Benoit Revil Baudard

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Books

• Cazacu, O., & Revil-Baudard, B. (2020). Plasticity of Metallic Materials: Modeling and Applications to Forming. doi:10.1016/b978-0-12-817984-0.01001-8
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  Plasticity of Metallic Materials presents a rigorous framework for description of plasticity phenomena, classic and recent models for isotropic and anisotropic materials, new original analytical solutions to various elastic/plastic boundary value problems and new interpretations of mechanical data based on these recent models. The book covers models for metals with both cubic and hexagonal crystal structures, presents the mechanical tests required to determine the model parameters, various identification procedures, verification, and validation tests, and numerous applications to metal forming.
• Lambert, D., Pasiliao, C., Erzar, B., Revil-Baudard, B., & Cazacu, O. (2019). Dynamic damage and fragmentation. doi:10.1002/9781119579311

Chapters

• Cazacu, O., Revil-Baudard, B., & Chandola, N. (2019). Anisotropic Plastic Potentials for Porous Metallic Materials. In Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials. doi:10.1007/978-3-319-92922-4_8
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  In all the constitutive models for porous plastic materials presented in previous chapters, it was presumed that the matrix can be regarded as isotropic. However, most engineering materials display plastic anisotropy (see Chaps. 5 and 6). In this chapter are presented key contributions toward understanding the role played by the matrix plastic anisotropy on yielding and damage evolution in single crystals and strongly textured polycrystalline materials containing randomly distributed spherical voids.
• Cazacu, O., Revil-Baudard, B., & Chandola, N. (2019). Constitutive equations for elastic–Plastic materials. In Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials. doi:10.1007/978-3-319-92922-4_2
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  While in the literature, there is ample exposure of elastic–plastic models formulated in the stress space, the dual formulations in the strain-rate space are less known. Chapter 2 presents the fundamental assumptions concerning the form of stress-based and strain-rate-based elastic–plastic models along with the corresponding numerical integration algorithms for solving boundary-value problems.
• Cazacu, O., Revil-Baudard, B., & Chandola, N. (2019). Mathematical framework. In Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials. doi:10.1007/978-3-319-92922-4_1
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  The theory of scalar- and tensor-valued functions constitutes the mathematical framework based on which modeling of the elasticity, plasticity, and damage in polycrystalline metallic materials is built. In this chapter, we provide the basic concepts and key mathematical results to be used in the rest of the book.
• Cazacu, O., Revil-Baudard, B., & Chandola, N. (2019). Plastic deformation of single crystals. In Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials. doi:10.1007/978-3-319-92922-4_3
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  Chapter 3 is devoted to constitutive relations for metallic single crystals. After introducing the key concepts of crystallography, an overview of the experimental evidence of plastic deformation mechanisms is presented. The yield criteria for description of the onset of plastic deformation in cubic crystals are introduced. Applications of the most recent single crystal yield criterion to the prediction of the directionality of the macroscopic tensile properties of polycrystalline sheets are also provided.
• Cazacu, O., Revil-Baudard, B., & Chandola, N. (2019). Plastic potentials for isotropic porous materials: Influence of the particularities of plastic deformation on damage evolution. In Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials. doi:10.1007/978-3-319-92922-4_7
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  In Chap. 7, key contributions toward elucidating the role of the plastic deformation on damage evolution in isotropic metallic materials are introduced. The ductile damage models presented are derived using rigorous upscaling techniques and limit-analysis methods. Previously unrecognized combined effects of the mean stress and third-invariant of the stress deviator on yielding of porous materials with matrix described by von Mises and Tresca yield criteria are presented. It is shown that the fastest rate of void growth or collapse occurs in a porous Tresca material. Most importantly, it is revealed that depending on the yield criterion for the matrix, the third-invariant effects (or Lode effects) on void evolution can be either enhanced or completely eliminated.
• Cazacu, O., Revil-Baudard, B., & Chandola, N. (2019). Strain-rate-based plastic potentials for polycrystalline materials. In Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials. doi:10.1007/978-3-319-92922-4_6
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  Although the existence of strain-rate based potentials which are work-conjugate of given stress potentials has been theoretically demonstrated, analytical expressions of strain-rate potentials are only known for a very few cases. In this chapter, closed-form expressions for strain-rate-based plastic potentials are derived for both isotropic and anisotropic fully-dense polycrystalline materials. Besides their intrinsic importance in design and optimization of metal forming processes, these analytic strain-rate potentials enable the development of the closed form expressions of plastic potentials for porous metallic materials that are presented in Chaps. 7 and 8.
• Cazacu, O., Revil-Baudard, B., & Chandola, N. (2019). Yield criteria for anisotropic polycrystals. In Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials. doi:10.1007/978-3-319-92922-4_5
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  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.
• Cazacu, O., Revil-Baudard, B., & Chandola, N. (2019). Yield criteria for isotropic polycrystals. In Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials. doi:10.1007/978-3-319-92922-4_4
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  Chapter 4 is devoted to modeling the plastic behavior of isotropic polycrystalline metallic materials. A review of the classic yield criteria and corresponding stress-based plastic potentials with discussion concerning the predicted mechanical response for various three-dimensional loadings is presented along with the most recent contributions devoted to the description of the behavior of incompressible materials displaying tension–compression asymmetry. On the basis of these new models, a new interpretation and explanation of the Swift phenomenon, occurring in monotonic and cyclic free-end torsion are provided.
• Kleiser, G., Revil-Baudard, B., & Cazacu, O. (2019). Plastic deformation of pure polycrystalline molybdenum. In Plasticity-Damage Couplings: From Single Crystal to Polycrystalline Materials. doi:10.1002/9781119579311.ch4
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  This chapter presents an overview of the experimental and theoretical investigations of the quasi-static and dynamic, room temperature, mechanical response of a commercial-purity polycrystalline Molybdenum material. It also presents the quasi-static monotonic tensile and compression data on the material. The chapter discusses Taylor impact tests. It describes the constitutive framework considered for modeling the observed behavior which simultaneously takes into account the anisotropy and the difference in yielding between uniaxial tension and compression. The chapter also describes the procedure for calibration of the parameters from compression and uniaxial tension data on smooth tensile specimens. To characterize the strain rate sensitivity of the material, high-strain-rate compression tests were conducted using a split Hopkinson pressure bar system. A comparison between the quasi-static uniaxial tension and compression data indicated that the material has tension-compression asymmetry.

Journals/Publications

• Cazacu, O., & Revil-Baudard, B. (2025). Analytical procedures for the determination of the anisotropy parameters of the non-quadratic orthotropic Yld91 yield function for extruded materials. European Journal of Mechanics-A/Solids, 111, 105577.
• Ghnatios, C., Cazacu, O., Revil-Baudard, B., & Chinesta, F. (2024). A new methodology for anisotropic yield surface description using model order reduction techniques and invariant neural network. Journal of the Mechanics and Physics of Solids, 184, 105542.
• Godoy, H., Revil-Baudard, B., & Cazacu, O. (2024). Influence of the sensitivity of plastic deformation to the third invariant on the stress state achievable during stretch forming of isotropic materials. International Journal of Material Forming, 17(3). doi:10.1007/s12289-024-01830-2
• Knaak, K. R., Cazacu, O., & Revil-Baudard, B. (2024). Correlation between the ratio between the tensile and shear yield strength on porosity evolution in isotropic ductile materials. Mechanics of Materials, 199, 105150.
• Revil-Baudard, B., Sable, P., Cazacu, O., Gaskey, B., & Soto-Medina, S. (2024). On the role of the retained porosity on the shock response of additively manufactured high-performance steel: Experiments, constitutive model and finite-element predictions. Journal of the Mechanics and Physics of Solids, 193, 105909.
• Corallo, L., Revil-Baudard, B., Cazacu, O., & Verleysen, P. (2023). Role of anisotropy on strain localization at high-strain rates in Ti6Al4V. European Journal of Mechanics-A/Solids, 97, 104856.
• Revil-Baudard, B. (2023). A new constitutive model for tetragonal crystals. Meccanica, 58(1), 233--244.
• Habraken, A., Aksen, T., Alves, J., Amaral, R., Betaieb, E., Chandola, N., Corallo, L., Cruz, D., Engel, B., Esener, E., Firat, M., Ghiabakloo, H., Kestens, L., Lian, J., Lingam, R., Liu, W., Ma, J., Menezes, L., Nguyen-Minh, T., , Miranda, S., et al. (2022). Analysis of ESAFORM 2021 cup drawing benchmark of an Al alloy, critical factors for accuracy and efficiency of FE simulations. International Journal of Material Forming, 15(5). doi:10.1007/s12289-022-01672-w
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  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), the punch force evolution and thickness in the cup wall are evaluated and analysed. The CPU time, the manpower for each step as well as the required tests versus the final prediction accuracy of more than 20 FE simulations are commented. The article aims to guide students and engineers in their choice of a constitutive law (yield locus, hardening law or plasticity approach) and data set used in the identification, without neglecting the other FE features, such as software, explicit or implicit strategy, element type and contact model.
• Revil-Baudard, B. (2022). Effects of anisotropy on dynamic void collapse and temperature rise in low-symmetry crystals. Mechanics Research Communications, 124. doi:10.1016/j.mechrescom.2022.103931
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  An investigation into the role of plastic anisotropy on dynamic void collapse and temperature rise in low-symmetry crystals is presented. To describe the influence of local deformation and thermal history on the dynamic process, in this paper, we use the new anisotropic model for low-symmetry crystals developed in [1]. This constitutive model accounts for the influence of the symmetries of tetragonal lattice on both the elastic and plastic response. Based on the results of the finite-element (FE) simulations of voided PETN crystals subjected to dynamic plain strain loadings, it can be concluded that there are significant effects of the crystal orientation on void collapse and on the location of the temperature peaks, which are potential sites for ignition.
• Revil-Baudard, B., & Cazacu, O. (2022). Dynamic response of polycrystalline high energetic systems: Constitutive modeling and application to impact. Journal of Applied Physics, 131(14). doi:10.1063/5.0080848
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  This paper presents a new polycrystalline model and Lagrangian computational framework for describing the large-scale thermo-mechanical response of energetic materials under dynamic loadings. In our multi-scale computational polycrystalline framework, at the grain level, the elastic response is modeled using an anisotropic Hooke's law, while the plastic behavior is described with a recently developed quadratic anisotropic single-crystal model that accounts for the intrinsic symmetries associated with the lattice of the constituent crystals. The orientation, plastic strains, and stresses in the individual grains are continuously updated, so the predicted macroscopic scale response takes into account the evolution of the thermo-mechanical state at the meso-scale. First, we illustrate the polycrystalline model capabilities by simulating the response of a pentaerythritol tetranitrate (PETN) polycrystalline high energetic system when subjected to dynamic compression. It is shown that there are strong differences in temperature and stresses between the constituent grains, depending on their relative orientation with respect to the wave direction. Moreover, it is shown that the rise in temperature in certain grains may be well in excess of the macroscopic value. We also present 3D finite element simulations of the impact of a penetrator made of a high-strength steel containing the same polycrystalline PETN system. Insights into the complex interactions between the energetic system and the metallic casing material are provided. Furthermore, it is shown that if the crystallinity is neglected, the predicted temperature rise and the extent of the zone of maximum heating in the energetic system during the impact event differ noticeably from those obtained with our polycrystalline model, which accounts for the crystallinity of the PETN material and the anisotropy in the plastic flow of its constituent crystals.
• Cazacu, O., & Revil-Baudard, B. (2021). Tension-compression asymmetry effects on the plastic response in bending: new theoretical and numerical results. Mechanics Research Communications, 114. doi:10.1016/j.mechrescom.2020.103596
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  At present, the analysis and interpretation of the bending response of isotropic elastic/plastic metallic materials is done based on the assumption that yielding and subsequent plastic deformation under tension and compression are the same. In this paper, we put into evidence analytically and verified through F.E. analyses that even a slight tension-compression asymmetry in yielding of isotropic pressure-insensitive materials leads to very specific behaviour under four-point bending. For this purpose, the isotropic version of Cazacu et al. [1] yield criterion is used. This yield criterion is pressure-insensitive, accounts for third-invariant effects, and involves a unique parameter k which depends solely on the ratio between the yield stress in simple tension and compression, σT/σC; k = 0 corresponding to the von Mises criterion. The theoretical analysis shows that for a material with σT < σC, yielding first occurs in tension at the bottom outer fiber while for a material with σT > σC yielding sets in at the top outer fiber. As the moment is further increased, a single plastic zone spreads into the cross section starting from the fiber where min (σT, σC) is first reached, the neutral axis being no longer located at the mid-height of the beam, but moving continuously during bending. If the applied load is sufficiently large, yielding also occurs at the other outer fiber and the plastic domain is comprised of two zones, one in tension and the other in compression. The extent of the plastic zones in tension and compression is not the same, namely the extent of each zone and the critical value of the moment when these two zones join being dictated by the tension-compression asymmetry ratio of the material. Most importantly, the stresses in the cross section during loading, and consequently the distribution of residual stresses that remain after unloading are completely different than in the case of a von Mises material. To the author's knowledge these features of the plastic response in bending, which are confirmed by F.E. analyses, have not been previously identified or reported.
• Revil-Baudard, B. (2021). Numerical investigation into the dynamic behavior of sands. Mechanics Research Communications, 114. doi:10.1016/j.mechrescom.2021.103664
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  The aim of this paper is to provide further understanding of the mechanical behavior of soils when subjected to high-pressure and high-rate loadings. To this end, finite-element (FE) analyses of dynamic compaction and penetration events were conducted using the advanced elastic/plastic soil model of Lade (1977) which was extrapolated to large pressures and implemented into the FE framework. To ensure improved accuracy of the results for conditions involving loading/unloading and stress path changes, an implicit integration scheme was adopted. The simulation results for dynamic densification show that the initial precompaction of the material has a strong influence on both the wave speed and the shape of the wave front. As concerns the initiation of penetration, the simulation results indicate that for the same material, the inception and nature of the localization bands are also strongly dependent on the level of precompaction of the target material. Namely, for a low precompaction level, upon impact multiple bands develop whereas for a larger initial precompaction level, a primary localization band develops.
• Revil-Baudard, B., Cazacu, O., & Massoni, E. (2021). Room-temperature plastic behavior and formability of a commercially pure titanium: Mechanical characterization, modeling, and validation. International Journal of Solids and Structures, 228. doi:10.1016/j.ijsolstr.2021.111121
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  Data on the room temperature behavior of titanium is limited. To assess the anisotropy of the plastic behavior of a commercially pure grade 2 hcp–titanium T40 for different strain paths, in this study both uniaxial tests in various orientations with respect to the rolling direction as well as bulging tests using different die apertures were conducted. Under uniaxial tension, the plastic anisotropy in yielding is moderate, while the anisotropy in plastic strains is very strong. The material also displays tension–compression asymmetry, irrespective of the orientation the flow stress in compression being higher than in tension. The bulging tests data, namely the evolution of the thickness with the fluid pressure complemented with post-test DIC measurements reveal that T40 has unusual deformation and failure characteristics as compared to common materials with cubic crystal structure. Irrespective of the die aperture, instabilities occur suddenly, the reduction in thickness being drastic (snap failure). However, the evolution of strains depends on the die aperture aspect ratio (hemispherical vs. elliptical). The anisotropy of the titanium T40 also leads to a different response depending on the orientation of the material axes with respect to the die axes. To explain these specific characteristics of the behavior of titanium T40 under bulging, two orthotropic criteria were used, one that neglects the tension–compression asymmetry of the material (Hill, 1948) and another that accounts for the combined effects of anisotropy and tension–compression asymmetry (Cazacu et al. (2006) yield criterion). Determination of the parameters involved in both criteria was done using only uniaxial test data. The F.E. results presented show that neglecting the tension–compression asymmetry of T40 leads to less accurate predictions of the fluid pressure and strains at which fracture occurs, and in some cases an incorrect orientation of the zone of localized deformation. Using the Cazacu et al. (2006) criterion, it is possible to accurately predict the sudden occurrence of instabilities, the distribution of plastic strains, and the correct orientation of the zone of localized deformation in both the hemispherical and elliptical bulge tests.
• Cazacu, O., Chandola, N., Revil-Baudard, B., Frodal, B., Børvik, T., & Hopperstad, O. (2020). Modeling the effect of notch geometry on the deformation of a strongly anisotropic aluminum alloy. European Journal of Mechanics, A/Solids, 82. doi:10.1016/j.euromechsol.2020.104004
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  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.
• Chandola, N., Cazacu, O., & Revil-Baudard, B. (2019). Prediction of strain distribution and four, six, or eight ears depending on single-crystal orientation using a new single crystal criterion. International Journal of Material Forming, 12(6). doi:10.1007/s12289-018-01465-0
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  Significant progress has been achieved on modeling the influence of plastic anisotropy on forming of polycrystalline metal sheets. In contrast, the effect of crystal orientation on forming of single-crystal sheets has been largely unexplored. In this paper, using a recently developed single crystal criterion, it is shown that the single-crystal orientation has a very strong influence on forming. Results of F.E. simulations of cup drawing and hole expansion are reported. The same set of values of the anisotropy coefficients, which correspond to Al single crystal (with 5% Cu) is used in all simulations. It is predicted that for the {100}〈001〉 orientation four ears develop whereas for the {111}〈11¯0〉 and {122}〈11¯0〉 crystal orientations six, and eight ears form. Moreover, correlations between the location of the ears and the variation of the Lankford coefficients in the plane of the respective single-crystal sheets are established. F.E. analysis of hole expansion also show a strong influence of crystal orientation on the distribution of thickness strains and strain localization.
• Cazacu, O., Chandola, N., & Revil-Baudard, B. (2018). Analytical expressions for the yield stress and Lankford coefficients of polycrystalline sheets based on a new single crystal model. International Journal of Material Forming, 11(4). doi:10.1007/s12289-017-1366-3
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  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.
• Cazacu, O., Revil-Baudard, B., & Chandola, N. (2018). A yield criterion for cubic single crystals. International Journal of Solids and Structures, 151. doi:10.1016/j.ijsolstr.2017.04.006
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  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 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.
• Chandola, N., Cazacu, O., & Revil-Baudard, B. (2018). Prediction of plastic anisotropy of textured polycrystalline sheets using a new single-crystal model. Comptes Rendus - Mecanique, 346(8). doi:10.1016/j.crme.2018.05.004
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  In this paper, we predict the effect of texture on the plastic anisotropy and consequently the drawing performance of polycrystalline metallic sheets. The constituent grain behavior is modeled using the new single-crystal yield criterion developed by [1]. 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 obtained with rotationally symmetric misorientations of scatter width of up to 35° from the ideal orientation, the numerical predictions have the same trend as those obtained analytically for an ideal texture, but the anisotropy is less pronounced. 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.
• Revil-Baudard, B., Cazacu, O., & Chandola, N. (2018). Effect of the yield stresses in uniaxial tension and pure shear on the size of the plastic zone near a crack. International Journal of Plasticity, 102. doi:10.1016/j.ijplas.2017.12.006
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  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.
• Cazacu, O., & Revil-Baudard, B. (2017). New analytic criterion for porous solids with pressure-insensitive matrix. International Journal of Plasticity, 89. doi:10.1016/j.ijplas.2016.11.002
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  In this paper, we address the question of how the relative weighting of the two invariants of the plastic deformation of the matrix influence the mechanical response of a porous metallic material. To this end, we first propose a new isotropic potential for description of the plastic behavior of the matrix that depends on both invariants of the strain-rate deviator. The relative weight of the two invariants is described by a material parameter β. Depending on the sign of the parameter β, the new plastic potential for the matrix is either interior to von Mises strain-rate potential (β < 0), coincides with it (β = 0) or it is exterior to it. Next, an analytic criterion for a porous solid with matrix governed by the new strain-rate potential is obtained using rigorous upscaling methods. Analysis is conducted for both tensile and compressive axisymmetric loading scenarios and spherical void geometry. No simplifying approximations are considered when estimating the local and overall plastic dissipation, respectively. It is shown that the value of β has a drastic influence on all aspects of the mechanical response. There is a value β = β* β*, the response of the porous material for tensile loadings and J3Σ≥0 is softer than that for loadings at J3Σ≤0. The reverse holds true for β
• Chandola, N., Cazacu, O., & Revil-Baudard, B. (2017). New polycrystalline modeling as applied to textured steel sheets. Mechanics Research Communications, 84. doi:10.1016/j.mechrescom.2017.07.001
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  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.
• Srivastava, A., Revil-Baudard, B., Cazacu, O., & Needleman, A. (2017). A model for creep of porous crystals with cubic symmetry. International Journal of Solids and Structures, 110-111. doi:10.1016/j.ijsolstr.2017.02.002
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  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.
• Kleiser, G., Revil-Baudard, B., & Pasiliao, C. (2016). High strain-rate plastic deformation of molybdenum: Experimental investigation, constitutive modeling and validation using impact tests. International Journal of Impact Engineering, 96. doi:10.1016/j.ijimpeng.2016.05.019
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  In this paper, an experimental study on the quasi-static behavior and dynamic behavior of a polycrystalline molybdenum material is presented. Due to the material's limited tensile ductility, successfully acquiring data for impact conditions is very challenging. For the first time, Taylor impact tests were successfully conducted on this material for impact velocities in the range of 140-165 m/s. For impact velocities beyond this range, the very high tensile pressures generated in the specimen immediately after impact lead to failure. A constitutive model accounting for the key features of the Mo plastic behavior, i.e. its tension-compression asymmetry and plastic anisotropy was developed. An implicit solver was used to simulate the impact deformation. A good agreement was obtained between predictions and experimental outlines of the specimens. Furthermore, it was shown that the model can be used to gain understanding of the dynamic deformation process in terms of time evolution of the pressure, the extent of the plastically deformed zone, distribution of the local plastic strain rates, and when the transition to quasi-stable deformation occurs.
• Revil-Baudard, B., Cazacu, O., Flater, P., Chandola, N., & Alves, J. (2016). Unusual plastic deformation and damage features in titanium: Experimental tests and constitutive modeling. Journal of the Mechanics and Physics of Solids, 88. doi:10.1016/j.jmps.2016.01.003
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  In this paper, we present an experimental study on plastic deformation and damage of polycrystalline pure HCP Ti, as well as modeling of the observed behavior. Mechanical characterization data were conducted, which indicate that the material is orthotropic and displays tension-compression asymmetry. The ex-situ and in-situ 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 the parameters involved in this model have a clear physical significance, being related to plastic properties, and are determined from 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. 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 being 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.
• Cazacu, O., & Revil-Baudard, B. (2015). New three-dimensional plastic potentials for porous solids with a von Mises matrix. Comptes Rendus - Mecanique, 343(2). doi:10.1016/j.crme.2014.12.001
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  In this paper, new 3-D plastic potentials for a porous solid with a von Mises matrix are obtained. First, a strain rate based potential is derived, the noteworthy result being its centro-symmetry. Moreover, it is revealed that the couplings between invariants are very specific, the most important influence of the third invariant being for axisymmetric states. It is demonstrated that the exact stress-based potential of the porous material should have the same key properties. Furthermore, it is deduced a new analytic 3-D stress-based potential that satisfies these properties. Compared to the existing criteria for porous solids with a von Mises matrix, this model is the only one that captures the specific couplings between all stress invariants and is exact for axisymmetric states.
• Chandola, N., Lebensohn, R., Cazacu, O., Revil-Baudard, B., Mishra, R., & Barlat, F. (2015). Combined effects of anisotropy and tension-compression asymmetry on the torsional response of AZ31 Mg. International Journal of Solids and Structures, 58. doi:10.1016/j.ijsolstr.2015.01.001
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  In this paper it is demonstrated that only by accounting for the combined effects of anisotropy and tension-compression asymmetry at polycrystal level, it is possible to explain and accurately predict the room-temperature torsional response of a strongly textured AZ31 Mg material. This is shown by using two modeling frameworks, namely: a viscoplastic self-consistent (VPSC) polycrystal model, and a macroscopic plasticity model based on an yield criterion, developed by Cazacu et al. (2006), that accounts for both orthotropy and tension-compression asymmetry in plastic flow. It is shown that unlike Hill's (1948) criterion, the latter macroscopic criterion quantitatively predicts the experimental results, namely: that the sample with axial direction along the rolling direction contracts, while the sample with axial direction along the normal direction elongates. Moreover, it is demonstrated that these experimentally observed axial strain effects can be quantitatively predicted with the VPSC polycrystal model, only if both slip and twinning are considered operational at single crystal level. On the other hand, if it is assumed that the plastic deformation is fully accommodated by crystallographic slip, the axial strains predicted by VPSC are very close with that predicted with Hill (1948) criterion, which largely underestimates the measured axial strain in the rolling direction, and predicts zero axial strain in the normal direction.
• Kleiser, G., Revil-Baudard, B., Cazacu, O., & Pasiliao, C. (2015). Experimental Characterization and Modeling of the Anisotropy and Tension–Compression Asymmetry of Polycrystalline Molybdenum for Strain Rates Ranging from Quasi-static to Impact. JOM, 67(11). doi:10.1007/s11837-015-1612-4
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  A systematic experimental investigation of the room-temperature quasi-static behavior and dynamic mechanical response of polycrystalline commercially pure molybdenum is presented. It was established that the material has ductility in tension at 10−5/s and that the failure strain is strongly dependent on the orientation. A specimen taken along the rolling direction (RD) sustains large axial strains (20%), while a specimen taken at an angle of 45° to the RD could only sustain 5% strain. It was observed that irrespective of the loading orientation the yield stress in uniaxial compression is larger than in uniaxial tension. While in tension, the material has a strong anisotropy in Lankford coefficients, while in uniaxial compression, it displays weak strain-anisotropy. Due to the material’s limited tensile ductility, successfully acquiring data for impact conditions is very challenging. For the first time, Taylor impact tests were successfully conducted on this material for impact velocities in the range 140–165 m/s. For impact velocities beyond this range, the very high tensile pressures generated in the specimen immediately after impact lead to failure. An elastic–plastic anisotropic model that accounts for all the specificities of the plastic deformation of the material was developed. Validation of the model was done through comparison with data on quasi-static notched specimens and Taylor impact specimens. Quantitative agreement with both global and local strain fields was obtained. In particular, the effect of loading orientation on the response was very well described for all strain rates.
• Kleiser, G., Revil-Baudard, B., Cazacu, O., & Pasiliao, C. (2015). Plastic deformation of polycrystalline molybdenum: Experimental data and macroscopic model accounting for its anisotropy and tension-compression asymmetry. International Journal of Solids and Structures, 75-76. doi:10.1016/j.ijsolstr.2015.08.021
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  In this paper a systematic experimental investigation of the room-temperature mechanical response of polycrystalline commercially pure molybdenum (Mo) is presented. It was established that the material has ductility in tension at 10-5/s and that the failure strain is strongly dependent on the orientation. A specimen taken along the rolling direction sustains large axial strains (20%), while a specimen taken at an angle of 45° to the rolling direction could only sustain 5% strain. It was observed that irrespective of the loading orientation the yield stress in uniaxial compression is larger than in uniaxial tension. While in tension the material has a strong anisotropy in Lankford coefficients, in uniaxial compression it displays weak strain-anisotropy. An elastic-plastic orthotropic model that accounts for all the specificities of the plastic deformation of the material was developed. Validation of the model was done through comparison with data on notched specimens. Quantitative agreement with both global and local strain fields was obtained. In particular, the effect of loading orientation on the response was very well described.
• Revil-Baudard, B., Cazacu, O., Flater, P., & Kleiser, G. (2015). Plastic deformation of high-purity α-titanium: Model development and validation using the Taylor cylinder impact test. Mechanics of Materials, 80. doi:10.1016/j.mechmat.2014.03.010
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  In this paper, results of an experimental study on the quasi-static and high-rate plastic deformation due to impact of a high-purity, polycrystalline, α-titanium material are presented. It was found that the material is transversely isotropic and displays strong strength differential effects. Split Hopkinson Pressure Bar tests in tension and compression and Taylor impact tests were conducted. For an impact velocity of 196 m/s, plastic deformation extended to 64% of the length of the deformed specimen, with little radial spreading. A three-dimensional constitutive model was developed. Key in the formulation was the use of a macroscopic yield function 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 α-titanium material for both quasi-static and high-rate loadings. In particular, the three-dimensional simulations of the Taylor impact test show a very good agreement with data, both the post-test major and minor side profiles and impact interface footprints are very well described.
• Alves, J., Revil-Baudard, B., & Cazacu, O. (2014). Importance of the coupling between the sign of the mean stress and the third invariant on the rate of void growth and collapse in porous solids with a von Mises matrix. Modelling and Simulation in Materials Science and Engineering, 22(2). doi:10.1088/0965-0393/22/2/025005
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  Recently, Cazacu et al (2013a J. Appl. Mech. 80 64501) demonstrated that the plastic potential of porous solids with a von Mises matrix containing randomly distributed spherical cavities should involve a very specific coupling between the mean stress and , the third invariant of the stress deviator. In this paper, the effects of this coupling on void evolution are investigated. It is shown that the new analytical model predicts that for axisymmetric stress states, void growth is faster for loading histories corresponding to than for those corresponding to J3Σ≥0. However, void collapse occurs faster for loadings where J3Σ≤0 than for those characterized by J3Σ≥0. Finite-element (FE) results also confirm these trends. Furthermore, comparisons between FE results and corresponding predictions of yielding and void evolution show the improvements provided by the new model with respect to Gurson's. Irrespective of the loading history, the predicted rate of void growth is much faster than that according to Gurson's criterion. © 2014 IOP Publishing Ltd.
• Cazacu, O., Chandola, N., Alves, J., & Revil-Baudard, B. (2014). Importance of the consideration of the specificities of local plastic deformation on the response of porous solids with Tresca matrix. European Journal of Mechanics, A/Solids, 47. doi:10.1016/j.euromechsol.2014.04.004
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  Based on rigorous limit-analysis theorems, very recently, Cazacu et al. (2014) have deduced an analytic plastic potential for porous solids with Tresca matrix. Key in the model development was the consideration of the specificities of the plastic flow of the matrix. In this paper, finite element calculations are conducted for a voided cubic cell obeying Tresca's criterion and compared with the predictions of the new model. The numerical calculations confirm the centro-symmetry of the yield locus of the porous Tresca material and the combined effects of the mean stress and the third-invariant of the stress deviator on void evolution. In particular, it is shown that the rate of void growth is faster for axisymmetric loading histories corresponding to the third-invariant J3Σ≥0 than for those corresponding to J3Σ≤0, while void collapse occurs faster for loadings such that J3Σ≤0 than for those characterized by J3Σ≥0. Irrespective of the loading history, it is found that neglecting the local plastic heterogeneity leads to a drastic underestimation of the rate of void evolution. © 2014 Elsevier Masson SAS. All rights reserved.
• Cazacu, O., Revil-Baudard, B., & Barlat, F. (2014). New interpretation of cyclic Swift effects. European Journal of Mechanics, A/Solids, 44. doi:10.1016/j.euromechsol.2013.10.005
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  The generally accepted view is that induced plastic anisotropy is the main reason for accumulation of axial strains during monotonic and cyclic free-end torsion. In this paper, analytical results and numerical simulations using an elastic/plastic model with yielding described by the isotropic form of Cazacu et al. (2006) criterion and isotropic hardening point to another important cause of this phenomenon. It is shown that such phenomenon can occur in an isotropic material, a slight difference between the uniaxial yield stresses in tension and compression of the material leading to a build-up of inelastic axial strains during cyclic torsion at constant strain amplitude. It is demonstrated that the ratio between the uniaxial yield stresses in tension and compression dictates whether permanent shortening or lengthening of the specimen occurs. Furthermore, it is predicted that by axially preloading the material below its plastic threshold and then subject it to strain controlled cyclic torsion under constant axial load, the axial effects may be either reinforced or reduced. Thus, for any given isotropic material it is possible to estimate the value of the constant load and the strain amplitude that need to be prescribed in order to eliminate these effects.© 2013 Elsevier Masson SAS. All rights reserved.
• Cazacu, O., Revil-Baudard, B., Chandola, N., & Kondo, D. (2014). New analytical criterion for porous solids with Tresca matrix under axisymmetric loadings. International Journal of Solids and Structures, 51(3-4). doi:10.1016/j.ijsolstr.2013.11.010
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  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. © 2013 Elsevier Ltd. All rights reserved.
• Revil-Baudard, B., & Cazacu, O. (2014). New three-dimensional strain-rate potentials for isotropic porous metals: Role of the plastic flow of the matrix. International Journal of Plasticity, 60. doi:10.1016/j.ijplas.2014.04.003
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  At present, modeling of the plastic response of porous solids is done using stress-based plastic potentials. To gain understanding of the combined effects of all invariants for general three-dimensional loadings, a strain-rate based approach appears more appropriate. In this paper, for the first time strain rate-based potentials for porous solids with Tresca and von Mises, matrices are obtained. The dilatational response is investigated for general 3-D conditions for both compressive and tensile states using rigorous upscaling methods. It is demonstrated that the presence of voids induces dependence on all invariants, the noteworthy result being the key role played by the plastic flow of the matrix on the dilatational response. If the matrix obeys the von Mises criterion, the shape of the cross-sections of the porous solid with the octahedral plane deviates slightly from a circle, and changes very little as the absolute value of the mean strain rate increases. However, if the matrix behavior is described by Tresca's criterion, the shape of the cross-sections evolves from a regular hexagon to a smooth triangle with rounded corners. Furthermore, it is revealed that the couplings between invariants are very specific and depend strongly on the particularities of the plastic flow of the matrix. © 2014 Elsevier Ltd. All rights reserved.
• Revil-Baudard, B., & Cazacu, O. (2014). Role of the plastic flow of the matrix on yielding and void evolution of porous solids: Comparison between the theoretical response of porous solids with Tresca and von Mises matrices. Mechanics Research Communications, 56. doi:10.1016/j.mechrescom.2013.11.008
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  Abstract In this paper, it is shown that yielding and void evolution in a porous metallic material is strongly influenced by the particularities of the plastic flow of the matrix. This is demonstrated by comparing the effective response of porous solids for which the matrix is described by Tresca and von Mises yield criterion, respectively. The effective response of the porous solid is calculated analytically using rigorous limit analysis theorems and upscaling techniques. Analysis is conducted for both tensile and compressive axisymmetric loading scenarios and spherical void geometry. For the first time it is demonstrated that if the matrix plastic response is governed by Tresca yield criterion, the overall response is softer, the combined effects of pressure and the third-invariant on yielding being much stronger than in a porous solid with von Mises matrix. Furthermore, the rate of void growth or collapse is much faster in a porous solid with Tresca matrix. © 2013 Elsevier Ltd.
• Revil-Baudard, B., Chandola, N., Cazacu, O., & Barlat, F. (2014). Correlation between swift effects and tension-compression asymmetry in various polycrystalline materials. Journal of the Mechanics and Physics of Solids, 70(1). doi:10.1016/j.jmps.2014.05.012
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  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 AZ31-Mg 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. © 2014 Elsevier Ltd.
• Cazacu, O., Revil-Baudard, B., & Barlat, F. (2013). New interpretation of monotonic Swift effects: Role of tension-compression asymmetry. Mechanics of Materials, 57. doi:10.1016/j.mechmat.2012.10.007
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  It is generally accepted that plastic anisotropy induced by texture development is the main cause of Swift effects in polycrystals subjected to monotonic free-end torsion. In this paper, analytical results and finite element simulations using a macroscopic model with yielding described by the isotropic form of Cazacu et al. (2006) criterion and isotropic hardening point to a new interpretation of Swift effects. Specifically, it is shown that a slight difference between the uniaxial yield stresses in tension and compression leads to irreversible length changes under monotonic free-end testing conditions. Furthermore, simulations using a self-consistent viscoplastic polycrystal model confirm the predictions obtained with the macroscopic model. Finally, a comparison between finite-element simulations and room temperature experiments on a commercially pure aluminum under free end torsion show that the model predicts that axial elongation occurs even at relatively small plastic strains. © 2012 Elsevier Ltd. All rights reserved.
• Cazacu, O., Revil-Baudard, B., Lebensohn, R., & Garajeu, M. (2013). On the combined effect of pressure and third invariant on yielding of porous solids with von mises matrix. Journal of Applied Mechanics, Transactions ASME, 80(6). doi:10.1115/1.4024074
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  In this work it is shown that the exact plastic potential for porous solids with von Mises perfectly plastic matrix containing spherical cavities should involve a very specific coupling between the mean stress and the third invariant of the stress deviator. Furthermore, a new approximate plastic potential that preserves this key feature of the exact one is developed. Unlike all existing analytical criteria for porous solids with von Mises matrix, this new criterion displays a lack of symmetry with respect to both the hydrostatic and deviatoric axes. A full-field approach is also used to generate numerical gauge surfaces. These calculations confirm the aforementioned new features of the dilatational response. Copyright © 2013 by ASME.
• Knezevic, M., Lebensohn, R., Cazacu, O., Revil-Baudard, B., Proust, G., Vogel, S., & Nixon, M. (2013). Modeling bending of α-titanium with embedded polycrystal plasticity in implicit finite elements. Materials Science and Engineering: A, 564. doi:10.1016/j.msea.2012.11.037
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  An accurate description of the mechanical response of α-titanium requires consideration of mechanical anisotropy. In this work we adapt a polycrystal self-consistent model embedded in finite elements to simulate deformation of textured α-titanium under quasi-static conditions at room temperature. Monotonic tensile and compressive macroscopic stress-strain curves, electron backscattered diffraction and neutron diffraction data are used to calibrate and validate the model. We show that the model captures with great accuracy the anisotropic strain hardening and texture evolution in the material. Comparisons between predictions and experimental data allow us to elucidate the role that the different plastic deformation mechanisms play in determining microstructure and texture evolution. The polycrystal model, embedded in an implicit finite element code, is then used to simulate geometrical changes in bending experiments of α-titanium bars. These predictions, together with results of a macroscopic orthotropic elasto-plastic model that accounts for evolving anisotropy, are compared with the experiments. Both models accurately capture the experimentally observed upward shift of the neutral axis as well as the rigidity of the material response along hard-to-deform crystallographic direction. © 2012 Elsevier B.V.
• Revil-Baudard, B., & Cazacu, O. (2013). On the effect of the matrix tension-compression asymmetry on damage evolution in porous plastic solids. European Journal of Mechanics, A/Solids, 37. doi:10.1016/j.euromechsol.2012.05.001
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  Strength differential effects (different behavior in tension versus compression) are observed at the polycrystal level, if either twinning or non-Schmid type slip are contributors to plastic deformation at the single crystal level. Despite recent progress in modeling the effects of this asymmetry on the plastic flow of the fully dense polycrystal, modeling the response of such polycrystals in the presence of voids remains a challenge. The aim of this paper is to numerically assess the influence of the tension-compression asymmetry of the plastic flow in the matrix (solid material) on void evolution and the location of the zone corresponding to maximum damage in round tensile specimens subject to uniaxial tension. It is shown that if the matrix tensile strength is higher than its compressive strength, void growth and damage distribution are similar to that in classical materials obeying Gurson's criterion. On the other hand, for certain porous polycrystals in which the matrix tensile strength is lower than its compressive strength, the rate of void growth rate is much slower. Damage distribution is significantly different, the location of the zone of maximum porosity shifts from the center of the specimen outwards. Furthermore, void growth is significantly affected by the rate of change of the tension-compression asymmetry of the matrix with accumulated plastic strain. © 2012 Elsevier Masson SAS. All rights reserved.
• Revil-Baudard, B., Cazacu, O., Thuillier, S., & Maire, E. (2013). Effect of stress triaxiality on porosity evolution in notched bars: Quantitative agreement between a recent dilatational model and X-ray tomography data. Mechanics Research Communications, 50. doi:10.1016/j.mechrescom.2013.04.005
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  In this paper, it is shown that a micromechanically motivated macroscopic model can predict with accuracy the role of the stress state on void evolution in engineering materials. Specifically, a recent criterion that accounts for the influence of all stress invariants on the dilatational response of porous metals is used to predict porosity evolution and strength reduction in aluminum alloy AA 6016-T4. A very good quantitative agreement between the simulation results and X-ray tomography damage measurements in specimens of different notch acuities is obtained. In contrast to existing models, the void volume fraction evolution correlates very well with the X-ray data for all stress triaxialities.
• Revil-Baudard, B., & Massoni, E. (2009). Simulation of the anisotropic behavior of titanium alloys during sheet metal forming. International Journal of Material Forming, 2(1). doi:10.1007/s12289-009-0535-4
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  This paper introduces a constitutive elastoplastic model based on anisotropic yield criterion. An evolving anisotropy during simulation is considered. The anisotropy axes are updated with the deformation gradient. An anisotropic yield criterion, an isotropic hardening and a kinematic hardening model the plastic behavior of titanium alloys. Different plastic yield criteria are compared to show the accuracy of each plasticity model for the simulation of forming processes. © Springer/ESAFORM 2009.

Proceedings Publications

• Cazacu, O., & Revil-Baudard, B. (2024). Effect of the Choice of Data Used for Analytical Identification of Orthotropic Criteria for Aluminum Extrusions. In 14th International Conference on the Technology of Plasticity - ICTP23.
• Revil-Baudard, B., & Cazacu, O. (2024). 3-D FE Forming Simulations Accounting for Texture Induced Anisotropy. In 14th International Conference on the Technology of Plasticity - ICTP23.
• Revil-Baudard, B., Godoy, H., & Cazacu, O. (2024). Stretch forming of isotropic materials: Influence of the ratio between yielding in pure shear and uniaxial tension on the stress state. In Esaform 2024 - International Conference on Material Forming.
• Cazacu, O., & Revil-Baudard, B. (2023). Effect of the Choice of Data Used for Analytical Identification of Orthotropic Criteria for Aluminum Extrusions. In International Conference on the Technology of Plasticity.
• Oliveira, M. C., Cazacu, O., Revil-Baudard, B., Neto, D. M., Frohn-S"orensen, P., Ma, J., Liu, W., Cruz, D. J., Santos, A. D., Van, B. A., & others, . (2023). ESAFORM 2021 cup drawing benchmark of an Al alloy: Critical follow up analysis of its potentials. In Conference on Material Forming--ESAFORM 2023.
• REVIL-BAUDARD, B., & CAZACU, O. (2023). Multi-scale modeling of the effect of crystallographic texture. In Conference on Material Forming--ESAFORM 2023.
• Revil-Baudard, B., & Cazacu, O. (2023, Fall). 3-D FE Forming Simulations Accounting for Texture Induced Anisotropy. In International Conference on the Technology of Plasticity.
• Godoy, H., Revil-Baudard, B., & Cazacu, O. (2022). Bulging of Isotropic Materials. In Esaform 2022 - 25th International Conference on Material Forming.
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  There is a large body of literature on both the techniques for bulge testing and experimental results for various metallic materials (see the book of Banabic [1]). Generally, the experimental data for isotropic materials are interpreted using the von Mises yield criterion [2]. In this paper, we investigate the role played by the third invariant of the stress deviator,J,3 on the response under bulging of isotropic materials that have the same mechanical response in tension and compression. To this end, we use the yield criterion developed by Cazacu [3] and our implementation of this model in the F.E. code Abaqus [4]. For isotropic materials, this yield criterion involves a unique parameter, denoted α; in the case when α = 0, it reduces to the von Mises yield criterion while for α ≠ 0, it involves dependence on J3 . The results of F.E. simulations of bulge tests for isotropic materials characterized by various values of the parameterα put into evidence new aspects concerning the stress states experienced by the respective materials under bulging.
• Revil-Baudard, B., Cazacu, O., & Chandola, N. (2022). Finite Element Analysis of AA 6016-T4 Sheet Metal Forming Operations Using a New Polycrystalline Model. In Esaform 2022 - 25th International Conference on Material Forming.
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  A major challenge in forming polycrystalline aluminum alloy sheets is their plastic anisotropy, namely the flow stresses and plastic strains depend on the loading direction. This plastic anisotropy is due to the anisotropy of the constituent crystals and the preferred orientations that they assume in the polycrystalline material i.e. crystallographic texture. Recently, in [1] we developed a single-crystal yield criterion that involves the correct number of anisotropy coefficients such as to satisfy the intrinsic symmetries of the constituent crystals and the condition of yielding insensitivity to hydrostatic pressure. This single-crystal criterion is defined for any stress state. It is shown that a polycrystalline model that uses this single-crystal criterion in conjunction with appropriate homogenization procedures leads to an improved prediction of the plastic anisotropy in macroscopic properties under uniaxial tension and shear loadings for polycrystalline aluminum alloy 6016-T4. Moreover, results of FE simulations of cup forming operations demonstrate the predictive capabilities of this polycrystalline model.
• Cazacu, O., & Revil-Baudard, B. (2021). Recent Advances on Modeling Plastic Deformation of Textured Metals with Applications to Metal Forming. In 13th International Conference on the Technology of Plasticity - ICTP21.
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  Due to the ease in calibration from simple tests and the reliability of the parameter identification, generally von Mises isotropic criterion and Hill orthotropic criterion are used in industry. While more advanced 3-D yield criteria have been developed, generally such criteria are written in terms of eigenvalues of transformed stress tensors, and as such the anisotropy coefficients are not directly related to mechanical properties. Therefore, the quality of the F.E. simulations depends on the experience of the analyst in calibrating these parameters. Very recently, it was shown that all advanced non-quadratic yield criteria are in fact polynomials in terms of stress components (see [1]). Moreover, for the 3-D orthotropic criteria involving one linear transformation (e.g. Yld91), the anisotropy coefficients can be determined using analytical formulas, involving only four yield points or three Lankford coefficients, respectively (see [2, 3]). In this paper, the predictive capabilities of the orthotropic criteria of Hill [4], Yld91 [5], and Cazacu [6] calibrated using both analytical and numerical minimization procedures are discussed. Moreover, simulation results of deep drawing of steel alloy DC06 are presented. The influence of the choice of the criterion, the procedure used for identification (analytical vs. numerical), and the type/extent of the data used for identification are analyzed in detail.
• Chandola, N., Cazacu, O., & Revil-Baudard, B. (2021). Effect of single crystal orientation on forming. In Esaform 2021 - 24th International Conference on Material Forming.
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  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 component on the anisotropy in uniaxial tensile properties of a polycrystal.
• Revil-Baudard, B. (2020). Forming of materials with cubic crystal structure. In Esaform 2020 - International Conference on Material Forming.
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  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.
• Chandola, N., Cazacu, O., & Revil-Baudard, B. (2018). Prediction of four, six or eight ears in drawn cups of single-crystal aluminum sheets. In NUMISHEET 2018: 11th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes.
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  The new single crystal criterion developed by Cazacu, Revil and Chandola (2017) was implemented in a finite-element (FE) code and applied to forming of single-crystal cups of aluminum. Drawing simulations were conducted for circular single-crystal blanks of three different orientations: {100} 〈 001 〉, {111} 〈 110 〉 and [112] 〈 110 〉 using the same set of parameters for the single-crystal yield criterion. A strong influence of anisotropy (single-crystal orientation) on the earing profile is found. While for the {100} 〈 001 〉 orientation it is predicted that four ears develop, for the {111} 〈 110 〉 and [112] 〈 110 〉 crystal orientations six and eight ears are predicted, respectively. The FE simulation results are consistent with experimental observations of Tucker (1961).
• Revil-Baudard, B., Chandola, N., & Cazacu, O. (2018). Prediction of the torsional response of HCP metals. In NUMISHEET 2018: 11th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes.
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  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.
• Revil-Baudard, B., Kleiser, G., Chandola, N., & Cazacu, O. (2018). Plastic deformation of metallic materials during dynamic events. In NUMISHEET 2018: 11th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes.
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  Recently, fully implicit computational capabilities have been developed to predict the plastic behavior of metallic materials (i.e. Ti, Mo) during dynamic events. It is to be noted that within this formulation framework, the equilibrium equations are solved for each time increment. The couplings of the numerical framework to the Cazacu et al. [1] plasticity model that accounts for all the key features of the plastic behavior of airframe materials, i.e. the tension-compression asymmetry and the orthotropic behavior, results in high fidelity prediction of the mechanical behavior during dynamic events. The improved predictive capabilities have been assessed for different strain rate conditions and different metallic materials. Furthermore, validation of the models and FE formulation for Taylor impact conditions through comparisons of experimental deformed profiles of Taylor specimens for Ti and Mo has been done. It is worth noting that for the first time, the extent of the zone of plastic deformation, change in geometry and the transition from transient to quasi-steady plastic wave propagation was captured with great fidelity. Furthermore, the model was used to gain understanding of the dynamic deformation process in terms of time evolution of the pressure, the extent of the plastically deformed zone, distribution of the local plastic strain rates, and when the transition to quasi-steady deformation occurs for different dynamic events. It was thus shown that this model has the potential to be used for virtual testing of complex systems.
• Cazacu, O., Revil-Baudard, B., & Chandola, N. (2017). New analytic criterion for FCC single crystals. In International Conference on the Technology of Plasticity, ICTP 2017.
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  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.
• Chandola, N., Cazacu, O., & Revil-Baudard, B. (2017). Prediction of Anisotropy of Textured Sheets Based on a New Polycrystal Model. In International Conference on the Technology of Plasticity, ICTP 2017.
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  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 45°. It is shown that the same fidelity in predictions is obtained for an ideal texture and for textures with misorientation scatter width up to 25°. 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.
• Chandola, N., Pasiliao, C., Cazacu, O., & Revil-Baudard, B. (2017). New Yield Criterion for Description of Plastic Deformation of Face-Centered Cubic Single Crystals. In Light Metals 2017, TMS.
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  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]).
• Cazacu, O., Revil-Baudard, B., & Chandola, N. (2016). Constitutive modelling of plastic deformation and damage in anisotropic high-purity titanium and validation using ex-situ and in-situ tomography data. In NUMISHEET 2016: 10th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes.
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  A study on plastic deformation and damage in titanium was conducted. The X-ray tomography data reveal that damage distribution and evolution in titanium is markedly different than for a FCC material. Theoretically, it is shown that only by modelling both the anisotropy and the tension-compression asymmetry in plastic behaviour it is possible to realistically predict titanium behaviour. For a smooth specimen under uniaxial tension, the model predicts that damage initiates at the centre of the specimen, and is diffuse; the level of damage close to failure being very low. In contrast, for a notched specimen under the same loading it is predicted that damage initiates at the outer surface of the specimen, and grows towards the centre of the specimen, which corroborates with XCMT data.
• Chandola, N., Pasiliao, C., Cazacu, O., & Revil-Baudard, B. (2016). On modeling the mechanical behavior and texture evolution of rolled AZ31 Mg for complex loadings involving strain path changes. In Magnesium Technology 2016, TMS Annual Meeting and Exhibition.
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  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. The general held belief is that without modeling de-twining it is impossible to describe the effect of the pre-strain on hardening behavior in low cycle compression-tension-compression and tension-compression-tension tests, respectively. In this paper, it is shown that using the viscoplastic self-consistent crystal plasticity model in conjunction with the pre-dominant twinning reorientation (PTR) scheme it is possible to accurately model the reorientation of the microstructure for such complex loadings. Comparison with recent data reported by Hama et al. [1, 2] shows that the stress-strain response is also very well predicted.
• Chandola, N., Revil-Baudard, B., & Cazacu, O. (2016). Plastic deformation of high-purity a-titanium: Model development and validation using the Taylor cylinder impact test. In NUMISHEET 2016: 10th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes.
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  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.
• Kleiser, G., Revil-Baudard, B., Cazacu, O., & Pasiliao, C. (2016). Constitutive modeling and simulation at room-temperature deformation and failure of polycrystalline molybdenum. In NUMISHEET 2016: 10th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes.
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  In this paper is presented a systematic experimental investigation of the mechanical response of polycrystalline commercially pure molybdenum (Mo). It was established that the material has ductility in tension at 10-5/s and that the failure strain is strongly dependent on the orientation. A specimen taken along the rolling direction sustains large axial strains (20%), while a specimen cut at an angle of 45° to the rolling direction could only sustain 5% strain. Irrespective of the loading orientation the yield stress in uniaxial compression is larger than in uniaxial tension. While in tension the material has a strong anisotropy in Lankford coefficients, in uniaxial compression it displays weak strain-anisotropy. An elastic- plastic orthotropic model that accounts for all the specificities of the plastic deformation of the material was developed. Validation of the model was done through comparison with data on notched specimens. Quantitative agreement with both global and local strain fields was obtained.
• Revil-Baudard, B., & Massoni, E. (2016). Constitutive modeling of a commercially pure titanium: Validation using bulge tests. In NUMISHEET 2016: 10th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming.
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  In this paper, mechanical tests aimed at characterizing the plastic anisotropy of a commercially pure α-titanium sheet are presented. Hemispheric and elliptic bulge tests conducted to investigate the forming properties of the material are also reported. To model the particularities of the plastic response of the material the classical Hill [1] yield criterion, and Cazacu et al. [2] yield criterion are used. Identification of the material parameters involved in both criteria is based only on uniaxial test data, while their predictive capabilities are assessed through comparison with the bulge tests data. Both models reproduce qualitatively the experimental plastic strain distribution and the final thickness of the sheet. However, only Cazacu et al. [2] yield criterion, which accounts for both the anisotropy and tension-compression asymmetry of the material captures correctly plastic strain localization, in particular its directionality. Furthermore, it is shown that accounting for the strong tension-compression asymmetry in the model formulation improves numerical predictions regarding the mechanical behavior close to fracture of a commercially pure titanium alloy under sheet metal forming processes.
• Chandola, N., Cazacu, O., & Revil-Baudard, B. (2015). New model predicting the unusual buckling behavior of AZ31 Mg. In Magnesium Technology 2015, TMS Annual Meeting and Exhibtion.
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  In this paper, for the first time it is demonstrated that only by accounting for the combined effects of the tension-compression asymmetry and strong anisotropy of AZ31 Mg it is possible to predict the very unusual buckling of this material, and most importantly capture the energy absorbed prior to buckling. It is shown that by using an elastic/plastic model based on Cazacu et al. [1] criterion that accounts for both anisotropy and strength differential effects, a strong influence of the direction of crushing is predicted. However, if Hill's [2] criterion is used i.e. strength differential effects are not taken into account, the predictions indicate that the orientation of the tube has no influence on the final geometry of the crushed specimen. Furthermore, the location and cross section of the buckle are not correctly captured by the Hill [2] yield criterion.
• Revil-Baudard, B., Cazacu, O., & Chandola, N. (2014). Role of the plastic flow of the matrix on yielding and void evolution of porous solids. In IDDRG 2014.
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  In this paper, it is shown that yielding and void evolution in a porous metallic material is strongly influenced by the particularities of the plastic flow of the matrix. This is demonstrated by comparing the effective response of porous solids for which the matrix is described by Tresca and von Mises yield criterion, respectively. The effective response of the porous solid is calculated analytically using rigorous limit analysis theorems and upscaling techniques. Analysis is conducted for both tensile and compressive axisymmetric loading scenarios and spherical void geometry. For the first time it is demonstrated that if the matrix plastic response is governed by Tresca yield criterion, the overall response is softer, the combined effects of pressure and the third-invariant on yielding being much stronger than in a porous solid with von Mises matrix. Furthermore, the rate of void growth or collapse is much faster in a porous solid with Tresca matrix.
• Revil-Baudard, B., Yoon, J., Stewart, J., & Cazacu, O. (2012). On the influence of damage evolution in an incompressible material with matrix displaying tension-compression asymmetry. In Procedia IUTAM.
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  A strong difference between the behavior in tension versus compression is observed at the polycrystal level, if either twinning or non-Schmid type slip are contributors to plastic deformation at the single crystal level. Despite recent progress in modeling the effects of this asymmetry in yielding, its influence on damage evolution remains a challenge. In a recent paper [1] we presented a new constitutive model for voided polycrystal that incorporates the effects of the tension-compression asymmetry of the incompressible matrix on the overall dilatational plastic behavior. In this contribution, this model is used to investigate the influence of the tension-compression asymmetry of the matrix on void evolution for uniaxial loading conditions. It is shown that if the matrix tensile strength is higher than its compressive strength, void growth and damage distribution are similar to that in classical materials obeying Gurson's [2] criterion. On the other hand, for certain porous polycrystals in which the matrix tensile strength is lower than its compressive strength, void growth rate is much slower. Damage distribution is significantly different; the location of the zone of maximum porosity shifts from the center of the specimen outwards. Furthermore, the influence of the evolving microstructure on void growth is studied. It is shown that void growth is significantly affected by the rate of change of the matrix strength differential with plastic strain. © 2012 Published by Elsevier B.V.
• Revil-Baudard, B., & Massoni, E. (2010). Implementation of an evolving non quadratic anisotropic behaviour for the closed packed materials. In NUMIFORM 2010: Proceedings of the 10th International Conference on Numerical Methods in Industrial Forming Processes Dedicated to Professor O. C. Zienkiewic.
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  In this paper, the mechanical behaviour of α-titanium alloys is modelised for the cold forming processes. The elasto-plastic constitutive law is decomposed in an anisotropic plastic criterion, an isotropic hardening and a kinematic hardening. Non quadratic criteria have been developed by Cazacu et al. [1], to model the plasticity of hexagonal closed packed materials. The implementation of this model in a finite element software switch between two bases, the equilibrium is calculated in a reference basis and the anisotropy axes define a local basis, updated by the deformation gradient. An identification procedure, based on tensile tests, allows defining all the parameters needed to model the elasto-plastic behaviour. Simulations of cold forming processes (bulging and deep drawing) have been done to validate this model. Numerical results are compared with experimental data, obtained from speckles analysis. © 2010 American Institute of Physics.
• Revil-Baudard, B., & Massoni, E. (2010). Simulation of titanium alloys behaviour for cold forming processes of metal sheets. In Mechanics & Industry.
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  In this paper, the mechanical behaviour of ? titanium alloys is modelised for the cold forming processes. The elasto-plastic constitutive law is decomposed in an anisotropic plastic criterion, an isotropic hardening and a kinematic hardening. Non quadratic criteria have been developed by Cazacu et al. (Orthotropic yield criterion for hexagonal closed packed metals, Int. J. Plasticity 22 (2006) 1171-1194), to model the plasticity of hexagonal closed packed materials. The implementation of this model in a finite element software switches between two bases, the equilibrium is calculated in a reference basis and the anisotropy axes define a local basis, updated by the deformation gradient. An identification procedure, based on tensile tests, allows to define all the parameters needed to model the elasto-plastic behaviour. Simulation of cold forming processes (bulging and deep drawing) have been done to validate this model. Numerical results are compared with experimental data, obtained from speckles analysis. © AFM, EDP Sciences 2010.

Presentations

• Revil Baudard, B. (2024). Modeling and Simulations of Energetic Materials under High Strain Rate Loadings. Energetic Material FY24 Tri-service Program Review. National Harbor, MD: AFOSR.
• Revil Baudard, B. (2024). Modeling and Simulations of Energetic Materials under High Strain Rate Loadings. IMECE 2024 - International Mechanical Engineering Congress. Portland, Oregon.
• Revil Baudard, B. (2024). Stretch Forming Of Isotropic Materials: Influence Of The Ratio Between Yielding In Pure Shear And Uniaxial Tension On The Stress State. Esaform 2024. Toulouse, France.
• Cazacu, O., & Revil Baudard, B. (2023, Fall). Effect of the choice of data used for analytical identification of orthotropic criteria for aluminum extrusions. ICTP 2023: the 14th International Conference on the Technology of Plasticity. Mandelieu la Napoule, France.
• Revil Baudard, B. (2023). Multi-scale modeling of the effect of crystallographic texture. ESAFORM 2023: European Conference on Material Forming. Krakow, Poland.
• Revil Baudard, B. (2023, fall). 3-D FE forming simulations accounting for texture induced anisotropy. ICTP 2023: 14th International Conference on the Technology of Plasticity. Mandelieu la Napoule, France.