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From microstructure to deformation and fracture behaviour of aluminium welded joints – a holistic modelling approach
Computational Materials Science 21 (2001) 429±435
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From microstructure to deformation and fracture behaviour of aluminium welded joints ± a holistic modelling approach Z.L. Zhang a,*, J. édeg ard a, O.R. Myhr b, H. Fjñr c a
SINTEF Materials Technology, N-7465 Trondheim, Norway b Hydro Automotive Structures, N-2831, Raufoss, Norway c Institute for Energy Technology, N-2027 Kjeller, Norway Received 1 March 2001; accepted 2 April 2001
Abstract In this study, a new modelling approach for aluminium weldments has been explored. In the approach, the microstructure data calculated from welding analysis are directly transferred to the deformation and damage analysis. With an interpolation equation between the properties of the base metal and the fully reverted heat aected zone (HAZ), the exact dimension and gradient of mechanical properties of the whole HAZ are automatically predicted. The overall eect of the microstructure evolution during welding, and the resulting deformation and damage capacity of the welded joint can then be analysed. This approach has been applied in two case studies, one cross weld tensile specimen, which is used for the parameter study, and one real T-joint from which test data are available. With a linear interpolation for the ¯ow stress and ductile damage parameter, the ®nite element results based on this new approach are in good agreement with the test data. Ó 2001 Published by Elsevier Science B.V.
1. Introduction ``Inhomogeneous'' is an important feature of welded joints. Not only the mechanical properties of weld metal, heat aected zone (HAZ) and base material are dierent, there is often a strong gradient in strength and ductility within the HAZ and weld metal. Conventional analyses often disregard the gradient by assuming the same properties throughout the HAZ. The dimension of the HAZ is often determined from hardness tests, or even ®tted from global load-deformation analyses. Apparently, more accurate modelling of strength and
*
Corresponding author. E-mail address: [email protected] Zhang).
(Z.L.
ductility gradients inside the HAZ is desired for realistic and direct prediction of the load-carrying and deformation capacity of welded joints. Basically there are two dierent approaches available for the analysis of welded joints. The ®rst approach can be called ``thermal±mechanical analysis''. Here the microstructure evolution is calculated for each material point of the HAZ during the welding process as described in [1±3]. Because there are large temperature gradients within the HAZ, there will be a corresponding variation in the resulting microstructure and yield strength after welding. In this approach the deformation capacity is based on the detailed strength distribution within the HAZ as calculated by the microstructure model. Another approach is called ``mechanical analysis''. In this approach, the strength and
0927-0256/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII: S 0 9 2 7 - 0 2 5 6 ( 0 1 ) 0 0 1 8 1 - 1
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Z.L. Zhang et al. / Computational Materials Science 21 (2001) 429±435
deformation capacity of the welded joint under external loading are calculated by assuming a uniform HAZ strength. Weld thermal simulation is often needed to determine the representative HAZ strength, and tensile testing of notched specimens is often applied to determine the damage parameters for ductile fracture [4,5]. The HAZ dimension is determined from hardness measurement. The HAZ properties are in fact controlled by the ®nal microstructure after welding. It becomes a natural idea to link the distribution of strength and deformation ability of the HAZ to the ®nal microstructure calculated from the thermal± mechanical analysis. The problem appears that the thermal±mechanical analyses and the further modelling of the load-deformation response are done by separate ®nite element codes with dierent meshes. This study is one step forward towards unifying the two models. For a selected alloy and given welding parameters, the microstructure data for a cross-weld tensile specimen and a real welded tubular T-joint are calculated by the WE L D S I M program [6] based on the microstructure model developed by Myhr [1,2]. Then by using a special technique, the microstructure data are transferred to AB A Q U S [7]. A parameter study was carried out on the interpolation function between the ®nal microstructure and the ¯ow strength and damage parameters. In this holistic approach the accurate gradient of properties and dimension of the HAZ are automatically modelled, and the microstructure data from thermal±mechanical analysis can be directly utilized.
2. Microstructure calculations In this study, welded joints of the aluminium alloy 6082-T6 are considered. The chemical composition of the alloy is shown in Table 1.
A weld simulation involves a coupled calculation of the heat ¯ow, the microstructure evolution and mechanical response during welding. The microstructure history as well as the ®nal microstructure is calculated using the WE L D S I M ®nite element program, where the microstructure model by Myhr and Grong is implemented [1,2]. Detailed information concerning the microstructure model and its implementation can be found in the references. The main idea of the model is to capture the microstructure evolution in terms of a time-dependent state variable ± the volume fraction of hardening particles, f. The ratio of the current volume fraction to its initial value, f =f0 is an indicator for its mechanical behaviour, in particular, the hardness. For the 6082 aluminium alloy the microstructure and hardness are not stable after welding. A process called natural ageing will change the microstructure by precipitation of hardening particles leading to some strength recovery in the HAZ [1,2]. The strength recovery will be most signi®cant close to the weld fusion boundary, and will gradually decrease at increasing distance from the weld, as illustrated in Fig. 1.
3. Transferring of microstructure data from WE L D to AB A Q U S
SIM
An important task is the transferring of the microstructure data from WE L D S I M to AB A Q U S . Because of the dierent nature of the calculations, dierent ®nite element meshes are generally used in these codes. It was decided to transfer the microstructure data to AB A Q U S at element level, where the whole element has the same microstructure, in accordance with the common practice in treating material inhomogeneity in ®nite element analyses. Step 1: Calculating the microstructure. Thermal±mechanical analyses were carried out with
Table 1 Chemical composition of the 6082-T6 alloy Element
Si
Fe
Cu
Mn
Mg
Cv
Zn
Ti
wt%
0.8±1.2
0.3
0.1
0.4±0.7
0.5±0.8
0.1
0.1
0.05
Z.L. Zhang et al. / Computational Materials Science 21 (2001) 429±435
431
4. Strength hardening and ductility
Fig. 1. Schematic diagram showing the ageing eect on the hardness pro®le of the HAZ of the aluminium alloy AA6082.
WE L D S I M for selected welding parameters, material data and given geometry. Solid elements were used. Mesh was designed according to thermal analyses rules. Step 2: Meshing in AB A Q U S . A very ®ne ®nite element mesh with 8-node elements was applied to the location where possible cracking under external loading will occur. (In order to communicate with WE L D S I M to obtain the microstructure data, 9-node elements were generated based on the original 8-node element mesh.) Step 3: Microstructure data for the AB A Q U S models. Microstructure data, at the locations of the element centre points in the AB A Q U S mesh, were estimated in WE L D S I M by interpolation in the microstructure result ®elds. Step 4: Microstructure data into AB A Q U S . In AB A Q U S the microstructure data are treated as ``state-dependent-variables (SDV)'' and related to the mechanical properties in a ``user-material-subroutine (UMAT)'' code which was originally developed for ductile damage/fracture analyses based on the Gurson model [8]. In the UMAT code, the ®rst ®ve SDVs are allocated for the damage parameters and other state-dependent-variables. The microstructure parameter f =f0 was assigned to the sixth state-dependent-variable, SDV6. Step 5: The remaining task is to link the microstructure data to the mechanical properties of HAZ. In this study, the properties of base material, weld metal and fully reverted HAZ are taken from a previous work [4,5]. Several interpolation functions have been studied.
Recently a so-called complete Gurson model has been developed for ductile damage/fracture analyses, where material ductile failure is linked to the microvoid nucleation parameter [9]. The complete Gurson model has been implemented in the AB A Q U S via the UMAT code. In order to predict the deformation and ductile fracture behaviour of a welded joint, three mechanical data sets for each material zone should be inputted into the AB A Q U S , the yield strength, hardening, and ductile damage parameters. Mechanical testing of the 6082-T6 base metal, a weld metal (AA5183) and weld thermal simulated HAZ has been performed in the previous work [4,5]. The ¯ow stress versus equivalent plastic strain curves are shown in Fig. 2 for the three materials. The HAZ curve in Fig. 2 was taken as that for the fully reverted HAZ in this study. From Fig. 2, we observe that the HAZ is the weakest material, and the base metal is the strongest. The weld metal has an identical yield stress as the HAZ, but a stronger hardening ability. In order to describe the ductility for each material, only one damage parameter is needed in the complete Gurson model ± the void nucleation parameter [9]. A so-called continuous void nucleation model has been used. The void nucleation
Fig. 2. The stress±strain curves used in the study, where HAZ is the weld thermal simulated HAZ, BM is the base material and WM represents the weld metal.
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Z.L. Zhang et al. / Computational Materials Science 21 (2001) 429±435
parameters are as follows [4,5]: Base metal, 0.001, weld metal 0.04, and fully reverted HAZ 0.02. For partly reverted HAZ, no equations were available for calculating the strength and ductility. In this study, a linear interpolation function and a parabolic interpolation function have been used for calculating the ¯ow stress and damage parameters for the partly reverted HAZ from the base metal and fully reverted HAZ, 8 m 6 mt ; MF HAZ > > < MF HAZ M ml MBM MF HAZ > > : m mt = 1:0 mt m > mt ; 1 and M mP
8 MF > > > :
HAZ
m 6 mt ;
F HAZ
MBM MF HAZ 2 m mt = 1:0 mt
m > mt ; 2
where m is the f =f0 , M represents the ¯ow strength or damage parameter of the partly reverted HAZ, MF HAZ for the fully reverted HAZ, and MBM for the base metal. In the above equation, a threshold value for microstructure, mt , has been used. The reason to use a threshold value is that the calculated minimum microstructure parameter f =f0 after welding which corresponds to the fully reverted HAZ was not zero, but larger than 0.3. Several threshold values of the microstructure have been tried. It is interesting to note that Fig. 2 shows that the stress±strain curves for the weld thermal simulated HAZ and base metal are nearly parallel to each other. This gives a good indication that the interpolation functions may be extended to the plastic regime.
tried ®rst. The geometry of the cross weld tensile specimen was taken from a previous study, and the materials are based in Fig. 2. The width, thickness, and total length of the cross weld tensile specimens are, 25, 4.1, 270 mm, respectively. No experimental results were compared. Fig. 3 shows the calculated microstructure at the centre versus axial distance. The minimum f =f0 value for the whole model is 0.36, rather than 0.0. This suggests that microstructure threshold value in the interpolation function (1, 2) should be at least 0.36, if the weld thermal simulated HAZ curve in Fig. 2 is taken as the fully reverted HAZ. By using the microstructure data and the interpolation functions, analyses have been carried out in AB A Q U S through the user material subroutine UMAT. Fig. 4 compares the results of four analyses. Case 1 represents the conventional approach analysis where the HAZ is treated by one uniform material zone, using the HAZ strength shown in Fig. 2. In this case, a uniform HAZ length 23 mm was used. Case 2 uses the holistic modelling approach with a linear interpolation function. The interpolation function range varies between 0.0 and 1.0 with zero threshold value. Because the minimum microstructure value is 0.36, which is larger than 0.0, therefore, the strength used in case 2 for the partly reverted HAZ is much higher than the HAZ strength shown in Fig. 2.
5. Applications 5.1. Cross weld tensile specimen In order to realize the holistic modelling approach, a cross weld tensile specimen has been
Fig. 3. Final microstructure distribution at the specimen centre along the longitudinal axis. The dimensions of the weld metal and HAZ were those used in the conventional analyses.
Z.L. Zhang et al. / Computational Materials Science 21 (2001) 429±435
433
Fig. 4. Load-displacement curves of four cases for the cross weld tensile specimen.
Fig. 5. Eect of uniform HAZ length in the conventional approach for the cross weld tensile specimen.
Because of this, the load-carrying capacity in case 2 is much higher than that in case 1. Cases 3 and 4 both use the same threshold microstructure value ± the minimum of the whole model, but dierent interpolation functions, case 3 is linear and case 4 is parabolic. It is interesting to notice that cases 4 and 1 are very close to each other. The dierent interpolations mainly change the loading levels, while the shapes of the load-displacement curves are nearly the same. The eect of HAZ length in the conventional approach, which uses a uniform HAZ material zone has also been studied and is illustrated in Fig. 5. Three material zone lengths, 23, 16 and 8 mm were studied. It can be observed that for the same stress±strain curves, small HAZ length, will increase the maximum loading carrying capacity, but decrease the overall ductility and the displacement at the maximum load. Combining Figs. 4 and 5, we may conclude that the dimensions of the HAZ primarily determine the shape of load-displacement curves, while the strength of HAZ in¯uences the loading level.
cates f =f0 1:0, which is the base metal. Fig. 6(b) shows the uniform HAZ dimensions used in [4,5]. It seems that a slightly larger volume of materials in the T-joint has been used as the fully reverted HAZ in the previous study [4,5], especially around the corners. Weld metal dimensions and properties were the same in both analyses. The eect of threshold microstructure value has also been studied in the T-joint case, Fig. 7. First of all, the shapes of the three curves are quite similar to each other. This is in accordance with the observation of the cross weld tensile specimen. The displacement at which fracture occurs is nearly unaected by the threshold value. In general threshold value has a large eect on the load-displacement behaviour. The larger the threshold value which indicates that more HAZ volume is taken as the fully reverted HAZ (lowest strength), the lower the load level. The ®nite element results of the holistic modelling approach have been compared with the experimental test results carried out in the previous study [4,5], together with the results of the conventional approach in Fig. 8. The general observation is that the numerical results overpredict the load-carrying capacity compared with the experimental results. It should be noted that rigid boundary conditions were assumed in the analyses, while the ®xtures in the experiments were not 100% rigid [4,5]. Some initial glide could be
5.2. A T-joint A real welded rectangular cross-section T-joint has been studied. Fig. 6(a) shows the calculated microstructure data. The minimum f =f0 for the Tjoint is found to be 0.31. The black colour indi-
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Z.L. Zhang et al. / Computational Materials Science 21 (2001) 429±435
(a)
(b)
Fig. 6. Microstructure distribution and uniform HAZ dimensions used in the conventional approach for the welded T-joint.
Fig. 7. Eect of threshold value on the load-displacement behaviour of the welded joint.
Fig. 8. Comparison of the results of the new model approach and the conventional approach with the experimental results [4,5].
present, which can explain the observed variations in the elastic stiness of the experimental and numerical load-displacement curves in Fig. 8. The prediction by the holistic modelling approach using a linear interpolation with threshold value taken as the minimum f =f0 found in the whole model predicts a higher loading capacity than that of the conventional approach where a larger volume of material has been assumed and all the material was treated as the fully reverted HAZ. This is understandable because in the ho-
listic modeling approach only the material with minimum f =f0 has the fully reverted HAZ properties, while the rest of the HAZ material has a higher ¯ow stress. Fig. 8 shows that when the threshold value is taken as 0.5, the prediction of the complete modelling approach is very close to that of the conventional approach, in terms of both the loading level and displacement at fracture. This indicates that if the weld thermal simulated HAZ properties in Fig. 2 are representative of the true fully reverted HAZ,
Z.L. Zhang et al. / Computational Materials Science 21 (2001) 429±435
not the material with minimum f =f0 , but a certain amount of volume f =f0 6 0:5 of the total HAZ needs to assume the fully reverted HAZ properties. 6. Concluding remarks In this study, it has been shown that two approaches, one for thermal±mechanical microstructure analysis and one for load-deformation mechanical analysis can be combined together into one. By using an interpolation function, the microstructure data calculated from WE L D S I M analysis can be used to automatically de®ne the HAZ dimensions of welded joints and determine the mechanical properties such as stress±strain curve and ductility. Although for the T-joint studied the new approach has not shown necessarily a better agreement with the experimental results than the conventional approach, where the whole HAZ has been taken as a uniform fully reverted zone and its dimension has been ®tted for the given uniform HAZ strength from a global load-deformation analysis. However, the main advantage of the new approach is that the gradient of the mechanical properties of the HAZ is better modelled than that previously and the corresponding dimensions can be automatically determined. An iterative process to match the balance between the dimension of the HAZ and its representative strength is eliminated. It has been shown that the dimensions of HAZ will determine the shape of load-displacement curves while the strength of HAZ will in¯uence the loading level of a weldment. In theory the yield strength and the hardening exponent as well as ductility (damage parameter) of a material are determined by its microstructure. No mechanical testing of HAZ is needed if a relation between microstructure and the mechanical properties exists. In practice, at least one test of the full HAZ with lowest f =f0 ratio should be tested to obtain the yield stress, hardening exponent and ductility. HAZ with an intermediate value of the f =f0 can be obtained by a linear or non-linear interpolation. It seems that a threshold value for the microstructure used in the interpolation functions is
435
necessary to get a good prediction compared with the experimental results for the T-joint. The relation of properties between the HAZ with minimum f =f0 and the thermal simulated HAZ should be better understood. It must be noted that the interpolation functions in this study have been applied not only to the yield strength, but also to the ¯ow strength (hardening) and damage parameters (ductility). The eect of microstructure on hardening and ductility is not well understood. Further investigation in this respect should be carried out. Acknowledgements The ®nancial support from the Norwegian Research Council via the PROSMAT project is greatly appreciated. References [1] O.R. Myhr, S. Klokkehaug, H.G. Fjñr, é. Grong, A.O. Kluken, Modelling of microstructure evolution and residual stress in processing and welding of 6082 and 7108 aluminium alloys, in: Proceedings of the 5th International Conference on Trends in Welding Research, Georgia, USA June 1±5, 1998. [2] O.R. Myhr, S. Klokkehaug, é. Grong, H.G. Fjñr, A.O. Kluken, Modelling of microstructure, evolution residual stress and distortions in 6082-T6 aluminium weldments, Weld. J. (1998) 286±289. [3] D. Radaj, H. Hauser, S. Braun, Numerical simulation of residual stress and distortion of welded joints in 6XXX alloys, Konstruktion 50 (1998) 30±38, heft 7/8. [4] J. édegard, Z.L. Zhang, A. Kluken, Prediction of the performance of welded aluminium nodes for car body applications, in: Proceedings of the International Body Engineering Conference, Body Design and Engineering (IBEC'96), 1996, pp. 17±24. [5] J. édegard, Z.L. Zhang, A. Kluken, The signi®cance of HAZ (heat aected zone) and weld metal properties on the performance of welded aluminium nodes, in: Proceedings of the International Body Engineering Conference, (IBEC'97), Stuttgart, 30/9±2/10, 1997. [6] WE L D S I M , User's manual, IFE, 1999. [7] AB A Q U S , User's Manual, version 5.8, 1998. [8] A. Gurson, J. Mater. Technol. (1968). [9] Z.L. Zhang, C. Thaulow, J. édeg ard, A complete Gurson model approach for ductile fracture, Eng. Fract. Mech. 67 (2000) 155±168.
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From microstructure to deformation and fracture behaviour of aluminium welded joints ± a holistic modelling approach Z.L. Zhang a,*, J. édeg ard a, O.R. Myhr b, H. Fjñr c a
SINTEF Materials Technology, N-7465 Trondheim, Norway b Hydro Automotive Structures, N-2831, Raufoss, Norway c Institute for Energy Technology, N-2027 Kjeller, Norway Received 1 March 2001; accepted 2 April 2001
Abstract In this study, a new modelling approach for aluminium weldments has been explored. In the approach, the microstructure data calculated from welding analysis are directly transferred to the deformation and damage analysis. With an interpolation equation between the properties of the base metal and the fully reverted heat aected zone (HAZ), the exact dimension and gradient of mechanical properties of the whole HAZ are automatically predicted. The overall eect of the microstructure evolution during welding, and the resulting deformation and damage capacity of the welded joint can then be analysed. This approach has been applied in two case studies, one cross weld tensile specimen, which is used for the parameter study, and one real T-joint from which test data are available. With a linear interpolation for the ¯ow stress and ductile damage parameter, the ®nite element results based on this new approach are in good agreement with the test data. Ó 2001 Published by Elsevier Science B.V.
1. Introduction ``Inhomogeneous'' is an important feature of welded joints. Not only the mechanical properties of weld metal, heat aected zone (HAZ) and base material are dierent, there is often a strong gradient in strength and ductility within the HAZ and weld metal. Conventional analyses often disregard the gradient by assuming the same properties throughout the HAZ. The dimension of the HAZ is often determined from hardness tests, or even ®tted from global load-deformation analyses. Apparently, more accurate modelling of strength and
*
Corresponding author. E-mail address: [email protected] Zhang).
(Z.L.
ductility gradients inside the HAZ is desired for realistic and direct prediction of the load-carrying and deformation capacity of welded joints. Basically there are two dierent approaches available for the analysis of welded joints. The ®rst approach can be called ``thermal±mechanical analysis''. Here the microstructure evolution is calculated for each material point of the HAZ during the welding process as described in [1±3]. Because there are large temperature gradients within the HAZ, there will be a corresponding variation in the resulting microstructure and yield strength after welding. In this approach the deformation capacity is based on the detailed strength distribution within the HAZ as calculated by the microstructure model. Another approach is called ``mechanical analysis''. In this approach, the strength and
0927-0256/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII: S 0 9 2 7 - 0 2 5 6 ( 0 1 ) 0 0 1 8 1 - 1
430
Z.L. Zhang et al. / Computational Materials Science 21 (2001) 429±435
deformation capacity of the welded joint under external loading are calculated by assuming a uniform HAZ strength. Weld thermal simulation is often needed to determine the representative HAZ strength, and tensile testing of notched specimens is often applied to determine the damage parameters for ductile fracture [4,5]. The HAZ dimension is determined from hardness measurement. The HAZ properties are in fact controlled by the ®nal microstructure after welding. It becomes a natural idea to link the distribution of strength and deformation ability of the HAZ to the ®nal microstructure calculated from the thermal± mechanical analysis. The problem appears that the thermal±mechanical analyses and the further modelling of the load-deformation response are done by separate ®nite element codes with dierent meshes. This study is one step forward towards unifying the two models. For a selected alloy and given welding parameters, the microstructure data for a cross-weld tensile specimen and a real welded tubular T-joint are calculated by the WE L D S I M program [6] based on the microstructure model developed by Myhr [1,2]. Then by using a special technique, the microstructure data are transferred to AB A Q U S [7]. A parameter study was carried out on the interpolation function between the ®nal microstructure and the ¯ow strength and damage parameters. In this holistic approach the accurate gradient of properties and dimension of the HAZ are automatically modelled, and the microstructure data from thermal±mechanical analysis can be directly utilized.
2. Microstructure calculations In this study, welded joints of the aluminium alloy 6082-T6 are considered. The chemical composition of the alloy is shown in Table 1.
A weld simulation involves a coupled calculation of the heat ¯ow, the microstructure evolution and mechanical response during welding. The microstructure history as well as the ®nal microstructure is calculated using the WE L D S I M ®nite element program, where the microstructure model by Myhr and Grong is implemented [1,2]. Detailed information concerning the microstructure model and its implementation can be found in the references. The main idea of the model is to capture the microstructure evolution in terms of a time-dependent state variable ± the volume fraction of hardening particles, f. The ratio of the current volume fraction to its initial value, f =f0 is an indicator for its mechanical behaviour, in particular, the hardness. For the 6082 aluminium alloy the microstructure and hardness are not stable after welding. A process called natural ageing will change the microstructure by precipitation of hardening particles leading to some strength recovery in the HAZ [1,2]. The strength recovery will be most signi®cant close to the weld fusion boundary, and will gradually decrease at increasing distance from the weld, as illustrated in Fig. 1.
3. Transferring of microstructure data from WE L D to AB A Q U S
SIM
An important task is the transferring of the microstructure data from WE L D S I M to AB A Q U S . Because of the dierent nature of the calculations, dierent ®nite element meshes are generally used in these codes. It was decided to transfer the microstructure data to AB A Q U S at element level, where the whole element has the same microstructure, in accordance with the common practice in treating material inhomogeneity in ®nite element analyses. Step 1: Calculating the microstructure. Thermal±mechanical analyses were carried out with
Table 1 Chemical composition of the 6082-T6 alloy Element
Si
Fe
Cu
Mn
Mg
Cv
Zn
Ti
wt%
0.8±1.2
0.3
0.1
0.4±0.7
0.5±0.8
0.1
0.1
0.05
Z.L. Zhang et al. / Computational Materials Science 21 (2001) 429±435
431
4. Strength hardening and ductility
Fig. 1. Schematic diagram showing the ageing eect on the hardness pro®le of the HAZ of the aluminium alloy AA6082.
WE L D S I M for selected welding parameters, material data and given geometry. Solid elements were used. Mesh was designed according to thermal analyses rules. Step 2: Meshing in AB A Q U S . A very ®ne ®nite element mesh with 8-node elements was applied to the location where possible cracking under external loading will occur. (In order to communicate with WE L D S I M to obtain the microstructure data, 9-node elements were generated based on the original 8-node element mesh.) Step 3: Microstructure data for the AB A Q U S models. Microstructure data, at the locations of the element centre points in the AB A Q U S mesh, were estimated in WE L D S I M by interpolation in the microstructure result ®elds. Step 4: Microstructure data into AB A Q U S . In AB A Q U S the microstructure data are treated as ``state-dependent-variables (SDV)'' and related to the mechanical properties in a ``user-material-subroutine (UMAT)'' code which was originally developed for ductile damage/fracture analyses based on the Gurson model [8]. In the UMAT code, the ®rst ®ve SDVs are allocated for the damage parameters and other state-dependent-variables. The microstructure parameter f =f0 was assigned to the sixth state-dependent-variable, SDV6. Step 5: The remaining task is to link the microstructure data to the mechanical properties of HAZ. In this study, the properties of base material, weld metal and fully reverted HAZ are taken from a previous work [4,5]. Several interpolation functions have been studied.
Recently a so-called complete Gurson model has been developed for ductile damage/fracture analyses, where material ductile failure is linked to the microvoid nucleation parameter [9]. The complete Gurson model has been implemented in the AB A Q U S via the UMAT code. In order to predict the deformation and ductile fracture behaviour of a welded joint, three mechanical data sets for each material zone should be inputted into the AB A Q U S , the yield strength, hardening, and ductile damage parameters. Mechanical testing of the 6082-T6 base metal, a weld metal (AA5183) and weld thermal simulated HAZ has been performed in the previous work [4,5]. The ¯ow stress versus equivalent plastic strain curves are shown in Fig. 2 for the three materials. The HAZ curve in Fig. 2 was taken as that for the fully reverted HAZ in this study. From Fig. 2, we observe that the HAZ is the weakest material, and the base metal is the strongest. The weld metal has an identical yield stress as the HAZ, but a stronger hardening ability. In order to describe the ductility for each material, only one damage parameter is needed in the complete Gurson model ± the void nucleation parameter [9]. A so-called continuous void nucleation model has been used. The void nucleation
Fig. 2. The stress±strain curves used in the study, where HAZ is the weld thermal simulated HAZ, BM is the base material and WM represents the weld metal.
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Z.L. Zhang et al. / Computational Materials Science 21 (2001) 429±435
parameters are as follows [4,5]: Base metal, 0.001, weld metal 0.04, and fully reverted HAZ 0.02. For partly reverted HAZ, no equations were available for calculating the strength and ductility. In this study, a linear interpolation function and a parabolic interpolation function have been used for calculating the ¯ow stress and damage parameters for the partly reverted HAZ from the base metal and fully reverted HAZ, 8 m 6 mt ; MF HAZ > > < MF HAZ M ml MBM MF HAZ > > : m mt = 1:0 mt m > mt ; 1 and M mP
8 MF > >
HAZ
m 6 mt ;
F HAZ
MBM MF HAZ 2 m mt = 1:0 mt
m > mt ; 2
where m is the f =f0 , M represents the ¯ow strength or damage parameter of the partly reverted HAZ, MF HAZ for the fully reverted HAZ, and MBM for the base metal. In the above equation, a threshold value for microstructure, mt , has been used. The reason to use a threshold value is that the calculated minimum microstructure parameter f =f0 after welding which corresponds to the fully reverted HAZ was not zero, but larger than 0.3. Several threshold values of the microstructure have been tried. It is interesting to note that Fig. 2 shows that the stress±strain curves for the weld thermal simulated HAZ and base metal are nearly parallel to each other. This gives a good indication that the interpolation functions may be extended to the plastic regime.
tried ®rst. The geometry of the cross weld tensile specimen was taken from a previous study, and the materials are based in Fig. 2. The width, thickness, and total length of the cross weld tensile specimens are, 25, 4.1, 270 mm, respectively. No experimental results were compared. Fig. 3 shows the calculated microstructure at the centre versus axial distance. The minimum f =f0 value for the whole model is 0.36, rather than 0.0. This suggests that microstructure threshold value in the interpolation function (1, 2) should be at least 0.36, if the weld thermal simulated HAZ curve in Fig. 2 is taken as the fully reverted HAZ. By using the microstructure data and the interpolation functions, analyses have been carried out in AB A Q U S through the user material subroutine UMAT. Fig. 4 compares the results of four analyses. Case 1 represents the conventional approach analysis where the HAZ is treated by one uniform material zone, using the HAZ strength shown in Fig. 2. In this case, a uniform HAZ length 23 mm was used. Case 2 uses the holistic modelling approach with a linear interpolation function. The interpolation function range varies between 0.0 and 1.0 with zero threshold value. Because the minimum microstructure value is 0.36, which is larger than 0.0, therefore, the strength used in case 2 for the partly reverted HAZ is much higher than the HAZ strength shown in Fig. 2.
5. Applications 5.1. Cross weld tensile specimen In order to realize the holistic modelling approach, a cross weld tensile specimen has been
Fig. 3. Final microstructure distribution at the specimen centre along the longitudinal axis. The dimensions of the weld metal and HAZ were those used in the conventional analyses.
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Fig. 4. Load-displacement curves of four cases for the cross weld tensile specimen.
Fig. 5. Eect of uniform HAZ length in the conventional approach for the cross weld tensile specimen.
Because of this, the load-carrying capacity in case 2 is much higher than that in case 1. Cases 3 and 4 both use the same threshold microstructure value ± the minimum of the whole model, but dierent interpolation functions, case 3 is linear and case 4 is parabolic. It is interesting to notice that cases 4 and 1 are very close to each other. The dierent interpolations mainly change the loading levels, while the shapes of the load-displacement curves are nearly the same. The eect of HAZ length in the conventional approach, which uses a uniform HAZ material zone has also been studied and is illustrated in Fig. 5. Three material zone lengths, 23, 16 and 8 mm were studied. It can be observed that for the same stress±strain curves, small HAZ length, will increase the maximum loading carrying capacity, but decrease the overall ductility and the displacement at the maximum load. Combining Figs. 4 and 5, we may conclude that the dimensions of the HAZ primarily determine the shape of load-displacement curves, while the strength of HAZ in¯uences the loading level.
cates f =f0 1:0, which is the base metal. Fig. 6(b) shows the uniform HAZ dimensions used in [4,5]. It seems that a slightly larger volume of materials in the T-joint has been used as the fully reverted HAZ in the previous study [4,5], especially around the corners. Weld metal dimensions and properties were the same in both analyses. The eect of threshold microstructure value has also been studied in the T-joint case, Fig. 7. First of all, the shapes of the three curves are quite similar to each other. This is in accordance with the observation of the cross weld tensile specimen. The displacement at which fracture occurs is nearly unaected by the threshold value. In general threshold value has a large eect on the load-displacement behaviour. The larger the threshold value which indicates that more HAZ volume is taken as the fully reverted HAZ (lowest strength), the lower the load level. The ®nite element results of the holistic modelling approach have been compared with the experimental test results carried out in the previous study [4,5], together with the results of the conventional approach in Fig. 8. The general observation is that the numerical results overpredict the load-carrying capacity compared with the experimental results. It should be noted that rigid boundary conditions were assumed in the analyses, while the ®xtures in the experiments were not 100% rigid [4,5]. Some initial glide could be
5.2. A T-joint A real welded rectangular cross-section T-joint has been studied. Fig. 6(a) shows the calculated microstructure data. The minimum f =f0 for the Tjoint is found to be 0.31. The black colour indi-
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(a)
(b)
Fig. 6. Microstructure distribution and uniform HAZ dimensions used in the conventional approach for the welded T-joint.
Fig. 7. Eect of threshold value on the load-displacement behaviour of the welded joint.
Fig. 8. Comparison of the results of the new model approach and the conventional approach with the experimental results [4,5].
present, which can explain the observed variations in the elastic stiness of the experimental and numerical load-displacement curves in Fig. 8. The prediction by the holistic modelling approach using a linear interpolation with threshold value taken as the minimum f =f0 found in the whole model predicts a higher loading capacity than that of the conventional approach where a larger volume of material has been assumed and all the material was treated as the fully reverted HAZ. This is understandable because in the ho-
listic modeling approach only the material with minimum f =f0 has the fully reverted HAZ properties, while the rest of the HAZ material has a higher ¯ow stress. Fig. 8 shows that when the threshold value is taken as 0.5, the prediction of the complete modelling approach is very close to that of the conventional approach, in terms of both the loading level and displacement at fracture. This indicates that if the weld thermal simulated HAZ properties in Fig. 2 are representative of the true fully reverted HAZ,
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not the material with minimum f =f0 , but a certain amount of volume f =f0 6 0:5 of the total HAZ needs to assume the fully reverted HAZ properties. 6. Concluding remarks In this study, it has been shown that two approaches, one for thermal±mechanical microstructure analysis and one for load-deformation mechanical analysis can be combined together into one. By using an interpolation function, the microstructure data calculated from WE L D S I M analysis can be used to automatically de®ne the HAZ dimensions of welded joints and determine the mechanical properties such as stress±strain curve and ductility. Although for the T-joint studied the new approach has not shown necessarily a better agreement with the experimental results than the conventional approach, where the whole HAZ has been taken as a uniform fully reverted zone and its dimension has been ®tted for the given uniform HAZ strength from a global load-deformation analysis. However, the main advantage of the new approach is that the gradient of the mechanical properties of the HAZ is better modelled than that previously and the corresponding dimensions can be automatically determined. An iterative process to match the balance between the dimension of the HAZ and its representative strength is eliminated. It has been shown that the dimensions of HAZ will determine the shape of load-displacement curves while the strength of HAZ will in¯uence the loading level of a weldment. In theory the yield strength and the hardening exponent as well as ductility (damage parameter) of a material are determined by its microstructure. No mechanical testing of HAZ is needed if a relation between microstructure and the mechanical properties exists. In practice, at least one test of the full HAZ with lowest f =f0 ratio should be tested to obtain the yield stress, hardening exponent and ductility. HAZ with an intermediate value of the f =f0 can be obtained by a linear or non-linear interpolation. It seems that a threshold value for the microstructure used in the interpolation functions is
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necessary to get a good prediction compared with the experimental results for the T-joint. The relation of properties between the HAZ with minimum f =f0 and the thermal simulated HAZ should be better understood. It must be noted that the interpolation functions in this study have been applied not only to the yield strength, but also to the ¯ow strength (hardening) and damage parameters (ductility). The eect of microstructure on hardening and ductility is not well understood. Further investigation in this respect should be carried out. Acknowledgements The ®nancial support from the Norwegian Research Council via the PROSMAT project is greatly appreciated. References [1] O.R. Myhr, S. Klokkehaug, H.G. Fjñr, é. Grong, A.O. Kluken, Modelling of microstructure evolution and residual stress in processing and welding of 6082 and 7108 aluminium alloys, in: Proceedings of the 5th International Conference on Trends in Welding Research, Georgia, USA June 1±5, 1998. [2] O.R. Myhr, S. Klokkehaug, é. Grong, H.G. Fjñr, A.O. Kluken, Modelling of microstructure, evolution residual stress and distortions in 6082-T6 aluminium weldments, Weld. J. (1998) 286±289. [3] D. Radaj, H. Hauser, S. Braun, Numerical simulation of residual stress and distortion of welded joints in 6XXX alloys, Konstruktion 50 (1998) 30±38, heft 7/8. [4] J. édegard, Z.L. Zhang, A. Kluken, Prediction of the performance of welded aluminium nodes for car body applications, in: Proceedings of the International Body Engineering Conference, Body Design and Engineering (IBEC'96), 1996, pp. 17±24. [5] J. édegard, Z.L. Zhang, A. Kluken, The signi®cance of HAZ (heat aected zone) and weld metal properties on the performance of welded aluminium nodes, in: Proceedings of the International Body Engineering Conference, (IBEC'97), Stuttgart, 30/9±2/10, 1997. [6] WE L D S I M , User's manual, IFE, 1999. [7] AB A Q U S , User's Manual, version 5.8, 1998. [8] A. Gurson, J. Mater. Technol. (1968). [9] Z.L. Zhang, C. Thaulow, J. édeg ard, A complete Gurson model approach for ductile fracture, Eng. Fract. Mech. 67 (2000) 155±168.