S.M. Keralavarma

Abstract: Plastic constitutive relations are derived for a class of anisotropic porous materials consisting of coaxial spheroidal voids, arbitrarily oriented relative to the embedding orthotropic matrix. The derivations are based on nonlinear homogenization, limit analysis and micromechanics. A variational principle is formulated for the yield criterion of the effective medium and specialized to a spheroidal representative volume element containing a confocal spheroidal void and subjected to uniform boundary deformation. To obtain closed form equations for the effective yield locus, approximations are introduced in the limit-analysis based on a restricted set of admissible microscopic velocity fields. Evolution laws are also derived for the microstructure, defined in terms of void volume fraction, aspect ratio and orientation, using material incompressibility and Eshelby-like concentration tensors. The new yield criterion is an extension of the well known isotropic Gurson model. It also extends previous analyses of uncoupled effects of void shape and material anisotropy on the effective plastic behavior of solids containing voids. Preliminary comparisons with finite element calculations of voided cells show that the model captures non-trivial effects of anisotropy heretofore not picked up by void growth models.

Abstract: The effect of loading path on the fracture locus was examined theoretically by means of cell model calculations. Two-dimensional axisymmetric finite element analyses were conducted to simulate plastic deformation of a material containing a periodic distribution of initially spherical voids. In the cell model, failure is defined to correspond to an abrupt loss of overall load bearing capacity. The cylindrical unit cells were subjected to loading along several radial paths, characterized by constant values of stress triaxiality. The strain-to-failure was recorded for each path and the locus relating it to triaxiality was thus uniquely determined. The process was repeated for a set of non-radial loading paths in which uniaxial loading was applied up to some strain level, followed by loading at constant triaxiality. For these cases, the time-weighted average value of stress triaxiality was used to plot the fracture locus. It was found that the failure locus for nonradial loadings differs substantially from that for radial paths. In fact, the nonradial locus does not represent a one-to-one relationship between average triaxiality and strain-to-failure. In addition, by varying the strain level E e ∗ at which the load path is changed, a family of failure loci is generated, indexed by E e ∗ .

Abstract: We report two-dimensional discrete dislocation dynamics simulations of combined dislocation glide and climb leading to "power-law" creep in a model aluminum crystal. The approach fully accounts for matter transport due to vacancy diffusion and its coupling with dislocation motion. The existence of quasiequilibrium or jammed states under the applied creep stresses enables observations of diffusion and climb over time scales relevant to power-law creep. The predictions for the creep rates and stress exponents fall within experimental ranges, indicating that the underlying physics is well captured.

Abstract: Experimental measurements and simulation results for the evolution of plastic deformation and hardening in micropillars are compared. The stress–strain response of high-symmetry Cu single crystals is experimentally determined using in situ micropillar compression. Discrete dislocation simulations are conducted within a two-dimensional plane-strain framework with the dislocations modeled as line singularities in an isotropic elastic medium. Physics-based constitutive rules are employed for an adequate representation of hardening. The numerical parameters entering the simulations are directly identified from a subset of experimental data. The experimental measurements and simulation results for the flow stress at various strain levels and the hardening rates are in good quantitative agreement. Both flow strength and hardening rate are size-dependent and increase with decreasing pillar size. The size effect in hardening is mainly caused by the build-up of geometrically necessary dislocations. Their evolution is observed to be size-dependent and more localized for smaller sample volumes, which is also reflected in local crystal misorientations.

Abstract: Large strain finite element calculations of unit cells subjected to triaxial axisymmetric loadings are presented for plastically orthotropic materials containing a periodic distribution of aligned spheroidal voids. The spatial distribution of voids and the plastic flow properties of the matrix are assumed to respect transverse isotropy about the axis of symmetry of the imposed loading so that a two-dimensional axisymmetric analysis is adequate. The parameters varied pertain to load triaxiality, matrix anisotropy, initial porosity and initial void shape so as to include the limiting case of penny-shaped cracks. Attention is focussed on comparing the individual and coupled effects of void shape and material anisotropy on the effective stress–strain response and on the evolution of microstructural variables. In addition, the effect of matrix anisotropy on the mode of plastic flow localization is discussed. From the results, two distinct regimes of behavior are identified: (i) at high triaxialities, the effect of material anisotropy is found to be persistent, unlike that of initial void shape and (ii) at moderate triaxialities the influence of void shape is found to depend strongly on matrix anisotropy. The findings are interpreted in light of recent, microscopically informed models of porous metal plasticity. Conversely, observations are made in relation to the relevance of these results in the development and calibration of a broader set of continuum damage mechanics models.

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

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Abstract: A model for the axisymmetric growth and coalescence of small internal voids in elastoplastic solids is proposed and assessed using void cell computations. Two contributions existing in the literature have been integrated into the enhanced model. The first is the model of Gologanu-Leblond-Devaux, extending the Gurson model to void shape effects. The second is the approach of Thomason for the onset of void coalescence. Each of these has been extended heuristically to account for strain hardening. In addition, a micromechanically-based simple constitutive model for the void coalescence stage is proposed to supplement the criterion for the onset of coalescence. The fully enhanced Gurson model depends on the flow properties of the material and the dimensional ratios of the void-cell representative volume element. Phenomenological parameters such as critical porosities are not employed in the enhanced model. It incorporates the effect of void shape, relative void spacing, strain hardening, and porosity. The effect of the relative void spacing on void coalescence, which has not yet been carefully addressed in the literature. has received special attention. Using cell model computations, accurate predictions through final fracture have been obtained for a wide range of porosity, void spacing, initial void shape, strain hardening, and stress triaxiality. These predictions have been used to assess the enhanced model. (C) 2000 Elsevier Science Ltd. All rights reserved.

Abstract: This is the first of three overviews on failure of metals. Here, brittle and ductile failure under monotonic loadings are addressed within the context of the local approach to fracture. In this approach, focus is on linking microstructure, physical mechanisms and overall fracture properties. The part on brittle fracture focuses on cleavage and also covers intergranular fracture of ferritic steels. The analysis of cleavage concerns both BCC metals and HCP metals with emphasis laid on the former. After a recollection of the Beremin model, particular attention is given to multiple barrier extensions and the crossing of grain boundaries. The part on ductile fracture encompasses the two modes of failure by void coalescence or plastic instability. Although a universal theory of ductile fracture is still lacking, this part contains a comprehensive coverage of the topic balancing phenomenology and mechanisms on one hand and microstructure-based modeling and simulation on the other hand, with application examples provided.

Abstract: Publisher Summary An important failure mechanism in ductile metals and their alloys is by growth and coalescence of microscopic voids. In structural materials, the voids nucleate at inclusions and second-phase particles by decohesion of the particle–matrix interface or by particle cracking. Void growth is driven by plastic deformation of the surrounding matrix. Early micromechanical treatments of this phenomenon considered the growth of isolated voids. Later, constitutive equations for porous ductile solids were developed based on homogenization theory. Among these, the most widely known model was developed by Gurson for spherical and cylindrical voids.