on modeling of the weld line in finite element analyses of tailor-welded blank forming operations

Journal of Materials Processing Technology 147 (2004) 28–37

On modeling of the weld line in finite element analyses oftailor-welded blank forming operations

Scott D. Raymond, Peter M. Wild∗, Christopher J. BayleyDepartment of Mechanical Engineering, Queen’s University, Kingston, Ont., Canada

Received 13 March 2002; received in revised form 20 March 2003; accepted 26 September 2003

Abstract

Finite element analyses of standard tailor-welded blank (TWB) forming tests were performed to determine the effects of weld modelingtechniques on simulation results. Finite element models of TWBs were created that either included a simple representation of the weldproperties and geometry or excluded both weld geometry or material properties. In all models, shell elements were used to representparent materials of the TWB. The models excluding weld properties and geometry used nodal rigid bodies to join the thin and thick parentmaterials. The models including weld properties and geometry used solid elements for the weld materials, and a novel method for joiningshells to solids. Simulations of three standard metal forming tests were performed: ASTM tensile test, in-plane plane strain test, and limitingdome height tests representing various biaxial strain states including: uniaxial tension, plane strain and biaxial tension. Results indicatethat there are a number of relatively subtle effects associated with the manner in which the weld line is modeled. Most of these effectsrelate to the constraining effect of the weld line with respect to strain along the axis of the weld line.© 2003 Elsevier B.V. All rights reserved.

Keywords: Finite element analysis; Tailor-welded blank forming test; Weld property

1. Introduction

Tailor-welded blanks (TWB) are comprised of two ormore sheets of metal with dissimilar strength and/or thick-ness that are welded into a single blank. TWBs are stampedinto automotive body panels and offer reduced part weightand improved material use. They are most commonly fabri-cated using a laser welding process, which creates a narrowweld and heat-affected zone (HAZ) at the junction of thedissimilar sheets.

In the published literature on finite element analysis (FEA)of TWB forming operations, methods of modeling of theweld line fall into two general categories. In the first cate-gory, weld properties and geometry are excluded from themodel[4,5,11,13–15]. A set of rigid links is used to tie ad-jacent nodes on the thin and thick sheets together. In thesecond category, models include various representations ofthe weld properties and geometry[9,10,12,13,15]. Saunders[13] and Zhao et al.[15] used shell elements to represent theweld line. Shell elements are limited in that they can onlyapproximate the weld geometry and are more suited to con-stant thickness geometries. In studies by Iwata et al.[9,12],

∗ Corresponding author.

beam elements were used to represent the weld. Beam ele-ments also limit the geometry that can be represented andthe refinement of the mesh in the weld zone. Jain[10] andZhao et al.[15] used solid elements to represent the weld.When using this technique, the parent materials were alsomodeled using solid elements. This approach is computa-tionally inefficient in the context of sheet metal forming op-erations, as several through-thickness solid elements mustbe used to accurately represent bending[7] throughout theparent metal.

In those references where the merits of inclusion of adetailed model of the weld are discussed, there is a consensusthat the additional computational cost is not justified[13,15].The Auto-steel Partnership guidelines on TWB stamping andprocess considerations summarize this consensus as follows:“When modeling a laser beam welded blank, the mechanicalproperties of the weld bead itself can be neglected with nosignificant loss of accuracy in the results[3]”. This viewis justified in the context of the majority of current TWBapplications in which the weld is isolated from regions ofhigh strain. As the variety of TWB applications increases,the effects of the weld on blank formability may becomemore significant and it will be important that these effectsare well understood. The objective of this research is toperform a systematic study of the influence of weld modeling

0924-0136/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2003.09.005

S.D. Raymond et al. / Journal of Materials Processing Technology 147 (2004) 28–37 29

techniques on results of FE simulations of TWB formingoperations.

2. TWB geometries

Finite element models were created for three differentstandard forming tests. The ASTM tensile test[2] was sim-ulated with a transverse weld orientation only. The in-planeplane strain test (IPPS)[10] was simulated with both longitu-dinal and transverse welds. The limiting dome height (LDH)test[6] was simulated with several blank geometries to ob-tain variations in the biaxial strain state. These variations inbiaxial strain were achieved by modeling blanks of varyingwidth, i.e. 25 (LDH25), 100 (LDH100), 125 (LDH125), and200 mm (LDH200). The LDH25 specimen simulated uniax-ial tension, while the LDH100 and LDH125 specimens sim-ulated plane strain and the LDH200 specimens simulatedbiaxial tension. For all LDH models, both longitudinal andtransverse weld orientations were simulated.

Thickness ratios for all these tests were varied to includea range from 1:1 up to 1:2.25. The thin parent material wasmaintained at 0.8 mm, while the thick parent material wasvaried in increments of 0.2 mm from 0.8 up to 1.8 mm.

The material properties used for the parent blanks corre-spond to AISI 1005 steel. The strain-hardening exponent andstrength coefficient used in the Ludwick–Hollomon equa-tions were obtained from a previous study on TWB proper-ties [1]. In this study, uniaxial tests on the parent materialspecimens and the integrated TWB were used to determinethe material properties of the weld. The material propertiesfor the parent and weld materials are shown inTable 1.

3. The finite element models

All simulations were performed using the dynamic-expl-icit FE code, LS-DYNA (Livermore Software Technol-ogy Corporation, Livermore, CA). The parent materialmodel was comprised of 4-node quadrilateral shell ele-ments of the Belytschko–Lin–Tsay formulation with threethrough-thickness integration points[8].

For the models excluding weld properties and geometry,nodal rigid bodies were used to connect adjacent nodes ofthe thin and thick parent materials. For the remainder of thisdocument, “NW” designates models excluding weld prop-erties.

The weld representation including weld properties used8-noded linear solid elements for the weld zone. These solid

Table 1Hardening characteristics for parent and weld materials[1]

Material Strength coefficient,K (MPa)

Strain-hardeningexponent,n

Parent 561 0.1757Weld 1165 0.1154

elements were constrained to move with the parent mate-rials using an interpolation constraint found in LS-DYNA(∗CONSTRAINEDINTERPOLATION) [8], as shown inFig. 1. When using this constraint, the motion of a singledependent node is interpolated from the motion of a set ofindependent nodes. In this study, the dependent node wason the parent material mesh, while the independent nodeslay on the adjacent weld material mesh. For the remainderof this document, “W” designates models including weldproperties.

For the ASTM test specimen, an additional model wasdeveloped in which the mesh is as described above for themodels including weld properties. However, the materialproperties assigned to the solid elements are identical to thematerial properties for the shell elements that define the par-ent material. The purpose of this model is to assess the ef-fects of mesh and element type on the results, independentof the material properties. For the remainder of this docu-ment, “NW-2” designates these models.

Prior to finalizing the finite element models, a sensitivitystudy was performed on element dimensions, formulationsand the number of integration points required. The results ofthese sensitivity studies formed the basis for the finite ele-ment models. A secondary sensitivity study was performedon model solution control techniques to determine the tool-ing speeds providing the most accurate and computationallyefficient solution.

Failure was determined by comparing the major and minorstrains in the thin parent material to the forming limit dia-gram (FLD) for the material. When the combination of majorand minor strains crossed the forming limit curve, failure wassaid to have occurred. The LS-POST post-processing soft-ware performs this procedure automatically. The FLD wascreated using the material thickness and strain-hardening ex-ponents of the parent material.

For models in which the weld was oriented with the axisof major strain, failure was expected to originate in the weldmaterial. However, the automatic comparison of major andminor strains to the FLD cannot be performed in LS-POSTfor the solid elements of which the weld is comprised. Alimiting effective plastic strain of 15% in the solid weldelements was, therefore, used to determine when failure hadoccurred. This is the ultimate strain for this weld materialas determined experimentally by Abdullah et al.[1].

4. Results

4.1. ASTM models

A number of relatively subtle differences were observedbetween the W and NW models for the ASTM specimen:

(1) The applied displacement causing failure in the NWspecimen was greater than the W specimen withthis difference diminishing as the thickness ratio in-

30 S.D. Raymond et al. / Journal of Materials Processing Technology 147 (2004) 28–37

Fig. 1. Schematic diagram of the interpolation constraint available in LS-DYNA.

creases, as shown inFig. 2. The NW and NW-2 resultsagreed well, except for the case of a 1:1 thicknessratio.

(2) As shown inFig. 3(a), for a thickness ratio of 1:1, thefailure location in the W specimen occurred away fromthe mid-span position (i.e. away from the weld) whereas,for the NW and NW-2 specimens, failure occurred atthe mid-span location (seeFig. 3(b) and (c)).

(3) For other thickness ratios, the measured failure locationfor all three models (W, NW and NW2) were identical,within measurement error (seeFig. 4). The error bars in

Fig. 2. Comparison of the applied displacement at failure for the ASTM simulations.

this figure indicate the resolution of the failure locationmeasurement which is determined by the mesh densityor element size.

(4) A significant difference in width reduction at the weldwas seen, as shown inFig. 5. The reduction in width inthe NW and NW2 specimens was higher than that forthe W specimens. The difference was the greatest at athickness ratio of 1:1, and diminishes as the thicknessratio increases.

(5) The weld displacements at failure are less (<3%) for theW model than for the NW and NW2 models, as shown


Fig. 3. Plots of effective plastic strain comparing peak strains and failure positions for ASTM: (a) W, (b) NW and (c) NW2 same gage specimens.

Fig. 4. Comparison of the failure location for the ASTM simulations.


Fig. 5. Comparison of the width reduction at failure for the ASTM simulations.

in Fig. 6. This difference diminishes as the thicknessratio increases.

(6) With the exception of the 1:1 and 1:2.25 thickness ratios,the weld displacements for the NW2 models are slightlygreater (<0.5%) than for the NW models.

4.2. IPPS models

For the IPPS simulations with transverse weld orienta-tions, a number of subtle differences were observed betweenthe W and NW models:

Fig. 6. Comparison of the weld displacement at failure for the ASTM simulations.

(1) The applied displacement causing failure in the NWspecimen was greater than the W specimen and thelargest difference was for a thickness ratio of 1:25, asshown inFig. 7.

(2) The effective plastic strain at failure was higher in theNW specimen, as shown inFig. 8.

(3) A significant difference in width reduction of the weldwas observed, as shown inFig. 9.

(4) Small differences in the weld displacement at failurewere observed, with a higher weld displacement for theNW specimens, as shown inFig. 10.


Fig. 7. Comparison of the overall displacement at failure for the IPPS simulations with transverse weld orientations.

For the IPPS simulations with longitudinal weld orienta-tions, weld modeling methods were seen to have essentiallyno effect as shown inFigs. 9 and 10.

4.3. LDH longitudinal models

For the longitudinal orientation of the weld, the followingobservations were made:

Fig. 8. Comparison of the effective plastic strain at failure for the IPPS simulations with transverse weld orientations.

(1) The distributions of effective plastic strains were similarfor all W and NW specimens. This is shown ifFig. 11for the LDH125 specimen with a thickness ratio of1:1.25.

(2) The weld displacements at failure are slightly higherfor the NW specimens than for the W specimens butthese differences are relatively insignificant for all blankwidths (no figure is presented).


Fig. 9. Comparison of the width reduction at failure for the IPPS simulations with transverse and longitudinal weld orientations.

4.4. LDH transverse models

For the transverse LDH tests, the following observationswere made:

(1) The failure position in the weld did not differ be-tween weld modeling methods for all blank widths.Failure generally occurred in the parent material inthe row of elements directly adjacent to the weldline.

Fig. 10. Comparison of the weld displacement at failure for the IPPS simulations with transverse and longitudinal weld orientations.

(2) W and NW specimens exhibited a difference in punchtravel causing failure, as shown for the LDH200 spec-imen in Fig. 12. This difference increased with the in-creasing blank width.

(3) The weld displacements at failure exhibit only slight dif-ferences for the plane strain specimens (i.e. LDH100 andLDH125), and more significant differences in the largerthickness ratios for the LDH25 and the LDH200 speci-mens. The weld displacement at failure for the LDH200specimen is shown inFig. 13.


Fig. 11. Comparison of effective plastic strain at failure for LDH125 specimens with longitudinal weld orientations (thickness ratio: 1:1.25).

5. Discussion

The results obtained with the NW and NW2 ASTM mod-els are consistent with each other. Any differences betweenthe results of these two models are, in almost all cases, less

than the differences between the NW and the W models.This confirms that differences that are seen between the re-sults for the NW and W models are due to the presence of theweld material in the W model and are not due to the differ-ence in mesh and element types in the vicinity of the weld.


Fig. 12. Comparison of the punch travel causing failure in the LDH200 specimens.

The higher yield strength and hardening behavior of theweld material in the W models impose a constraining effecton the deformation of these models. This constraining ef-fect is the most significant factor contributing to differencesbetween W and NW specimens. Examples of this effect arethe failure locations in ASTM models with a 1:1 thicknessratio (Figs. 3 and 4). The NW model fails at the mid-spanposition whereas the W model fails away from the mid-spanposition. Another example is the higher elongation at failureseen in the ASTM-W model compared with the NW model

Fig. 13. Comparison of the weld displacements at failure for the LDH200 specimens.

for a thickness ratio of 1:1. In the W model, thinning andnecking occur on both sides of the weld since there is nopreferential necking location. The presence of two regionsof necking leads to greater overall elongation of the speci-men at failure.

The importance of the constraining effect of the weld linediminishes as the thickness ratio increases. This is illustratedby the decreasing difference between the NW and the Wdata inFigs. 2 and 7. For large thickness ratios, the thickermaterial becomes as significant a constraint on deformation


as the weld and, as a result, plastic deformation is increas-ingly localized in the thinner material.

A more subtle manifestation of the constraining effect isthat the thinner material adjacent to the modeled weld inthe transverse IPPS and LDH tests is not free to draw in,resulting in lower effective plastic strains at failure in themodels that include the weld. The constraining effect alsointeracts with the thickness ratio of the parent materials.As the thickness ratio increases, the relative importance ofthe constraining effect of the weld diminishes as the thickmaterial acts in the same manner as a weld line to restrictdeformation adjacent to the weld.

In all the IPPS and LDH models, failure occurred imme-diately adjacent to the weld whereas in practice, failure inthese tests generally occurs a small distance from the weldin the thinner material. In order to more completely capturethe effect of the weld on failure, the model that includesweld properties requires further refinement, i.e. a finer meshof solid elements and inclusion of the gradient of materialproperties in the HAZ.

6. Conclusions

The work presented here is an examination of the effectsof weld modeling techniques on the results of FE simula-tions of TWB forming operations. Results indicate that thereare a number of relatively subtle effects associated with themanner in which the weld is modeled. Most of these effectsrelate to the constraining effect of the weld line with respectto strain along the axis of the weld line.

The scope of this study was limited to standard formingtests, i.e. ASTM, IPPS, and LDH. These tests represent therange of biaxial strain states typically occurring in sheetmetal forming operations. In current tailor-welded blanking,welds are generally placed in low strain regions to minimizethe effects of the limited ductility of the weld. In that context,the subtle effects identified in this study identified may notbe important. However, as the design of TWB componentsevolves, there may be benefits associated with locating weldsin higher strain regions. In addition, the development ofnon-linear welds may lead to additional effects that may notbe captured in models that exclude the weld line.

Acknowledgements

The Centre for Automotive Materials and Manufacturing(Kingston, Ont.) is gratefully acknowledged for funding thisresearch.

References

[1] K. Abdullah, P.M. Wild, J.J. Jeswiet, A. Ghasempoor, Tensile testingfor weld properties in tailor welded blanks using the rule of mixtures,Received from author, 2000.

[2] American Society for Testing and Materials, ASTM E 646-93: stan-dard test method for tensile strain-hardening exponents (n-values) ofmetallic sheet metals, Annual Book of ASTM Standards, 1993.

[3] Auto/Steel Partnership, Tailor welded blank design and manufactur-ing manual, Auto/Steel Partnership, Southfield, MI, 1995.

[4] A. Buste, X. Lalbin, M.J. Worswick, Prediction of strain distributionin aluminium tailor welded blanks for different welding techniques,Proc. Light Met. 99 (1999) 485–500.

[5] A. Buste, X. Lalbin, M.J. Worswick, J.A. Clarke, M. Finn, B. Alt-shuller, M. Jain, Prediction of strain distribution in aluminium tai-lor welded blanks, in: Proceedings of the International Conference,NUMISHEET, Besancon, 1999, pp. 455–460.

[6] CamSys Incorporated, Fact sheet: forming limit curve generation(online), October 22, 2001.http://www.camsysinc.com/documents/service.pdf.

[7] C. Galbraith, Sheet Metal Forming Simulation Using LS-DYNA,Metal Forming Analysis Corporation, Kingston, Ont., 1999.

[8] J.O. Hallquist, LS-DYNA Keyword User’s Manual, Version 940,Livermore Software Technology Corporation, Livermore, CA, 1997.

[9] N. Iwata, M. Matsui, N. Nakagawa, S. Ikura, Improvements infinite-element simulation for stamping and application to the formingof laser-welded blanks, J. Mater. Process. Technol. 50 (1995) 335–347.

[10] M. Jain, A simple test to asses the formability of tailor-weldedblanks, Int. J. Form. Processes 3 (3–4) (2000) 185–212.

[11] Y. Lee, M.J. Worswick, M. Finn, W. Christy, M. Jain, Simulated andexperimental deep drawing of aluminum alloy tailor welded blanks,in: Proceedings of the International Deep Drawing Group, June 2000.

[12] N. Nakagawa, S. Ikura, F. Natsumi, Finite element simulation ofstamping a laser-welded blank, SAE Technical Paper Series: 930522,1993.

[13] F.I. Saunders, Forming of tailor-welded blanks, Ph.D. Dissertation,Ohio State University, Columbus, OH, USA, 1994.

[14] K.M. Zhao, B.K. Chun, J.K. Lee, Finite element analysis oftailor-welded blanks, Finite Elem. Anal. Des. 37 (2000) 117–130.

[15] K.M. Zhao, B.K. Chun, J.K. Lee, Numerical modeling technique fortailor welded blanks, SAE Technical Paper Series: 2000-01-0410,2000.

http://www.camsysinc.com/documents/service.pdf

http://www.camsysinc.com/documents/service.pdf

on modeling of the weld line in finite element analyses of tailor-welded blank forming operations

Documents