Analytical determination of cyclic hydrostatic stress-strain relations for a composite sphere with a soft inclusion and a hard bilinear, isotropically hardening matrix (Q1570854)

The authors determine analytically cyclic hydrostatic stress-strain relations for a composite sphere with a soft inclusion and a hard bilinear isotropically hardening matrix. In doing this, they took both phases elastically isotropic, assuming that the inclusion is softer than the matrix. Yielding is assumed to ocur in the matrix in accordance with von Mises criterion. Using Hill's approach as a starting point, an exact solution is first determined for the first five sequences of the loading. Based on the observation of the first five loading, the authors suggest an analytical relation for the overall hydrostatic stress and strain for the \(n\)th loading. Using the equations so developed, the authors are able to study the Bauschinger effect for the composite sphere. They observe that, irrespective of the inclusion volume fraction or the work hardening nature of the matrix, the response of the composite is initially governed by isotropic hardening, whereas an asymptotic response is approached where both kinematic and isotropic mechanisms play equally important roles. Such an evolution in the composite response is attributed to the evolution in the internal stress of the composite sphere.