Elastic-Plastic Analysis of Directionally Solidified Lamellar Eutectic Composites

Yielding in a crystal structure occurs with plastic slip on preferential planes. It is similar to yielding on maximum shear planes in an isotropic continuum, but in this case the slip is anisotropic. The anisotropic slip is described by 24 piecewise, continuous yield functions, also known as the generalized Schmid’s law for FCC crystals. The plastic strain increment for any one slip mechanism is assumed given by the potential flow law of plasticity. However, there are combined slip situations where two or more slip mechanisms are activated simultaneously. In this paper, the plastic strains for all the possible intersections in FCC crystals are derived, i.e., for intersections of two, four, and eight yield surfaces of compatible stress states. A strain hardening modulus H^′ is included by defining an equivalent shear stress τ and an equivalent plastic shear strain γ^p for each slip system. The analysis is programmed for finite-element solution on the computer, by defining a strain “vector” {dε}, a stress “vector” {dσ}, and an elastic-plastic compliance [C] for each element, relating the strain and stress vectors. The analysis is applied to the elastic-plastic yielding of directionally solidified eutectic systems of Co-CoAl which solidify into a lamellar structure. A plane strain analysis is compared with experiments and good correlation is found for the stress concentration effect when the lamellae have termination points.