Elastic-plastic ductile damage model based on strain-rate plastic potential

Modeling of ductile damage is generally done using analytical potentials, which are expressed in the stress space. In this paper, for the first time it is shown that strain rate potentials which are exact conjugate of the stress-based potentials can be instead used to model the dilatational response of porous polycrystals. A new integration algorithm is also developed. It is to be noted that a strain-rate based formulation is most appropriate when the plastic flow of the matrix is described by a criterion that involves dependence on all stress invariants. In such cases, although a strain-rate potential is known, the stress-based potential cannot be obtained explicitly. While the proposed framework based on strain-rate potentials is general, for comparison purposes in this work we present an illustration of the approach for the case of a porous solid with von Mises matrix containing randomly distributed spherical cavities. Comparison between simulations using the strain-rate based approach and the classical stress-based Gurson’s criterion in uniaxial tension is presented. These results show that the model based on a strain-rate potential predicts the dilatational response with the same level of accuracy

Micromechanical study of the dilatational response of porous solids with pressure-insensitive matrix displaying tension-compression asymmetry

In this paper, the dilatational response of porous solids with pressure-insensitive matrix displaying strength differential (SD) effects is investigated. To this end, micromechanical finite-element analyses of three-dimensional unit cells are carried out. The matrix behavior is governed by the isotropic form of Cazacu et al. (2006) criterion that accounts for SD effects through a parameter k. Simulation results are presented for axisymmetric tensile loadings corresponding to fixed values of the stress triaxiality for the two possible values of the Lode parameter, LP. For moderate and high stress triaxialities, it is shown that for materials for which the matrix tensile strength is larger than its compressive strength (k > 0), under tensile loadings corresponding at LP=1 the void growth rate is much faster than in the case of tensile loadings at LP=-1. The opposite holds true for materials with matrix tensile strength lower than its compressive strength (k< 0). This drastic difference in porosity evolution is explained by the distribution of the local plastic strain and stresses, which are markedly different than in a von Mises material (i.e. no SD effects of the matrix).info:eu-repo/semantics/publishedVersio

Analytical yield criterion for an anisotropic material containing spherical voids and exhibiting tension–compression asymmetry

AbstractA significant difference between the behavior in tension versus compression is obtained at the polycrystal level if either twinning or non-Schmid effects are contributors to the plastic deformation at the single crystal level. Examples of materials that exhibit tension–compression asymmetry include hexagonal close-packed (HCP) polycrystals and intermetallics (e.g., molybdenum compounds). Despite recent progress in modeling their yield behavior in the absence of voids, the description of coupling between plasticity and damage by void growth in these materials remains a challenge.This paper is devoted to the development of a macroscopic anisotropic yield criterion for a porous material when the matrix material is incompressible, anisotropic and displays tension–compression asymmetry. The analytical yield criterion is obtained based on micromechanical considerations and non-linear homogenization. The matrix plastic behavior is described by the Cazacu et al. (2006) anisotropic yield criterion that is pressure-insensitive and accounts for strength–differential effects. Comparison between finite element cell calculations and theory show the predictive capabilities of the developed anisotropic model in terms of modeling the combined effects of anisotropy, tension–compression asymmetry of the matrix and voids on the overall yielding of the porous aggregate. It is shown that if the matrix material does not display tension–compression asymmetry, the developed criterion reduces to that of Benzerga and Besson (2001). If the matrix is isotropic, it reduces to the isotropic criterion developed in Cazacu and Stewart (2009)

On Modeling Plasticity-damage Couplings in Polycrystalline Materials

AbstractAt 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

Elastic-plastic ductile damage model based on strain-rate plastic potential

Modeling of ductile damage is generally done using analytical potentials, which are expressed in the stress space. In this paper, for the first time it is shown that strain rate potentials which are exact conjugate of the stress-based potentials can be instead used to model the dilatational response of porous polycrystals. A new integration algorithm is also developed. It is to be noted that a strain-rate based formulation is most appropriate when the plastic flow of the matrix is described by a criterion that involves dependence on all stress invariants. In such cases, although a strain-rate potential is known, the stress-based potential cannot be obtained explicitly. While the proposed framework based on strain-rate potentials is general, for comparison purposes in this work we present an illustration of the approach for the case of a porous solid with von Mises matrix containing randomly distributed spherical cavities. Comparison between simulations using the strain-rate based approach and the classical stress-based Gurson’s criterion in uniaxial tension is presented. These results show that the model based on a strain-rate potential predicts the dilatational response with the same level of accuracy

The role of tension-compression asymmetry of the plastic flow on ductility and damage accumulation of porous polycrystals

The influence of the tension-compression asymmetry of the plastic flow, due to intrinsic single-crystal deformation mechanisms, on porosity evolution and the overall ductility of voided metallic polycrystals is assessed. To this end, detailed micromechanical finite-element analyses of three-dimensional unit cells containing a single initially spherical cavity are carried out. The plastic flow of the matrix (fully-dense material) is described by a criterion that accounts for strength-differential effects induced by deformation twinning of the constituent grains of the metallic polycrystalline materials. The dilatational response of porous polycrystals are calculated for macroscopic axisymmetric tensile loadings corresponding to a fixed value of the stress triaxiality and the two possible values of the Lode parameter. It is shown that damage accumulation, and ultimately ductility of the porous polycrystals are markedly different as compared to the case when the matrix is governed by von Mises criterion. Most importantly, a direct correlation is established between the macroscopic material parameter k that is intimately related to the particularities of the plastic flow of the matrix and the rate of damage accumulation. (C) 2017 Portuguese Society of Materials (SPM). Published by Elsevier Espana, S.L.U.. All rights reserved.The authors gratefully acknowledge the financial support of the Portuguese Foundation for Science and Technology (FCT) via the project PTDC/EMETEC/1805/2012.This work has been supported by FCT (Fundacao para a Ciencia e Tecnologia) in the scope of the project UID/EEA/04436/2013.info:eu-repo/semantics/publishedVersio