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Finite element analysis of a tailored blanks stamping process
Journal of Materials Processing Technology 106 (2000) 254±260
Finite element analysis of a tailored blanks stamping process Z. Zimniaka,*, A. Pielab a
Department of Engineering Forming Processes, Faculty of Mechanical Engineering, Wroclaw University of Technology, ul. Lukasiewicza 3/5, 50-371 Wroclaw, Poland b Silesian University of Technology, ul. Krasinskiego 8, 40-019 Katowice, Poland
Abstract This paper describes the computer simulation methodology for applying the method of ®nite elements in the sheet stamping of a new type of sheet. Simulation of the cup stamping process by a punch of square section has been chosen for testing. The modelling of such a stamping process was carried out using a complete thermomechanical analysis including the modelling of the sheet welding process and the modelling of the stamping process. It has been assumed that the criteria for evaluating the quality of the theoretical solution is the displacement of welding line after stamping. The stress after the welding process and the deformation are essential for further stage of the stamping process. # 2000 Elsevier Science B.V. All rights reserved. Keywords: Finite element simulation; Sheet metal forming; Laser welded blank
1. Introduction Forming more complex parts of sheet metal in a single stamping operation is very ef®cient in cost reduction and dimensional accuracy. The introduction of new materials for stamping, such as tailored blanks, has become a common practice in the automotive industry. Tailored blanks combine many features of the above mentioned materials in respect of their application. The concept of such a type of charge for stamping requires the application of laser welding in order to join different sheets of steel. Their geometrical and physical features are being matched on the basis of the economics and the constructional requirement of the stamped elements. Introducing tailored blanks for stamping should be preceded by a series of careful examinations which ought to be of multilevel character. Examinations of this kind are both timeconsuming and expensive because the production and processing of tailored blanks has not yet been fully examined and developed. The risk of negative application of new materials can be reduced only if their performance can be correctly assessed during the stamping process. The cost reduction of the process technological examination of the new materials can be achieved by modelling examinations and computer simulation. Therefore charge modelling methodology for stamping should be developed, since these charges have *
Corresponding author.
different mechanical properties and geometrical features of sheet constituent elements. 2. Experimental work Stamping-process examinations, i.e. identi®cation of the problem of the in¯uence of the weld on the process of sheet material ¯ow in stamping, have been carried out applying the technological evaluation of drawability. Tools for the cupping test, Erichsen tests, tensile tests in a cup bottom hole Ð KWI, and hydraulic bulge tests were used for examination purposes. A test for uniaxial sample bumping with the weld being positioned crosswise and lengthwise against the direction of blocking was carried out. The frontal welding process with blanks being positioned as shown in Fig. 1 has been completed by CO2 gas laser with a mirror head which re¯ects the rays from the root of weld. The examination of weld joints established that the material is of ferritic structure with diversi®ed band system. Welds of the examined joints feature a dendritic structure with a distinctly noticeable crystallisation axis. The shape of the welds is narrow (just as it should be) which is characteristic of laser welding. Measurements of local strains carried out by marking nets on the sheets before deformation, revealed that the process of sheet material ¯ow has been considerably disturbed because of the difference in the stamped sheet thickness and the in¯uence of weld itself. Characteristic blocking of lengthwise metal ¯ow in a weld (Fig. 2) and characteristic
0924-0136/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 0 ) 0 0 6 2 6 - 9
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
255
Fig. 1. Microstructure of weld zone (mag.: 20).
distortion of the weld line (Figs. 3 and 4) in the direction of the thicker sheet have been observed similar to the observations presented in [1,2]. Displacements of the weld line shown in the above mentioned ®gures are due to the diversi®ed material ¯ow in similar zones of the drawpiece both on the thicker and thinner side of the sheet. The weld limits lengthwise deformation also. This causes the puckering of a drawpiece ¯ange into the side surface zone (Fig. 4) and there is also a considerably smaller narrowing of the sample at the weld line as compared to the neighbouring zones, as shown in Fig. 2. The observed dependencies con®rm the local strain distribution which has been presented in Fig. 5. These distributions result from ball-shaped punch bulge tests of a sheet restrained by a clamp. The relationships between the degree of sheet deformation in the weld zone and the analogical places of a drawpiece on the thicker and thinner side of the sheet depend on: (i) the thickness relationships of the tailored blanks, (ii) the properties of sheet hardening values with these values depending on yield stress change characteristics, and (iii) the weld quality (also the level of hardening in the heataffected zone) and the size of the welding stresses. Whether the tailored blanks are completely suitable for stamping depends on the compound sheet characteristics and weld quality. Therefore drawability is dif®cult to de®ne
Fig. 2. Break of the sample and a crosswise weld resulting from a bumping test.
Fig. 3. The KWI test: (a) distortion of a weld line in the area of punch stamping towards a thicker sheet; (b) a break of the sheet near the weld on its thinner part from the edge of a bumped hole.
for this type of charge, taking into consideration all possible variations of sheet tailoring. It seems necessary to develop a method of heterogeneous material ¯ow analysis for tailored blanks in the process of stamping. This process can be
Fig. 4. (a) A cupping test using a 40 mm square punch with a ¯at bottom; (b) break of the sheet near the weld line in the area of the punch bottom; (c) distortion of the weld line in a side surface zone and punch ¯ange zone.
256
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
Fig. 5. Local strain distribution in a sheet welded after bulging by a ballshaped punch.
characterised by changeable geometry, and the state of stress and strain of the deformation zone based on the compound sheets characteristics. Hence, it is justi®ed to apply simulation techniques for the analysis of such non-de®ned sheet material ¯ow. 3. Simulation of the tailored blanks stamping process by FEM A full computer simulation of the stamping process for laser welded sheet requires ®nding a solution for: the initial modelling of the charge welding and the modelling of the stamping process. In a simpli®ed version of analysis, the charge welding can be neglected in favour of establishing de®ned features of stamped material in the weld area [3±5]. Refs. [6,7] give evidence that the designing of a tailored blanks stamping process is different from the designing of a conventional blank stamping process. The breaks occur in different places of the drawpieces and it is also necessary to use sectional blankholders. The position of the weld line is important for the level of local strains. In most of the above mentioned publications a simpli®ed version of the tailored blanks stamping process was presented and a suitable model for the weld zone was also provided. Buste et al. [7] applied gradually increasing thickness elements in the place where a thin sheet joins a thick sheet. Also presented was a new solution using rigid links which join sheets of various thickness. Experimental measurements of strains along a line which is perpendicular to a weld line give evidence that if such simpli®cations are applied, considerable divergence between experimental and theoretical results can occur.
Fig. 6. Simulation of the welding process with temperature distribution.
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
257
Fig. 7. Stress which remained in a linked sheet after the welding and cooling process.
3.1. Calculation model The FEM simulation of the square drawpiece stamping process of a laser weld charge using the MARC programme supported by users sub-programs was performed. The following assumptions were made: 1. The charge for stamping consists of two deep drawn sheets of 1 and 1.5 mm thickness which have different material properties;
2. Heat produced by the laser is modelled by a heat stream which is let in at linked material contact areas and is of a de®ned radius of laser spot resulting from a Gaussian distribution (the user's sub-program was introduced); 3. Not all heat reaches the sheet (the absorption coef®cients for sheet materials have been used for calculations); 4. Heat is removed from the sheet by convection and radiation;
Fig. 8. Distribution of sheet thickness in a modelled drawpiece.
258
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
Fig. 9. Substitute strain distribution at the ®nal stage of stamping.
Fig. 10. Substitute stress distribution at the ®nal stage of stamping.
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
5. Latent heat resulting from sheet material phase transformation was taken into account. This was done in accordance with the Brown and Song [8] concept; 6. A constant temperature of 208C for linked sheet before welding was assumed; 7. The sheet cooling time after welding was established experimentally and it ensured total cooling up to the temperature before welding; 8. A constant welding speed was assumed (introduced by the user's computer programme); 9. Simulation was carried out for a full three-dimensional model. The application of thermomechanical analysis allowed taking into account all the phenomena occurring in a sheet during welding and also applying such a charge model for stamping process simulation. 3.2. Calculation results Fig. 6 presents subsequent stages for the laser welding of a preform with a distinctly visible sheet temperature distribution. The stresses in a sheet after the welding process and after cooling are shown in Fig. 7. The stresses which remain in the material after the welding process in¯uence considerably the material ¯ow during the stamping process. This has been con®rmed by simulation results of the analysed drawpiece forming process, these results being presented in Figs. 8±11.
259
Characteristic changes of sheet thickness, especially in the weld zone, are shown in Fig. 8, whilst Figs. 9 and 10 present substitute strain and stress distribution, respectively. A particular way of sheet ¯ow in the stamping process right from the beginning causes bigger strains in the thicker part of the drawpiece. The ®nal effect of such material ¯ow results in signi®cant diversi®cation of sheet thickness in different parts of a drawpiece Ð Fig. 11. There can also be noticed a characteristic displacement and distortion of weld line towards the thicker sheet. The ¯ang part of a drawpiece is of a speci®c shape that can be found in drawpieces formed from welded sheets. Such a shape is formed because there is a bigger ¯ang strain in a thinner part of the drawpiece than in the thicker part. 4. Conclusions The simulation results of the linked sheet stamping process require practical veri®cation. The presented experimental results and calculations are in quantitative agreement. The character of the weld line displacement acquired in the simulation con®rms that noticed in experiments in the weld line displacement of the drawpieces. Quantitative evaluation seems to be a far more complicated problem. The displacement diagram of a weld line (Fig. 12) is quite a good evaluation criterion of a solution consistence. One axis of the diagram in Fig. 12 represents the length of the original weld line and the other its displacement from the initial
Fig. 11. Distribution of sheet thickness with a distinct weld line displacement.
260
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
tion carried out, both for thickness changes and local strains. The automatic picture analysis technique for measuring local strains on the entire area of the drawpiece has been developed and is getting ready for application. References
Fig. 12. Weld line displacement diagram.
position just after welding process. The examinations carried out on this subject demonstrate satisfactory agreement of measurements and calculation results for the simulated example of a square cup. Local strain changes and local changes of thickness were also used as a criterion of calculation accuracy. The comparison of calculation and measurement results for selected places of a drawpiece con®rmed the validity of the simula-
[1] A. Mustafa, D. Ahmetoglu, L. Brouwers, L. Shulkin, G. Taupin, L. Kinzel, T. Altan, Deep drawing of round cups from tailor-welded blanks, J. Mater. Process. Technol. 53 (1995) 684. [2] F.I. Saunders, R.H. Wagoner, Forming of tailor-welded blanks, Metall. Mater. Trans. A 27 (9) (1996) 2605. [3] D.T. Swift-Hook, A.E.F. Gick, Penetration welding with lasers, Weld. J. 52 (11) (1973) 492. [4] J.S. Park, S.J. Na, Heat transfer in a stud-to-plate laser braze considering ®ller metal movement, Weld. J. 77 (4) (1998) 155. [5] M.R. Frewin, D.A. Scott, Finite element simulation of welding of large structures, J. Eng. Ind. 114 (11) (1992) 441. [6] L. Taupin, G.L. Kinzel, T. Altan, Deep drawing of round coups from tailor-welded blanks, J. Mater. Process. Technol. 53 (3/4) (1995) 684. [7] 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, p. 455. [8] S. Brown, H. Song, Finite element simulation of welding of large structures, J. Eng. Ind. 114 (11) (1992) 441.
Finite element analysis of a tailored blanks stamping process Z. Zimniaka,*, A. Pielab a
Department of Engineering Forming Processes, Faculty of Mechanical Engineering, Wroclaw University of Technology, ul. Lukasiewicza 3/5, 50-371 Wroclaw, Poland b Silesian University of Technology, ul. Krasinskiego 8, 40-019 Katowice, Poland
Abstract This paper describes the computer simulation methodology for applying the method of ®nite elements in the sheet stamping of a new type of sheet. Simulation of the cup stamping process by a punch of square section has been chosen for testing. The modelling of such a stamping process was carried out using a complete thermomechanical analysis including the modelling of the sheet welding process and the modelling of the stamping process. It has been assumed that the criteria for evaluating the quality of the theoretical solution is the displacement of welding line after stamping. The stress after the welding process and the deformation are essential for further stage of the stamping process. # 2000 Elsevier Science B.V. All rights reserved. Keywords: Finite element simulation; Sheet metal forming; Laser welded blank
1. Introduction Forming more complex parts of sheet metal in a single stamping operation is very ef®cient in cost reduction and dimensional accuracy. The introduction of new materials for stamping, such as tailored blanks, has become a common practice in the automotive industry. Tailored blanks combine many features of the above mentioned materials in respect of their application. The concept of such a type of charge for stamping requires the application of laser welding in order to join different sheets of steel. Their geometrical and physical features are being matched on the basis of the economics and the constructional requirement of the stamped elements. Introducing tailored blanks for stamping should be preceded by a series of careful examinations which ought to be of multilevel character. Examinations of this kind are both timeconsuming and expensive because the production and processing of tailored blanks has not yet been fully examined and developed. The risk of negative application of new materials can be reduced only if their performance can be correctly assessed during the stamping process. The cost reduction of the process technological examination of the new materials can be achieved by modelling examinations and computer simulation. Therefore charge modelling methodology for stamping should be developed, since these charges have *
Corresponding author.
different mechanical properties and geometrical features of sheet constituent elements. 2. Experimental work Stamping-process examinations, i.e. identi®cation of the problem of the in¯uence of the weld on the process of sheet material ¯ow in stamping, have been carried out applying the technological evaluation of drawability. Tools for the cupping test, Erichsen tests, tensile tests in a cup bottom hole Ð KWI, and hydraulic bulge tests were used for examination purposes. A test for uniaxial sample bumping with the weld being positioned crosswise and lengthwise against the direction of blocking was carried out. The frontal welding process with blanks being positioned as shown in Fig. 1 has been completed by CO2 gas laser with a mirror head which re¯ects the rays from the root of weld. The examination of weld joints established that the material is of ferritic structure with diversi®ed band system. Welds of the examined joints feature a dendritic structure with a distinctly noticeable crystallisation axis. The shape of the welds is narrow (just as it should be) which is characteristic of laser welding. Measurements of local strains carried out by marking nets on the sheets before deformation, revealed that the process of sheet material ¯ow has been considerably disturbed because of the difference in the stamped sheet thickness and the in¯uence of weld itself. Characteristic blocking of lengthwise metal ¯ow in a weld (Fig. 2) and characteristic
0924-0136/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 0 ) 0 0 6 2 6 - 9
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
255
Fig. 1. Microstructure of weld zone (mag.: 20).
distortion of the weld line (Figs. 3 and 4) in the direction of the thicker sheet have been observed similar to the observations presented in [1,2]. Displacements of the weld line shown in the above mentioned ®gures are due to the diversi®ed material ¯ow in similar zones of the drawpiece both on the thicker and thinner side of the sheet. The weld limits lengthwise deformation also. This causes the puckering of a drawpiece ¯ange into the side surface zone (Fig. 4) and there is also a considerably smaller narrowing of the sample at the weld line as compared to the neighbouring zones, as shown in Fig. 2. The observed dependencies con®rm the local strain distribution which has been presented in Fig. 5. These distributions result from ball-shaped punch bulge tests of a sheet restrained by a clamp. The relationships between the degree of sheet deformation in the weld zone and the analogical places of a drawpiece on the thicker and thinner side of the sheet depend on: (i) the thickness relationships of the tailored blanks, (ii) the properties of sheet hardening values with these values depending on yield stress change characteristics, and (iii) the weld quality (also the level of hardening in the heataffected zone) and the size of the welding stresses. Whether the tailored blanks are completely suitable for stamping depends on the compound sheet characteristics and weld quality. Therefore drawability is dif®cult to de®ne
Fig. 2. Break of the sample and a crosswise weld resulting from a bumping test.
Fig. 3. The KWI test: (a) distortion of a weld line in the area of punch stamping towards a thicker sheet; (b) a break of the sheet near the weld on its thinner part from the edge of a bumped hole.
for this type of charge, taking into consideration all possible variations of sheet tailoring. It seems necessary to develop a method of heterogeneous material ¯ow analysis for tailored blanks in the process of stamping. This process can be
Fig. 4. (a) A cupping test using a 40 mm square punch with a ¯at bottom; (b) break of the sheet near the weld line in the area of the punch bottom; (c) distortion of the weld line in a side surface zone and punch ¯ange zone.
256
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
Fig. 5. Local strain distribution in a sheet welded after bulging by a ballshaped punch.
characterised by changeable geometry, and the state of stress and strain of the deformation zone based on the compound sheets characteristics. Hence, it is justi®ed to apply simulation techniques for the analysis of such non-de®ned sheet material ¯ow. 3. Simulation of the tailored blanks stamping process by FEM A full computer simulation of the stamping process for laser welded sheet requires ®nding a solution for: the initial modelling of the charge welding and the modelling of the stamping process. In a simpli®ed version of analysis, the charge welding can be neglected in favour of establishing de®ned features of stamped material in the weld area [3±5]. Refs. [6,7] give evidence that the designing of a tailored blanks stamping process is different from the designing of a conventional blank stamping process. The breaks occur in different places of the drawpieces and it is also necessary to use sectional blankholders. The position of the weld line is important for the level of local strains. In most of the above mentioned publications a simpli®ed version of the tailored blanks stamping process was presented and a suitable model for the weld zone was also provided. Buste et al. [7] applied gradually increasing thickness elements in the place where a thin sheet joins a thick sheet. Also presented was a new solution using rigid links which join sheets of various thickness. Experimental measurements of strains along a line which is perpendicular to a weld line give evidence that if such simpli®cations are applied, considerable divergence between experimental and theoretical results can occur.
Fig. 6. Simulation of the welding process with temperature distribution.
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
257
Fig. 7. Stress which remained in a linked sheet after the welding and cooling process.
3.1. Calculation model The FEM simulation of the square drawpiece stamping process of a laser weld charge using the MARC programme supported by users sub-programs was performed. The following assumptions were made: 1. The charge for stamping consists of two deep drawn sheets of 1 and 1.5 mm thickness which have different material properties;
2. Heat produced by the laser is modelled by a heat stream which is let in at linked material contact areas and is of a de®ned radius of laser spot resulting from a Gaussian distribution (the user's sub-program was introduced); 3. Not all heat reaches the sheet (the absorption coef®cients for sheet materials have been used for calculations); 4. Heat is removed from the sheet by convection and radiation;
Fig. 8. Distribution of sheet thickness in a modelled drawpiece.
258
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
Fig. 9. Substitute strain distribution at the ®nal stage of stamping.
Fig. 10. Substitute stress distribution at the ®nal stage of stamping.
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
5. Latent heat resulting from sheet material phase transformation was taken into account. This was done in accordance with the Brown and Song [8] concept; 6. A constant temperature of 208C for linked sheet before welding was assumed; 7. The sheet cooling time after welding was established experimentally and it ensured total cooling up to the temperature before welding; 8. A constant welding speed was assumed (introduced by the user's computer programme); 9. Simulation was carried out for a full three-dimensional model. The application of thermomechanical analysis allowed taking into account all the phenomena occurring in a sheet during welding and also applying such a charge model for stamping process simulation. 3.2. Calculation results Fig. 6 presents subsequent stages for the laser welding of a preform with a distinctly visible sheet temperature distribution. The stresses in a sheet after the welding process and after cooling are shown in Fig. 7. The stresses which remain in the material after the welding process in¯uence considerably the material ¯ow during the stamping process. This has been con®rmed by simulation results of the analysed drawpiece forming process, these results being presented in Figs. 8±11.
259
Characteristic changes of sheet thickness, especially in the weld zone, are shown in Fig. 8, whilst Figs. 9 and 10 present substitute strain and stress distribution, respectively. A particular way of sheet ¯ow in the stamping process right from the beginning causes bigger strains in the thicker part of the drawpiece. The ®nal effect of such material ¯ow results in signi®cant diversi®cation of sheet thickness in different parts of a drawpiece Ð Fig. 11. There can also be noticed a characteristic displacement and distortion of weld line towards the thicker sheet. The ¯ang part of a drawpiece is of a speci®c shape that can be found in drawpieces formed from welded sheets. Such a shape is formed because there is a bigger ¯ang strain in a thinner part of the drawpiece than in the thicker part. 4. Conclusions The simulation results of the linked sheet stamping process require practical veri®cation. The presented experimental results and calculations are in quantitative agreement. The character of the weld line displacement acquired in the simulation con®rms that noticed in experiments in the weld line displacement of the drawpieces. Quantitative evaluation seems to be a far more complicated problem. The displacement diagram of a weld line (Fig. 12) is quite a good evaluation criterion of a solution consistence. One axis of the diagram in Fig. 12 represents the length of the original weld line and the other its displacement from the initial
Fig. 11. Distribution of sheet thickness with a distinct weld line displacement.
260
Z. Zimniak, A. Piela / Journal of Materials Processing Technology 106 (2000) 254±260
tion carried out, both for thickness changes and local strains. The automatic picture analysis technique for measuring local strains on the entire area of the drawpiece has been developed and is getting ready for application. References
Fig. 12. Weld line displacement diagram.
position just after welding process. The examinations carried out on this subject demonstrate satisfactory agreement of measurements and calculation results for the simulated example of a square cup. Local strain changes and local changes of thickness were also used as a criterion of calculation accuracy. The comparison of calculation and measurement results for selected places of a drawpiece con®rmed the validity of the simula-
[1] A. Mustafa, D. Ahmetoglu, L. Brouwers, L. Shulkin, G. Taupin, L. Kinzel, T. Altan, Deep drawing of round cups from tailor-welded blanks, J. Mater. Process. Technol. 53 (1995) 684. [2] F.I. Saunders, R.H. Wagoner, Forming of tailor-welded blanks, Metall. Mater. Trans. A 27 (9) (1996) 2605. [3] D.T. Swift-Hook, A.E.F. Gick, Penetration welding with lasers, Weld. J. 52 (11) (1973) 492. [4] J.S. Park, S.J. Na, Heat transfer in a stud-to-plate laser braze considering ®ller metal movement, Weld. J. 77 (4) (1998) 155. [5] M.R. Frewin, D.A. Scott, Finite element simulation of welding of large structures, J. Eng. Ind. 114 (11) (1992) 441. [6] L. Taupin, G.L. Kinzel, T. Altan, Deep drawing of round coups from tailor-welded blanks, J. Mater. Process. Technol. 53 (3/4) (1995) 684. [7] 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, p. 455. [8] S. Brown, H. Song, Finite element simulation of welding of large structures, J. Eng. Ind. 114 (11) (1992) 441.