A rate-dependent damage model for brittle materials based on the dominant crack

Abstract

A rate-dependent, continuum damage model is developed for brittle materials under dynamic loading. This model improves on the approach (ISOSCM) of [Addessio, F.L., Johnson, J.N., 1990. A constitutive model for the dynamic response of brittle materials. Journal of Applied Physics 67, 3275–3286] in several respects. (1) A new damage surface is found by applying the generalized Griffith instability criterion to the dominant crack (having the most unstable orientation), rather than by averaging the instability condition over all crack orientations as done previously. The new surface removes a discontinuity in the damage surface in ISOSCM when the pressure changes sign. (2) The strain due to crack opening is more consistent with crack mechanics, with only the tensile principal stresses contributing to the crack opening strain. This is achieved by incorporating a projection operator in the equation for the crack opening strain. One consequence of incorporating the projection operator is a prediction of shear dilatancy, which is not accounted for in ISOSCM. (3) The evolution of damage, which is based on the energy-release rate for the dominant crack, has a physical basis, whereas in the previous approach the damage growth rate was assumed to be an exponential function of the distance from the stress state to the damage surface without specific physical justification. An implicit algorithm has been developed so that a larger time step can be used than with the explicit algorithm used in ISOSCM. The numerical results of a silicon carbide (SiC) ceramic under several loading paths (hydrostatic tension/compression, uniaxial strain, uniaxial stress, and shear) and strain rates are presented to illustrate the main features of the model.