A Theory of Crack Growth in Viscoelastic Media

Abstract

Abstract : A theory is developed for predicting the time-dependent size and shape of cracks in linearly viscoelastic, isotropic media, and its validity is demonstrated by applying the theory to crack growth and failure of unfilled and particulate-filled polymers. Starting with a bounded solution for the stress distribution near a crack tip in an elastic body and the extended correspondence principle for viscoelastic media with moving boundaries, a simple equation is derived for predicting instantaneous crack tip velocity in terms of the opening- mode stress intensity factor; although the undamaged portion of the continuum is assumed linear, no significant restrictions are placed on the nature of the disintegrating material near the crack tip and, therefore, this material may be highly nonlinear, rate- dependent, and even discontinuous. A further analysis is made to predict the time at which a crack starts to grow, and then some explicit solutions are given for this so- called fracture initiation time, the time- dependent crack growth, and the time at which gross failure occurs under time- varying applied forces and environmental parameters. Following a derivation of the linear cumulative damage rule, an examination of its theoretical range of validity, and a discussion of the experimental determination of fracture properties, the theory is applied to monolithic and composite materials under constant and varying loads. Some concluding remarks deal with extensions of the theory to include finite strain effects, crack growth in the two shearing modes and in combined opening and shearing modes, and adhesive fracture.