The main goal of this work is to present a three-dimensional mechanical model for the numerical s... more The main goal of this work is to present a three-dimensional mechanical model for the numerical simulation of the deep-drawing process. The model takes into account the large elastoplastic strains and rotations that occur in the deep-drawing process. Hill’s orthotropic yield criteria with isotropic and kinematics hardening describes the anisotropic plastic properties of the sheet. Coulomb’s classical law models the frictional contact problem treated with an augmented Lagrangian approach. This method yields a mixed system where the final unknowns of the problem are static (frictional contact forces) and kinematic (displacements) variables. To solve this problem use is made of a fully implicit algorithm of Newton–Raphson type. Three-dimensional isoparametric finite elements with a selective reduced integration are used for the spatial discretization of the deformed body. The geometry of the forming tools is modelled by Bézier surfaces. The numerical results of the deep-drawing of a square cup are presented to focus their good agreement with the results of experiment.
International Journal of Solids and Structures, 2006
The development of depth sensing indentation equipment has allowed easy and reliable determinatio... more The development of depth sensing indentation equipment has allowed easy and reliable determination of two of the most popular measured mechanical properties of materials: the hardness and the Young’s modulus. However, some difficulties emerge in the experimental procedure to calculate accurate values of these properties. This is related to, for example, the tip geometrical imperfections of the diamond pyramidal indenter and the definition of the contact area at the maximum load. Being so, numerical simulation of ultramicrohardness tests can be a helpful tool for better understanding of the influence of these parameters on procedures for determining the hardness and the Young’s modulus. For this purpose, specific finite element simulation software, HAFILM, was developed to simulate the ultramicrohardness tests. Different mesh refinements were tested because of the dependence between the values of the mechanical properties and the size of the finite element mesh. Another parameter studied in this work is the value of the friction coefficient between the indenter and the sample in the numerical simulation. In order to obtain numerical results close to reality, a common geometry and size of the imperfection of the tip of Vickers indenter was taken into account for the numerical description of the indenter.
This paper presents two procedures for the identification of material parameters, a genetic algor... more This paper presents two procedures for the identification of material parameters, a genetic algorithm and a gradient-based algorithm. These algorithms enable both the yield criterion and the work hardening parameters to be identified. A hybrid algorithm is also used, which is a combination of the former two, in such a way that the result of the genetic algorithm is considered as the initial values for the gradient-based algorithm. The objective of this approach is to improve the performance of the gradient-based algorithm, which is strongly dependent on the initial set of results. The constitutive model used to compare the three different optimization schemes uses the Barlat'91 yield criterion, an isotropic Voce type law and a kinematic Lemaitre and Chaboche law, which is suitable for the case of aluminium alloys. In order to analyse the effectiveness of this optimization procedure, numerical and experimental results for an EN AW-5754 aluminium alloy are compared.
The deformation behaviour of prestrained metal sheets is analysed in this work. The non-uniform d... more The deformation behaviour of prestrained metal sheets is analysed in this work. The non-uniform deformation observed during reloading in tension was studied, by following deformation in different regions of the samples. It takes into account the presence of geometrical defects in the samples and explains the importance of mechanical behaviour. A simplified analysis was used, to model the behaviour in tension of a metallic specimen with geometrical imperfection. The flow behaviour is described using a Swift law equation, which includes strain-rate sensitivity. A modified law was used for prestrained materials and this incorporates the plastic prestrain value, adjusted to the path change. The model predicts imperfection growth kinetics with strain, and strain saturation in the homogeneous region, due to the onset of necking.
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 1999
The effect of cross section variation on formability of prestrained samples has been investigated... more The effect of cross section variation on formability of prestrained samples has been investigated using finite element simulations of a standard sheet tensile test. The mechanical model takes into account large elastoplastic strains and rotations that occur during deformation. Hill’s orthotropic yield criterion with isotropic hardening describes the anisotropic plastic properties of the sheet. The isotropic hardening is modelled by a modified Swift law that describes the response of prestrained materials in reloading. Two different situations were simulated: reloading in tension of samples with constant cross sectional area and reloading in tension of samples with two zones of slightly different cross sectional areas. The results show that the strain distribution along the tensile axis of a prestrained sample depends on the level of the prestrain and also on the presence and size of geometrical fluctuations in the cross section, which always occur in experimental samples. This dependence is higher for materials with lower work-hardening rates.
This paper seeks to present a new approach to reverse analysis in depth-sensing indentation which... more This paper seeks to present a new approach to reverse analysis in depth-sensing indentation which makes use of numerical simulation. This methodology allows the results of experimental hardness tests acquired with single indenter geometry to be used to determine the plastic properties of materials. Forward and reverse analyses of high deformation three-dimensional numerical simulations of Vickers indentation tests are used to determine different mechanical properties of materials: Young’s modulus, yield stress and strain-hardening exponent. The Vickers indenter used in the numerical simulations is formulated as a rigid body and takes into account the presence of the most common imperfection of the tip, so-called offset. The contact friction between the Vickers indenter and the deformable body is also considered. The forward analysis uses materials with Young’s modulus values from 50 to 600 GPa, yield stress values from 0.3 to 10 GPa and strain-hardening exponents from 0 to 0.6; the Poisson ratio did not vary from 0.3. The representative plastic strain εr and the correspondent stress σr, as previously defined by other authors [Dao M, Chollacoop N, Vliet KJ, Venkatesh TA, Suresh S. Acta Mater 2001;49:3899], were identified by an independent numerical method. The values of the representative plastic strain εr obtained for the Vickers indenter confirm those of the above-mentioned authors, despite showing a slight influence from the Young’s modulus values. The forward study enables the production of a unique plot of the hardness HIT vs. representative stress σr, where both are normalized by the Young’s modulus E. The proposed reverse analysis provides a unique solution to the representative stress σr and the strain-hardening exponent, n, given that the Young’s modulus is predetermined from the experimental hardness test. Depending on the material properties, the value of n can be more or less sensitive to the scatter of the experimental results obtained using the depth-sensing equipment, particularly the stiffness of the unloading curve. The validity of the proposed reverse analysis method is checked using three real materials: stamping quality steel (DC 06), stainless AISI 304 steel and BK7 glass.
Tailor-welded blanks made of dissimilar, uniform or non-uniform thickness materials have potentia... more Tailor-welded blanks made of dissimilar, uniform or non-uniform thickness materials have potential applications in automobile industries. Compared to the base metal, the formability of tailor-welded blank is less due to the presence of weld area and strength mismatch between component blanks. Most sheet metals used to produce tailor-welded blanks have anisotropy induced during pre-processing stage due to large deformation. The orientation of the blank sheet rolling direction and the combination of the blank sheet materials has significant influence on the deformation behaviour. The effect of anisotropy in the tailor-welded blank and the orientation of blank sheets rolling direction during deep-drawing process are investigated in this study. Finite element analysis of deep-drawing mild steel and dual-phase steel tailor-welded blank models was carried out using research purpose FE code DD3IMP; to form a basis for tailor-welded blank design and development for a part. Anisotropy in the blank sheets has moderate influence and its contribution to increased material flow depends on the mechanical properties of the blank sheets. Appropriate combination of the blank sheets rolling direction orientation can significantly improve the formability of the tailor-welded blank in the deep-drawing of square cup.
Depth-sensing indentation equipment is widely used for evaluation of the hardness and Young&a... more Depth-sensing indentation equipment is widely used for evaluation of the hardness and Young's modulus of materials. The depth resolution of this technique allows the use of ultra-low loads. However, aspects related to the determination of the contact area under indentation should be cautiously considered when using this equipment. These are related to the geometrical imperfections of the tip, the diamond
This study deals with the experimental and numerical reverse re-drawing of cylindrical cups. Expe... more This study deals with the experimental and numerical reverse re-drawing of cylindrical cups. Experiments were carried out on a classical tensile test machine of maximum load 100 kN. Experimental data consist of force–displacement curves of the punch and thickness distribution in the cup wall at 0°, 45° and 90° to the rolling direction (RD). The drawing process was simulated using both the dynamic explicit finite element code Pam-Stamp and the static implicit home code DD3IMP. Two extreme cases have been considered: a dynamic explicit calculation with shell elements, leading to low CPU times and a static implicit calculation with solid elements, which is CPU time-consuming. The accuracy of these numerical results, when compared to experimental ones, is then studied. Moreover, the occurrence of strain path changes during the first and the second stage is also investigated in order to estimate their influence.
A modified Swift law to describe the evolution of the mechanical behaviour in reloading of prestr... more A modified Swift law to describe the evolution of the mechanical behaviour in reloading of prestrained materials is proposed in this work. This equation is deduced from the original Swift law by including a parameter that accounts for the effect of strain path change. This parameter depends on the value of the yield stress and the subsequent work-hardening behaviour in reloading. The new equation predicts well the general mechanical behaviour in the second path for copper and steel. In particular, it predicts accurately the strain value for which necking occurs during reloading and fits experimental stress-strain curves well. The flow equation formulated remains sufficiently simple to be applied in finite element modelling of prestrained materials. However, since the parameter, which is needed for the modified Swift law, must be previously known, the strain path change itself cannot be part of the simulation.
Optimization of process parameters in sheet metal forming is an important task to reduce manufact... more Optimization of process parameters in sheet metal forming is an important task to reduce manufacturing cost. To determine the optimum values of the process parameters, it is essential to find their influence on the deformation behaviour of the sheet metal. The significance of three important process parameters namely, die radius, blank holder force and friction coefficient on the deep-drawing characteristics of a stainless steel axi-symmetric cup was determined. Finite element method combined with Taguchi technique form a refined predictive tool to determine the influence of forming process parameters. The Taguchi method was employed to identify the relative influence of each process parameter considered in this study. A reduced set of finite element simulations were carried out as per the Taguchi orthogonal array. Based on the predicted thickness distribution of the deep drawn circular cup and analysis of variance test, it is evident that die radius has the greatest influence on the deep drawing of stainless steel blank sheet followed by the blank holder force and the friction coefficient. Further, it is shown that a blank holder force application and local lubrication scheme improved the quality of the formed part.
The present paper aims at reviewing some recent progress in developing advanced constitutive mode... more The present paper aims at reviewing some recent progress in developing advanced constitutive models which are devoted to the description of the anisotropic work-hardening behaviour under strain-path changes at large strains of metallic materials. After reviewing some microscopic and macroscopic experimental evidence, a physically-based phenomenological model using four internal state tensor variables is presented. This model can be simplified into several classical phenomenological models in order to take into account either the isotropic or the kinematic hardening or both. The implementation of the proposed models in the in-house finite element code DD3IMP is briefly recalled. Numerical simulations of the stamping of a curved rail are carried out in order to evaluate the accuracy and the efficiency of the proposed models in modelling the springback.
The last decade has witnessed many advances and a lot of improvement in FE codes for simulation o... more The last decade has witnessed many advances and a lot of improvement in FE codes for simulation of sheet metal forming processes. Such advances could be followed mainly by benchmarks proposed in Numisheet conferences. It was possible to notice that the scatter of results among numerical codes has decreased so significantly that recently scattering of experimental results among different corporations was evident. However in order to pursue further developments and validate numerical results it is fundamental to have reliable reference experimental data. This is one of the objectives of a current IMS project called 3DS-Digital Die Design System.In this paper such objectives are presented as well as some of the proposed benchmarks. It is intended to show part of the developed work concerning tool design and manufacturing methodology. Also an experimental case study about the use of piercing holes in parts and the use of counter-punch is presented. Finally some simulation results are also shown concerning one of the proposed benchmarks.
The deformation behaviour of prestrained metal sheets is analysed in this work. The non-uniform d... more The deformation behaviour of prestrained metal sheets is analysed in this work. The non-uniform deformation observed during reloading in tension was studied, by following deformation in different regions of the samples. It takes into account the presence of geometrical defects in the samples and explains the importance of mechanical behaviour. A simplified analysis was used, to model the behaviour in tension of a metallic specimen with geometrical imperfection. The flow behaviour is described using a Swift law equation, which includes strain-rate sensitivity. A modified law was used for prestrained materials and this incorporates the plastic prestrain value, adjusted to the path change. The model predicts imperfection growth kinetics with strain, and strain saturation in the homogeneous region, due to the onset of necking.
The main goal of this study is to evaluate the influence of work-hardening modeling in springback... more The main goal of this study is to evaluate the influence of work-hardening modeling in springback prediction in the first phase of the Numisheet’05 “Benchmark 3”: the U-shape “Channel Draw”. Several work-hardening constitutive models are used in order to allow the different materials’ mechanical behavior to be better described: the Swift law (a power law) or a Voce type saturation law to describe the classical isotropic work-hardening; a Lemaître and Chaboche type law to model the non-linear kinematic hardening, which can be combined with the previous two; and Teodosiu’s microstructural work-hardening model. This analysis was carried out using two steels currently used in the automotive industry: mild (DC06) and dual phase (DP600). Haddadi et al. [Haddadi, H., Bouvier, S., Banu, M., Maier, C., Teodosiu, C., 2006. Towards an accurate description of the anisotropic behaviour of sheet metals under large plastic deformations: Modelling, numerical analysis and identification. Int. J. Plasticity 22 (12), 2226-2271] performed the mechanical characterization of these steels, as well as the identification of the constitutive parameters of each work-hardening model, based on an appropriate set of experimental data such as uniaxial tensile tests, monotonic and Bauschinger simple shear tests and orthogonal strain-path change tests, all at various orientations with respect to the rolling direction of the sheet. All the simulations were carried out with the in-house FE code DD3IMP. The selected sheet metal formed component induces high levels of equivalent plastic strain. However, for the several work-hardening models tested, the differences in springback prediction are not significantly higher than those previously reported for components with lower equivalent plastic strain levels. It is shown that these differences can be related to the predicted through-thickness stress gradients. The comparative significance of both equivalent plastic strain levels and strain-path changes in the through-thickness stress gradients is discussed.
The influence of the mismatch between material properties and constraint on the plastic deformati... more The influence of the mismatch between material properties and constraint on the plastic deformation behaviour of the heat affected zone of welds in high strength steels is investigated in this study, using finite element simulations. An elastoplastic implicit three-dimensional finite element code (EPIM3D) was used in the analysis. The paper presents the mechanical model of the code and the methodology used for the numerical simulation of the tensile test of welded joints. Numerical results of the tensile test of welded samples with different hypothetical widths for the Heat Affected Zone and various material mismatch levels are shown. The analysis concerns the overall strength and ductility of the joint and in relation to the plastic behaviour of the heat affected zone. The influence of the yield stress, tensile strength and constraint on the stress and plastic strain distribution in the soft heat affected zone is also discussed.
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 1999
The effect of cross section variation on formability of prestrained samples has been investigated... more The effect of cross section variation on formability of prestrained samples has been investigated using finite element simulations of a standard sheet tensile test. The mechanical model takes into account large elastoplastic strains and rotations that occur during deformation. Hill’s orthotropic yield criterion with isotropic hardening describes the anisotropic plastic properties of the sheet. The isotropic hardening is modelled by a modified Swift law that describes the response of prestrained materials in reloading. Two different situations were simulated: reloading in tension of samples with constant cross sectional area and reloading in tension of samples with two zones of slightly different cross sectional areas. The results show that the strain distribution along the tensile axis of a prestrained sample depends on the level of the prestrain and also on the presence and size of geometrical fluctuations in the cross section, which always occur in experimental samples. This dependence is higher for materials with lower work-hardening rates.
Deep drawing is one of the most used sheet metal forming processes in the production of automotiv... more Deep drawing is one of the most used sheet metal forming processes in the production of automotive components, LPG bottles and household goods, among others. The formability of a blank depends on the process parameters such as blank holder force, lubrication, punch and die radii, die-punch clearance, in addition to material properties and thickness of the sheet metal. This paper presents a numerical study made on the deep drawing of LPG bottles. In particular, the application of both variable blank holder forces and contact friction conditions at specific location during deep drawing are considered. The numerical simulations were carried out with DD3IMP FE code. A variable blank holder force strategy was applied and the numerical results were compared with results from other blank holder force schemes. It is evident that the proposed variable blank holder force scheme reduces the blank thinning when compared to other schemes; the friction coefficient also has a significant influence on the stress–strain distribution.
The main goal of this work is to present a three-dimensional mechanical model for the numerical s... more The main goal of this work is to present a three-dimensional mechanical model for the numerical simulation of the deep-drawing process. The model takes into account the large elastoplastic strains and rotations that occur in the deep-drawing process. Hill’s orthotropic yield criteria with isotropic and kinematics hardening describes the anisotropic plastic properties of the sheet. Coulomb’s classical law models the frictional contact problem treated with an augmented Lagrangian approach. This method yields a mixed system where the final unknowns of the problem are static (frictional contact forces) and kinematic (displacements) variables. To solve this problem use is made of a fully implicit algorithm of Newton–Raphson type. Three-dimensional isoparametric finite elements with a selective reduced integration are used for the spatial discretization of the deformed body. The geometry of the forming tools is modelled by Bézier surfaces. The numerical results of the deep-drawing of a square cup are presented to focus their good agreement with the results of experiment.
International Journal of Solids and Structures, 2006
The development of depth sensing indentation equipment has allowed easy and reliable determinatio... more The development of depth sensing indentation equipment has allowed easy and reliable determination of two of the most popular measured mechanical properties of materials: the hardness and the Young’s modulus. However, some difficulties emerge in the experimental procedure to calculate accurate values of these properties. This is related to, for example, the tip geometrical imperfections of the diamond pyramidal indenter and the definition of the contact area at the maximum load. Being so, numerical simulation of ultramicrohardness tests can be a helpful tool for better understanding of the influence of these parameters on procedures for determining the hardness and the Young’s modulus. For this purpose, specific finite element simulation software, HAFILM, was developed to simulate the ultramicrohardness tests. Different mesh refinements were tested because of the dependence between the values of the mechanical properties and the size of the finite element mesh. Another parameter studied in this work is the value of the friction coefficient between the indenter and the sample in the numerical simulation. In order to obtain numerical results close to reality, a common geometry and size of the imperfection of the tip of Vickers indenter was taken into account for the numerical description of the indenter.
This paper presents two procedures for the identification of material parameters, a genetic algor... more This paper presents two procedures for the identification of material parameters, a genetic algorithm and a gradient-based algorithm. These algorithms enable both the yield criterion and the work hardening parameters to be identified. A hybrid algorithm is also used, which is a combination of the former two, in such a way that the result of the genetic algorithm is considered as the initial values for the gradient-based algorithm. The objective of this approach is to improve the performance of the gradient-based algorithm, which is strongly dependent on the initial set of results. The constitutive model used to compare the three different optimization schemes uses the Barlat'91 yield criterion, an isotropic Voce type law and a kinematic Lemaitre and Chaboche law, which is suitable for the case of aluminium alloys. In order to analyse the effectiveness of this optimization procedure, numerical and experimental results for an EN AW-5754 aluminium alloy are compared.
The deformation behaviour of prestrained metal sheets is analysed in this work. The non-uniform d... more The deformation behaviour of prestrained metal sheets is analysed in this work. The non-uniform deformation observed during reloading in tension was studied, by following deformation in different regions of the samples. It takes into account the presence of geometrical defects in the samples and explains the importance of mechanical behaviour. A simplified analysis was used, to model the behaviour in tension of a metallic specimen with geometrical imperfection. The flow behaviour is described using a Swift law equation, which includes strain-rate sensitivity. A modified law was used for prestrained materials and this incorporates the plastic prestrain value, adjusted to the path change. The model predicts imperfection growth kinetics with strain, and strain saturation in the homogeneous region, due to the onset of necking.
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 1999
The effect of cross section variation on formability of prestrained samples has been investigated... more The effect of cross section variation on formability of prestrained samples has been investigated using finite element simulations of a standard sheet tensile test. The mechanical model takes into account large elastoplastic strains and rotations that occur during deformation. Hill’s orthotropic yield criterion with isotropic hardening describes the anisotropic plastic properties of the sheet. The isotropic hardening is modelled by a modified Swift law that describes the response of prestrained materials in reloading. Two different situations were simulated: reloading in tension of samples with constant cross sectional area and reloading in tension of samples with two zones of slightly different cross sectional areas. The results show that the strain distribution along the tensile axis of a prestrained sample depends on the level of the prestrain and also on the presence and size of geometrical fluctuations in the cross section, which always occur in experimental samples. This dependence is higher for materials with lower work-hardening rates.
This paper seeks to present a new approach to reverse analysis in depth-sensing indentation which... more This paper seeks to present a new approach to reverse analysis in depth-sensing indentation which makes use of numerical simulation. This methodology allows the results of experimental hardness tests acquired with single indenter geometry to be used to determine the plastic properties of materials. Forward and reverse analyses of high deformation three-dimensional numerical simulations of Vickers indentation tests are used to determine different mechanical properties of materials: Young’s modulus, yield stress and strain-hardening exponent. The Vickers indenter used in the numerical simulations is formulated as a rigid body and takes into account the presence of the most common imperfection of the tip, so-called offset. The contact friction between the Vickers indenter and the deformable body is also considered. The forward analysis uses materials with Young’s modulus values from 50 to 600 GPa, yield stress values from 0.3 to 10 GPa and strain-hardening exponents from 0 to 0.6; the Poisson ratio did not vary from 0.3. The representative plastic strain εr and the correspondent stress σr, as previously defined by other authors [Dao M, Chollacoop N, Vliet KJ, Venkatesh TA, Suresh S. Acta Mater 2001;49:3899], were identified by an independent numerical method. The values of the representative plastic strain εr obtained for the Vickers indenter confirm those of the above-mentioned authors, despite showing a slight influence from the Young’s modulus values. The forward study enables the production of a unique plot of the hardness HIT vs. representative stress σr, where both are normalized by the Young’s modulus E. The proposed reverse analysis provides a unique solution to the representative stress σr and the strain-hardening exponent, n, given that the Young’s modulus is predetermined from the experimental hardness test. Depending on the material properties, the value of n can be more or less sensitive to the scatter of the experimental results obtained using the depth-sensing equipment, particularly the stiffness of the unloading curve. The validity of the proposed reverse analysis method is checked using three real materials: stamping quality steel (DC 06), stainless AISI 304 steel and BK7 glass.
Tailor-welded blanks made of dissimilar, uniform or non-uniform thickness materials have potentia... more Tailor-welded blanks made of dissimilar, uniform or non-uniform thickness materials have potential applications in automobile industries. Compared to the base metal, the formability of tailor-welded blank is less due to the presence of weld area and strength mismatch between component blanks. Most sheet metals used to produce tailor-welded blanks have anisotropy induced during pre-processing stage due to large deformation. The orientation of the blank sheet rolling direction and the combination of the blank sheet materials has significant influence on the deformation behaviour. The effect of anisotropy in the tailor-welded blank and the orientation of blank sheets rolling direction during deep-drawing process are investigated in this study. Finite element analysis of deep-drawing mild steel and dual-phase steel tailor-welded blank models was carried out using research purpose FE code DD3IMP; to form a basis for tailor-welded blank design and development for a part. Anisotropy in the blank sheets has moderate influence and its contribution to increased material flow depends on the mechanical properties of the blank sheets. Appropriate combination of the blank sheets rolling direction orientation can significantly improve the formability of the tailor-welded blank in the deep-drawing of square cup.
Depth-sensing indentation equipment is widely used for evaluation of the hardness and Young&a... more Depth-sensing indentation equipment is widely used for evaluation of the hardness and Young's modulus of materials. The depth resolution of this technique allows the use of ultra-low loads. However, aspects related to the determination of the contact area under indentation should be cautiously considered when using this equipment. These are related to the geometrical imperfections of the tip, the diamond
This study deals with the experimental and numerical reverse re-drawing of cylindrical cups. Expe... more This study deals with the experimental and numerical reverse re-drawing of cylindrical cups. Experiments were carried out on a classical tensile test machine of maximum load 100 kN. Experimental data consist of force–displacement curves of the punch and thickness distribution in the cup wall at 0°, 45° and 90° to the rolling direction (RD). The drawing process was simulated using both the dynamic explicit finite element code Pam-Stamp and the static implicit home code DD3IMP. Two extreme cases have been considered: a dynamic explicit calculation with shell elements, leading to low CPU times and a static implicit calculation with solid elements, which is CPU time-consuming. The accuracy of these numerical results, when compared to experimental ones, is then studied. Moreover, the occurrence of strain path changes during the first and the second stage is also investigated in order to estimate their influence.
A modified Swift law to describe the evolution of the mechanical behaviour in reloading of prestr... more A modified Swift law to describe the evolution of the mechanical behaviour in reloading of prestrained materials is proposed in this work. This equation is deduced from the original Swift law by including a parameter that accounts for the effect of strain path change. This parameter depends on the value of the yield stress and the subsequent work-hardening behaviour in reloading. The new equation predicts well the general mechanical behaviour in the second path for copper and steel. In particular, it predicts accurately the strain value for which necking occurs during reloading and fits experimental stress-strain curves well. The flow equation formulated remains sufficiently simple to be applied in finite element modelling of prestrained materials. However, since the parameter, which is needed for the modified Swift law, must be previously known, the strain path change itself cannot be part of the simulation.
Optimization of process parameters in sheet metal forming is an important task to reduce manufact... more Optimization of process parameters in sheet metal forming is an important task to reduce manufacturing cost. To determine the optimum values of the process parameters, it is essential to find their influence on the deformation behaviour of the sheet metal. The significance of three important process parameters namely, die radius, blank holder force and friction coefficient on the deep-drawing characteristics of a stainless steel axi-symmetric cup was determined. Finite element method combined with Taguchi technique form a refined predictive tool to determine the influence of forming process parameters. The Taguchi method was employed to identify the relative influence of each process parameter considered in this study. A reduced set of finite element simulations were carried out as per the Taguchi orthogonal array. Based on the predicted thickness distribution of the deep drawn circular cup and analysis of variance test, it is evident that die radius has the greatest influence on the deep drawing of stainless steel blank sheet followed by the blank holder force and the friction coefficient. Further, it is shown that a blank holder force application and local lubrication scheme improved the quality of the formed part.
The present paper aims at reviewing some recent progress in developing advanced constitutive mode... more The present paper aims at reviewing some recent progress in developing advanced constitutive models which are devoted to the description of the anisotropic work-hardening behaviour under strain-path changes at large strains of metallic materials. After reviewing some microscopic and macroscopic experimental evidence, a physically-based phenomenological model using four internal state tensor variables is presented. This model can be simplified into several classical phenomenological models in order to take into account either the isotropic or the kinematic hardening or both. The implementation of the proposed models in the in-house finite element code DD3IMP is briefly recalled. Numerical simulations of the stamping of a curved rail are carried out in order to evaluate the accuracy and the efficiency of the proposed models in modelling the springback.
The last decade has witnessed many advances and a lot of improvement in FE codes for simulation o... more The last decade has witnessed many advances and a lot of improvement in FE codes for simulation of sheet metal forming processes. Such advances could be followed mainly by benchmarks proposed in Numisheet conferences. It was possible to notice that the scatter of results among numerical codes has decreased so significantly that recently scattering of experimental results among different corporations was evident. However in order to pursue further developments and validate numerical results it is fundamental to have reliable reference experimental data. This is one of the objectives of a current IMS project called 3DS-Digital Die Design System.In this paper such objectives are presented as well as some of the proposed benchmarks. It is intended to show part of the developed work concerning tool design and manufacturing methodology. Also an experimental case study about the use of piercing holes in parts and the use of counter-punch is presented. Finally some simulation results are also shown concerning one of the proposed benchmarks.
The deformation behaviour of prestrained metal sheets is analysed in this work. The non-uniform d... more The deformation behaviour of prestrained metal sheets is analysed in this work. The non-uniform deformation observed during reloading in tension was studied, by following deformation in different regions of the samples. It takes into account the presence of geometrical defects in the samples and explains the importance of mechanical behaviour. A simplified analysis was used, to model the behaviour in tension of a metallic specimen with geometrical imperfection. The flow behaviour is described using a Swift law equation, which includes strain-rate sensitivity. A modified law was used for prestrained materials and this incorporates the plastic prestrain value, adjusted to the path change. The model predicts imperfection growth kinetics with strain, and strain saturation in the homogeneous region, due to the onset of necking.
The main goal of this study is to evaluate the influence of work-hardening modeling in springback... more The main goal of this study is to evaluate the influence of work-hardening modeling in springback prediction in the first phase of the Numisheet’05 “Benchmark 3”: the U-shape “Channel Draw”. Several work-hardening constitutive models are used in order to allow the different materials’ mechanical behavior to be better described: the Swift law (a power law) or a Voce type saturation law to describe the classical isotropic work-hardening; a Lemaître and Chaboche type law to model the non-linear kinematic hardening, which can be combined with the previous two; and Teodosiu’s microstructural work-hardening model. This analysis was carried out using two steels currently used in the automotive industry: mild (DC06) and dual phase (DP600). Haddadi et al. [Haddadi, H., Bouvier, S., Banu, M., Maier, C., Teodosiu, C., 2006. Towards an accurate description of the anisotropic behaviour of sheet metals under large plastic deformations: Modelling, numerical analysis and identification. Int. J. Plasticity 22 (12), 2226-2271] performed the mechanical characterization of these steels, as well as the identification of the constitutive parameters of each work-hardening model, based on an appropriate set of experimental data such as uniaxial tensile tests, monotonic and Bauschinger simple shear tests and orthogonal strain-path change tests, all at various orientations with respect to the rolling direction of the sheet. All the simulations were carried out with the in-house FE code DD3IMP. The selected sheet metal formed component induces high levels of equivalent plastic strain. However, for the several work-hardening models tested, the differences in springback prediction are not significantly higher than those previously reported for components with lower equivalent plastic strain levels. It is shown that these differences can be related to the predicted through-thickness stress gradients. The comparative significance of both equivalent plastic strain levels and strain-path changes in the through-thickness stress gradients is discussed.
The influence of the mismatch between material properties and constraint on the plastic deformati... more The influence of the mismatch between material properties and constraint on the plastic deformation behaviour of the heat affected zone of welds in high strength steels is investigated in this study, using finite element simulations. An elastoplastic implicit three-dimensional finite element code (EPIM3D) was used in the analysis. The paper presents the mechanical model of the code and the methodology used for the numerical simulation of the tensile test of welded joints. Numerical results of the tensile test of welded samples with different hypothetical widths for the Heat Affected Zone and various material mismatch levels are shown. The analysis concerns the overall strength and ductility of the joint and in relation to the plastic behaviour of the heat affected zone. The influence of the yield stress, tensile strength and constraint on the stress and plastic strain distribution in the soft heat affected zone is also discussed.
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 1999
The effect of cross section variation on formability of prestrained samples has been investigated... more The effect of cross section variation on formability of prestrained samples has been investigated using finite element simulations of a standard sheet tensile test. The mechanical model takes into account large elastoplastic strains and rotations that occur during deformation. Hill’s orthotropic yield criterion with isotropic hardening describes the anisotropic plastic properties of the sheet. The isotropic hardening is modelled by a modified Swift law that describes the response of prestrained materials in reloading. Two different situations were simulated: reloading in tension of samples with constant cross sectional area and reloading in tension of samples with two zones of slightly different cross sectional areas. The results show that the strain distribution along the tensile axis of a prestrained sample depends on the level of the prestrain and also on the presence and size of geometrical fluctuations in the cross section, which always occur in experimental samples. This dependence is higher for materials with lower work-hardening rates.
Deep drawing is one of the most used sheet metal forming processes in the production of automotiv... more Deep drawing is one of the most used sheet metal forming processes in the production of automotive components, LPG bottles and household goods, among others. The formability of a blank depends on the process parameters such as blank holder force, lubrication, punch and die radii, die-punch clearance, in addition to material properties and thickness of the sheet metal. This paper presents a numerical study made on the deep drawing of LPG bottles. In particular, the application of both variable blank holder forces and contact friction conditions at specific location during deep drawing are considered. The numerical simulations were carried out with DD3IMP FE code. A variable blank holder force strategy was applied and the numerical results were compared with results from other blank holder force schemes. It is evident that the proposed variable blank holder force scheme reduces the blank thinning when compared to other schemes; the friction coefficient also has a significant influence on the stress–strain distribution.
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Papers by Luis Menezes