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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 of tailor-welded blank forming operations Scott D. Raymond, Peter M. Wild∗ , Christopher J. Bayley Department 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 modeling techniques on simulation results. Finite element models of TWBs were created that either included a simple representation of the weld properties and geometry or excluded both weld geometry or material properties. In all models, shell elements were used to represent parent materials of the TWB. The models excluding weld properties and geometry used nodal rigid bodies to join the thin and thick parent materials. The models including weld properties and geometry used solid elements for the weld materials, and a novel method for joining shells to solids. Simulations of three standard metal forming tests were performed: ASTM tensile test, in-plane plane strain test, and limiting dome height tests representing various biaxial strain states including: uniaxial tension, plane strain and biaxial tension. Results indicate that there are a number of relatively subtle effects associated with the manner in which the weld line is modeled. Most of these effects relate 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 or more sheets of metal with dissimilar strength and/or thickness that are welded into a single blank. TWBs are stamped into automotive body panels and offer reduced part weight and improved material use. They are most commonly fabricated using a laser welding process, which creates a narrow weld and heat-affected zone (HAZ) at the junction of the dissimilar sheets. In the published literature on finite element analysis (FEA) of TWB forming operations, methods of modeling of the weld line fall into two general categories. In the first category, weld properties and geometry are excluded from the model [4,5,11,13–15]. A set of rigid links is used to tie adjacent nodes on the thin and thick sheets together. In the second category, models include various representations of the weld properties and geometry [9,10,12,13,15]. Saunders [13] and Zhao et al. [15] used shell elements to represent the weld line. Shell elements are limited in that they can only approximate the weld geometry and are more suited to constant thickness geometries. In studies by Iwata et al. [9,12],
∗
Corresponding author.
0924-0136/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2003.09.005
beam elements were used to represent the weld. Beam elements also limit the geometry that can be represented and the refinement of the mesh in the weld zone. Jain [10] and Zhao et al. [15] used solid elements to represent the weld. When using this technique, the parent materials were also modeled using solid elements. This approach is computationally inefficient in the context of sheet metal forming operations, as several through-thickness solid elements must be used to accurately represent bending [7] throughout the parent metal. In those references where the merits of inclusion of a detailed model of the weld are discussed, there is a consensus that the additional computational cost is not justified [13,15]. The Auto-steel Partnership guidelines on TWB stamping and process considerations summarize this consensus as follows: “When modeling a laser beam welded blank, the mechanical properties of the weld bead itself can be neglected with no significant loss of accuracy in the results [3]”. This view is justified in the context of the majority of current TWB applications in which the weld is isolated from regions of high strain. As the variety of TWB applications increases, the effects of the weld on blank formability may become more significant and it will be important that these effects are well understood. The objective of this research is to perform a systematic study of the influence of weld modeling
S.D. Raymond et al. / Journal of Materials Processing Technology 147 (2004) 28–37
techniques on results of FE simulations of TWB forming operations.
2. TWB geometries Finite element models were created for three different standard forming tests. The ASTM tensile test [2] was simulated with a transverse weld orientation only. The in-plane plane strain test (IPPS) [10] was simulated with both longitudinal and transverse welds. The limiting dome height (LDH) test [6] was simulated with several blank geometries to obtain variations in the biaxial strain state. These variations in biaxial strain were achieved by modeling blanks of varying width, i.e. 25 (LDH25), 100 (LDH100), 125 (LDH125), and 200 mm (LDH200). The LDH25 specimen simulated uniaxial tension, while the LDH100 and LDH125 specimens simulated plane strain and the LDH200 specimens simulated biaxial tension. For all LDH models, both longitudinal and transverse weld orientations were simulated. Thickness ratios for all these tests were varied to include a range from 1:1 up to 1:2.25. The thin parent material was maintained at 0.8 mm, while the thick parent material was varied in increments of 0.2 mm from 0.8 up to 1.8 mm. The material properties used for the parent blanks correspond to AISI 1005 steel. The strain-hardening exponent and strength coefficient used in the Ludwick–Hollomon equations were obtained from a previous study on TWB properties [1]. In this study, uniaxial tests on the parent material specimens and the integrated TWB were used to determine the material properties of the weld. The material properties for the parent and weld materials are shown in Table 1.
3. The finite element models All simulations were performed using the dynamic-explicit FE code, LS-DYNA (Livermore Software Technology Corporation, Livermore, CA). The parent material model was comprised of 4-node quadrilateral shell elements of the Belytschko–Lin–Tsay formulation with three through-thickness integration points [8]. For the models excluding weld properties and geometry, nodal rigid bodies were used to connect adjacent nodes of the thin and thick parent materials. For the remainder of this document, “NW” designates models excluding weld properties. The weld representation including weld properties used 8-noded linear solid elements for the weld zone. These solid Table 1 Hardening characteristics for parent and weld materials [1] Material
Strength coefficient, K (MPa)
Strain-hardening exponent, n
Parent Weld
561 1165
0.1757 0.1154
29
elements were constrained to move with the parent materials using an interpolation constraint found in LS-DYNA (∗ CONSTRAINED INTERPOLATION) [8], as shown in Fig. 1. When using this constraint, the motion of a single dependent node is interpolated from the motion of a set of independent nodes. In this study, the dependent node was on the parent material mesh, while the independent nodes lay on the adjacent weld material mesh. For the remainder of this document, “W” designates models including weld properties. For the ASTM test specimen, an additional model was developed in which the mesh is as described above for the models including weld properties. However, the material properties assigned to the solid elements are identical to the material properties for the shell elements that define the parent material. The purpose of this model is to assess the effects of mesh and element type on the results, independent of the material properties. For the remainder of this document, “NW-2” designates these models. Prior to finalizing the finite element models, a sensitivity study was performed on element dimensions, formulations and the number of integration points required. The results of these sensitivity studies formed the basis for the finite element models. A secondary sensitivity study was performed on model solution control techniques to determine the tooling speeds providing the most accurate and computationally efficient solution. Failure was determined by comparing the major and minor strains in the thin parent material to the forming limit diagram (FLD) for the material. When the combination of major and minor strains crossed the forming limit curve, failure was said to have occurred. The LS-POST post-processing software performs this procedure automatically. The FLD was created using the material thickness and strain-hardening exponents of the parent material. For models in which the weld was oriented with the axis of major strain, failure was expected to originate in the weld material. However, the automatic comparison of major and minor strains to the FLD cannot be performed in LS-POST for the solid elements of which the weld is comprised. A limiting effective plastic strain of 15% in the solid weld elements was, therefore, used to determine when failure had occurred. This is the ultimate strain for this weld material as determined experimentally by Abdullah et al. [1].
4. Results 4.1. ASTM models A number of relatively subtle differences were observed between the W and NW models for the ASTM specimen: (1) The applied displacement causing failure in the NW specimen was greater than the W specimen with this difference diminishing as the thickness ratio in-
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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 in Fig. 2. The NW and NW-2 results agreed well, except for the case of a 1:1 thickness ratio. (2) As shown in Fig. 3(a), for a thickness ratio of 1:1, the failure location in the W specimen occurred away from the mid-span position (i.e. away from the weld) whereas, for the NW and NW-2 specimens, failure occurred at the mid-span location (see Fig. 3(b) and (c)). (3) For other thickness ratios, the measured failure location for all three models (W, NW and NW2) were identical, within measurement error (see Fig. 4). The error bars in
this figure indicate the resolution of the failure location measurement which is determined by the mesh density or element size. (4) A significant difference in width reduction at the weld was seen, as shown in Fig. 5. The reduction in width in the NW and NW2 specimens was higher than that for the W specimens. The difference was the greatest at a thickness ratio of 1:1, and diminishes as the thickness ratio increases. (5) The weld displacements at failure are less (<3%) for the W model than for the NW and NW2 models, as shown
Fig. 2. Comparison of the applied displacement at failure for the ASTM simulations.
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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.
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Fig. 5. Comparison of the width reduction at failure for the ASTM simulations.
in Fig. 6. This difference diminishes as the thickness ratio increases. (6) With the exception of the 1:1 and 1:2.25 thickness ratios, the weld displacements for the NW2 models are slightly greater (<0.5%) than for the NW models. 4.2. IPPS models For the IPPS simulations with transverse weld orientations, a number of subtle differences were observed between the W and NW models:
(1) The applied displacement causing failure in the NW specimen was greater than the W specimen and the largest difference was for a thickness ratio of 1:25, as shown in Fig. 7. (2) The effective plastic strain at failure was higher in the NW specimen, as shown in Fig. 8. (3) A significant difference in width reduction of the weld was observed, as shown in Fig. 9. (4) Small differences in the weld displacement at failure were observed, with a higher weld displacement for the NW specimens, as shown in Fig. 10.
Fig. 6. Comparison of the weld displacement at failure for the ASTM simulations.
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Fig. 7. Comparison of the overall displacement at failure for the IPPS simulations with transverse weld orientations.
For the IPPS simulations with longitudinal weld orientations, weld modeling methods were seen to have essentially no effect as shown in Figs. 9 and 10. 4.3. LDH longitudinal models For the longitudinal orientation of the weld, the following observations were made:
(1) The distributions of effective plastic strains were similar for all W and NW specimens. This is shown if Fig. 11 for the LDH125 specimen with a thickness ratio of 1:1.25. (2) The weld displacements at failure are slightly higher for the NW specimens than for the W specimens but these differences are relatively insignificant for all blank widths (no figure is presented).
Fig. 8. Comparison of the effective plastic strain at failure for the IPPS simulations with transverse weld orientations.
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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 observations were made: (1) The failure position in the weld did not differ between weld modeling methods for all blank widths. Failure generally occurred in the parent material in the row of elements directly adjacent to the weld line.
(2) W and NW specimens exhibited a difference in punch travel causing failure, as shown for the LDH200 specimen in Fig. 12. This difference increased with the increasing blank width. (3) The weld displacements at failure exhibit only slight differences for the plane strain specimens (i.e. LDH100 and LDH125), and more significant differences in the larger thickness ratios for the LDH25 and the LDH200 specimens. The weld displacement at failure for the LDH200 specimen is shown in Fig. 13.
Fig. 10. Comparison of the weld displacement at failure for the IPPS simulations with transverse and longitudinal weld orientations.
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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 models are consistent with each other. Any differences between the 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 results for the NW and W models are due to the presence of the weld material in the W model and are not due to the difference in mesh and element types in the vicinity of the weld.
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Fig. 12. Comparison of the punch travel causing failure in the LDH200 specimens.
The higher yield strength and hardening behavior of the weld material in the W models impose a constraining effect on the deformation of these models. This constraining effect is the most significant factor contributing to differences between W and NW specimens. Examples of this effect are the failure locations in ASTM models with a 1:1 thickness ratio (Figs. 3 and 4). The NW model fails at the mid-span position whereas the W model fails away from the mid-span position. Another example is the higher elongation at failure seen in the ASTM-W model compared with the NW model
for a thickness ratio of 1:1. In the W model, thinning and necking occur on both sides of the weld since there is no preferential necking location. The presence of two regions of necking leads to greater overall elongation of the specimen at failure. The importance of the constraining effect of the weld line diminishes as the thickness ratio increases. This is illustrated by the decreasing difference between the NW and the W data in Figs. 2 and 7. For large thickness ratios, the thicker material becomes as significant a constraint on deformation
Fig. 13. Comparison of the weld displacements at failure for the LDH200 specimens.
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as the weld and, as a result, plastic deformation is increasingly localized in the thinner material. A more subtle manifestation of the constraining effect is that the thinner material adjacent to the modeled weld in the transverse IPPS and LDH tests is not free to draw in, resulting in lower effective plastic strains at failure in the models that include the weld. The constraining effect also interacts with the thickness ratio of the parent materials. As the thickness ratio increases, the relative importance of the constraining effect of the weld diminishes as the thick material acts in the same manner as a weld line to restrict deformation adjacent to the weld. In all the IPPS and LDH models, failure occurred immediately adjacent to the weld whereas in practice, failure in these tests generally occurs a small distance from the weld in the thinner material. In order to more completely capture the effect of the weld on failure, the model that includes weld properties requires further refinement, i.e. a finer mesh of solid elements and inclusion of the gradient of material properties in the HAZ.
6. Conclusions The work presented here is an examination of the effects of weld modeling techniques on the results of FE simulations of TWB forming operations. Results indicate that there are a number of relatively subtle effects associated with the manner in which the weld is modeled. Most of these effects relate to the constraining effect of the weld line with respect to strain along the axis of the weld line. The scope of this study was limited to standard forming tests, i.e. ASTM, IPPS, and LDH. These tests represent the range of biaxial strain states typically occurring in sheet metal forming operations. In current tailor-welded blanking, welds are generally placed in low strain regions to minimize the effects of the limited ductility of the weld. In that context, the subtle effects identified in this study identified may not be important. However, as the design of TWB components evolves, there may be benefits associated with locating welds in higher strain regions. In addition, the development of non-linear welds may lead to additional effects that may not be captured in models that exclude the weld line.
37
Acknowledgements The Centre for Automotive Materials and Manufacturing (Kingston, Ont.) is gratefully acknowledged for funding this research. References [1] K. Abdullah, P.M. Wild, J.J. Jeswiet, A. Ghasempoor, Tensile testing for 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: standard test method for tensile strain-hardening exponents (n-values) of metallic sheet metals, Annual Book of ASTM Standards, 1993. [3] Auto/Steel Partnership, Tailor welded blank design and manufacturing manual, Auto/Steel Partnership, Southfield, MI, 1995. [4] A. Buste, X. Lalbin, M.J. Worswick, Prediction of strain distribution in 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. Altshuller, M. Jain, Prediction of strain distribution in aluminium tailor 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 in finite-element simulation for stamping and application to the forming of laser-welded blanks, J. Mater. Process. Technol. 50 (1995) 335– 347. [10] M. Jain, A simple test to asses the formability of tailor-welded blanks, Int. J. Form. Processes 3 (3–4) (2000) 185–212. [11] Y. Lee, M.J. Worswick, M. Finn, W. Christy, M. Jain, Simulated and experimental 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 of stamping 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 of tailor-welded blanks, Finite Elem. Anal. Des. 37 (2000) 117–130. [15] K.M. Zhao, B.K. Chun, J.K. Lee, Numerical modeling technique for tailor welded blanks, SAE Technical Paper Series: 2000-01-0410, 2000.
On modeling of the weld line in finite element analyses of tailor-welded blank forming operations Scott D. Raymond, Peter M. Wild∗ , Christopher J. Bayley Department 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 modeling techniques on simulation results. Finite element models of TWBs were created that either included a simple representation of the weld properties and geometry or excluded both weld geometry or material properties. In all models, shell elements were used to represent parent materials of the TWB. The models excluding weld properties and geometry used nodal rigid bodies to join the thin and thick parent materials. The models including weld properties and geometry used solid elements for the weld materials, and a novel method for joining shells to solids. Simulations of three standard metal forming tests were performed: ASTM tensile test, in-plane plane strain test, and limiting dome height tests representing various biaxial strain states including: uniaxial tension, plane strain and biaxial tension. Results indicate that there are a number of relatively subtle effects associated with the manner in which the weld line is modeled. Most of these effects relate 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 or more sheets of metal with dissimilar strength and/or thickness that are welded into a single blank. TWBs are stamped into automotive body panels and offer reduced part weight and improved material use. They are most commonly fabricated using a laser welding process, which creates a narrow weld and heat-affected zone (HAZ) at the junction of the dissimilar sheets. In the published literature on finite element analysis (FEA) of TWB forming operations, methods of modeling of the weld line fall into two general categories. In the first category, weld properties and geometry are excluded from the model [4,5,11,13–15]. A set of rigid links is used to tie adjacent nodes on the thin and thick sheets together. In the second category, models include various representations of the weld properties and geometry [9,10,12,13,15]. Saunders [13] and Zhao et al. [15] used shell elements to represent the weld line. Shell elements are limited in that they can only approximate the weld geometry and are more suited to constant thickness geometries. In studies by Iwata et al. [9,12],
∗
Corresponding author.
0924-0136/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2003.09.005
beam elements were used to represent the weld. Beam elements also limit the geometry that can be represented and the refinement of the mesh in the weld zone. Jain [10] and Zhao et al. [15] used solid elements to represent the weld. When using this technique, the parent materials were also modeled using solid elements. This approach is computationally inefficient in the context of sheet metal forming operations, as several through-thickness solid elements must be used to accurately represent bending [7] throughout the parent metal. In those references where the merits of inclusion of a detailed model of the weld are discussed, there is a consensus that the additional computational cost is not justified [13,15]. The Auto-steel Partnership guidelines on TWB stamping and process considerations summarize this consensus as follows: “When modeling a laser beam welded blank, the mechanical properties of the weld bead itself can be neglected with no significant loss of accuracy in the results [3]”. This view is justified in the context of the majority of current TWB applications in which the weld is isolated from regions of high strain. As the variety of TWB applications increases, the effects of the weld on blank formability may become more significant and it will be important that these effects are well understood. The objective of this research is to perform a systematic study of the influence of weld modeling
S.D. Raymond et al. / Journal of Materials Processing Technology 147 (2004) 28–37
techniques on results of FE simulations of TWB forming operations.
2. TWB geometries Finite element models were created for three different standard forming tests. The ASTM tensile test [2] was simulated with a transverse weld orientation only. The in-plane plane strain test (IPPS) [10] was simulated with both longitudinal and transverse welds. The limiting dome height (LDH) test [6] was simulated with several blank geometries to obtain variations in the biaxial strain state. These variations in biaxial strain were achieved by modeling blanks of varying width, i.e. 25 (LDH25), 100 (LDH100), 125 (LDH125), and 200 mm (LDH200). The LDH25 specimen simulated uniaxial tension, while the LDH100 and LDH125 specimens simulated plane strain and the LDH200 specimens simulated biaxial tension. For all LDH models, both longitudinal and transverse weld orientations were simulated. Thickness ratios for all these tests were varied to include a range from 1:1 up to 1:2.25. The thin parent material was maintained at 0.8 mm, while the thick parent material was varied in increments of 0.2 mm from 0.8 up to 1.8 mm. The material properties used for the parent blanks correspond to AISI 1005 steel. The strain-hardening exponent and strength coefficient used in the Ludwick–Hollomon equations were obtained from a previous study on TWB properties [1]. In this study, uniaxial tests on the parent material specimens and the integrated TWB were used to determine the material properties of the weld. The material properties for the parent and weld materials are shown in Table 1.
3. The finite element models All simulations were performed using the dynamic-explicit FE code, LS-DYNA (Livermore Software Technology Corporation, Livermore, CA). The parent material model was comprised of 4-node quadrilateral shell elements of the Belytschko–Lin–Tsay formulation with three through-thickness integration points [8]. For the models excluding weld properties and geometry, nodal rigid bodies were used to connect adjacent nodes of the thin and thick parent materials. For the remainder of this document, “NW” designates models excluding weld properties. The weld representation including weld properties used 8-noded linear solid elements for the weld zone. These solid Table 1 Hardening characteristics for parent and weld materials [1] Material
Strength coefficient, K (MPa)
Strain-hardening exponent, n
Parent Weld
561 1165
0.1757 0.1154
29
elements were constrained to move with the parent materials using an interpolation constraint found in LS-DYNA (∗ CONSTRAINED INTERPOLATION) [8], as shown in Fig. 1. When using this constraint, the motion of a single dependent node is interpolated from the motion of a set of independent nodes. In this study, the dependent node was on the parent material mesh, while the independent nodes lay on the adjacent weld material mesh. For the remainder of this document, “W” designates models including weld properties. For the ASTM test specimen, an additional model was developed in which the mesh is as described above for the models including weld properties. However, the material properties assigned to the solid elements are identical to the material properties for the shell elements that define the parent material. The purpose of this model is to assess the effects of mesh and element type on the results, independent of the material properties. For the remainder of this document, “NW-2” designates these models. Prior to finalizing the finite element models, a sensitivity study was performed on element dimensions, formulations and the number of integration points required. The results of these sensitivity studies formed the basis for the finite element models. A secondary sensitivity study was performed on model solution control techniques to determine the tooling speeds providing the most accurate and computationally efficient solution. Failure was determined by comparing the major and minor strains in the thin parent material to the forming limit diagram (FLD) for the material. When the combination of major and minor strains crossed the forming limit curve, failure was said to have occurred. The LS-POST post-processing software performs this procedure automatically. The FLD was created using the material thickness and strain-hardening exponents of the parent material. For models in which the weld was oriented with the axis of major strain, failure was expected to originate in the weld material. However, the automatic comparison of major and minor strains to the FLD cannot be performed in LS-POST for the solid elements of which the weld is comprised. A limiting effective plastic strain of 15% in the solid weld elements was, therefore, used to determine when failure had occurred. This is the ultimate strain for this weld material as determined experimentally by Abdullah et al. [1].
4. Results 4.1. ASTM models A number of relatively subtle differences were observed between the W and NW models for the ASTM specimen: (1) The applied displacement causing failure in the NW specimen was greater than the W specimen with this 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 in Fig. 2. The NW and NW-2 results agreed well, except for the case of a 1:1 thickness ratio. (2) As shown in Fig. 3(a), for a thickness ratio of 1:1, the failure location in the W specimen occurred away from the mid-span position (i.e. away from the weld) whereas, for the NW and NW-2 specimens, failure occurred at the mid-span location (see Fig. 3(b) and (c)). (3) For other thickness ratios, the measured failure location for all three models (W, NW and NW2) were identical, within measurement error (see Fig. 4). The error bars in
this figure indicate the resolution of the failure location measurement which is determined by the mesh density or element size. (4) A significant difference in width reduction at the weld was seen, as shown in Fig. 5. The reduction in width in the NW and NW2 specimens was higher than that for the W specimens. The difference was the greatest at a thickness ratio of 1:1, and diminishes as the thickness ratio increases. (5) The weld displacements at failure are less (<3%) for the W model than for the NW and NW2 models, as shown
Fig. 2. Comparison of the applied displacement at failure for the ASTM simulations.
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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.
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Fig. 5. Comparison of the width reduction at failure for the ASTM simulations.
in Fig. 6. This difference diminishes as the thickness ratio increases. (6) With the exception of the 1:1 and 1:2.25 thickness ratios, the weld displacements for the NW2 models are slightly greater (<0.5%) than for the NW models. 4.2. IPPS models For the IPPS simulations with transverse weld orientations, a number of subtle differences were observed between the W and NW models:
(1) The applied displacement causing failure in the NW specimen was greater than the W specimen and the largest difference was for a thickness ratio of 1:25, as shown in Fig. 7. (2) The effective plastic strain at failure was higher in the NW specimen, as shown in Fig. 8. (3) A significant difference in width reduction of the weld was observed, as shown in Fig. 9. (4) Small differences in the weld displacement at failure were observed, with a higher weld displacement for the NW specimens, as shown in Fig. 10.
Fig. 6. Comparison of the weld displacement at failure for the ASTM simulations.
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Fig. 7. Comparison of the overall displacement at failure for the IPPS simulations with transverse weld orientations.
For the IPPS simulations with longitudinal weld orientations, weld modeling methods were seen to have essentially no effect as shown in Figs. 9 and 10. 4.3. LDH longitudinal models For the longitudinal orientation of the weld, the following observations were made:
(1) The distributions of effective plastic strains were similar for all W and NW specimens. This is shown if Fig. 11 for the LDH125 specimen with a thickness ratio of 1:1.25. (2) The weld displacements at failure are slightly higher for the NW specimens than for the W specimens but these differences are relatively insignificant for all blank widths (no figure is presented).
Fig. 8. Comparison of the effective plastic strain at failure for the IPPS simulations with transverse weld orientations.
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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 observations were made: (1) The failure position in the weld did not differ between weld modeling methods for all blank widths. Failure generally occurred in the parent material in the row of elements directly adjacent to the weld line.
(2) W and NW specimens exhibited a difference in punch travel causing failure, as shown for the LDH200 specimen in Fig. 12. This difference increased with the increasing blank width. (3) The weld displacements at failure exhibit only slight differences for the plane strain specimens (i.e. LDH100 and LDH125), and more significant differences in the larger thickness ratios for the LDH25 and the LDH200 specimens. The weld displacement at failure for the LDH200 specimen is shown in Fig. 13.
Fig. 10. Comparison of the weld displacement at failure for the IPPS simulations with transverse and longitudinal weld orientations.
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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 models are consistent with each other. Any differences between the 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 results for the NW and W models are due to the presence of the weld material in the W model and are not due to the difference in mesh and element types in the vicinity of the weld.
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Fig. 12. Comparison of the punch travel causing failure in the LDH200 specimens.
The higher yield strength and hardening behavior of the weld material in the W models impose a constraining effect on the deformation of these models. This constraining effect is the most significant factor contributing to differences between W and NW specimens. Examples of this effect are the failure locations in ASTM models with a 1:1 thickness ratio (Figs. 3 and 4). The NW model fails at the mid-span position whereas the W model fails away from the mid-span position. Another example is the higher elongation at failure seen in the ASTM-W model compared with the NW model
for a thickness ratio of 1:1. In the W model, thinning and necking occur on both sides of the weld since there is no preferential necking location. The presence of two regions of necking leads to greater overall elongation of the specimen at failure. The importance of the constraining effect of the weld line diminishes as the thickness ratio increases. This is illustrated by the decreasing difference between the NW and the W data in Figs. 2 and 7. For large thickness ratios, the thicker material becomes as significant a constraint on deformation
Fig. 13. Comparison of the weld displacements at failure for the LDH200 specimens.
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as the weld and, as a result, plastic deformation is increasingly localized in the thinner material. A more subtle manifestation of the constraining effect is that the thinner material adjacent to the modeled weld in the transverse IPPS and LDH tests is not free to draw in, resulting in lower effective plastic strains at failure in the models that include the weld. The constraining effect also interacts with the thickness ratio of the parent materials. As the thickness ratio increases, the relative importance of the constraining effect of the weld diminishes as the thick material acts in the same manner as a weld line to restrict deformation adjacent to the weld. In all the IPPS and LDH models, failure occurred immediately adjacent to the weld whereas in practice, failure in these tests generally occurs a small distance from the weld in the thinner material. In order to more completely capture the effect of the weld on failure, the model that includes weld properties requires further refinement, i.e. a finer mesh of solid elements and inclusion of the gradient of material properties in the HAZ.
6. Conclusions The work presented here is an examination of the effects of weld modeling techniques on the results of FE simulations of TWB forming operations. Results indicate that there are a number of relatively subtle effects associated with the manner in which the weld is modeled. Most of these effects relate to the constraining effect of the weld line with respect to strain along the axis of the weld line. The scope of this study was limited to standard forming tests, i.e. ASTM, IPPS, and LDH. These tests represent the range of biaxial strain states typically occurring in sheet metal forming operations. In current tailor-welded blanking, welds are generally placed in low strain regions to minimize the effects of the limited ductility of the weld. In that context, the subtle effects identified in this study identified may not be important. However, as the design of TWB components evolves, there may be benefits associated with locating welds in higher strain regions. In addition, the development of non-linear welds may lead to additional effects that may not be captured in models that exclude the weld line.
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Acknowledgements The Centre for Automotive Materials and Manufacturing (Kingston, Ont.) is gratefully acknowledged for funding this research. References [1] K. Abdullah, P.M. Wild, J.J. Jeswiet, A. Ghasempoor, Tensile testing for 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: standard test method for tensile strain-hardening exponents (n-values) of metallic sheet metals, Annual Book of ASTM Standards, 1993. [3] Auto/Steel Partnership, Tailor welded blank design and manufacturing manual, Auto/Steel Partnership, Southfield, MI, 1995. [4] A. Buste, X. Lalbin, M.J. Worswick, Prediction of strain distribution in 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. Altshuller, M. Jain, Prediction of strain distribution in aluminium tailor 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 in finite-element simulation for stamping and application to the forming of laser-welded blanks, J. Mater. Process. Technol. 50 (1995) 335– 347. [10] M. Jain, A simple test to asses the formability of tailor-welded blanks, Int. J. Form. Processes 3 (3–4) (2000) 185–212. [11] Y. Lee, M.J. Worswick, M. Finn, W. Christy, M. Jain, Simulated and experimental 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 of stamping 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 of tailor-welded blanks, Finite Elem. Anal. Des. 37 (2000) 117–130. [15] K.M. Zhao, B.K. Chun, J.K. Lee, Numerical modeling technique for tailor welded blanks, SAE Technical Paper Series: 2000-01-0410, 2000.