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The interpretation of optical caustics in the presence of dynamic non-uniform crack-tip motion histories: A study based on a higher order transient crack-tip expansion

1993; Elsevier BV; Volume: 30; Issue: 7 Linguagem: Inglês

10.1016/0020-7683(93)90017-2

1879-2146

Cheng Liu, Ares J. Rosakis, L. B. Freund,

Optical measurement and interference techniques

The optical method of caustics is re-examined by considering the presence of dynamic non-uniform crack-tip motion histories. Based on the higher order transient expansion obtained by Freund and Rosakis (1990, Eleventh National Congress of Applied Mechanics; 1992, J. Mech. Phys. Solids40(3), 699–719) and Rosakis et al. (1991, Int. J. Fract. 50, R39–R45), in which dynamic transient effects were included in the near-tip deformation field, the exact mapping equations of caustics are derived for non-uniformly propagating cracks. The resulting equations indicate that the classical analysis of caustics based on the assumption of KId-dominance, is inadequate to interpret the experimental caustic patterns when dynamic transient effects become significant. In this paper, an explicit relation between the instantaneous value of the dynamic stress intensity factor KId(t) and the geometrical characteristics of the caustic is established. This relation shows that for the case of non-uniformly propagating cracks, the relation between the dynamic stress intensity factor and the geometrical characteristics of the caustic pattern depends on the crack-tip acceleration and on KId(t). It also reduces to the classical relation between KId(t) and the caustic diameter for the case of KId-dominance (when the crack-tip fields are well described by the r−½ singularity in stresses). 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 the value of the dynamic stress intensity factor obtained by the proposed method agrees remarkably well with the exact analytical value while large errors are introduced when the classical analysis (KId-dominant) of the method of caustics is used.