This article details the ESAFORM Benchmark 2021. The deep drawing cup of a 1 mm thick, AA 6016-T4... more This article details the ESAFORM Benchmark 2021. The deep drawing cup of a 1 mm thick, AA 6016-T4 sheet with a strong cube texture was simulated by 11 teams relying on phenomenological or crystal plasticity approaches, using commercial or self-developed Finite Element (FE) codes, with solid, continuum or classical shell elements and different contact models. The material characterization (tensile tests, biaxial tensile tests, monotonic and reverse shear tests, EBSD measurements) and the cup forming steps were performed with care (redundancy of measurements). The Benchmark organizers identified some constitutive laws but each team could perform its own identification. The methodology to reach material data is systematically described as well as the final data set. The ability of the constitutive law and of the FE model to predict Lankford and yield stress in different directions is verified. Then, the simulation results such as the earing (number and average height and amplitude), th...
Chapter 5 is devoted to modeling the elastic–plastic behavior of anisotropic polycrystalline meta... more Chapter 5 is devoted to modeling the elastic–plastic behavior of anisotropic polycrystalline metals. After introducing the only two rigorous methodologies for extending isotropic formulations such as to account for anisotropy, the most versatile three-dimensional orthotropic yield criteria for materials with the same response in tension and in compression are presented. While the need for analytic yield criteria that account for both anisotropy and tension–compression asymmetry in the plastic deformation of hexagonal materials such as magnesium, zirconium, and titanium alloys has been long recognized, only recently models that describe these key features have been developed. These contributions along with applications for a variety of loadings are discussed.
Among processes involving plastic deformation, sheet metal forming requires a most accurate descr... more Among processes involving plastic deformation, sheet metal forming requires a most accurate description of plastic anisotropy. One of the main sources of mechanical anisotropy is the intrinsic anisotropy of the constituent crystals. In this paper, we present the single-crystal yield criterion recently developed by Cazacu et al. [1] and its application to the prediction of anisotropy in uniaxial tension of strongly textured polycrystalline sheets. Namely, it is shown that using this single crystal yield criterion the Lankford coefficients exist and have finite values for all loading orientations. Moreover, the variation of both the yield stress and Lankford coefficients with the crystallographic direction can be expressed analytically. An application of this criterion to forming a cylindrical cup from a single crystal of (100) orientation is presented. Finally, we show that using this single-crystal model, one can describe well the effect of the spread around an ideal texture compone...
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.
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 a three-dimensional analytical criterion for description of the onset of plastic de... more In this paper a three-dimensional analytical criterion for description of the onset of plastic deformation in cubic single crystals is presented. The criterion is pressure-insensitive and form-invariant to any transformation belonging to the symmetry class of the given crystal. For most FCC single crystals the criterion involves five independent coefficients, which can be determined based on the yield stresses in different crystal orientations. Comparisons with single crystal data on aluminum and copper single crystals show that the criterion can successfully describe the difference in yielding anisotropy between FCC crystals.
One of the greatest challenges that a researcher in the field of the theory of plasticity is faci... more One of the greatest challenges that a researcher in the field of the theory of plasticity is facing is that it has to establish general mathematical relations between the stresses and strains that should be applicable to any loading, although the experimental information available is generally restricted to uniaxial tension and/or compression tests. In particular, it has been long recognized that classic yield criteria cannot accurately capture the torsional response of hcp metals. In this paper, it is shown that Cazacu et al. [1] orthotropic yield criterion, identified based on uniaxial tests, captures the unusual characteristics of the torsional response of hcp AZ31 Mg. Furthermore, for the first time, on the basis of the same criterion, it is predicted the shape of the yield surface of this material for combined tension-torsion and combined compression-torsion loadings. Most importantly, it is shown that from the analysis of the stress-strain responses in a few very simple mechanical tests, using this criterion one can predict whether axial strains develop in torsion.
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.
Among processes involving plastic deformation, sheet metal forming requires a most accurate descr... more Among processes involving plastic deformation, sheet metal forming requires a most accurate description of plastic anisotropy. One of the main sources of mechanical anisotropy is crystallographic texture. In this paper, using the new single crystal yield criterion developed by Cazacu et al. (Int J Solids Struct, 2017), we provide analytical expressions for the variation of the uniaxial flow properties of polycrystalline sheets. It is shown that irrespective of the ideal texture component, Lankford coefficients exist and have finite values for all loading directions. The illustrative examples presented show that using this approach, the anisotropy in polycrystalline behavior can be estimated accurately in a very efficient manner. Another added advantage is that 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, 2017
In this paper a three-dimensional analytical criterion for description of the onset of plastic de... more In this paper a three-dimensional analytical criterion for description of the onset of plastic deformation in cubic single crystals is presented. The criterion is pressure-insensitive and forminvariant to any transformation belonging to the symmetries of the material. Specialization of this criterion for each class of the cubic system is presented. For most metallic single crystals, the criterion involves five independent parameters, which can be determined based on the yield stresses in different crystal orientations. Comparisons with single crystal data show that the criterion can successfully describe the difference in yielding anisotropy between FCC crystals.
Abstract It has been long recognized that the preferred orientation of the grains, arising from p... more Abstract It has been long recognized that the preferred orientation of the grains, arising from processing of metallic materials, result in anisotropic plastic behavior. An accurate assessment of the resulting macroscopic plastic anisotropy is thus essential in predicting the mechanical performance of alloys. This paper presents a new approach for modeling polycrystalline behavior. A key aspect in the formulation is the use of the single-crystal yield criterion recently developed by Cazacu et al., 2017 for the description of the plastic properties of the constituent grains. The capabilities of the polycrystalline model in predicting the directionality of macroscopic tensile properties are illustrated by comparing the theoretical predictions with mechanical data on steel sheets of various textures. There is a good agreement between experimental and theoretical predictions.
Results of an experimental study on the quasi-static and high-rate plastic deformation due to imp... more Results of an experimental study on the quasi-static and high-rate plastic deformation due to impact of a high-purity, polycrystalline, a-titanium material are presented. To quantify the plastic anisotropy and tension-compression asymmetry of the material, first monotonic uniaxial compression and tension tests were carried out at room temperature under quasi-static conditions. It was found that the material is transversely isotropic and displays strong strength differential effects. To characterize the material's strain rate sensitivity, Split Hopkinson Pressure Bar tests in tension and compression were also conducted. Taylor impact tests were performed for impact velocity of 196 m/s. Plastic deformation extended to 64% of the length of the deformed specimen, with little radial spreading. To model simultaneously the observed anisotropy, strain-rate sensitivity, and tension-compression asymmetry of the material, a three-dimensional constitutive model was developed. Key in the formulation is a macroscopic yield function [1] that incorporates the specificities of the plastic flow, namely the combined effects of anisotropy and tension-compression asymmetry. Comparison between model predictions and data show the capabilities of the model to describe with accuracy the plastic behavior of the a-Ti material for both quasi-static and dynamic loadings, in particular, a very good agreement was obtained between the simulated and experimental post-test Taylor specimen geometries.
Journal of the Mechanics and Physics of Solids, 2016
In this paper, we present an experimental study on plastic deformation and damage of polycrystall... more In this paper, we present an experimental study on plastic deformation and damage of polycrystalline pure Ti, as well as modeling of the observed behavior. From the mechanical characterization data, it can be concluded that the material displays anisotropy and tensioncompression asymmetry. As concerns damage, the X-ray tomography measurements conducted reveal that damage distribution and evolution in this HCP Ti material is markedly different than in a typical FCC material such as copper. Stewart and Cazacu (2011) anisotropic elastic/plastic damage model is used to describe the behavior. All material parameters involved in this model have a clear physical significance, being related to plastic properties, and are determined based on very few simple mechanical tests. It is shown that this model predicts correctly the anisotropy in plastic deformation, and its strong influence on damage distribution and damage accumulation in Ti. Specifically, for a smooth axisymmetric specimen subject to uniaxial tension, damage initiates at the center of the specimen and is diffuse; the level of damage close to failure is very low. On the other hand, for a notched specimen subject to the same loading, the model predicts that damage initiates at the outer surface of the specimen, and further grows from the outer surface to the center of the specimen, which corroborates with the in-situ tomography data.
At room temperature, titanium materials display deformation and failure properties that are quite... more At room temperature, titanium materials display deformation and failure properties that are quite different from that of typical materials with cubic crystalline structure (aluminium, steels, etc). Rolled or extruded products exhibit a strong anisotropy and very pronounced difference in yielding and work-hardening evolution between tension and compression loadings. In this paper, a macroscopic elastic/plastic model that accounts for the key features of the plastic deformation of Ti, in particular the distortion of the yield surface induced by texture evolution is presented. Comparison with data demonstrates that the model predicts with accuracy the plastic response for a variety of loading conditions. Furthermore, it is shown that the model can be extended such as to incorporate damage. In contrast to existing approaches, the plasticity-damage couplings are deduced and not postulated. Hence, all material parameters have a clear physical significance, being related to plastic propert...
In this paper, a new analytic criterion for porous solids with matrix obeying Tresca yield criter... more In this paper, a new analytic criterion for porous solids with matrix obeying Tresca yield criterion is derived. The criterion is micromechanically motivated and relies on rigorous upscaling theorems. Analysis is conducted for both tensile and compressive axisymmetric loading scenarios and spherical void geometry. Finite element cell calculations are also performed for various triaxialities. Both the new model and the numerical calculations reveal a very specific coupling between the mean stress and the third invariant of the stress deviator that results in the yield surface being centro-symmetric and void growth being dependent on the third-invariant of the stress deviator. Furthermore, it is verified that the classical Gurson's criterion is an upper bound of the new criterion with Tresca matrix.
ABSTRACT The Swift phenomenon, which refers to the occurrence of permanent axial deformation duri... more ABSTRACT The Swift phenomenon, which refers to the occurrence of permanent axial deformation during monotonic free-end torsion, has been known for a very long time. While plastic anisotropy is considered to be its main cause, there is no explanation as to why in certain materials irreversible elongation occurs while in others permanent shortening is observed. In this paper, a correlation between Swift effects and the stress-strain behavior in uniaxial tension and compression is established. It is based on an elastic-plastic model that accounts for the combined influence of anisotropy and tension-compression asymmetry. It is shown that, if for a given orientation the uniaxial yield stress in tension is larger than that in compression, the specimen will shorten when twisted about that direction; however, if the yield stress in uniaxial compression is larger than that in uniaxial tension, axial elongation will occur. Furthermore, it is shown that on the basis of a few simple mechanical tests it is possible to predict the particularities of the plastic response in torsion for both isotropic and initially anisotropic materials. Unlike other previous interpretations of the Swift effects, which were mainly based on crystal plasticity and/or texture evolution, it is explained the occurrence of Swift effects at small to moderate plastic strains In particular, the very good quantitative agreement between model and data for a strongly anisotropic AZ31Mg alloy confirm the correlation established in this work between tension-compression asymmetry and Swift effects. Furthermore, it is explained why the sign of the axial plastic strains that develop depends on the twisting direction.
This article details the ESAFORM Benchmark 2021. The deep drawing cup of a 1 mm thick, AA 6016-T4... more This article details the ESAFORM Benchmark 2021. The deep drawing cup of a 1 mm thick, AA 6016-T4 sheet with a strong cube texture was simulated by 11 teams relying on phenomenological or crystal plasticity approaches, using commercial or self-developed Finite Element (FE) codes, with solid, continuum or classical shell elements and different contact models. The material characterization (tensile tests, biaxial tensile tests, monotonic and reverse shear tests, EBSD measurements) and the cup forming steps were performed with care (redundancy of measurements). The Benchmark organizers identified some constitutive laws but each team could perform its own identification. The methodology to reach material data is systematically described as well as the final data set. The ability of the constitutive law and of the FE model to predict Lankford and yield stress in different directions is verified. Then, the simulation results such as the earing (number and average height and amplitude), th...
Chapter 5 is devoted to modeling the elastic–plastic behavior of anisotropic polycrystalline meta... more Chapter 5 is devoted to modeling the elastic–plastic behavior of anisotropic polycrystalline metals. After introducing the only two rigorous methodologies for extending isotropic formulations such as to account for anisotropy, the most versatile three-dimensional orthotropic yield criteria for materials with the same response in tension and in compression are presented. While the need for analytic yield criteria that account for both anisotropy and tension–compression asymmetry in the plastic deformation of hexagonal materials such as magnesium, zirconium, and titanium alloys has been long recognized, only recently models that describe these key features have been developed. These contributions along with applications for a variety of loadings are discussed.
Among processes involving plastic deformation, sheet metal forming requires a most accurate descr... more Among processes involving plastic deformation, sheet metal forming requires a most accurate description of plastic anisotropy. One of the main sources of mechanical anisotropy is the intrinsic anisotropy of the constituent crystals. In this paper, we present the single-crystal yield criterion recently developed by Cazacu et al. [1] and its application to the prediction of anisotropy in uniaxial tension of strongly textured polycrystalline sheets. Namely, it is shown that using this single crystal yield criterion the Lankford coefficients exist and have finite values for all loading orientations. Moreover, the variation of both the yield stress and Lankford coefficients with the crystallographic direction can be expressed analytically. An application of this criterion to forming a cylindrical cup from a single crystal of (100) orientation is presented. Finally, we show that using this single-crystal model, one can describe well the effect of the spread around an ideal texture compone...
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.
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 a three-dimensional analytical criterion for description of the onset of plastic de... more In this paper a three-dimensional analytical criterion for description of the onset of plastic deformation in cubic single crystals is presented. The criterion is pressure-insensitive and form-invariant to any transformation belonging to the symmetry class of the given crystal. For most FCC single crystals the criterion involves five independent coefficients, which can be determined based on the yield stresses in different crystal orientations. Comparisons with single crystal data on aluminum and copper single crystals show that the criterion can successfully describe the difference in yielding anisotropy between FCC crystals.
One of the greatest challenges that a researcher in the field of the theory of plasticity is faci... more One of the greatest challenges that a researcher in the field of the theory of plasticity is facing is that it has to establish general mathematical relations between the stresses and strains that should be applicable to any loading, although the experimental information available is generally restricted to uniaxial tension and/or compression tests. In particular, it has been long recognized that classic yield criteria cannot accurately capture the torsional response of hcp metals. In this paper, it is shown that Cazacu et al. [1] orthotropic yield criterion, identified based on uniaxial tests, captures the unusual characteristics of the torsional response of hcp AZ31 Mg. Furthermore, for the first time, on the basis of the same criterion, it is predicted the shape of the yield surface of this material for combined tension-torsion and combined compression-torsion loadings. Most importantly, it is shown that from the analysis of the stress-strain responses in a few very simple mechanical tests, using this criterion one can predict whether axial strains develop in torsion.
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.
Among processes involving plastic deformation, sheet metal forming requires a most accurate descr... more Among processes involving plastic deformation, sheet metal forming requires a most accurate description of plastic anisotropy. One of the main sources of mechanical anisotropy is crystallographic texture. In this paper, using the new single crystal yield criterion developed by Cazacu et al. (Int J Solids Struct, 2017), we provide analytical expressions for the variation of the uniaxial flow properties of polycrystalline sheets. It is shown that irrespective of the ideal texture component, Lankford coefficients exist and have finite values for all loading directions. The illustrative examples presented show that using this approach, the anisotropy in polycrystalline behavior can be estimated accurately in a very efficient manner. Another added advantage is that 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, 2017
In this paper a three-dimensional analytical criterion for description of the onset of plastic de... more In this paper a three-dimensional analytical criterion for description of the onset of plastic deformation in cubic single crystals is presented. The criterion is pressure-insensitive and forminvariant to any transformation belonging to the symmetries of the material. Specialization of this criterion for each class of the cubic system is presented. For most metallic single crystals, the criterion involves five independent parameters, which can be determined based on the yield stresses in different crystal orientations. Comparisons with single crystal data show that the criterion can successfully describe the difference in yielding anisotropy between FCC crystals.
Abstract It has been long recognized that the preferred orientation of the grains, arising from p... more Abstract It has been long recognized that the preferred orientation of the grains, arising from processing of metallic materials, result in anisotropic plastic behavior. An accurate assessment of the resulting macroscopic plastic anisotropy is thus essential in predicting the mechanical performance of alloys. This paper presents a new approach for modeling polycrystalline behavior. A key aspect in the formulation is the use of the single-crystal yield criterion recently developed by Cazacu et al., 2017 for the description of the plastic properties of the constituent grains. The capabilities of the polycrystalline model in predicting the directionality of macroscopic tensile properties are illustrated by comparing the theoretical predictions with mechanical data on steel sheets of various textures. There is a good agreement between experimental and theoretical predictions.
Results of an experimental study on the quasi-static and high-rate plastic deformation due to imp... more Results of an experimental study on the quasi-static and high-rate plastic deformation due to impact of a high-purity, polycrystalline, a-titanium material are presented. To quantify the plastic anisotropy and tension-compression asymmetry of the material, first monotonic uniaxial compression and tension tests were carried out at room temperature under quasi-static conditions. It was found that the material is transversely isotropic and displays strong strength differential effects. To characterize the material's strain rate sensitivity, Split Hopkinson Pressure Bar tests in tension and compression were also conducted. Taylor impact tests were performed for impact velocity of 196 m/s. Plastic deformation extended to 64% of the length of the deformed specimen, with little radial spreading. To model simultaneously the observed anisotropy, strain-rate sensitivity, and tension-compression asymmetry of the material, a three-dimensional constitutive model was developed. Key in the formulation is a macroscopic yield function [1] that incorporates the specificities of the plastic flow, namely the combined effects of anisotropy and tension-compression asymmetry. Comparison between model predictions and data show the capabilities of the model to describe with accuracy the plastic behavior of the a-Ti material for both quasi-static and dynamic loadings, in particular, a very good agreement was obtained between the simulated and experimental post-test Taylor specimen geometries.
Journal of the Mechanics and Physics of Solids, 2016
In this paper, we present an experimental study on plastic deformation and damage of polycrystall... more In this paper, we present an experimental study on plastic deformation and damage of polycrystalline pure Ti, as well as modeling of the observed behavior. From the mechanical characterization data, it can be concluded that the material displays anisotropy and tensioncompression asymmetry. As concerns damage, the X-ray tomography measurements conducted reveal that damage distribution and evolution in this HCP Ti material is markedly different than in a typical FCC material such as copper. Stewart and Cazacu (2011) anisotropic elastic/plastic damage model is used to describe the behavior. All material parameters involved in this model have a clear physical significance, being related to plastic properties, and are determined based on very few simple mechanical tests. It is shown that this model predicts correctly the anisotropy in plastic deformation, and its strong influence on damage distribution and damage accumulation in Ti. Specifically, for a smooth axisymmetric specimen subject to uniaxial tension, damage initiates at the center of the specimen and is diffuse; the level of damage close to failure is very low. On the other hand, for a notched specimen subject to the same loading, the model predicts that damage initiates at the outer surface of the specimen, and further grows from the outer surface to the center of the specimen, which corroborates with the in-situ tomography data.
At room temperature, titanium materials display deformation and failure properties that are quite... more At room temperature, titanium materials display deformation and failure properties that are quite different from that of typical materials with cubic crystalline structure (aluminium, steels, etc). Rolled or extruded products exhibit a strong anisotropy and very pronounced difference in yielding and work-hardening evolution between tension and compression loadings. In this paper, a macroscopic elastic/plastic model that accounts for the key features of the plastic deformation of Ti, in particular the distortion of the yield surface induced by texture evolution is presented. Comparison with data demonstrates that the model predicts with accuracy the plastic response for a variety of loading conditions. Furthermore, it is shown that the model can be extended such as to incorporate damage. In contrast to existing approaches, the plasticity-damage couplings are deduced and not postulated. Hence, all material parameters have a clear physical significance, being related to plastic propert...
In this paper, a new analytic criterion for porous solids with matrix obeying Tresca yield criter... more In this paper, a new analytic criterion for porous solids with matrix obeying Tresca yield criterion is derived. The criterion is micromechanically motivated and relies on rigorous upscaling theorems. Analysis is conducted for both tensile and compressive axisymmetric loading scenarios and spherical void geometry. Finite element cell calculations are also performed for various triaxialities. Both the new model and the numerical calculations reveal a very specific coupling between the mean stress and the third invariant of the stress deviator that results in the yield surface being centro-symmetric and void growth being dependent on the third-invariant of the stress deviator. Furthermore, it is verified that the classical Gurson's criterion is an upper bound of the new criterion with Tresca matrix.
ABSTRACT The Swift phenomenon, which refers to the occurrence of permanent axial deformation duri... more ABSTRACT The Swift phenomenon, which refers to the occurrence of permanent axial deformation during monotonic free-end torsion, has been known for a very long time. While plastic anisotropy is considered to be its main cause, there is no explanation as to why in certain materials irreversible elongation occurs while in others permanent shortening is observed. In this paper, a correlation between Swift effects and the stress-strain behavior in uniaxial tension and compression is established. It is based on an elastic-plastic model that accounts for the combined influence of anisotropy and tension-compression asymmetry. It is shown that, if for a given orientation the uniaxial yield stress in tension is larger than that in compression, the specimen will shorten when twisted about that direction; however, if the yield stress in uniaxial compression is larger than that in uniaxial tension, axial elongation will occur. Furthermore, it is shown that on the basis of a few simple mechanical tests it is possible to predict the particularities of the plastic response in torsion for both isotropic and initially anisotropic materials. Unlike other previous interpretations of the Swift effects, which were mainly based on crystal plasticity and/or texture evolution, it is explained the occurrence of Swift effects at small to moderate plastic strains In particular, the very good quantitative agreement between model and data for a strongly anisotropic AZ31Mg alloy confirm the correlation established in this work between tension-compression asymmetry and Swift effects. Furthermore, it is explained why the sign of the axial plastic strains that develop depends on the twisting direction.
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