Modeling Crack Growth Resistance Using Computational Cells with Microstructurally—Based Length Scales Available to Purchase

Many metals which fail by void growth mechanism display a macroscopically planar fracture process zone of one or two void spacing in thickness characterized by intense plastic flow in the ligaments between the voids. To model this process cell elements, each of which contains a void, are employed on the plane ahead of the initial crack. The linear dimension of these elements is D. We use Gurson model to describe the hole growth in a cell resulting in material softening and, ultimately, loss of stress carrying capacity leading to void coalescence and formation of new crack surface thereby advancing the crack. The void-free material surrounding the cells is described by the J₂ flow theory of plasticity. The two cell parameters, D and f₀, characterize the mean spacing and volume fraction of voids in the material lying in the plane of fracture.

Finite element calculations have been carried out for plane strain, mode I crack growth under small scale yielding. A wide range of fracture behavior is captured by proper combinations of D and f₀ Resistance curves are calculated for crack extensions two orders of magnitude larger than D. The parameters affecting fracture resistance are discussed emphasizing the roles of microstructural parameters and continuum properties of the material. Geometry effects on fracture resistance are investigated by way of the T-stress. As a final application, resistance curves for a deep and a shallow crack bend bar are computed. These are compared with experimental data.