SUMMARYThe cohesive finite element method (CFEM) allows explicit modelling of fracture processes. One form of CFEM models integrates cohesive surfaces along all finite element boundaries, facilitating the explicit resolution of arbitrary fracture paths and fracture patterns. This framework also permits explicit account of arbitrary microstructures with multiple length scales, allowing the effects of material heterogeneity, phase morphology, phase size and phase distribution to be quantified. However, use of this form of CFEM with cohesive traction-separation laws with finite initial stiffness imposes two competing requirements on the finite element size. On one hand, an upper bound is needed to ensure that fields within crack-tip cohesive zones are accurately described. On the other hand, a lower bound is also required to ensure that the discrete model closely approximates the physical problem at hand. Both issues are analysed in this paper within the context of fracture in multi-phase composite microstructures and a variable stiffness bilinear cohesive model. The resulting criterion for solution convergence is given for meshes with uniform, cross-triangle elements. A series of calculations is carried out to illustrate the issues discussed and to verify the criterion given. These simulations concern dynamic crack growth in an Al 2 O 3 ceramic and in an Al 2 O 3 /TiB 2 ceramic composite whose phases are modelled as being hyperelastic in constitutive behaviour.

Dynamic fracture in two-phase Al 2 O 3 /TiB 2 ceramic composite microstructures is analyzed explicitly using a cohesive finite element method (CFEM). This framework allows the effects of microstructural heterogeneity, phase morphology, phase distribution, and size scale to be quantified. The analyses consider arbitrary microstructural phase morphologies and entail explicit tracking of crack growth and arbitrary fracture patterns. The approach involves the use of CFEM models that integrate cohesive surfaces along all finite element boundaries as an intrinsic part of the material description. This approach obviates the need for any specific fracture criteria and assigns models the capability of predicting fracture paths and fracture patterns. Calculations are carried out using idealized phase morphologies as well as real phase morphologies in actual material microstructures. Issues analyzed include the influence of microstructural morphology on the fracture behavior, the influence of phase size on fracture resistance, the effect of interphase bonding strength on failure, and the effect of loading rate on fracture.

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