DUCTILE CRACK-GROWTH .1. A NUMERICAL STUDY USING COMPUTATIONAL CELLS WITH MICROSTRUCTURALLY-BASED LENGTH SCALES

Many metals which fail by a void growth mechanism display a macroscopically planar fracture process zone of one or two void spacings in thickness characterized by intense plastic flow in the ligaments between the voids; outside this region, the voids exhibit little or no growth. To model this process a material layer containing a pre-existing population of similar sized voids is assumed. The thickness of the layer, D, can be identified with the mean spacing between the voids. This layer is represented by an aggregate of computational cells of linear dimension D. Each cell contains a single void of some initial volume. The Gurson constitutive relation for dilatant plasticity describes the hole growth in a cell resulting in material softening and, ultimately, loss of stress carrying capacity. The collection of cells softened by hole growth constitutes the fracture process zone of length I-1. Two fracture mechanism regimes can be identified corresponding to l(1) approximate to D and l(1) >> D. The connection between these mechanisms and fracture resistance is discussed. Finite element calculations have been carried out to determine crack growth resistance curves for plane strain, mode I crack growth under small scale yielding. A row of voided cells is placed on the symmetry plane ahead of the initial crack. These cell elements are embedded within a conventional elastic-plastic continuum. Under increasing load, the voids in the cells grow and coalesce to form a new crack surface thereby advancing the crack. Resistance curves are calculated for crack growth exceeding many multiples of D. The parameters affecting fracture resistance are discussed emphasizing the roles of microstructural parameters and continuum properties of the material. The effect of crack tip constraint on fracture resistance is examined under small scale yielding 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.