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    Effective yield criterion for a porous single crystal accounting for void size effects
    (01-09-2021)
    Khavasad, Prakash H.
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    The growth of sub-grain voids in crystalline materials is affected by plastic anisotropy as well as void size effects. In this paper, an effective yield criterion is derived for a porous single crystal using homogenization theory and limit analysis. A two dimensional planar model of a single crystal containing a random distribution of cylindrical voids is assumed. The effective yield criterion is derived using plastic limit load analysis of a hollow cylindrical representative volume element, containing a concentric cylindrical void in a single crystalline matrix. A conventional strain gradient plasticity model with an embedded material length scale is assumed for the matrix, in order to account for the void size dependence of yielding. The yield loci and void growth rates predicted by the model under plane strain conditions are validated by comparison with numerical results obtained using finite elements, as well as prior analytical results for the special case of size independent matrix behavior. The model predictions for the size dependence of the yield stress as well as void growth under proportional loading conditions are discussed with reference of known results from experiments and lower scale dislocation dynamics simulations.
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    Publication
    Numerical assessment of an anisotropic porous metal plasticity model
    (01-11-2015) ;
    Benzerga, A. A.
    The objective of this paper is to perform numerical assessment of a micromechanical model of porous metal plasticity developed previously by the authors. First, upper bound estimates for the yield loci are computed using homogenization and limit analysis of a spheroidal representative volume element containing a confocal spheroidal void, neglecting elasticity. Unlike in the development of the analytical model, the computational limit analysis is performed without recourse to approximations so that the obtained yield loci are rigorous upper bounds for the true criterion. Next, the model's macroscopic dilatancy at incipient plastic flow is compared against that of the numerical limit analysis approach. Finally, finite-element calculations, with elasticity included, are presented for transversely isotropic porous unit-cells loaded axisymmetrically. The effective stress-strain response as well as evolution of the unit-cell porosity and void aspect ratio are compared with theoretical predictions.
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    Publication
    Micromechanical modeling and simulation of the loading path dependence of ductile failure by void growth to coalescence
    (01-07-2019)
    Vishwakarma, Vishal
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    The loading path dependence of ductile failure by void growth to coalescence is studied using a unit cell model of a porous material, containing a periodic distribution of voids in an elasto-plastic power law hardening matrix. The unit cell is subjected to triaxial proportional loading paths, and predictions for the strains to failure, defined as the onset of void coalescence by plastic strain localization in the inter-void ligaments, are obtained as a function of the loading path parameters, the stress triaxiality and the Lode parameter. Analogous simulations of a macroscopic material element subjected to proportional loading are performed using a multi-surface plasticity model, which accounts for void growth by diffuse plastic flow and void coalescence by the localization of plastic strains inside a micro-scale representative volume element. A phenomenological hardening law that approximately accounts for the physics of strain hardening during both pre- and post-coalescence deformation is proposed. The strains to failure in the continuum simulations are determined as the equivalent strains to the onset of void coalescence at the micro-scale of the voids. It is shown that the multi-surface plasticity model quantitatively predicts the loading path dependence of the strains to failure obtained from the cell model simulations over a wide range of values of the Lode parameter, from axisymmetric to shear dominated states, and moderate to large values of the stress triaxiality. Quantitative agreement with cell model simulations is obtained for two representative values of the strain hardening exponent, and in the absence of heuristic adjustable parameters in the model.