A Nonlinear Analysis of an Equilibrium Craze: Part I—Problem Formulation and Solution

This study investigates the effect of nonlinear cohesive forces on crack growth with the special problem of craze mechanics in mind. The work is presented in two parts. In the first and present one, we develop a numerical method for determining the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement (P-V) behavior, including strain softening characteristics. The second part of this study deals with the numerical simulation of craze and crack growth (Ungsuwarungsri and Knauss, 1986).¹ The problem formulation is based on the superposition of the relevant elasticity Green’s function and the solution for the resulting nonlinear problem is effected by using Picard’s successive approximation scheme. Both field equilibrium and the Barenblatt condition for vanishing stress and strain singularities are satisfied simultaneously, rendering the craze tip profile cusp-like. The formulation allows the stress distribution profile and the corresponding P-V relation to be computed from experimentally measured craze/crack displacement contours; it also allows the computation of the craze or crack/craze profile if the P-V relation, far-field load, and craze or crack size are specified. Numerical investigations indicate that only certain classes of the fibril P-V relations are consistent with measured craze profiles. In addition, it is found that for a given P-V relation, nontrivial solutions exist only for certain ranges of craze lengths.