Finite Element Modeling of Residual Stress due to Welding: Study on Full-scale Testing of Swaged Steel Bulkheads

Kenneth Gauthier | University of Florida REU Institution: University of California at San Diego

REU Advisor: Dr. Uang

September 28, 2013

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Abstract Several countries have begun using swaged bulkheads for commercial ship construction. The purpose of this research is to determine the strength characteristics, optimum dimensions, and buckling behavior of swaged bulkheads so that they may be used in ship design and construction in the United States. Finite element models were created with ABAQUS and validated with testing results. The primary focus of this paper was to determine the effect of welding residual stress by incorporating them into the ABAQUS model. A method of doing so was developed, verified, and can be applied to other projects where residual stress near a weld are of interest.

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Table of Contents 1. Project Outline ............................................................................................................................ 1

1.1 Phase Descriptions ................................................................................................................ 1

1.2 Testing Methods.................................................................................................................... 2

2. Literature Review........................................................................................................................ 2

2.1 Buckling Modes .................................................................................................................... 3

2.2 Welding ................................................................................................................................. 3

2.3 Residual Stress ...................................................................................................................... 3

3. Finite Element Modeling and Verifications ................................................................................ 3

3.1 Modeling of Welding Process ............................................................................................... 4

3.2 Verification of Model ........................................................................................................... 4

4. Applications ................................................................................................................................ 6

4.1 NASSCO ............................................................................................................................... 6

4.2 SOM ...................................................................................................................................... 6

5. Future Work ................................................................................................................................ 8

6. Contact Information .................................................................................................................... 9

7. Acknowledgements ..................................................................................................................... 9

8. References ................................................................................................................................. 10

9. Appendices ................................................................................................................................ 12

Appendix A – Nomenclature .................................................................................................... 12

Appendix B – Temperature-Dependent Material Properties .................................................... 13

Appendix C – Heat Transfer Equations .................................................................................... 15

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1. Project Outline

NASSCO, a division of the company General Dynamics, specializes in the design and construction of auxiliary and support ships for the U.S. Navy as well as oil tanker and dry cargo carriers for the commercial market. NASSCO’s shipyard in the San Diego Bay is the only full service shipyard on the west coast (General Dynamics, 2013). The outline of this project was determined by the engineers at NASSCO after a thorough feasibility report determined the cost benefit of using swaged steel plates in ship construction and design. A swaged plate is a steel plate that is pressed to form U-shapes as shown in Figure 1. The plates will be used as structural members within the interior of ships. The NAASCO report took into account factors such as transportation, painting, and elimination of welding and then projected those savings over the next 10 and 30 years using average production values.

Figure 1: Swaged steel plate with large height and width

1.1 Phase Descriptions

The project is separated into three phases, each phase consisting of a design, performance prediction through finite element analysis, physical testing, and validation of actual and finite element model results. The first phase of testing was designed for a comparative study of swaged and stiffened panels. This phase compared testing results of bulb stiffener and swaged steel plates, both composed of high strength structural steel, DH36. Testing was finished in 2012 and showed that the swaged plates have a 35% higher ultimate load strength than plates with stiffeners (Ozkula et al., 2012).

The second phase was designed to determine the effects of swage geometry, thickness, and grade. This phase compared testing results of two swaged shapes of differing height, both composed of mild steel, A36. Testing of this phase finished in August 2013 and showed that the swage shape with a larger height had a 30% higher ultimate compressive strength than the swaged shape with a smaller height. It was also observed that the swaged plate with smaller height displayed no signs of local buckling and the plate with a larger swaged shape height had local buckling before global buckling developed. Phase three is designed to determine the effects of irregularities such as cutouts and stiffeners, and is due to begin testing in 2014.

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1.2 Testing Methods

Two specimens of each geometry were tested in Phase 2. One was subjected to compressive loading using three 500-kip actuators applying a load perpendicular to the flange on one side of the plate with the flange on the other side being anchored to a concrete block being held in place by post-tensioning rods. The other plates were subjected to lateral loading with just two 500-kip actuators. This was done by using rigid connections to indirectly apply a shear load as shown in Figure 2. The dashed lines on the plate represent the swaged shape or stiffener. String pots and strain gauges were used to measure displacement and strain at key points on the plate. All testing was conducted in the Charles Lee Powell Structural Laboratories at U.C. San Diego.

Figure 2: Test setup for compression loading (left) and lateral loading (right)

2. Literature Review

Stiffened steel plates are used in large quantity as structural members for many types of structures which require a high strength to weight ratio such as commercial cargo ships and tankers. Although there is no publically available research into plates with a swaged geometry, it is possible to use the vast amount of research focused on stiffened plates to help analyze the testing results from this investigation. Over the last two decades great effort has been made to create accurate analytical equations and finite element models that can predict buckling modes and their corresponding ultimate load for stiffened steel plates of various dimensions. Grondin et al. (1998a) were one of the first to create a finite element model that could predict ultimate loads, deformation, and buckling failure modes of stiffened plates with great accuracy. This model made use of measured material properties, initial imperfections, and residual stresses typical of the stiffened plate under examination. It is noted, however, that if other arrangements of plate and stiffener proportions are to be explored, the magnitude and distribution of both initial imperfections and residual stresses must be examined on a case basis. Continued research of stiffened steel plates was carried out at the University of Alberta by Sheikh et al. (2001, 2002, 2003). They used a finite element model, validated by tests on full size stiffened steel plates, to conduct a very detailed dimensional analysis of different dimensionless parameters for stiffened steel plates.

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2.1 Buckling Modes

The use of high strength steel in ships leads to thinner plates which are more vulnerable to buckling. Buckling due to compression can be classified as plate induced overall buckling, stiffener induced overall buckling, plate buckling, or stiffener tripping. Buckling due to shear can be classified as local buckling, global buckling, or interactive buckling (Yi et al., 2008). Stiffener tripping is the torsional buckling in stiffeners of frames with high flexural rigidity and low torsional rigidity which results in an abrupt reduction in capacity past peak load (Danielson et al., 1990). This sudden drop in capacity makes the buckling failure mode very important and why the causes of stiffener tripping are crucial information for design so that stiffener tripping may always be prevented. Local buckling is desirable as it will occur isolated in a sub-panel and result in minor capacity loss. Stiffened steel plates in ships are designed so that local panel buckling occurs before overall buckling and stiffener tripping (Fujikobo and Yao, 1999).

2.2 Welding

One of the advantages of swaged plates is the elimination of welding required to produce them. Steel plates are typically strengthened by longitudinal and transverse stiffeners which are connected using continuous fillet welds. This welding process results in residual stress which generally reduces the elastic local buckling strength of a stiffened plate. The elastic buckling strength of a local panel between stiffeners is increased by the presence of stiffeners, but due to the presence of welding residual stress the actual strength is almost the same as that of a simply supported plate (Grondin et al., 1998a).

2.3 Residual Stress

Steel members are molded to their designed shape by heating them to near melting temperatures of 1650 ˚F (melting point is 2700 ˚F) and rolling them through a form and then allowing them to cool. If a rigid moment connection is required, members are commonly welded together. These and other factors involved in the production of steel members result in the development of stress ingrained into the steel. A large temperature gradient is created as a result of the high temperature applied to a localized section of steel during welding. As metal heats up it expands and as it cools down it contracts; this difference in temperature creates tensile and compressive forces. The geometry of the member, cooling environment, and heat source all affect the magnitude and distribution of resulting residual stress, but it is a general rule of thumb that areas that cool first will be in compression and areas that cool last will be in tension (Ueda et al., 2012).

3. Finite Element Modeling and Verifications

It was of interest to the project to find a method to incorporate residual stress due to welding into the finite element model (FEM) to determine how much effect, if any, it has on the ultimate load. Several papers were found that outline successful attempts at simulating the welding process but none gave a step-by-step process on how it was done. The task of the author of this paper was to develop and verify a process to incorporate welding residual stress into the FEM of several projects.

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3.1 Modeling of Welding Process

A three-dimensional ABAQUS finite element model was made of the testing specimen using solid elements of type Coupled Temperature-Displacement, an 8-node thermally coupled brick, tri-linear displacement and temperature. The geometry of additional weld material was included in this model and partitioned into segments of equal length in the weld direction. The different materials and welding volume were partitioned and assigned their corresponding properties. It is necessary to use temperature-dependent property values of steel as they vary drastically at high temperatures. Determination of coefficient of thermal expansion, yield and tensile stress, modulus of elasticity, thermal conductivity, specific heat, and density is outlined in Appendix B – Temperature-Dependent Material Properties.

Heat transfer due to convection was applied through a Surface Film Condition Interaction, which uses Equation C.2, found in Appendix C. Heat transfer due to radiation was applied through a Surface Radiation Interaction, which uses Equation C.3. The initial temperature of all material was set by a Predefine Field => Temperature. These functions, along with the coefficient of thermal conduction for each material, will accurately transfer heat through the model and allow for it to cool properly.

The process for modeling heat transfer of the weld consists of multiple steps. In the first step, the weld volume is removed using the Change Model Interaction. In the second step, a single segment of the weld is added back using the Change Model Interaction. A Body Heat Flux Load is then applied to this weld segment using Equation C.1 and the time length of the step is determined by Equation C.4. In the subsequent steps, another single segment of the weld is added back using the Change Model Interaction. A Body Heat Flux Load is applied to the weld segment using Equation C.1 and the time length of the step is determined by Equation C.4, and the Body Heat Flux Load from the previous step is deactivated. This step-by-step method simulated the application of high heat and weld material continuously along the member.

Pause steps are added between welding of separate sides of a T-joint to simulate the delay of machinery repositioning for another pass. A final cool down step is added to allow the entire model to cool approximately to room temperature.

3.2 Verification of Model

Tonkovic et al. (2012) is used as the primary verification of the weld modeling method. They were able to use infrared cameras, thermocouples (type K), and non-contact 3D image correlation systems ARAMIS 4M for deformation analysis to record the temperature and strain at specific locations during a live weld. The longitudinal residual stress values shown in Figure 3 were determined along the same reference line and any slight difference could be explained by a difference in mesh. Temperature histories were recorded at five different locations, TC-101(-5), on the T-joint as shown in Figure 4. The temperature values of the ABAQUS model are higher than those found in Tonković et al (2012). One possible cause for this is the size of weld segment used. In the ABAQUS model, a segment size of 63mm was used while the model in the Tonković et al used a segment size of

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7mm. This means that with the larger segment a smaller heat flux is applied for a much longer time for each segment, which may result in slightly higher temperatures in certain locations.

Figure 3: Residual stress results from ABAQUS model (left) and Tonković et al (2012) (right)

Figure 4: Temperature histories from ABAQUS model (above) and Tonković et al (2012) (below)

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4. Applications

4.1 NASSCO

Several problems were encountered while trying to replicate the testing results of static loading. Initial stiffness of the FEM is almost double that which was observed in laboratory testing. Initial imperfections such as minute initial buckling and slightly offset boundary conditions were applied in the FEM but neither had a significant effect to account for the extra stiffness. It was suggested by a graduate student researcher more familiar with ABAQUS that sometimes the use of solid elements is not valid as it does not allow normal buckling behavior for thin plates. Slight tweaking of these initial imperfections may solve this problem but as of the time this paper was written it was not resolved.

4.2 SOM

A study into built-up box columns was conducted in order to use a new design approach outside of the AISC 358 code. This project is pertinent to the focus of this paper as it was determined that a sudden fracture, which occurred during testing, was caused by electro-slag welding (Sarkisian et al., 2013). Electro-slag welding is a specific type of weld typically used for joining heavy castings and forgings. It consists of extremely high temperatures, upwards of 2500˚F, and large amounts of welding material which results in a very large heat-affected zone where base metal properties are negatively affected. These high temperatures then cool in room temperature and result in a change of steel microstructure within the heat-affected zone. Martensite is commonly formed, which has greater strength characteristics but is less ductile and thus more prone to sudden fracture than steel (Ueda et al., 2012).

While it is beyond the scope of this work to go into the material properties of every finite element within the heat-affected zone and change them to their resulting values, it is possible to apply the residual stress from welding. The ABAQUS model is shown in Figure 5. Figure 6 shows the laboratory testing results and notes the sudden drop in resistance strength when the sudden fracture occurred. Figure 7 shows the ABAQUS model hysteresis without the welding residual stress which resulted in a peak resistance strength of 467 kips. Figure 8 shows the ABAQUS model hysteresis with the welding residual stress incorporated, which resulted in a peak resistance strength of 452 kips. While the model with residual stress failed to duplicate the fracture it does result in a 3.2% decrease in ultimate load capacity.

Figure 5: FEM of column and I-beam with reduced area moment connection; results are stress in direction of I-beam at the final loading step

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Figure 6: Hysteresis plot of laboratory testing of swaged plate subjected to lateral loading. Note the sudden drop in resistance strength when the sudden fracture occurred

Figure 7: Hysteresis plot of ABAQUS model without residual stress from welding. The peak resistance strength was 467-kips, compared to 504-kips for the experimental model.

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Peak Resistance Strength = 504kips Sudden Fracture

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Figure 8: Hysteresis plot of ABAQUS model with residual stress from welding. The peak resistance strength was 452-kips, compared to 467-kips for ABAQUS model without residual stress.

Further details of the moment connection may be required to achieve results more similar to those seen in laboratory testing, but it is clearly shown that the addition of welding residual stress to the ABAQUS model mimics the decrease in strength known to be there.

5. Future Work

The process of creating multiple steps for each weld segment can be very time consuming. If fewer segments of larger length were used then the modeling and run time could be reduced by several hours. Thus a convergence study should be conducted to determine what length is required to achieve accurate results.

The swaged plate does not have any residual stress due to welding but it does have residual stress due to the press forming of the steel plate to form that shape. A method of simulating the press forming of the steel plate could be developed and incorporated into the testing model in order to add the residual stress and get more accurate results. It would be interesting to know whether the lack of welding actually results in less residual stress in the swaged plates.

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6. Contact Information

For further information or comments and suggestions contact Kenneth Gauthier at kenneth.gauthier@gmail.com. For updated information on the NASSCO project contact Gulen Ozkula at gozkula@ucsd.edu. There is a power point detailing the finite element welding process with ABAQUS available if anyone is interested in applying it to their research.

7. Acknowledgements

This project was partially supported by the National Science Foundation through the Research Experience for Undergraduates program (EEC-1263155) and the George E. Brown Jr. Network for Earthquake Engineering Simulation (NEES) Cooperative Agreement CMMI-0927178

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Special thanks to Kelli Walters, Thalia Anagnos, Alicia Lyman-Holt, and for continuous feedback and direction; Gulen Ozkula, Dong-Won Kim, and Dr. Uang at U.C.S.D. for guidance, encouragement, and critique.

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8. References

American Institute of Steel Construction (2011). Steel Construction Manual, 14th Edition. United States of America: AISC. Cengel, Y.A., Cimbala, J.M., Turner, R.H. (2012). Fundamentals of Thermal-Fluid Science, 4th Edition. United States of America: McGraw-Hill Companies, Inc. Danielson, D.A., Kihl, D.P., and Hodges, D.H. (1990). “Tripping of Thin-Walled Plating Stiffeners in Axial Compression.” Thin-Walled Structures, Vol. 10, pp. 121-142. Fujikobo, M. and Yao, T. (1999). “Elastic Local Buckling Strength Stiffened Plates Considering Plate/Stiffener Interaction and Welding Residual Stress.” Marine Structures, Vol. 12, pp. 543-564. General Dynamics (2013). “Company Overview.” < http://www.nassco.com/who-we-are/company-overview.html> (September 3, 2013). Grondin, G. Y., Elwi, A. E. and Cheng, J.J.R. (1998a). “Buckling of Stiffened Steel Plates: a Parametric Study.” Journal of Construction Steel Research, Vol. 50, No. 2, pp. 151-175. Grondin, G. Y., Chen Q., Elwi, A. E. and Cheng, J.J.R. (1998b). “Stiffened Steel Plates under Compression and Bending.” Journal of Construction Steel Research, Vol. 45, No. 2, pp. 125-148. Ozkula, G., Kim, D., Uang, C. (2012). “Progress Report to NASSCO.” Department of Structural Engineering, University of California, San Diego. Ruddy, J.L., Marlo, J.P., Ioannides, S.A. and Alfawakhiri, F. (2003). Fire Resistance of Structural Steel Framing, Design Guide 19. AISC, Chicago, IL. Sarkisian, M., Lee, P., Garai, R., Ozkula, G., Uang, C. (2013). “Effect of Built-up Box Column Electro-slag Welding on Cyclic Performance of Welded Steel Moment Connections.” SEAOC 2013 Convention Proceedings. Sheikh, I.A., Grondin G.Y. and Elwi A.E. (2001). “Stiffener Tripping in Stiffened Steel Plates.” Structural Engineering Report No. 236, Department of Civil and Environmental Engineering, University of Alberta, April. Sheikh, I.A., Grondin, G.Y. and Elwi, A.E. (2002). “Stiffened Steel Plates under Uniaxial Compression.” Journal of Construction Steel Research, Vol. 58, pp. 1061-1080. Sheikh, I.A., Elwi, A.E., and Grondin, G.Y. (2003). “Stiffened Steel Plates under Combined Compression and Bending.” Journal of Construction Steel Research, Vol. 59, pp. 911-930.

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Tonkovic, Z., Peric, M., Surjak, M. (2012). “Numerical and Experimental Modeling of a T-joint Fillet Welding Process.” 11th International Conference on Quantitative InfraRed Thermography, Naples, Italy. Ueda, Yukio. (2012). Welding Deformation and Residual Stress Prevention. Waltham, MA : Elsevier/Butterworth-Heinemann. Yi, J., Gil, H., Youm, K. and Lee H. (2008). “Interactive Shear Buckling Behavior of Trapezoidally Corrugated Steel Webs.” Engineering Structures, Vol. 30, pp. 1656-166

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9. Appendices

Appendix A – Nomenclature cP, specific heat at constant pressure Asurf, surface area h, convection heat transfer coefficient I, weld current k, coefficient of thermal conductivity L, original length Lseg, length of weld segment qweld, weld heat transfer qcond, conductive heat transfer qconv, convection heat transfer qrad, radiation heat transfer tseg, duration of body heat flux Tc, surface temperature Tsur, ambient temperature T∞, ambient temperature U, weld voltage Vweld, weld velocity V, volume of weld segment α, coefficient of thermal expansion Δq, heat energy transferred per mass ΔT, temperature differential ΔL, change in length ε, emissivity η, weld efficiency ρ, density σ, Steffan-Boltzmann constant

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Appendix B – Temperature-Dependent Material Properties Coefficient of Thermal Expansion, α

𝛥𝐿𝐿

= 𝛼 × 𝛥𝑇 (AISC, 2011) (B.1)

68 – 104 ˚F 𝛼 = 6.5 × 10−6 104 – 1200 ˚F 𝛼 = (6.1 + 0.0019 × 𝑡) × 10−6

Yield Stress, Fy, and Modulus of Elasticity, E – (Ruddy et al., 2003)

Thermal Conductivity, k

𝑞𝑐𝑜𝑛𝑑 = 𝑘 ∗ 𝛥𝑇𝐿

(Cengel et al., 2012) (B.2)

Example: Carbon-Manganese-Silicon Steel ( 1% < Mn < 1.65% ; 0.1% < Si < 0.6% ) Temperature, ᵒC (ᵒF) k (W/m*K)

127 (260.6) 42.2

327 (620.6) 39.7

527 (980.6) 35.0

727 (1340.6) 27.6

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Specific Heat, cP

𝑐𝑃 = 𝛥𝑞𝛥𝑇

(Cengel et al., 2012) (B.3) Example: Carbon-Manganese-Silicon Steel ( 1% < Mn < 1.65% ; 0.1% < Si < 0.6% ) Temperature, ᵒC (ᵒF) Cp (J/kg*K)

127 (260.6) 487

327 (620.6) 559

527 (980.6) 685

727 (1340.6) 1090 Density, ρ Relatively constant, 7850 𝑘𝑔

𝑚3, for all grades of steel at increasing temperatures (AISC, 2011).

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Appendix C – Heat Transfer Equations Body Heat Flux

𝑞𝑤𝑒𝑙𝑑 = 𝐼∗𝑈∗𝜂𝑉

(Ueda et al., 2012) (C.1) Convection Heat Transfer

𝑞𝑐𝑜𝑛𝑣 = ℎ ∗ 𝐴𝑠𝑢𝑟𝑓 ∗ (𝑇𝐶 − 𝑇∞) (Cengel et al., 2012) (C.2) h ≈ 13 𝑊

𝑚2𝐾 (Tonkovic et al., 2012)

Radiation Heat Transfer

𝑞𝑟𝑎𝑑 = 𝜀 ∗ 𝐴𝑠𝑢𝑟𝑓 ∗ 𝜎 ∗ (𝑇𝐶4 − 𝑇𝑠𝑢𝑟4 ) (Cengel et al., 2012) (C.3) ε = emissivity = 0.9 σ = Stefan-Boltzmann constant = 5.67 × 10−8 𝑊

𝑚2𝐾4

Duration of Body Heat Flux (Ueda et al., 2012)

𝑡𝑠𝑒𝑔 = 𝐿𝑠𝑒𝑔×60𝑉𝑤𝑒𝑙𝑑

(Ueda et al., 2012) (C.4)