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In the present paper, ductile crack growth in an aluminium alloy is numerically simulated using a cohesive zone model under both plane stress and plane strain conditions for two different fracture types, shear and normal modes. The cohesive law for ductile fracture consists of two parts—a specific material’s separation traction and energy. Both are assumed to be constant during ductile fracture (stable crack growth). In order to verify the assumed cohesive law to be suitable for ductile fracture processes, experimental records are used as control curves for the numerical simulations. For a constant separation traction, determined experimentally from tension test data, the corresponding cohesive energy was determined by finite element calculations. It is confirmed that the cohesive zone model can be used to characterize a single ductile fracture mode and is roughly independent of stable crack extention. Both the cohesive traction and the cohesive fracture energy should be material specific parameters. The extension of the cohesive zone is restricted to a very small region near the crack tip and is in the order of the physical fracture process. Based on the present observations, the cohesive zone model is a promising criterion to characterize ductile fracture.

An elastoplastic solution with higher-order terms for cracks in materials exhibiting pressure-sensitive yielding and plastic volumetric deformation is presented in this paper. Two-term expansions of the plane strain and plane stress solutions for a crack in a homogeneous material are obtained. It is shown that a variable-separable solution form under plane strain conditions exists only for weakly pressure-sensitive materials and the limit values of the pressure-sensitivity factor depend on the strain-hardening exponent. The second-order plane strain terms have to be solved as an eigenvalue problem and the elastic terms enter the second-order solutions only when the material has substantial strain-hardening. It follows that the second stress amplitude factor must be determined by the applied load. The values of the second exponents in the stress expansion are slightly larger than zero for most hardening materials and behave as an increasing function of the pressure-sensitivity factor. The finite element computations confirm that the second-order terms under plane strain conditions will increase dominance of the asymptotic solution remarkably. The plane stress analysis shows that the amplitudes of both leading-order and second-order solution are determined by the J-integral for most pressure-sensitive dilatant materials. The variable-separable asymptotic solution exists for all available values of the pressure-sensitivity factor. Because of rapid changes in leading-order terms of the stress component trrr at ,9 t> 160 ° the second-order solution will not significantly improve the prediction of the asymptotic solution in the whole tip field. Numerical results based on the incremental theory of plasticity show that the asymptotic solution characterizes the near-tip fields. Finite strains dominate in the region r/(J/~ro) < 1 under plane strain conditions. The two-parameter boundary layer formulation with different T-stresses predicts that the higher-order terms are only weakly dependent on the distance to the crack tip and vary significantly with ,9 in the forward sector.

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