Interpretation of optical caustic patterns obtained during unsteady crack growth: an analysis based on a higher-order transient expansion

Abstract

The optical caustic method is re-examined considering the presence of transient effects. Based on the higher-order asymptotic expansion provided by Freund and Rosakis, regarding the stress field near a non-uniformly propagating crack tip, the caustic mapping and the initial curve equations are derived. The dynamic stress intensity factor, K^d_I(t), is related to experimentally measurable quantities of the caustic pattern by an explicit expression. It is shown that the classical analysis of caustics is a special case of the new interpretation method. The Broberg problem is used as an example problem to check the feasibility of analysing caustics in the presence of higher-order transient terms. It is shown that the caustic patterns are sensitive to transient effects, and that use of the classical analysis of caustics in the interpretation of the optical patterns for this problem may result in large errors in the value of the stress intensity factor, especially at short times after initiation.