This paper presents an experimental characterization of the quasi-static mechanical response of a... more This paper presents an experimental characterization of the quasi-static mechanical response of a TA-6V titanium alloy in sheet form. Monotonic tests, such as uniaxial tension and compression, plane strain and simple shear, were conducted along several orientations in the plane of the sheet in order to investigate the plastic anisotropy and the tension-compression asymmetry displayed by the material at the macroscopic scale. It was observed a moderate anisotropy in yielding while the anisotropy in rratios is very pronounced. Initial yielding is described using criteria that account for both plastic anisotropy and strength differential effects. Comparison between experimental data and FE simulation results illustrates the ability of the model to predict the mechanical response of TA-6V.
An accurate description of the deformation response of AZ31 Mg under changing strain paths requir... more An accurate description of the deformation response of AZ31 Mg under changing strain paths requires consideration of its strong anisotropy and its evolution with accumulated plastic deformation. In this paper, the viscoplastic self-consistent mean field crystal plasticity model, VPSC, is used for modeling the room-temperature deformation of rolled AZ31 Mg for a variety of loading paths. First, a step-by-step procedure, to calibrate the material parameters based on simple monotonic tensile and compressive mechanical test data is outlined. The good agreement between measured and predicted textures for these strain paths attest to the robustness of the identification. Next, it is investigated whether with the same set of parameters it is possible to predict the response of a thinner AZ31 Mg sheet. Specifically, it is shown that the model can predict with accuracy the macroscopic stress-strain response and texture evolution for loadings involving stress path changes. The interplay between slip and twinning and its influence on work hardening are well described.
In this paper an analytical yield criterion for description of the plastic behavior of face-cente... more In this paper an analytical yield criterion for description of the plastic behavior of face-centered cubic single crystals is presented. The new criterion is written in terms of the generalized invariants of the stress deviator proposed by Cazacu and Barlat (Int J Eng Sci 41:1367–1385, 2003 [1]), specialized to cubic symmetry. The octahedral projections of the yield surfaces for different crystal orientations according to the new model are presented, and compared with the yield surfaces according to the regularized Schmid law (Bishop and Hill, in Lond Edinb Dublin Philos Mag J Sci 42:1298–1307 (1951) [2], Darrieulat and Piot, in Int J Plas 12:575–612 (1996) [3]).
An anisotropic viscoplastic constitutive model was developed for the description of the high-stra... more An anisotropic viscoplastic constitutive model was developed for the description of the high-strain rate behaviour of zirconium, a HCP metal that exhibits strength differential effects and strong anisotropic strain hardening. The evolution laws for the strength differential parameter and the anisotropy coefficients involved in the expression of the yield criterion were obtained based on numerical tests performed with a crystal plasticity model. The strain rate dependent parameters involved in the formulation were determined from results of dynamic in-plane tests performed on a high purity zirconium plate [9, 10] on a Split Hopkinson Pressure Bar (SHPB). Simulations of the Taylor impact test were conducted using the finite element code ABAQUS with the anisotropic viscoplastic model. The very good agreement between the simulated and experimental post-test geometries of the Taylor specimens in terms of major and minor side profiles and impact interface footprints shows the ability of the phenomenological model to capture the influence of twinning on texture evolution.
The paper is dealing with a general, invariant, formulation of a failure condition for an anisotr... more The paper is dealing with a general, invariant, formulation of a failure condition for an anisotropic compressible rock. The invariant formulation is thought in conjunction with a general formulation of a viscoplastic constitutive equation for that rock, where this failure condition will play the role of {open_quotes}short-term{close_quotes} failure condition. The data available (due to H. Niandou and obtained at the laboratory LML Lille URA CNRS 1444 from France) were obtained in triaxial tests and provide the stress at failure for various orientations of the bedding planes with respect to the axial loading direction. We use the well known representation theorem according to which the failure function must depend not only on the invariants of the stress tensor, but also on the mixed invariants: tr M{sigma} and tr M{sigma}{sup 2}, where M = s{sub 1} {direct_product} s{sub 1} and s{sub 1} is the normal to the bedding plane. Using the data we first determine the form of the failure condition formulated in terms of stress invariants, for several orientations of the bedding planes with respect to the direction in which acts the main compressive stress, and which is defined by an angle 0. Then the coefficients of these failure conditions aremore » made functions on this angle 0, which in turn is expressed as a function of the mixed invariants tr M{sigma}{prime} and II{sub {sigma}{prime}} (the second invariant of the stress deviator). All the coefficients involved in this generally formulated criterion are fully determined from the data.« less
In this paper, the new single crystal yield criterion developed by Cazacu et al. [1] is used to s... more In this paper, the new single crystal yield criterion developed by Cazacu et al. [1] is used to study the effect of the initial texture on the anisotropy in plastic properties of metal sheets. The directional dependence of the yield stresses and Lankford coefficients in uniaxial tension is calculated for polycrystalline sheets with textures described in terms of a Gaussian distribution of misorientations with scatter width increasing from zero (single crystal) to 45º. It is shown that the same fidelity in predictions is obtained for an ideal texture and for textures with misorientation scatter width up to 25º. Furthermore, irrespective of the number of grains in the sample, Lankford coefficients have finite values for all loading orientations. Therefore, using this new single crystal yield criterion for the description of the plastic behavior of the constituent grains, the polycrystalline behavior can be predicted with accuracy, and at a very low computational cost. Most importantly, once the single crystal behavior is known, no additional calibration or macroscopic mechanical tests are needed in order to predict the effect of different texture components on the polycrystalline behavior.
International Journal of Solids and Structures, Apr 1, 2017
A model for description of the creep response of porous cubic single crystal is presented. The pl... more A model for description of the creep response of porous cubic single crystal is presented. The plastic potential is obtained by specializing the orthotropic potential of Stewart and Cazacu (Int. J. Solids Struct., 48, 357, 2011) to cubic symmetry. The crystal matrix material response is characterized by power law creep. The predictions of this porous plastic constitutive relation are presented for various values of stress triaxiality (mean normal stress divided by Mises effective stress) and various values of the Lode parameter L (a measure of the influence of the third invariant of the stress deviator). A strong influence of crystal orientation on the evolution of the creep strain and the porosity is predicted. For loadings along the < 100 > directions of the cubic crystal, void growth is not influenced by the value of the Lode parameter. However, for loadings such that the maximum principal stress is aligned with the [110] direction there is a strong influence of the values of the Lode parameter and the fastest rate of void growth occurs for shear loadings (one of the principal values of the applied stress deviator is zero). For loadings such that the maximum applied stress is along the [111] crystal direction the fastest rate of void growth corresponds to L=-1, while the slowest rate corresponds to L=1. These predictions are compared with corresponding predictions of the three dimensional finite deformation unit cell analysis of Srivastava and Needleman (Mech. Mater., 90, 10, 2015). It is found that the phenomenological model predicts the same trends as the cell model calculations and, in some cases, gives good quantitative agreement.
Journal of Engineering Materials and Technology-transactions of The Asme, Aug 6, 2015
Accurate description of the mechanical response of AZ31 Mg requires consideration of its strong a... more Accurate description of the mechanical response of AZ31 Mg requires consideration of its strong anisotropy both at the single crystal and polycrystal levels, and its evolution with accumulated plastic deformation. In this paper, a self-consistent mean field crystal plasticity model, viscoplastic self-consistent (VPSC), is used for modeling the room-temperature deformation of AZ31 Mg. A step-by-step procedure to calibrate the material parameters based on simple tensile and compressive mechanical test data is outlined. It is shown that the model predicts with great accuracy both the macroscopic stress–strain response and the evolving texture for these strain paths used for calibration. The stress–strain response and texture evolution for loading paths that were not used for calibration, including off-axis uniaxial loadings and simple shear, are also well described. In particular, VPSC model predicts that for uniaxial tension along the through-thickness direction, the stress–strain curve should have a sigmoidal shape.
This book details recent advances in all aspects related to scale transition in crystal plasticit... more This book details recent advances in all aspects related to scale transition in crystal plasticity and damage, with a particular focus on the challenges associated with the characterization and modeling of this class of complex interactions. The following topics are included: - Innovative characterization techniques (multi-scale characterization, SEMTEM coupling, TEM-micro-diffraction coupling, in-situ mechanical tests, localization, image correlation, displacement field measurements, tomography, etc.). - Computational crystal plasticity and damage (dislocation dynamics and ab initio calculations, microstructure evolution of polycrystals, comparison between FE, fast Fourier transform and self-consistent approaches, intragranular slip, heterogeneities, discrete approaches, etc.). The book gathers together selected papers from the invited lectures presented at the 3rd and 4th US-France Symposia organized by the editors under the auspices of the International Center for Applied Computa...
In this paper, we predict the effect of texture on the anisotropy in plastic properties of polycr... more In this paper, we predict the effect of texture on the anisotropy in plastic properties of polycrystalline metallic sheets. The constituent grain behavior is modelled using the new single crystal yield criterion developed by Cazacu, Revil, and Chandola (2017). For ideal texture components, the yield stress and plastic strain ratios can be obtained analytically. For the case of strongly textured sheets containing a spread about the ideal texture components, the polycrystalline response is obtained numerically on the basis of the same single-crystal criterion. It is shown that for textures with misorientation scatter width up to 25º, the numerical predictions are very close to those obtained analytically for an ideal texture. Furthermore, irrespective of the number of grains in the sample, Lankford coefficients have finite values for all loading orientations. Illustrative examples for sheets with textures containing a combination of few ideal texture components are also presented. The simulations of the predicted polycrystalline behavior based on the new description of the plastic behavior of the constituent grains capture the influence of individual texture components on the overall degree of anisotropy. The polycrystalline simulation results are also compared to analytical estimates obtained using the closed-form formulas for the ideal components present in the texture in conjunction with a simple law of mixtures. The analytical estimates show the same trends as the simulation results. Therefore, the trends in plastic anisotropy of the macroscopic properties can be adequately estimated analytically.
This extended comment is in response to the letter of Barlat (Int J Mater Form 2020 ) concerning ... more This extended comment is in response to the letter of Barlat (Int J Mater Form 2020 ) concerning our recent article (Chandola et al. (Int J Mater Form 12(6):943–954 2019 )). The main issue raised is an apparent “mismatch” between some of the F.E. results presented and cup forming data of Tucker (Acta Metall 9:275-286 1961 ). There is no mismatch because the simulation results presented in our paper correspond to a different material than the one used by Tucker (Acta Metall 9:275-286 1961 ). Specifically, the F.E. results correspond to an Al-Cu single crystal for which uniaxial tension characterization data were reported in Karnop and Sachs (Z Für Phys 49:480–497 1928 ) and was processed differently than Tucker’s material. Furthermore, in the letter of Barlat (Int J Mater Form 2020 ), the scope and findings of our study are misrepresented, and all the quotations from our paper are taken out of context. Detailed responses to the issues raised by Barlat (Int J Mater Form 2020 ) are given.
Generally, the plastic behavior of orthotropic metallic materials with cubic crystal structure is... more Generally, the plastic behavior of orthotropic metallic materials with cubic crystal structure is modelled with yield criteria that predict the same response in tension and compression. One drawback associated to using orthotropic yield criteria for simulation of forming processes is related to the uncertainties introduced by the methods used for parameter identification. Very recently, it was shown that advanced non-quadratic criteria such as Yld91 can be represented as polynomials in terms of stress components. Using this equivalent expression, the anisotropy coefficients involved in Yld91 can be obtained using analytical formulas in terms of only experimental flow stresses, or alternatively in terms of only Lankford coefficients for three orientations. In this paper, the predictive capabilities of Hill, Yld 91 and Cazacu calibrated using different identification procedures, either analytical or by numerical minimization are discussed. Moreover, simulation results of deep drawing are presented.
In this study, an elastic-plastic model with yielding described by a newly proposed orthotropic y... more In this study, an elastic-plastic model with yielding described by a newly proposed orthotropic yield criterion was used to model the unusual deformation of a strongly textured AA6060 alloy. Available experimental data from tension tests and results of crystal plasticity simulations were used to determine the anisotropy coefficients involved in the yield criterion. Virtual material tests using a recent polycrystalline model were performed to obtain flow stresses for loadings where experimental data were not available. The capability of the elastic-plastic model to account for the distinct anisotropy of the material is demonstrated through comparison of finite element simulations and experimental tests on both smooth and notched axisymmetric specimens of the AA6060 alloy. Specifically, for the smooth specimen, the model predicts that the minimum cross-section evolves from a circle to an ellipse while for the notched specimens, the minimum cross-section evolves from a circular shape to an approximately rectangular, or rhomboidal shape, respectively as observed in the experiments. This model can be easily implemented in finite element codes, requires reduced CPU time compared to crystal plasticity finite element simulations, and can be applied in simulations of large-scale structural applications.
In this paper, we make use of complex potentials for the problem of an elliptic hole subject to f... more In this paper, we make use of complex potentials for the problem of an elliptic hole subject to far field uniaxial tension to obtain the elastic stress distribution in the vicinity of a crack. Unlike the classical Westergaard stress distribution, the new stress field obtained is not axisymmetric in the crack plane. Using this new elastic stress field, it is possible to assess the effect of the particularities of yielding on the extent of the plastic zone near a crack. Analysis is done considering yielding governed by von Mises, Tresca, and Drucker yield criterion, respectively. It is demonstrated that the ratio between the yield stresses in uniaxial tension and pure shear of a material has a great influence on the size of the plastic zone around the crack. Specifically, the larger this ratio the larger is the plastic zone. Finite-element calculations confirm the theoretical predictions. Moreover, we derive new analytic relations between the length of the plastic zone, measured from the crack tip in the crack plane, and the external applied load for the case when yielding is governed by the von Mises and Tresca criterion, respectively.
This paper presents an experimental characterization of the quasi-static mechanical response of a... more This paper presents an experimental characterization of the quasi-static mechanical response of a TA-6V titanium alloy in sheet form. Monotonic tests, such as uniaxial tension and compression, plane strain and simple shear, were conducted along several orientations in the plane of the sheet in order to investigate the plastic anisotropy and the tension-compression asymmetry displayed by the material at the macroscopic scale. It was observed a moderate anisotropy in yielding while the anisotropy in rratios is very pronounced. Initial yielding is described using criteria that account for both plastic anisotropy and strength differential effects. Comparison between experimental data and FE simulation results illustrates the ability of the model to predict the mechanical response of TA-6V.
An accurate description of the deformation response of AZ31 Mg under changing strain paths requir... more An accurate description of the deformation response of AZ31 Mg under changing strain paths requires consideration of its strong anisotropy and its evolution with accumulated plastic deformation. In this paper, the viscoplastic self-consistent mean field crystal plasticity model, VPSC, is used for modeling the room-temperature deformation of rolled AZ31 Mg for a variety of loading paths. First, a step-by-step procedure, to calibrate the material parameters based on simple monotonic tensile and compressive mechanical test data is outlined. The good agreement between measured and predicted textures for these strain paths attest to the robustness of the identification. Next, it is investigated whether with the same set of parameters it is possible to predict the response of a thinner AZ31 Mg sheet. Specifically, it is shown that the model can predict with accuracy the macroscopic stress-strain response and texture evolution for loadings involving stress path changes. The interplay between slip and twinning and its influence on work hardening are well described.
In this paper an analytical yield criterion for description of the plastic behavior of face-cente... more In this paper an analytical yield criterion for description of the plastic behavior of face-centered cubic single crystals is presented. The new criterion is written in terms of the generalized invariants of the stress deviator proposed by Cazacu and Barlat (Int J Eng Sci 41:1367–1385, 2003 [1]), specialized to cubic symmetry. The octahedral projections of the yield surfaces for different crystal orientations according to the new model are presented, and compared with the yield surfaces according to the regularized Schmid law (Bishop and Hill, in Lond Edinb Dublin Philos Mag J Sci 42:1298–1307 (1951) [2], Darrieulat and Piot, in Int J Plas 12:575–612 (1996) [3]).
An anisotropic viscoplastic constitutive model was developed for the description of the high-stra... more An anisotropic viscoplastic constitutive model was developed for the description of the high-strain rate behaviour of zirconium, a HCP metal that exhibits strength differential effects and strong anisotropic strain hardening. The evolution laws for the strength differential parameter and the anisotropy coefficients involved in the expression of the yield criterion were obtained based on numerical tests performed with a crystal plasticity model. The strain rate dependent parameters involved in the formulation were determined from results of dynamic in-plane tests performed on a high purity zirconium plate [9, 10] on a Split Hopkinson Pressure Bar (SHPB). Simulations of the Taylor impact test were conducted using the finite element code ABAQUS with the anisotropic viscoplastic model. The very good agreement between the simulated and experimental post-test geometries of the Taylor specimens in terms of major and minor side profiles and impact interface footprints shows the ability of the phenomenological model to capture the influence of twinning on texture evolution.
The paper is dealing with a general, invariant, formulation of a failure condition for an anisotr... more The paper is dealing with a general, invariant, formulation of a failure condition for an anisotropic compressible rock. The invariant formulation is thought in conjunction with a general formulation of a viscoplastic constitutive equation for that rock, where this failure condition will play the role of {open_quotes}short-term{close_quotes} failure condition. The data available (due to H. Niandou and obtained at the laboratory LML Lille URA CNRS 1444 from France) were obtained in triaxial tests and provide the stress at failure for various orientations of the bedding planes with respect to the axial loading direction. We use the well known representation theorem according to which the failure function must depend not only on the invariants of the stress tensor, but also on the mixed invariants: tr M{sigma} and tr M{sigma}{sup 2}, where M = s{sub 1} {direct_product} s{sub 1} and s{sub 1} is the normal to the bedding plane. Using the data we first determine the form of the failure condition formulated in terms of stress invariants, for several orientations of the bedding planes with respect to the direction in which acts the main compressive stress, and which is defined by an angle 0. Then the coefficients of these failure conditions aremore » made functions on this angle 0, which in turn is expressed as a function of the mixed invariants tr M{sigma}{prime} and II{sub {sigma}{prime}} (the second invariant of the stress deviator). All the coefficients involved in this generally formulated criterion are fully determined from the data.« less
In this paper, the new single crystal yield criterion developed by Cazacu et al. [1] is used to s... more In this paper, the new single crystal yield criterion developed by Cazacu et al. [1] is used to study the effect of the initial texture on the anisotropy in plastic properties of metal sheets. The directional dependence of the yield stresses and Lankford coefficients in uniaxial tension is calculated for polycrystalline sheets with textures described in terms of a Gaussian distribution of misorientations with scatter width increasing from zero (single crystal) to 45º. It is shown that the same fidelity in predictions is obtained for an ideal texture and for textures with misorientation scatter width up to 25º. Furthermore, irrespective of the number of grains in the sample, Lankford coefficients have finite values for all loading orientations. Therefore, using this new single crystal yield criterion for the description of the plastic behavior of the constituent grains, the polycrystalline behavior can be predicted with accuracy, and at a very low computational cost. Most importantly, once the single crystal behavior is known, no additional calibration or macroscopic mechanical tests are needed in order to predict the effect of different texture components on the polycrystalline behavior.
International Journal of Solids and Structures, Apr 1, 2017
A model for description of the creep response of porous cubic single crystal is presented. The pl... more A model for description of the creep response of porous cubic single crystal is presented. The plastic potential is obtained by specializing the orthotropic potential of Stewart and Cazacu (Int. J. Solids Struct., 48, 357, 2011) to cubic symmetry. The crystal matrix material response is characterized by power law creep. The predictions of this porous plastic constitutive relation are presented for various values of stress triaxiality (mean normal stress divided by Mises effective stress) and various values of the Lode parameter L (a measure of the influence of the third invariant of the stress deviator). A strong influence of crystal orientation on the evolution of the creep strain and the porosity is predicted. For loadings along the < 100 > directions of the cubic crystal, void growth is not influenced by the value of the Lode parameter. However, for loadings such that the maximum principal stress is aligned with the [110] direction there is a strong influence of the values of the Lode parameter and the fastest rate of void growth occurs for shear loadings (one of the principal values of the applied stress deviator is zero). For loadings such that the maximum applied stress is along the [111] crystal direction the fastest rate of void growth corresponds to L=-1, while the slowest rate corresponds to L=1. These predictions are compared with corresponding predictions of the three dimensional finite deformation unit cell analysis of Srivastava and Needleman (Mech. Mater., 90, 10, 2015). It is found that the phenomenological model predicts the same trends as the cell model calculations and, in some cases, gives good quantitative agreement.
Journal of Engineering Materials and Technology-transactions of The Asme, Aug 6, 2015
Accurate description of the mechanical response of AZ31 Mg requires consideration of its strong a... more Accurate description of the mechanical response of AZ31 Mg requires consideration of its strong anisotropy both at the single crystal and polycrystal levels, and its evolution with accumulated plastic deformation. In this paper, a self-consistent mean field crystal plasticity model, viscoplastic self-consistent (VPSC), is used for modeling the room-temperature deformation of AZ31 Mg. A step-by-step procedure to calibrate the material parameters based on simple tensile and compressive mechanical test data is outlined. It is shown that the model predicts with great accuracy both the macroscopic stress–strain response and the evolving texture for these strain paths used for calibration. The stress–strain response and texture evolution for loading paths that were not used for calibration, including off-axis uniaxial loadings and simple shear, are also well described. In particular, VPSC model predicts that for uniaxial tension along the through-thickness direction, the stress–strain curve should have a sigmoidal shape.
This book details recent advances in all aspects related to scale transition in crystal plasticit... more This book details recent advances in all aspects related to scale transition in crystal plasticity and damage, with a particular focus on the challenges associated with the characterization and modeling of this class of complex interactions. The following topics are included: - Innovative characterization techniques (multi-scale characterization, SEMTEM coupling, TEM-micro-diffraction coupling, in-situ mechanical tests, localization, image correlation, displacement field measurements, tomography, etc.). - Computational crystal plasticity and damage (dislocation dynamics and ab initio calculations, microstructure evolution of polycrystals, comparison between FE, fast Fourier transform and self-consistent approaches, intragranular slip, heterogeneities, discrete approaches, etc.). The book gathers together selected papers from the invited lectures presented at the 3rd and 4th US-France Symposia organized by the editors under the auspices of the International Center for Applied Computa...
In this paper, we predict the effect of texture on the anisotropy in plastic properties of polycr... more In this paper, we predict the effect of texture on the anisotropy in plastic properties of polycrystalline metallic sheets. The constituent grain behavior is modelled using the new single crystal yield criterion developed by Cazacu, Revil, and Chandola (2017). For ideal texture components, the yield stress and plastic strain ratios can be obtained analytically. For the case of strongly textured sheets containing a spread about the ideal texture components, the polycrystalline response is obtained numerically on the basis of the same single-crystal criterion. It is shown that for textures with misorientation scatter width up to 25º, the numerical predictions are very close to those obtained analytically for an ideal texture. Furthermore, irrespective of the number of grains in the sample, Lankford coefficients have finite values for all loading orientations. Illustrative examples for sheets with textures containing a combination of few ideal texture components are also presented. The simulations of the predicted polycrystalline behavior based on the new description of the plastic behavior of the constituent grains capture the influence of individual texture components on the overall degree of anisotropy. The polycrystalline simulation results are also compared to analytical estimates obtained using the closed-form formulas for the ideal components present in the texture in conjunction with a simple law of mixtures. The analytical estimates show the same trends as the simulation results. Therefore, the trends in plastic anisotropy of the macroscopic properties can be adequately estimated analytically.
This extended comment is in response to the letter of Barlat (Int J Mater Form 2020 ) concerning ... more This extended comment is in response to the letter of Barlat (Int J Mater Form 2020 ) concerning our recent article (Chandola et al. (Int J Mater Form 12(6):943–954 2019 )). The main issue raised is an apparent “mismatch” between some of the F.E. results presented and cup forming data of Tucker (Acta Metall 9:275-286 1961 ). There is no mismatch because the simulation results presented in our paper correspond to a different material than the one used by Tucker (Acta Metall 9:275-286 1961 ). Specifically, the F.E. results correspond to an Al-Cu single crystal for which uniaxial tension characterization data were reported in Karnop and Sachs (Z Für Phys 49:480–497 1928 ) and was processed differently than Tucker’s material. Furthermore, in the letter of Barlat (Int J Mater Form 2020 ), the scope and findings of our study are misrepresented, and all the quotations from our paper are taken out of context. Detailed responses to the issues raised by Barlat (Int J Mater Form 2020 ) are given.
Generally, the plastic behavior of orthotropic metallic materials with cubic crystal structure is... more Generally, the plastic behavior of orthotropic metallic materials with cubic crystal structure is modelled with yield criteria that predict the same response in tension and compression. One drawback associated to using orthotropic yield criteria for simulation of forming processes is related to the uncertainties introduced by the methods used for parameter identification. Very recently, it was shown that advanced non-quadratic criteria such as Yld91 can be represented as polynomials in terms of stress components. Using this equivalent expression, the anisotropy coefficients involved in Yld91 can be obtained using analytical formulas in terms of only experimental flow stresses, or alternatively in terms of only Lankford coefficients for three orientations. In this paper, the predictive capabilities of Hill, Yld 91 and Cazacu calibrated using different identification procedures, either analytical or by numerical minimization are discussed. Moreover, simulation results of deep drawing are presented.
In this study, an elastic-plastic model with yielding described by a newly proposed orthotropic y... more In this study, an elastic-plastic model with yielding described by a newly proposed orthotropic yield criterion was used to model the unusual deformation of a strongly textured AA6060 alloy. Available experimental data from tension tests and results of crystal plasticity simulations were used to determine the anisotropy coefficients involved in the yield criterion. Virtual material tests using a recent polycrystalline model were performed to obtain flow stresses for loadings where experimental data were not available. The capability of the elastic-plastic model to account for the distinct anisotropy of the material is demonstrated through comparison of finite element simulations and experimental tests on both smooth and notched axisymmetric specimens of the AA6060 alloy. Specifically, for the smooth specimen, the model predicts that the minimum cross-section evolves from a circle to an ellipse while for the notched specimens, the minimum cross-section evolves from a circular shape to an approximately rectangular, or rhomboidal shape, respectively as observed in the experiments. This model can be easily implemented in finite element codes, requires reduced CPU time compared to crystal plasticity finite element simulations, and can be applied in simulations of large-scale structural applications.
In this paper, we make use of complex potentials for the problem of an elliptic hole subject to f... more In this paper, we make use of complex potentials for the problem of an elliptic hole subject to far field uniaxial tension to obtain the elastic stress distribution in the vicinity of a crack. Unlike the classical Westergaard stress distribution, the new stress field obtained is not axisymmetric in the crack plane. Using this new elastic stress field, it is possible to assess the effect of the particularities of yielding on the extent of the plastic zone near a crack. Analysis is done considering yielding governed by von Mises, Tresca, and Drucker yield criterion, respectively. It is demonstrated that the ratio between the yield stresses in uniaxial tension and pure shear of a material has a great influence on the size of the plastic zone around the crack. Specifically, the larger this ratio the larger is the plastic zone. Finite-element calculations confirm the theoretical predictions. Moreover, we derive new analytic relations between the length of the plastic zone, measured from the crack tip in the crack plane, and the external applied load for the case when yielding is governed by the von Mises and Tresca criterion, respectively.
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Papers by Oana Cazacu