V. Tvergaard

Flow Localization in the Plane Strain Tensile Test

Abstract The deformations in a plane strain tensile test are analyzed numerically, both for a solid characterized by a phenomenological corner theory of plasticity and for a nonlinear elastic solid. As opposed to the simplest flow theory of plasticity with a smooth yield surface, both these material models exhibit shear band instabilities at a realistic level of strain. Initial imperfections are specified in the form of thickness inhomogeneities. A long-wavelength imperfection grows into the well-known necking mode and subsequently, at a sufficiently high local strain level, bands of intense shear deformations develop in the necking region. The location of these shear bands is strongly influenced by the location of small strain concentrations near the surface, induced by various short-wave patterns of initial thickness imperfections. In accord with the non-uniform straining in the neck it is found that the intensity of the localized deformations varies along the bands, and some of the shear bands end inside the material.

Nonlocal effects on localization in a void-sheet

Abstract For a nonlocal damage model it is expected that the characteristic material length relates to the damage mechanism. In the case of ductile fracture the most relevant length scales would be the average void radius or spacing. Cell model computations representing a single row of voids in an infinite solid under plane strain conditions are here used to compare with predictions of a nonlocal version of a porous ductile material model. Both the critical strain for the onset of plastic flow localization and the slope of the stress-strain curve in the post-localization range are compared, and it is found that both of these are affected by the value of the material length in the nonlocal model. Comparison with predictions of the void-sheet cell model are carried out for an inclined row of voids, leading to shear band failure, as well as a row of transversely aligned voids. For shear bands the material characteristic length scales with the void radius, whereas for transversely aligned voids the scaling is with the void spacing.

Void Growth in Plastic Solids

An overview is given of the continuum mechanics of void growth pertaining to room temperature ductile fracture processes. Analyses of the growth of isolated voids and of void interaction effects are reviewed. A framework for phenomenological constitutive relations for porous plastic solids is discussed. Calculations of localization and failure in porous plastic solids are reviewed that illustrate the progressive development of ductile failure. Additional considerations, including the effect of the constraint provided by contact between the growing void and the void-nucleating particle, cavitation, and the effect of non-uniform porosity distributions are briefly noted.