HIGHER-ORDER CRACK-TIP ASYMPTOTIC SOLUTIONS FOR QUASI-STATIC STEADY CRACK-GROWTH IN NONLINEAR VISCOUS SOLIDS

A METHODOLOGY for the determination of higher order terms in the asymp totic expansion of the crack tip fields for the problem of quasi-stati c steady-state crack growth in an elastic-nonlinear-viscous solid is d eveloped. The creep strain rate is assumed to be proportional to stres s raised to some power. The possibility of each term in the asymptotic expansion being separable in r and theta, where (r, theta) are polar coordinates at the crack tip, is examined, and the first two terms in the asymptotic series are obtained. Anti-plane shear (mode-III) and pl ane strain solutions for a crack in a homogeneous material as well as for a crack lying along the interface between an elastic-viscous solid and a rigid substrate are obtained. In all cases analysed, both the f irst and the second terms of the asymptotic expansion of the crack lip stress fields are singular in r as r --> 0, when the creep exponent i s in the range 3 < n < 4. For the case of the steady-state crack growt h along the interface of an elastic-nonlinear-viscous solid and a rigi d substrate, we find that both the amplitude of the leading term and t he crack tip ''mode-mix'' are completely determined by the asymptotic solution alone, when n greater than or equal to 3. For each value of t he creep exponent, there are two distinct solutions with a very differ ent mode-mix on the interfacial line ahead of the crack; one of the so lutions is mode-I-like, whereas the other has a substantial mode-II co mponent.