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Procedia Materials Science 3 ( 2014 ) 855 860

Available online at www.sciencedirect.com

2211-8128 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/3.0/ ).Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of Structural Engineeringdoi: 10.1016/j.mspro.2014.06.139

ScienceDirect

20th European Conference on Fracture (ECF20)

Ductile fracture simulation of full-scale circumferential cracked pipes: (I) Carbon steel

Jae-Jun Han a, Ho-Wan Ryu a, Yun-Jae Kim a,*, Nak-Hyun Kim b and Jong-Hyun Kim c

a Korea University, Mechanical Engineering Dept., Seoul 136-713, KOREAb KEPCO E&C, Structural Integrity and Materials Dept., Yongin 446-713, Gyeonggi-Do, KOREA

c KAERI, Fast Reactor Design Division., Daejeon 305-353, KOREA

Abstract

This paper reports ductile fracture simulation and comparison with carbon steel test data of full-scale cracked pipes via 3-D finiteelement damage analysis based on stress-modified fracture strain model. Although there are few test results and discussion offull-scale cracked pipes, it is not an easy task to properly evaluate fracture behaviour of large-scale components for various pipesizes with different shape of a crack-like defect. In such a situation, finite element (FE) damage analysis can be a competitivealternative to characterize the fracture behaviour of cracked components such as crack initiation and maximum loads. In recentyears, a simple FE method [1] to simulate ductile fracture has been developed based on the stress-modified fracture strain model[2,3]. The technique appropriately simulated ductile failure for miscellaneous cracked components [4,5]. However, for somecases, large-scale components using small element size, FE analysis couldn't give reliable values because of numerical instability.Element-size-dependent critical damage model enhanced by taking the effect of element-size on the ductile fracture damage

analysis is introduced to overcome this problem and to be applicable to the large-scale structures. In order to validate proposedmethod, two types of carbon steel (A106 Gr. B and SA333 Gr. 6) pipes with a circumferential crack taken from [6] areconsidered, subjected to four-point bending only and combined loading. It is shown that predicted crack initiation and maximumloads are compared with experimentally measured values, showing overall good agreements. 2014 The Authors. Published by Elsevier Ltd.Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department ofStructural Engineering.

Keywords: Ductile fracture, Finite element analysis, Stress-modified fracture strain model, Damage analysis, Full-scale cracked pipes.

* Corresponding author. Tel.: +82-3290-3372; fax: +82-929-1718. E-mail address: [email protected]

2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/3.0/ ).Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Departmentof Structural Engineering
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856 Jae-Jun Han et al. / Procedia Materials Science 3 ( 2014 ) 855 860

Nomenclature

a a crack length and extension in the radial direction, respectivelyr, D o mean pipe radius and outer pipe diameter, respectivelyt pipe thickness, mm

half circumferential angle e p incremental equivalent plastic strain

f fracture strain 1 2 3 principal stress components e m effective stress and hydrostatic stress, respectively

accumulated damage and incremental damage c critical damage for cracking

material constant for stress-modified fracture strain Le element size, mm J J -integral

P exp initiation or maximum loads from experimental data P pred initiation or maximum loads from finite element damage simulation

Introduction

In structural integrity assessment, full-scale test is an accurate and reliable way to evaluate fracture behaviour ofcomponents containing crack-like defects. However, from a cost-effectiveness perspective, it is consequentlyeconomically unfavourable. One efficient way to replace such extensive test programmes is to use finite element(FE) damage analyses. Recently a simple FE method has been proposed [1] to implement fracture simulation basedon the well-known stress-modified fracture strain model [2,3]. Although the technique appropriately simulatedductile failure for miscellaneous cracked components [4,5], the failure simulations using small element size causenumerical instability. In order to overcome this problem and to be applicable to the large-scale structures, this paperintroduces element-size-dependent critical damage model [8]. In the subsequent section, test results of full-scale

pipes are briefly summarized with tensile and fracture toughness ones extracted from the pipes under the samemanufacturing processes. Section 3 describes the damage model and FE technique to simulate ductile fracture

behaviour. From the results of tensile and fracture toughness tests, damage criteria can be determined in section 4.Section 5 gives simulated results compared with full-scale test data of circumferential cracked pipes taken from PipeFracture Encyclopedia [6] to validate the proposed method. Section 6 concludes the paper with a discussion of themain results.

1. Summary of Full-Scale Pipe Test Data

Battelle memorial institute has performed various test data sets consisted of tensile test, fracture toughness testand full-scale circumferential cracked pipe under four-point bending test [7]. Two material sets of full-scale pipetest data at 288 oC were chosen from Pipe Fracture Encyclopedia [6] for SA333 Grade 6 and A106 Grade B carbonsteels. For the sake of space, only for A106 Gr. B, geometric variables, dimensions and schematic figures of cracked

pipes are sh own in Table 1 and Fig. 1. Three types of cracks are considered, including through-wall, surface andcomplex cracks. The complex crack indicates the cross section of the circumferential crack, consisting part ofthrough-wall crack with remaining surface crack depicted in Fig. 1d and Fig. 1e. For A106 Gr. B, the 0.2% proof(yield) strength, ultimate tensile strength and reduction of area are 320MPa, 621MPa and 34.4%, respectively. In thesame order, 239MPa, 527MPa and 60.0%, respectively for SA333 Gr. 6. Full-scale pipe tests are comprise of fivetests of A106 Gr. B and four test of SA333 Gr.6.

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(a) (b) (c)

(d) (e)Fig. 1. Schematic of the cross-sectional view for A106 Gr. B pipes in Table 1: (a) through-wall cracked pipe, (b)-(c)surface cracked pipes and (d)-(e) complex cracked pipes.

Table 1. Summary of specimen dimensions for circumferential cracked A106 Gr. B pipes at 288 oC.

Specimen Do (mm)t

(mm) r/t a/t /

Through-wall crack (1.2-7) 168.0 14.0 5.50 - 0.360Surface crack (4112-6) 167.5 14.8 5.16 0.680 0.503

Surface crack (1.1-9) w/ pressure 167.4 14.0 5.48 0.721 0.419Complex crack (4113-5) 168.0 14.2 5.42 0.313 0.37/1.0Complex crack (4113-6) 168.0 14.2 5.42 0.643 0.37/1.0

2. Ductile Fracture Simulation

3.1 Damage modelThe damage model used in this paper is based on the phenomenological ductile fracture model which is also

known as the stress-modified fracture strain model [2,3]. In this model, fracture strain f for dimple fracture isassumed to depend exponentially on the stress triaxiality m/ e:

1 2 3exp ;3

m m f

e e e

(1)

where i (i=1-3) are principle stress components; and , and are material constants. Damage can be calculated by summing incremental damage , given by

pe

f

(2)

where pe is the equivalent plastic strain increment, calculated from FE analysis implemented in ABAQUS usinguser subroutines [9]. Determined fracture strain model (crit1) is shown in Fig. 2 based on tearing modulus data fromexperimental data. This technique enables a criterion for ductile fracture simulation to be determined by tensile andfracture toughness test only.

3.2 Element size effectIn the conventional damage analysis, a proper element size for the material calibrated corresponds to the case of

c=1. The main concept of the proposed method is that the critical accumulated damage for fracture, c, is assumed

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(a) (b)Fig. 2. Determination of criteria for ductile fracture simulation: (a) Assumed stress-modified fracture strain modelsfor the A 106 Gr. B steel at 288 oC and (b) effect of fracture strain criteria on simulated data for determining tearingmodulus of the C(T) specimen.

Fig. 3. Dependence of the critical accumulated damage, c, on the element size.

to vary with the element size. Then the failure criterion is

(element size) c (3)

When a larger element is used, a smaller c value can be used to produce the same cracking rate as shown in Fig. 3.Figure 2 shows that one criterion has unique ductile fracture behaviour regardless of the element size. Therefore,

proper criterion can be determined by tensile and fracture toughness test data. The element-size-dependent criticaldamage model provides a solution to overcome the problem due to numerical instability.

3. FE analysis and Results

To enable ductile fracture simulation of full-scale pipes, the pipes were modelled with the element size of 0.6mmand 0.8mm for A106 Gr. B and SA106 Gr. 6, respectively. A quarter model was used considering symmetryconditions. Eight-node brick elements with full integrations (element type C3D8 in ABAQUS [9]) were uniformlyspaced in the cracked section as shown in Fig. 4a. Damage analysis was performed with the non-linear geometrychange option.

Figure 4b and 4c show that simulated crack growth are coloured in black at maximum load and sufficiently longcrack extension, respectively. For the complex cracked pipe, load versus load line displacement (LLD) data andcrack extension versus LLD are plotted in Fig. 5. Without damage analyses (conventional elastic plastic analysis),the results continuously increased. On the other hand, with damage analyses, FE results are simulated well

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with experimental ones including crack initiation and maximum loads. Predicted crack initiation and maximumloads for four different tests of SA333 Gr. 6 pipes and five different tests of A106 Gr. B pipes are compared withexperimentally measured values, in Fig. 6, showing overall good agreements less than 11% for the crack initiationload and 6% for the maximum load.

4. Conclusions

Full-scale pipes with a circumferential crack for SA333 Gr. 6 and A106 Gr. B carbon steels are simulated usingFE damage analysis based on the stress-modified fracture strain model. The criteria for ductile fracture simulationcan be determined by tensile and fracture toughness test data only. To overcome numerical instability problem dueto the small element size and to be applicable to the large-scale structures, a concept of the element-size-dependentcritical damage model is introduced. The present method can predict well crack initiation and maximum loads offull-scale pipe tests. This method offers significant advantages in simulating long, stable crack growth in large-scalecomponents.

Acknowledgement

This research was supported by National Research Foundation of Korea (NRF) funded by the Ministry of Science,

ICT and Future Planning. (NRF- 2013M2A7A1076396, NRF-2013M2A8A1040924)

References

[1] Oh, C.-S., N.-H. Kim, Y.-J. Kim, J.-H. Baek, Y.-P. Kim, and W.-S. Kim, 2011. A finite element ductile failure simulation method using stress-modified fracture strain model. Engineering Fracture Mechanics 78:124-137.[2] McClintock, F. A, 1968. A Criterion for Ductile Fracture by the Growth of Holes. Journal of Applied Mechanics 35:363-371.[3] Hancock, J. W. and A. C. Mackenzie, 1976. On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states.Journal of the Mechanics and Physics of Solids 24:147-160.[4] Kim, N.-H., C.-S. Oh, Y.-J. Kim, 2011. A numerical method to simulate ductile failure of tensile plates with interacting through-wall cracks.Fatigue & Fracture of Engineering Materials & Structures 34:215-226.[5] Kim, N.-H., C.-S. Oh, Y.-J. Kim, K.-B. Yoon, and Y.-H. Ma, 2011. Comparison of fracture strain based ductile failure simulation withexperimental results. International Journal of Pressure Vessels and Piping 88:434-447.

[6] Pipe Fracture Encyclopedia. 1997. Volume 3: Pipe Fracture Test Data. Battelle.[7] Wilkowski, G. M., J. Ahmad, D. Broek, F. Brust, G. Kramer, M. Landow, C. W. Marschall, W. Maxey, M. Nakagaki, V. Papaspyropoulos, V.Pasupathi, C. Popelar, and P. Scott, 1985. Analysis and low-energy test results of degraded piping. Nuclear Engineering and Design 89:257-269.[8] Kim, J. H., N. H. Kim, Y. J. Kim, K. Hasegawa, and K. Miyazaki, 2013. Ductile fracture simulation of 304 stainless steel pipes with twocircumferential surface cracks. Fatigue & Fracture of Engineering Materials & Structures.[9] ABAQUS Version 6.11, 2011. Analysis Users Manual . Dassault Systemes Simulia Corp., Providence, RI.

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