 for US Navy applications. The DTRC data is summarized in Appendix A for the plate size of construction in the LANL vessels. The lower-bound IcJ value obtained in all test sequences for a range of temperatures between 72oF and -160oF base metal was

IcJ = 2177 in.-lb/in.2 A correlation between the elastic-plastic (i.e., J -integral), IcJ and the brittle fracture parameter IcK [22-24] is as follows:

( )

EK

J IcIc

221 υ−= , (E.2)

where υ = Poisson’s ratio and E = Young’s modulus, (lb/in.2).



The corresponding lowest quasi-static plane-strain fracture toughness value, IcK :

inksi 265=IcK Dynamic plane-strain fracture toughness, IdK , is numerically equal to the quasi-static plane-strain fracture toughness, except that the toughness curve is displaced upward in the temperature scale by a specified amount. Thus, the corresponding dynamic plane-strain fracture toughness to use in calculations is

inksi 265=IdK E.2 Strain-Rate Temperature Shift Transition in temperature is indicated from the following equation [24] where the upward temperature shift (i.e., from static to dynamic) is applicable for steels within the range of yield strengths specified. The temperature shift effect is idealized in Figure E.1 between static and dynamic toughness: yshiftT σ5.1215 −=∆ ksiksi y 14036 ≤≤ σ (E.3) Barsom and Rolfe [24] conclude that for steels with yield strengths less than 140 ksi and for intermediate strain-rates within the range 10 10 3 ≤≤− ε , the temperature shift is ( )( ) 17.0150 εσ ysshiftT −=∆ (E.4) For the LANL vessel, strain-rates in the vicinity of 3010 ≤≤ ε are quite common. Thus, this correlation may be outside the range of validity. Wallin [57] has developed similar correlations based on crack initiation and crack arrest for materials having a nickel content %3.1≤Ni :

⎥⎦

⎤⎢⎣

⎡ ++−=∆ MPa3.6833.136

2735exp yso

o

CTT

σ (E.5)

While Wallin’s correlation might be the most applicable, crack arrest toughness is not available for HSLA-100. Nonetheless, in the range of similar high-strength steels noted by Wallin, HY-80 was included which has similar characteristics as HSLA. Wallin further modified his equation to account for materials whose nickel content exceeded 1.3%, as shown in Equation (E.6);

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−++−=∆

91.2

%5.2%

MPa3.6601.1362735exp Ni

CTT ys

oo σ

(E.6)



Using the actual nickel content for the HSLA-100 material (i.e., 3.5%) in equation (E.6), results in the temperature shift shown in Table E.2. The notional temperature shift between the dynamic and static plane-strain fracture toughness is shown in Figure E.1.

Frac

t ur e

To u

ghne

s s, K

I

Temperature, (°F)

∆T

KIc KId

Figure E.1 - Static to dynamic toughness temperature shift.

Table E.2 – Correlations and shiftT∆ Ref. Eq. shiftT∆

(oF) 24 E.3 55 24 E.4 81 55 E.5 147 55 E.6 4

It is evident that a wide range of possible temperature shifts are obtained by the diverse forms noted in literature. However, because the fracture-safe methodology is based upon the dynamic tear (DT) test method, the temperature shifts associated with that presented in Section 3 of this report are maintained. Conclusion Fracture testing of HSLA-100 with DTTE has determined that the material can withstand large flaw sizes and that a LBB condition exists. Elastic-plastic fracture toughness testing at DTRC using the J-integral methodology, IcJ , shows that the critical plane-strain stress intensity factor, IcK , is within the range of 250 to 300 ksi-in.1/2. The lowest

IcJ value obtained from J-integral testing corresponds to a IcK of 265 ksi-in.1/2. This value will be used in subsequent critical minimum flaw size analyses to determine the susceptibility of HSLA-100 to brittle fracture.



APPENDIX F

CRITICAL FLAW SIZES FOR SHELL, NOZZLE, AND WELD Introduction This Appendix provides detailed analytical calculations for critical flaw sizes for the shell, nozzle, and weld/HAZ. Estimates of potential slow, stable, crack extension are provided where J-R curve information is available. Amount of crack extension is only taken to 0.1-inch corresponding to guidance in Sec. VIII, Div. 3 [58]. Linear-elastic solutions contained herein are taken from API 579 [25] and from recent work by Anderson [42]. Ductile fracture is addressed herein through elastic-plastic fracture mechanics using the J -integral method. Critical flaw sizes will be determined by the static, IcJ , or dynamic,

IdJ , crack initiation parameters. Furthermore, the elastic portion, elJ , includes an estimate of the effective crack length to account for small-scale crack-tip plasticity, and denoted by; yeff raa φ+= (F.1)

where, ( )2/11

oPP+=φ (F.2)

P = Applied load oP = Limit load of flawed structure and

2

111

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

+−=

oy

Kmmr

σβπ (F.3)

where, yr = Radius of crack-tip plastic zone β = Constraint factor for plane-stress or, plane-strain m = Ramberg-Osgood exponent K = Elastic stress intensity factor oσ = Yield strength The above form for effa is used in lieu of the crack depth a in the linear-elastic portion of the crack-driving force, where



( )E

KJ el

221 ν−= (F.4)

and

⎟⎟⎠

⎞⎜⎜⎝

⎛=

ta

FQa

K effeffπσ (F.5)

Figure F.1 shows a graph of yr φ as a function of the load ratio oPP / for a range of stress intensity factors. The figure reveals that small-scale crack-tip plasticity correction size increases with increasing stress intensity factor and decreases with increasing load ratio.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Crack-Tip Plasticity Correction

50100150200250275300

P / Po

K

Figure F.1 – Crack-tip plasticity correction. As stated above the elastic stress intensity factor solutions, elJ , are derived from closed-form solutions for typical flaw geometries and orientation [22,25,42], while the fully plastic stress intensity factor solutions, plJ , use appropriate influence functions from several sources, including Anderson [22], Kanninen and Popelar [23], Kumar and Shih [39,40], and Kim [59] for the structure and flaw geometry. The fully-plastic crack driving force plJ is upper-bounded by assuming the influence function ( )Wah /1 solution for a semi-elliptical surface crack in a tension-loaded plate [59]. The fully-plastic crack driving force is denoted as;



( )1

1 ,/+

⎥⎦

⎤⎢⎣

⎡=

m

ooopl P

PmWabhJ εασ (F.6)

where: aWb −= = Uncracked ligament =W Thickness of plate ( ) =mWah ,/1 Influence function m = Ramberg-Osgood exponent =P Applied load =oP Limit load of flawed structure Section 5 of this report provides a summary of the solution scheme. All calculations are accomplished for the dual-axis vessel design incorporating a 2.5-inch wall thickness. However, several figures are also included comparing critical crack sizes for the 2-inch single-axis vessel and the 2.5-inch dual-axis vessel designs. Because many of the stress-intensity factor solutions are rather complex, computations tend to be tedious and laborious. As such, some of the solutions in Appendix F have been calculated with the aid of FractureGraphic [60] from Structural Reliability Technology. This is an integrated software package for performing fitness-for-service assessments. F.1 Vessel Shell Two separate postulated flaws are evaluated for the vessel to determine the limiting critical crack size, at two separate temporal locations. During the early-time event, i.e., 0.5 ms, secondary membrane stress of approximately 40 ksi is developed. At late time, the only membrane stress is the residual gas pressure. The two flaws evaluated are for the shell away from the welds, (1) a semi-elliptical flaw on the inner surface and (2) a through-wall flaw. Both these solutions are contained in API 579 [25] and Anderson, et al. [42]. An effective crack length, effa , is included in the elastic portion ( )elJ to account for small-scale crack-tip plasticity, where the total crack driving force pleltot JJJ += is then determined. It should be emphasized that because the major contribution to the state-of-stress are secondary stresses, a grossly conservative assumption is made herein to use a flawed structure limit-load solution in determining the fully-plastic contribution ( )plJ . As described by Kumar, German, and Shih [39], and reiterated in Section 5, the limit load of a structure based on a deformation-controlled situation is much higher than the limit load of a load-controlled structure. For the plJ contribution only, a limit load oP , equivalent to either the yield or true-ultimate is employed.



Lastly, as described in Section 4 of this report, at specific times during the transient, secondary membrane fluctuates between zero and ~25 ksi and secondary bending stresses fluctuate between zero and ~90 ksi. However, the total secondary stress remains below 100 ksi throughout the transient response. As a conservative measure, secondary bending stresses of 100 ksi are applied to the flaw geometry for further calculations. Semi-elliptical Inside Surface Flaw Flaw geometry size for the vessel is conservatively assumed to be a semi-elliptical flaw on the inner surface as shown in Figure F.2. The governing closed-form solution for the semi-elliptical surface flaw is based on the crack width ( 2c), depth a [25,42]. See API 579 [25] for the solution scheme.

Figure F.2 - Semi-elliptical surface flaw [25,42]. Figures F.3 and F.4 show the elastic stress intensity factors (with crack-tip plasticity) for a semi-elliptical surface flaw. Figure F.5 shows comparisons of the 2-inch and 2.5-inch thick vessel shells for the single-axis and dual-axis vessels. Figure F.6 shows the plJ

contribution for specific Wa / and ca / ratios for crack locations at o0=φ (free surface) and o90=φ (maximum depth). Based on above plJ functions, the 0o and 90o crack locations stress intensity values are combined with the elastic solutions. A linear interpolation is used to obtain values at

27.7=m for the HSLA-100 Ramberg-Osgood model. Solutions are shown in Figure F.6 using upper-bound influence function values at both crack locations, i.e., o0=φ and

o90=φ , assuming a limit load equivalent to the yield strength of the material.



It is evident that for actual “primary” loads affecting the flaw and assuming a yield-load limit, where ksiP 13= and ksiPo 105= (i.e., 12.0/ =oPP ), the fully-plastic solution can be neglected altogether. The increase in crack-driving force for a fully-plastic solution at the two load ratios of interest (i.e., early-time 4.0/ =oPP and late-time 12.0/ =oPP ), are considered negligible. Also, the true limit-load of a flawed structure under deformation-controlled condition is unknown, but is presumed to be much higher than load-controlled conditions, and certainly much higher than the yield strength limit load assumed here.

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5 2 2.5

Semi-Elliptical Flaw - Inner Vessel Surface

2c=32c=62c=12

Stre

ss In

tens

ity F

acto

r, (k

si-in

1/2 )

Crack Depth, (in.)

Elastic Solution with Plasticity Correction

Primary Membrane Stress = 13 ksi

Secondary Stress = 100 ksi (Bending)

KI at φ=0o

Figure F.3 – Stress intensity factor for (2.5-inch shell thickness).

Table F.1 – Influence Functions Semi-Elliptical Surface Flaw in Tension Plate [59]

5=m 10=m Wa / ca / 0o 45o 90o 0o 45o 90o

0.2 0.2 0.164 0.789 1.117 0.198 0.996 1.416 0.2 0.6 0.286 0.570 0.672 0.324 0.715 0.847 0.2 1.0 0.321 0.446 0.435 0.358 0.565 0.556 0.5 0.2 1.325 6.371 8.516 2.539 11.99 14.811 0.5 0.6 1.502 2.086 2.976 2.319 5.128 5.186 0.5 1.0 1.377 1.839 1.630 2.007 3.218 2.804



-50

0

50

100

150

200

0 0.5 1 1.5 2 2.5

Semi-Elliptical Flaw - Inner Vessel Surface

2c=32c=62c=12

Stre

ss In

tens

ity F

acto

r, (k

si-i

n1/2 )

Crack Depth, (in)




KI at φ=90o

Figure F.4 – Stress intensity factor for (2.5-inch shell thickness).

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5 2 2.5

Semi-Elliptical Flaw Comparison -2" and 2.5" Shell

2c=3 (2-inch)2c=6 (2-inch)2c=3 (2.5-inch)2c=6 (2.5-inch)

Stre

ss In

tens

ity F

acto

r, (k

si-i

n1/2 )

Crack Depth, (in)




KI at φ=0o

Figure F.5 – Comparison of 2-inch and 2.5-inch thick shell.



Assuming the limit load, oP , is anchored to the true-ultimate strength such that a “primary” load ratio resulting in 067.0/ =oPP (where, ksiPo 13= and ksiPo 185= ), the plastic crack-driving force, shown in Figure F.6, would be negligible. Although there is no definitive data on limit loads of flawed structures under “deformation-controlled” conditions, the notional assumption of a limit load at true-ultimate strength provides a measure of crack-driving force effect for fully-plastic conditions. Using this notional premise, it is evident that plJ is negligible. Lastly, assuming that larger HE loads are

used in a detonation event, such that the deformation-controlled membrane stresses ( smQ )

reach 80% to 100% of yield, where 55.0/ =oPP , the plJ contribution would still be negligible. Although this particular load ratio (i.e., ultimate strength limit load) is not used anywhere in the ensuing calculations, it is worth noting the large conservatism employed in the calculations.

-0.5

0

0.5

1

1.5

2

2.5

3

0.3 0.4 0.5 0.6 0.7 0.8

Fully Plastic J -Solution for Semi Elliptical Flaw

Phi=0Phi=90

J-Pl

astic

, (ks

i-in

)

P / Po

Late-time Load Ratio

P / Po = 0.12 (Yield-limit)

Figure F.6 – Fully-plastic J-solution for semi-elliptical surface

crack in a tension-loaded plate Assuming a yield strength-anchored limit load oP where the deformation-controlled membrane stresses are 80% of yield and a load ratio of 80.0/ =oPP , Figure F.6 shows a crack driving force 2650=plJ psi-in at o90=φ . From Figure F.3, the IK portion at

o90=φ is about 150 ksi-in1/2, or 700=elJ psi-in. The total crack driving force,

plel JJ + , is 3350=totJ psi-in.



Referring to Figure A.10 for HSLA-100 plate material RJ − curve, the slow, stable crack extension associated with this crack-driving force is about 0.05 inch. This is an acceptable crack extension, and rather conservative due to the arguments relative to deformation-controlled limit loads. Figure F.7 shows the critical flaw size solution using the Failure Assessment Diagram (FAD) approach in FractureGraphic [60], which accounts for both unstable fracture and limit loads. It is apparent that for small-length flaws, the critical depth is about 2.3-in., and for long flaws the critical depth is about 2-in.

2

2.1

2.2

2.3

2.4

2.5

0 10 20 30 40 50

Critical Flaw for Spherical Shell

Critical Flaw

Cra

ck D

epth

(a),

(in.

)

Crack Length (2c), (in.)

Primary Membrane

Secondary Stress

Figure F.7 – Critical flaw size for 2.5-inch thick shell [25]. Through-wall Flaw Assume a through-wall flaw with a crack-tip stress intensity factor solution per API 579 [25], as shown in Figure F.8. Using similar procedures as above, Figure F.9 shows the stress intensity factor with an elastic crack-tip plasticity correction.



Figure F.8 - Through-wall flaw [25].

50

100

150

200

250

300

350

400

450

0 1 2 3 4 5 6 7

Spherical Shell Through-Wall Flaw Solution

Stress Intensity Factor

Stre

ss In

tens

ity F

acto

r, (k

si-i

n1/2 )

Effective Crack Length, (in)


Primary Stress = 13 ksi

Secondary Stress = 100 ksi (bending)

Figure F.9 – Stress intensity factor solution for through-wall flaw.

Recognizing that the linear-elastic crack-tip plasticity correction follows the Figure F.1 relationship, a maximum correction of 0.25-inch is applied to this flaw geometry. For the fully-plastic crack-driving force, plJ , the correction is negligible. Thus, the critical flaw size for the through-wall flaw is

inacrit 5.3=



As a point of interest, the FAD approach in API-579 shows that for this given set of applied primary and secondary loads, the critical flaw size is 4.75-in. long. This is larger than shown above, yet the conservative measure is used for design purposes. F.3 Nozzle Forging Critical crack sizes have been conservatively calculated for the nozzle corner region. This is notably a location of potential high-stress due in part to the structural discontinuity, thereby assuring a triaxial state of stress, i.e., true plane-strain condition. Thumbnail Corner Surface Flaw Figure F.10 shows the postulated part through-wall nozzle flaw emanating from the inside corner. The most accurate solution for a nozzle corner crack under an impulsively-driven loading would be obtained with the use of a full-3D FEA model. However, an approximate stress-intensity factor solution from API 579 [25] is used herein, which was originally developed by Guozhong and Qichao [61,62], accounting for both front surface,

fM , and back surface, bM , correction. The stress-intensity factor solutions has the following form;

( )ππσ apkMMK nomtabfI

2+= (F.7)

where, ( )ϕϕ cossin24.043.1 +−=fM (F.8)

2

2215.01

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

++=

nb

ttaM (F.9)

( ) ( )( )

B

nntnta td

akk−

⎥⎦

⎤⎢⎣

⎡−++−+=

2cossin111 ϕϕπ (F.10)

and nom

tnkσσ max= (F.11)

For a nozzle on a spherical shell, the exponent to the stress concentration tak (i.e., factor B ) is represented by

n

n

dtB 22 −= (F.12)



P

a

Figure F.10 - Nozzle region and postulated flaw. The above forms are conditional on the flaw depth-to-thickness ratio, of both the shell and nozzle, and the maximum orientation flaw-angle (See Figure F.11).

(1) 5.0/0.0 ≤≤ ta (2) 5.0/0.0 ≤≤ nta (3) o45=ϕ

where, t = Spherical shell thickness nd = Nozzle diameter at mid-thickness nt = Nozzle thickness ϕ = Angular orientation from shell horizontal axis.

Figure F.11 – Nozzle-to-Shell junction.



The “local” elastic stress concentration factor, tak , for a nozzle corner is a function of the stress concentration factor, tnk , of a hole in either a plate, cylinder, or sphere. For this flaw calculation, the stress concentration factor for a hole in a sphere is derived from both a static and dynamic pressure analysis by Ballard and Shunk [63], and Shunk [64]. Figure F.12 below depicts a 2D model of the entry-port nozzle with a double bolting ring. The LANL vessel design parameters are, . 5.2 int = . 72 inD = . 0.5 intn = . 30 indn =

Figure F.12 – 2D Model of Dual-Axis vessel; entry-port nozzle.

Results show that both, for static internal pressure and the dynamic transient (i.e., HE impulse loading) analysis, the SCF’s are, 5.1=tnk . This is slightly lower than Decock’s approximation [65] for stress-concentration factor (SCF) of nozzle-to-shell junction, where;

( ) ( )( ) TDTdtt

DTDdDDTdtdktn //1//25.1//22 2/12/1

+++= (F.13)

05.2=tnk (for the LANL vessel geometry) As such, the lower SCF, 5.1=tnk , based on FEA modeling will be used in the calculations. Stated in Section 4 and reiterated here, the spherical vessel shell and the nozzle forgings are designed by limiting (secondary) membrane stresses to yS0.1 and

yS5.0 respectively.



It’s worth noting that the quasi-static residual pressure of 1,740 psi, resulting from a 40-lb PBX-9501 HE detonation, produces primary membrane stresses in the spherical vessel shell of ~13 ksi and the cylindrical nozzle forging of ~5.0 ksi. Solving for the stress-intensity factor, Equation F.7, and using a flaw angle of o45=ϕ thus maximizing the front surface correction, results representative of a 25-inch inner diameter nozzle are shown in Figures F.13.

0

50

100

150

200

0 1 2 3 4 5

Nozzle Corner Flaw Stress Intensity Factor

Stress Intensity Factor

Stre

ss In

tens

ity F

acto

r, (k

si-in

1/2 )

Effective Crack Depth, (in.)

Primary Stress

Crack-Tip Plasticity Correction

Pm= 0.5σy

Figure F.13 - Nozzle corner flaw stress-intensity factor: ymP σ5.0= , [25].

Figure F.13 shows that a stress-intensity factor of ~180 ksi-in1/2 is developed for a 4.-in. deep crack assuming a primary membrane stress of ymP σ5.0= . The material fracture toughness, as shown in Appendices A, and E, is ~265 ksi-in1/2, or a inpsiJel −= 2177 . This implies that a 4-in. long corner flaw will not propagate unstably. Noting that the nozzle is 5-in. thick, this implies that the crack can be 80% of the thickness or greater before it extends unstably.



Longitudinal Part Through-wall Flaw Figure F.14 depicts a longitudinal flaw inside the nozzle, with a crack length of “ a .” The solution is given in API-579 [25];

Figure F.14 - Part through-wall longitudinal nozzle flaw [25]. The part through-wall longitudinal flaw solution is shown in Figure F.15 for different initial crack lengths. Figure F.15 is based on the Failure Analysis Diagram (FAD) approach using FractureGraphic [60] for the analytical solution. The method is based on meeting two separate criteria; unstable fracture and limit loads. Figure F.16 provides the stress intensity factor for a number of different flaw-depths to flaw-widths. The data shows that the critical flaw size is about 1.9-in. at a given stress intensity factor of ~265 ksi-in1/2. The longitudinal part-through-wall nozzle flaw results show a critical crack size at about 1.75-inch depth for a flaw length of ~5-inches. Because the cylindrical portion of the nozzle is 8-inches long, and assuming the flaw length 82 =c , then the critical flaw size is 1.5-inch. Therefore, this appears to be the limiting flaw geometry for NDE inspection of the nozzle. This flaw size is large and detectable by visual inspection alone. However the detectable limit of NDE is 1/32nd of an inch using UT and RT methods. Thus, the critical flaw size is;

. 5.1 inacrit =



0.5

1

1.5

2

2.5

3

0 5 10 15 20

Longitudinal Flaw on Inner Surface of Nozzle

Limiting Flaw Size

Cra

ck D

epth

, (in

)


Pm = 0.5σy

Primary Stress

Secondary Stress

Q = 1.0 σy

Figure F.15 - Critical flaw size for a longitudinal part-through-wall nozzle flaw [25].

50

100

150

200

250

300

350

400

0 1 2 3 4 5

Longitudinal Flaw on Inner Surface of Nozzle

2c=42c=52c=62c=72c=8

Stre

ss In

tens

ity F

acto

r, (k

si-i

n1/2 )

Crack Depth, (in.)

Crack Length (2c)

Figure F.16 - Critical flaw size for small-length part-through-wall nozzle flaw [25].



F.4 Welds Mechanical properties for HSLA-100 weld metal are described in Appendix D. Flow characteristics in the elastic-plastic regime are idealized as a power-law approximation (See Appendix D), and described by Equations D.1a and D.1b. Using the Ramberg-Osgood constitutive equation, as described in Section 5 for the parent metal, parameters are derived from Equations D.1a and D.1b power-law for welds. Table F.2 shows the RO parameters derived from Eq. (F.14) below.

n

o

o

o

K1

1−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

σεα (F.14)

Table F.2 – Ramberg-Osgood Parameters for HSLA-100 Weld Design oσ

(ksi) oε oK

(ksi) n m α

Single-Axis 90 0.002 125 0.0617 16.2 2.44 Dual-Axis 99 0.002 150 0.0752 13.3 1.99

With the parameters in Table F.2, the effective crack size, effa , under elastic crack-tip plasticity and the fully plastic crack driving force, plJ , can now be computed for a given applied load, P , and a normalizing limit load, oP of a flawed structure. Elastic-plastic dynamic crack driving force, IdJ , reported in Appendix D for weld metal showed an average of 2350 psi-in and a lower-bound value of 2057 psi-in. Thus, in the calculations that follow, the lower-bound value will be used throughout. Residual Weld Stress As described in Appendix D for the LANL vessels, weld heat input for HSLA-100 was accomplished at an average of 40 kJ/in. Per API 579 guidance on residual weld stresses, and applying the vessel geometry parameters, the maximum residual stress is a gradient of 100 ksi on the outer surface and 35 ksi on the inner surface. This produces the following; ksiQr

m 5.32= ksiQr

b 5.67= For simplicity, these values will be rounded upward as 70 ksi bending and 35 ksi membrane.



Secondary Bending Stress As performed for the vessel shell and nozzle, the detonation loading produces secondary bending stresses reaching yield. Thus, bending stress of 100 ksi will also be applied, or; ksiQs

b 100= Results are shown in Figure F.17 and F.18 for a number of crack-depth versus crack-lengths using FractureGraphic [60] for the analytical solution, which is based on the FAD approach. A critical flaw size of 1.25-in. results for short-length flaws. These results are based on an applied residual and secondary stress field along with a small primary membrane loading from the static gas pressure. For longer flaws, the critical flaw-depths are slightly greater than 0.75-in.

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 10 20 30 40 50 60 70

Critical Weld Flaw Sizes

Critical Flaw

Cra

ck D

eth

(a),

(in.

)


Residual Weld Stress

Secondary Stress

Primary Membrane

Figure F.17 - Critical flaw size for weld flaw [25].



50

100

150

200

250

300

350

400

0 0.5 1 1.5 2 2.5

Critical Weld Flaw Size

2c=42c=82c=122c=162c=20

Stre

ss In

tens

ity F

acto

r, (k

si-i

n1/2 )

Crack Depth, (in)

Residual Weld Stress

Secondary Stress

Primary Membrane

Crack Length

Figure F.18 - Critical flaw size for short-length weld flaws [25]. For short-length flaws, the critical depth is 1.25-inch and for longer flaws, the critical depth is 0.75-inch.

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