Assessment of Numerical Procedures for Residual Stress Analysis of Multipass Welds

Transcription

1 Assessment of Numerical Procedures for Residual Stress Analysis of Multipass Welds The effects of heat input magnitudes and prescribed initial temperature conditions for welds on residual stresses are discussed BY J. K. HONG, C.-L. TSAI AND P. DONG ABSTRACT. Two-dimensional finite element modeling procedures are addressed to predict the residual stresses for multipass welds. A generalized plane strain model with a five-pass weld in a plate and an axisymmetric model with a six-pass girth weld in a pipe are considered. Element rebirth and pass-lumping techniques are employed in both models. The combined heat input using surface and body flux components is applied in simulating arc heat effects. In the generalized plane strain model, the calculated temperature histories and stresses are compared with the measured ones. Residual stress results are compared between non-lumped and lumped models. In the pipe girth-weld model, the calculated residual stresses are compared with the experimental data. The effects of heat input magnitudes and prescribed initial temperature conditions for welds on residual stresses are discussed in this article. Introduction Researchers have attempted to establish empirical approaches for understanding the behavior of materials during welding. To date, due to the complexity of the welding process, thermal and mechanical behaviors of weldment are not completely understood. Considerable effort has been devoted to develop numerical solutions to predict the thermal and mechanical responses in weldments. Although some insightful results have been obtained, most of the numerical procedures are usually extremely complex and difficult to implement in dealing with realistic welded structures. J. K. HONG and P. DONG are with the Center for Welded Structures Research, Battelle Memorial Institute, Columbus, Ohio. C.-L. TSAI is with the Department of Industrial, Welding and System Engineering at the Ohio State University, Columbus, Ohio. There are many publications on weld modeling using finite element analysis (FEA) techniques (Refs. 1-13). Recently, additional effort (Refs. 11, 12) has been made to develop simplified FEA procedures so that realistic temperature/stress histories in a weldment can be simulated with commonly available FEA packages. Representative publications on FEA techniques for the multipass welds can be found (Refs. 1-6). The thermal and mechanical response of a weldment is a three-dimensional (3- D) problem that requires a considerable amount of computational time. The computational time required to simulate a multipass weld increases in proportion to the number of weld passes. Therefore, it is necessary to develop cost-effective procedures to reduce the computational time while preserving the accuracy of the solution. To reduce the computational time, a two-dimensional (2-D) analysis can be carried out with appropriate simplifying assumptions depending upon the nature of the problem (Refs. 1,2, 5). To introduce welding travel speed effect in the 2-D model, the ramp heat input function has been developed (Ref. 1). Furthermore, some investigators have recently studied lumped pass modeling techniques (Refs ) to reduce the computing times for multipass welding cases. KEY WORDS Combined Heat Input Element Rebirth Technique Finite Element Analysis Initial Temperature Condition Multipass Welds Ramp Heat Input Function Residual Stress Pass-Lumping Technique To include the multipass effect, the element rebirth technique can be used as one of the few reasonable methods that can be readily incorporated in the existing commercial FEA packages. In this technique, the element groups representing each weld pass are generated along with the FEA meshes for the workpiece. These element groups are kept inactive until a designated "rebirth" time, according to specified pass sequences, is approached in the simulation (Refs. 1, 5). These techniques are applied to the residual stress analysis of a given welded joint. Considerable care needs to be exercised by an experienced analyst to correctly implement these numerical procedures, particularly for multipass welds. The simulation becomes even more complicated if phase transformation effects need to be incorporated (Refs. 7-10), although simplified numerical procedures have been investigated (Refs. 11, 12). In this study, simplified numerical procedures based on a commercial FE package, ABAQUS (Ref. 17), were investigated for residual stress analysis in multipass welds. A generalized plane strain model for a five-pass weld in a plate and an axisymmetric model for a six-pass girth weld in a pipe were used for this purpose. Element rebirth and pass-lumping techniques were employed in both models. Finite Element Modeling Procedures Heat Source Model To simulate arc heating effects during welding, the equivalent heat input can be assumed as the combination of both surface and body heat flux components (Ref. 5). Therefore, the total heat input can be written as Q = Q s + QB (1) 372-s I SEPTEMBER 1998

2 Table 1 -- Pass Sequences and Welding Parameters of Each Pass for a Five-Pass Welded Plate ~'~ Pass sequence I1 12" EfJ'J'IJ'A Welding parameters Pass No. Current (A) Voltage (V) Speed (in./min) Ref. 1. Heat Flux / Fig. I -- Ramped heat input function,z tl / n t,,--z5 i=i n t2 t2 Time ~,<-- t3 --~ 1-,.,-1 n gliti iffil qeq n ~ t~ln Fig Definition of ramp functions for heat flux before and after lumping (Re 16): A -- Ramp functions of welding passes before lumping; g -- ramp function after lumping. iffil Time (sec.) where (~s and (~B indicate heat contents resulting from a specified surface flux and body heat flux, respectively. In addition, the surface heat flux was assumed to be in the form of a Gaussian thermal distribution (Ref. 5), while the body heat flux was assumed constant in this study. The ratio of Qs/QB can be adjusted to achieve an accurate representation of fusion zone. Ramped Heat Input A ramp heat input function has been developed to Time gradually apply the heat flux with a variable amplitude to the model, as discussed by a number of earlier publications (Ref. 1, 2). In addition, to avoid numerical divergence problems due to a sudden increase in temperature, the ramped heat input procedure enables a 2-D cross-section model to include the effect of a 3-D moving arc in a consistent manner. The ramp function considers the out-of-plane heat transfer effects on a specified 2-D cross section as the arc approaches, travels across and departs from it. As shown in Fig. 1, the actual welding time for the arc to travel across the unit thickness of the model is tl + t2. The term t3 indicates the rampdown time and is assumed to be the same as tl. The temperature profiles can be affected by the ratio of the ramp-up time, tl, over the time period, tl + t2, i.e., tl --xl00 (%). tl + t2 According to the previous work (Ref. 1 ), it was observed that a ramp-up time, tl, of 20 % of the actual weld time, tl + t2, gave the best correlation with the gas metal arc welding (GMAW) experimental data. The total area under the curve (Fig. 1) is kept constant to ensure that the same total heat input to the model is maintained. In this study, if the total time and the percentage of ramp heat time were determined, the ramped heat input effects were calculated by a user subroutine (Ref. 17). Weld Metal Initial Temperature Conditions In simulating GMA welding processes, weld metal can be assumed to be deposited at melting temperature. However, this often complicates the finite element procedures using some of the commercial finite element codes (e.g., ABAQUS) and requires additional solution steps in the thermal analysis. As a result, some authors in previous publications only assumed ambient temperature as the initial temperature conditions for the weld metal. However, in studies by Karlsson, et al., (Refs. 18, 19), the authors adopted melting temperature as the initial temperature for the reborn elements (deposited weld metal) in calculating the resulting thermal strains. Josefson (Ref. 20) used a similar approach. In this study, two different prescribed initial temperature conditions, i.e., room temperature and melting temperature, were employed for the weld metal and their effects on predicted residual stresses were compared. Temperature Solution Procedures According to Lindgren, et al (Ref. 21 ), if the residual stresses are of primary interest, the temperature history can be calculated from simple analytical solutions. As such, the thermal material properties are assumed to be independent of the temperature. In addition, Landau, et al. (Ref. 22), discussed that the residual stress solutions are not sensitive to the de- WELDING RESEARCH SUPPLEMENT I 373-s

3 tails of the temperature distributions. In this study, various finite element heat flow solution procedures were investigated for the stress analysis of a sixpass girth weld. The effects on residual stress predictions were discussed. Element Rebirth Technique The element rebirth technique (Ref. 5) was employed to include the multipass weld metal deposition effects. With this technique, the elements simulating each weld pass are grouped at model generation stage. During analysis, these element groups (i.e., weld passes) are first removed and then reactivated at a specified moment to simulate a given deposition sequence of weld passes. When a group of weld elements are activated, specified initial temperatures are imposed for all the nodes associated with the weld elements. Lumped (Grouped) Weld Passes Residual stress analysis for complex welded structures with multipass welds often requires the use of lumped passes to reduce computational time and simplify analysis procedures. Along this line, Rybicki, et al. (Ref. 14), studied multipass girth welds by combining all passes in lumped layers each of which represented several welds. Ueda, et al (Ref. 15), also investigated the lumped-pass technique for a narrow-groove weld. They concluded that the number of welding passes in thick plates can be significantly reduced without affecting the accuracy of the analysis Lee (Ref. 16) proposed a lumpedpass procedure with which heat flux magnitudes were calculated in an accumulative manner and heating duration was determined in an averaged sense-- Fig. 2. In this study, Lee's lumped-pass procedure was analyzed in detail to compare with the results without using lumped-pass procedures. Case Studies To investigate the adequacy of various numerical procedures as discussed above, detailed case studies on a fivepass weld in a plate and a six-pass pipe girth weld are presented below. A Five-PassWeld in a Plate Assumptions and Analvsis Procedures The details of the five-pass weld are given in Table 1 (Ref. 1 ). The weldment is 15 in. long, 8 in. wide and Y2 in. thick. The gas metal arc welding (GMAW) process was simulated according to the pass se- quence and welding parameters xl~ 8 shown. The thermal and mechanical material prop- ~ _ e erties for both base ~ s and weld metal were assumed i based on ASTM A36 mild steel, as shown in Fig. 3 as a function of temper- o, ature. The strainhardening behav ior at room temperature is shown in Fig. 4. An isotropic hardening plasticity model was used. 4o A 2-D plane 35 model was used, 30 shown in Figs. 5 ~ 2s and 6. The total "-~ number of ele- a+, 20 ments used in the "~,5 model is 867. Gen-, o eralized plane s strain conditions were assumed in o the residual stress o analysis to take into account of the deformation behavior in the outof-plane direction. ABAQUS (Ref. 17) was employed for the transient temperature and sub- sequent residual stress analyses. In "~ performing the.~ temperature analy- sis, it was further assumed that the initial temperature conditions for both base and weld metal were at a uniform temperature 70 F (21.1 C), i.e., room temperature, in the heat flow analysis. The heat loss coefficient assumed for all surfaces is Btu/in2 F. Other heat loss mechanisms such as radiation and forced convection due to shielding gas were neglected. Similarly, radiation and convection influences on the microstructures and cooling rates of weld metal, as well as heat losses or gains from phase transformation, were neglected. I! I i I o0 160o o0 Y *kl rams (XlO ~) Younm'* ModUlU* 011o ) TemPerature (F) Tempermture (F) ~ !., Fig Temperature-dependent material properties of ASTM A36 mild steel for finite element analysis (Ref. 1): A -- Thermal material properties; B -- mechanical material properties oy 1.15 oy Oy Fig Strain hardening effect used for ASTM A36 steel. Plastic strain Total heat input was assumed to be in the form of 20% of surface flux and 80% body flux. The heat input was imposed onto the specified newly activated elements representing a depositing pass at a given time. The surface heat flux was followed by the modified Gaussian distrib S I SEPTEMBER 1998

4 4 15 inches Fig View of entire mode/for a five-pass welded plate. I i i i X ~ - - ~ Weld toe "--"-t----'~ Fig Finite element mode/for a five-pass welded plate: A -- Weld detail, five-pass model (nonlumped model); B -- weld detail, three-pass model (lumped model). y Y uted heat flux over the length of each weld (Ref. 5). Body heat flux was uniformly distributed over the length of each weld layer. An arc efficiency of 85% was considered for the net heat input to the weldment. A ramp time consisting of 20% of total heat input time was used (Ref. 1). The maximum allowable temperature change between time increments was set to be 300 F (149 C). Interpass temperature was assumed to be at room temperature. Three lumpedpass procedures were investigated for this case: A five-pass model (without lumping) (Fig. 6A) ; a three lumped-pass model (Fig. 6B) with an equivalent heat input from Lee's study (Ref. 16); and, a three lumped-pass model (Fig. 6B) but with a lumped heat input modified by a weight factor to avoid overheating around the weld area. Results and Discussions Thermal Analysis The transient temperature histories during the first pass at '/~ in. and 1~ in. from the weld toe on the top surface are shown in Figs. 7A and 7B. The measured temperature data (Ref. 1) at the same positions are also plotted against the predicted results. Note Fig. 7A shows the temperature histories within the first 20 s, while Fig. 7B gives the entire temperature histories up to the steady-steady state, e.g., room temperature. A good agreement between the finite element results and experimental measurements is evident. Stress Analysis Five-Pass Model vs. Three Lumped-Pass Model Figure 8 shows the transverse residual stresses (perpendicular to the welding direction) along the bottom and top surfaces after final weld pass. The results of the five-pass model and the three-pass model (lumped) are compared. The discrepancy between the five-pass and three-pass models appears to be significant near the weld toe. The measured transverse stress from Tsai, et al. (Ref. 2), showed a higher magnitude than the finite element results -- Fig. 8B. The threepass models predicted lower stresses and a wider tensile stress zone than the fivepass model, since the lumped models tend to introduce a higher heat content to the weldment. The discrepancy becomes less significant away from the weld toe. Figure 9 shows the corresponding longitudinal residual stress distributions (along the welding direction) on both the bottom and top surfaces. The three-pass 6OO oe A 7OO r Measured(1/2")I1]j.. I ~FEReeub(1P2") I B e& O I Time (Sec.) OI Time (See.) Fig Comparison of measured (Ref. 1) and calculated temperature profiles for the first weld pass at ~ in. and ~,~ in. from the weld toe on top surface of a Vs-in.-thick plate model: A -- During heating; B -- during heating and cooling. WELDING RESEARCH SUPPLEMENT I 375-s

5 model without modification shows higher compressive stresses away from the weld toe and a larger tensile stress zone within the weld area compared with the five-pass model. The experimentally measured value (Ref. 2) is also shown -- Fig. 9B. Figures 10A and 10B show the through-thickness distributions of the transverse and longitudinal stress at % in. from the weld centerline. It can be seen that all three models predicted a similar general trend for the transverse residual stress component. However, the throughthickness variation from the five-pass model is more significant than those from the three-pass models in which the stress magnitudes at both surfaces and the middle section of the weld were underestimated. As for the longitudinal component, the lumped-pass models overestimated the residual stresses through the plate thickness. Lumoed-Pass Models As shown in Figs. 8 and 9, the increased tensile zone sizes were attributed to the lumped heat input effects. This clearly demonstrates that the equivalent heat contents associated with lumped passes should be carefully defined to obtain a reasonable residual stress prediction, particularly for transverse residual stress components. In the lumped-pass model with a modified weight function (reduced by 15% as a weight factor), the improvement in residual stress predictions can be seen, particularly for the longitudinal components. Pass by Pass Residual Stress Develooment Through Figs , the detailed residual stress development is further illustrated using the five-pass model. Figures 11A and 11 B show the transverse stresses along the bottom and top sur- faces of the weldment after each pass. The transverse residual stresses at the weld toe were compressive in the beginning and became highly tensile after the final (fifth) pass. Figures 12A and 12B show the longitudinal residual stresses along the bottom and top surfaces. The longitudinal residual stresses maintained a relatively high magnitude throughout the five-pass deposition process. The increase in magnitude was relatively small comparing 15 with transverse residual stresses. f0 Figures 13A and ~ 13B show the 5 through-thickness transverse and lon- 50 gitudinal stress variation at 2/5 in. -5 from the weld toe. A Six-Pass Girth- Welded Pipe Model Definition A six-pass girthwelded pipe was considered in this section. This model definition was consistent with that investigated by Brust, et al. (Ref. 23), as shown in Fig. 14. The pipe was made of Type 304 stainless steel. The corresponding material properties are given in Fig. 15 (Ref. 23). The weld metal properties were assumed to -10 ~Z m 10 15! ]o -10 be the same as the base material. The detailed weld pass data with welding parameters are summarized in Table 2. Axisymmetry assumptions were used. Furthermore, symmetry conditions were assumed with respect to the weld centerline. The total number of elements and nodes within the model are 294 and 999, respectively pass model ] x ~.. ~. ~. l k ~ ~3 pass model (w/o mo~cation) _x 3pas_s mod~l_ (with m o(~/ification~j Distance from weld toe on bottom surface (in.) -- 5 pass moded ~ 3 pass model (w/o modification) x 3 pass model (with modification) Measured 2] x ~... _-llkllm~ it I ~ X, ll ii ill Distance from ~ toe on top surface (in.) Fig Residual transverse stress distributions for a plate mode/: A -- On bottom surface; B -- on top surface. o) pass model ~ : t ~ ~ x ~ 3 pass model (WO modification) I \.\ x 3 pass model (with modification 30 I -~p~=de' J I \ = \ I~ 3 palm model (~0 modlfk~tion) I z~ ] \ ~ X I x 3 pass model (v, tthmodlflcation) I \ I f o ~,<~J~.~xxx x x ~ ~ ~ ~ _~ ~ ~ x -20 J Distance from '~,e Id toe on bottom surface (in.) Distance from ~ld toe on bottom surface (in.) Fig Residual longitudinal stress distributions for a plate model: A -- On bottom surface; B -- on top surface. 376-s I SEPTEMBER 1998

6 7.5 ~ 5 ix 3passmodel(w~modlfication) I / ~ 2.5..' '.'~_o2, o.',5 o2~.~zi.' i ~45 "4 t4o f --~-- ~ =: mm~o~)l (w/o modlf' ation) ] x 3 pass model (with modfflcatjon)~ x ~ Distnace from bottom to top surface (in.) O 0.C , ,5 Distance from bottom to top surface (in.) Fig Through-thickness residual stress distributions at 2~ in. from the weld toe for a plate model: A -- Transverse stress distributions; B -- longitudinal stress distributions pus model 3 pass model (w/o modification) x 3pass mode withmodifinason -5 ~ ~35-10 J Distance from ~ toe on bottom audace (in.) Distance from bottom to top surface (in.) Fig Residual transverse stress distributions after immediate passes for a plate model: A -- On bottom surface; B -- on top surface. 30 "- 1ol Distance from wek:l toe on bottom surface (in,) _~ =.. _ ~ ~ = D~lance from ~ toe cn top surface (in.) Fig Residual longitudinal stress distributions after immediate passes for a plate model: A -- On bottom surface; B -- on top surface. WELDING RESEARCH SUPPLEMENT 377-S

7 6 10 q io ' i. i ' i.' i Distar~ce from bottom to top surface (in.) D~tarTce from r~torn to top sudace (in,) Fig Through-thickness stress distribution at 2,~ in. from the weld toe after immediate passes for a plate model: A -- Transverse stress distributions; B -- longitudinal stress distributions. The analysis procedures are similar to those described in the above, except that (1) weld metal initial temperature at deposition was assumed at either room or melting temperature; (2) various arc efficiency factors were assumed, (see Table 3, note that Case D with 108% arc efficiency was arbitrarily selected); and (3) linear kinematic hardening was assumed. Results and Discussions Predictions vs. Measurements Figures 16 and 17 show the comparison between the finite element results (Case A) and experimental data (Ref. 23). Figures 16A and 16B show the axial residual stress distributions along the outer and inner surfaces, respectively. In Figure 16A, the FEA results show a good agreement with the experimental measurements. In Figure 16B, the predictions gave higher values than those obtained from experiments. Figures 17A and 17B show the circumferential (hoop) residual stress distributions along the outer and inner surfaces, respectively. The predicted and measured hoop residual stresses on the outer surface showed a significant variation (Fig. 17A), particularly at the weld toe. However, the overall trends between the predictions and measurements appear in reasonable agreement. Hoop residual stresses with a high magnitude were predicted for the inner surface, extending a few weld widths from the weld centerline -- Fig. 17A. In what follows, various heat input conditions (see Table 3) and their effects on residual stress predictions will be examined with respect to Case A. Table 2 -- Pass Sequences and Welding Parameters of Each Pass for a Six-Pass Girth-Welded Pipe Model ~ Welding parameters Pass No. Layer No. Heat input (kj/mm) Speed (mm/s) , 3 4, 5, Ref. 23. Effects of Heat Input Figures 18 and 19 show the residual stress distributions along the inner and outer surfaces with various conditions described in Table 3, with prescribed room temperature conditions for weld metal. Note that the predicted residual stress distributions are rather similar. Among them, Case D (with an unrealisti- o.3_ I Passea 4 = Passes 2-3 Root Pass Centcrline! 5.0"! I I It;/ll',','~lLIl~ R=6.0" Fig Finite element model for a six-pass girth-welded pipe: A -- View of weld area; B -- entire view of the axisymmetric pipe model. cally high heat input) showed a little more deviation far away from the weld. Note that the weld metal initial temperatures in these cases were assumed to be at room temperature. Effects of Weld Metal Initial Temperature Figures 20 and 21 show the predicted residual stress distributions along outer and inner surfaces with different heat I i i ' 378-s I SEPTEMBER 1998

8 o'u, o'y, E~ET, v ksj ksi_ psi 0.34~ ~ ' ~ 0"33 ~ " 28 r ~ o, "~ ~y ;,.2,1-~ -,~ -,, r ~ ~ \ ~,,. o o.2,,-,0 -,o., ~ ~ j ~.... ~ \ \ I o.2~- ~ -,,,,2 r ~ ~,.,.\ \ ~,oo 02,_~0_,~,o r / \ ~ \ \ I o.,,_~o_,o: ~r / \ ~ ~ \ t ", 0.~,_,,. o,,r/ ~ ~ \\i..o o~o_,oj_ ~: 2!_ ~-~----~-~ ~"~.1 o,.-~-2~ o 2oo.oo ~oo ~OOm.~r, OO%.~2oo,.oo,~oo,~oo 2ooo ~ Fig Temperature-dependent material properties of 304 stainless steel for finite element stress analysis (Ref. 23). Table 3 -- Combination of Heat Inputs for a Six-Pass Girth-Welded Pipe Case A B C D E F G Percent heat input Initial prescribed temperature conditions (%) Weld metal Base metal 72 Room temperature Room temperature 62 Room temperature Room temperature 82 Room temperature Room temperature 108 Room temperature Room temperature 50 Melting temperature Room temperature 40 Melting temperature Room temperature 72 Melting temperature Room temperature inputs, as shown in Table 3, and the prescribed melting temperature initial conditions for weld metal. Again, the results are essentially similar among all the cases. Case G showed some deviations from the rest starting from about 2 in. away from the weld centerline., From a practical standpoint, the results (Figs ) suggest that the predicted residual stress distributions do not seem sensitive to the detailed heat input parameters and the prescribed initial temperature conditions for weld metal deposio 60 4O 2o Weld =l I--FE Results (Case A) I =' 1 ~ i'u"'~~] I I, t 0 ol, ~., o:= ~.~-,.~,.,,.~,.,, '2;-'"- ~-20 ~ --FE Reeults (Case A) Measured 23 i Distance from we~l centerlble on OUter surface (in.) Distance tom weld centedine on inner surface (in.) Fig Comparison of the calculated (Case A heat input) and measured (Ref. 23) residual axial stresses for a pipe model: A -- On outer surface; B -- on inner surface. WELDING RESEARCH SUPPLEMENT I 379-s

9 607 --FE Results (Case A) 40~ Measured FE Results (Case A) Measured 23] :or If o, 120~ W~ld ~' _:~\*' 20 ~o ~-20 I ' i I 0.2 I (--~," Weld J Distance from weld centedlne on outer surface (in.) -60 Distance from weld centerline on inner surface (in.) Fig Comparison of the calculated (Case A heat input) and measured, Ref. 23) residual hoop stresses for a pipe model: A -- On outer surface; B -- on inner surface ~ 0, i o 1 5 J ~ -20 ~ 21' Distance from weld centerllne on outer surface (in.) 20- o, ~-20 ~ ~ "... i ' i ' ' ' 7.~ -~ 5 Distance from weld centedine on inner surface (in.) Fig Residual axial stresses for different heat input magnitudes for a pipe model (prescribed initial temperature for weld metal is room temperature): A -- On outer surface; B -- on inner surface. 6O 6O..=-20 ~20~ ] Distance from w@d centedine on outer surface (in.).60 Distance from weld centerine on inner sudace (in.) Fig Residual hoop stresses for different heat input magnitudes for a pipe model (prescribed initial temperature for weld metal is room temperature): A -- On outer surface; B -- on inner surface. 380-s I SEPTEMBER 1998

10 : 5 j 1 : 5 ' 2 2 : 5 ' 3 3 : " 4'.~"- : ~" 5 ~ ~ ~ -60 J Distance from weld centerune on outer surface (in.) ~. 20 ~o -40~ I -60 ~ Distance from weld centedine on inner surface (in.) Fig Residual axial stresses for different heat input magnitudes for a pipe model (prescribed initial temperature for weld metal is melting temperature): A -- On outer surface; B -- on inner surface. 60 4O 40 0 ~, ~.~ 2O J 1 ~-2o -40 Distance from weld centerune on outer surface (in.) -60 Distarce from weld centedine on inner surface (in.) Fig Residual hoop stresses for different heat input magnitudes for a pipe model (prescribed initial temperature for weld metal is melting temperature): A -- On outer surface; B -- on inner surface. tion effects, as long as the fusion zone for each pass is adequately modeled. Conclusions In this article, various simplified residual stress modeling procedures were examined in detail using two multipass weld examples. The following observations can be made in light of the case studies performed: 1 ) If lumped-pass models are used, the transverse residual stresses tend to be underestimated due to the higher amount equivalent heat input. However, the corresponding longitudinal residual stresses can still be reasonably predicted. Further improvement can be achieved by introducing the weighted factor approach presented in this study. 2) The modeled weld pass profile in terms of both size and shape dominates the final residual stress distributions. Spe- cial care must be exercised in defining and presenting weld pass profiles to achieve an adequate accuracy in residual stress predictions. 3) Predicted residual stress results in this study are shown to be insensitive to the detailed heat input parameters and initial temperature settings for deposited passes. Advantages can be taken to simplify the thermal analysis procedures without jeopardizing the accuracy of residual stress solutions. This will be extremely beneficial for analyzing complex structures. Acknowledgement The presented work was sponsored in part by the Edison Welding Institute under the EWl Cooperative Research Program. References 1. Shim, Y. L., Feng, Z., Lee, S., Kim D., Jaeger, J., Papritan, J. C., and Tsai C.-L Determination of residual stresses in thick-section weldments. Welding Journal 71 (9): 305-s to 312-s. 2. Tsai, C.-L., Kim, D. S., Shim, Y. L., Feng, Z., Lee, S., and Jaeger, J Determination of Residual Stress and Effects in Thick Section Weldments for Hydraulic Structures. Research Report of Army Corps of Engineers. 3. Feng, Z., Jaeger, J., Kim, D., Lee, S., Papritan, J., Shim, Y. L., and Tsai, C.-L Finite Element Modeling of Welded Thick Plates for Bonneville Navigation Lock. Research Report of Army Corps of Engineers. 4. Tsai, C.-L., Lee, S. G., Shim, Y. L., Jaeger, J., and Chasten, C Experimental Verification of Modeling Techniques of Thermal-Related Welding Problems. The Winter Annual Meeting of the ASME, Orlando, Fla. 5. Hong, J. K., Dong, P., and Tsai, C.-L. Finite element simulation of residual stresses in muhipass welds International Conference Proceedings on Modeling and Control of Jointing Processes, ed. T. Zachria, American Welding Society, Miami, Fla., pp Dong, Y., Hong, J. K., Tsai, C.-L., and Dong, P Finite element modeling of residual stresses in austenitic stainless steel WELDING RESEARCH SUPPLEMENT 381-s

11 pipe girth welds. Welding Journal 76(10): 442- s to 449-s. 7. Josefson, B. L Stress redistribution during annealing of a multi-pass butt-welded pipe. Journal of Pressure Vessel Technology 105: Karlsson, L Thermal stresses in welding. Thermal Stresses, ed. R. B. Hetnarski,Vol. 1, pp North-Holland, Amsterdam, The Netherlands. 9. Goldak, J. Modeling thermal stresses and distortions in welds Recent Trends in Welding Science and Technology, eds. S. A. David and I. M. Vitek, pp ASM International, Material Parks, Ohio. 10. Andersson, B. A. B Thermal stresses in a submerged-arc welded joint considering phase transformations. Journal of Engineering Materials and Technology 100(4): Hibbitt, H. D., and Marcal, P. V A numerical, thermo-mechanical model for the welding and subsequent loading of a fabricated structure. Computer & Structures 3: Argyris, J. H., Szimmat, J., Willam, K. J Computational aspects of welding stress analysis. Computer Methods in Applied Mechanics and Engineering 33: Leung C. K., and Pick, R.J Finite element analysis of multipass welds. Welding Research Council Bulletin 356: Rybicki, E. F., and Stonesifer, R. B Computation of residual stresses due to multipass welds in piping systems. Journal of Pressure Vessel Technology 101 : Ueda, Y., and Nakacho, K Simplifying methods for analysis of transient and residual stresses and deformations due to multi-pass welding. Trans. of JWRI 11: Lee, S. G Modeling of Residual Stress In Thick Section Weldments, Ph.D. ds., The Ohio State University. 17. ABAQUS User's Manual Hibbitt, Karlsson & Sorensen, Inc., Province, R.I. 18. Karlsson, C. T Finite element analysis of temperatures and stresses in a single-pass butt-welded pipe -- influence of mesh density and material modeling. Engi- neering Computations 6: Karlsson, R. I., and Josefson, B. L Three-dimensional finite element analysis of temperatures and stresses in a single-pass butt-welded pipe. Journal of Pressure Vessel Technology 112: Josefson, g. L Residual stresses and their redistribution during annealing of a girth-butt welded thin-walled pipe. Journal of Pressure Vessel Technology 104: Lindgren, L.-E Temperature fields in simulation of butt-welding of large plates. Communications in Applied Numerical Methods, Vol. 2, pp Landau, H. G., Weiner, J. H., and Zwicky, E. E., Jr Thermal stress in a viscoelastic-plastic plate with temperature-dependent yield stress. Journal of Applied Mechanics 27(2): Brust, F. W., and Stonesifer R. B. Effect of Weld Parameters on Residual Stresses in BWR Piping Systems. NP-1747, Final report by Battelle, Columbus Laboratories to Electric Power Research Institute, March s SEPTEMBER 1998