Computational Modeling of Material Failure

Division of Engineering. Brown University, Providence Rl 02912 Analyses of fracture are discussed where the initial-boundary value problem for­mulation allows for the possibility of a complete loss of stress carrying capacity, with the associated creation of new free surface. No additional failure criterion is employed so that fracture arises as a natural outcome of the deformation process. Two types of analyses are reviewed. In one case, the material's constitutive de­scription incorporates a model of the failure mechanism; the nucleation, growth and coalescence of microvoids for ductile fracture in structural metals. In some analyses this is augmented with a simple characterization of failure by cleavage to analyze ductile-brittle transitions. The other class of problems involves specifying separation relations for one or more cohesive surfaces present in the continuum. The emphasis is on reviewing recent work on dynamic failure phenomena and the discussion centers around issues of length scales, size effects and the convergence of numerical solutions. INTRODUCTION The main focus of quantitative theories of mechanical behavior is the determination of the deformations and stresses in a solid subject to a given history of loading. Failure due to loss of stability, as in buckling under compressive loading or localized necking under tensile loading, can emerge as a direct outcome of a stress and deformation analysis. Fracture, which involves the cre­ation of new free surface, is generally treated by car­rying out a conventional stress analysis with a fracture criterion specified separately. There has been increasing interest in developing the­ories where fracture emerges as a natural outcome of the deformation history. One motivation stems from the progressive nature of fracture in many engineering materials; local failure causes a redistribution of the stress and deformation fields, which affects the course of subsequent failure, which causes a further stress and deformation redistribution, etc. Accounting for this progression is often essential for predicting final failure. Another motivation is to relate phenomenological mea­sures of ductility and fracture toughness to measurable (and controllable) features of a material's microstruc-ture, to provide a basis for the design of stronger and tougher materials. Ultimately, of course, separation takes place on an atomic scale. However, in many circumstances the processes that are key for determining the mechanical performance of engineering materials take place on a much larger length scale, say of the order of a micron or larger, for example, on the size scale of grains in a polycrystalline metal, and the use of a continuum ap­proach is justified. The main ingredients required for the theoretical framework are constitutive descriptions of inelastic flow, equations for damage evolution and crack mechanics. The direct prediction of failure has been pursued for diverse materials and from a variety of perspec­tives. One approach, often termed continuum dam­age mechanics, see e.g., Kachanov (1958), Lemaitre (1986), introduces one or more phenomenological pa­rameters to characterize failure. The evolution equa­tions and parameters for damage evolution are cho­sen from experiment and are usually not directly re­lated to the michromechanical processes of failure. An­other approach is based on incorporating a model of the failure process into the constitutive description of the continuum in order to make a more direct connec­tion to the physical mechanisms of fracture. Such the­ories have been developed for microcracking of ceram­ics, Charalambides and McMeeking (1987) and Ortiz and Giannakopoulos (1990), ductile fracture of metals by void nucleation, growth and coalescence, Tvergaard (1990a), and for failure modes of metal-matrix compos­ites, Needleman et al. (1993). Initial-boundary value problems are formulated and solved where the loss of load carrying capacity emerges as an outcome of com­puting the deformation history. Analyses carried out within such a framework have given both qualitative and quantitative descriptions of fracture processes. Attention in this review is mainly focused on analy­ses of ductile failure processes and ductile-brittle tran­sitions in structural metals. The fracture mechanisms