A three dimensional computational model of the mechanical response of a dual-phase ceramic

This paper presents a constitutive model of a fired ceramic consisting of two phases each with a different thermal expansion coefficient. Each phase is linear elastic but the stiffness of one of the phases is progressively reduced anisotropically to simulate the growth of microcracks under tension. This damage, in any orientation, is proportional to the normal tensile traction in that direction and no damage is produced by compressive stresses. The damage is recorded as a damage orientation function held numerically at 20 orientations. del is specifically designed to be used in the pre-peak region of the stress–strain curve and to be robust in use in finite element programs. To this end, while the stresses in the phases are determined assuming that the strains in each phase are equal, the overall compliance of the composite is calculated from the complementary energy. del reproduces non-linear stress–strain behaviour when loaded in tension and, because of the thermal mismatch, also shows permanent deformation on the removal of the load. A user defined subroutine has been written for the commercial finite element program ABAQUS and used to simulate an experimental test on a commercial refractory and the results compared with experimental data. The UMAT is also used to simulate a hollow axisymmetric cylinder in generalised plane strain subject to moderately rapid heating on the inner surface; and the results for linear elasticity and the damaging model are compared.