Failure of metals I : brittle and ductile fracture

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.

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Ductile Fracture by Void Growth to Coalescence

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.

An extended model for void growth and coalescence - application to anisotropic ductile fracture

On the path-dependence of the fracture locus in ductile materials - Analysis

An effective yield function is derived for a porous ductile solid near a state of failure by microvoid coalescence. Homogenization theory combined with limit analysis are used to that end. A cylindrical cell is taken to contain a coaxial cylindrical void of finite height. Plastic flow in the intervoid matrix is described by J2 theory while regions above and below the void remain rigid. Velocity boundary conditions are employed which are compatible with an overall uniaxial straining for the cell, a postlocalization kinematics that is ubiquitous during the coalescence of neighboring microvoids in rate-independent solids. Such boundary conditions are not of the uniform strain rate kind, as is the case for Gursonlike models. A similar limit analysis problem for a square-prismatic cell containing a square-prismatic void was posed long ago (Thomason, P. F., 1985, “Three-Dimensional Models for the Plastic Limit–Loads at Incipient Failure of the Intervoid Matrix in Ductile Porous Solids,” Acta Metallurgica, 33, pp. 1079–1085). However, to date a closed-form solution to this problem has been lacking. Instead, an empirical expression of the yield function proposed therein has been widely used in the literature. The fully analytical expression derived here is intended to be used concurrently with a Gursonlike yield function in numerical simulations of ductile fracture.

S. Hoelscher

Papers

Void growth and coalescence in anisotropic plastic solids