Abstract
Through detailed three-dimensional (3D) finite element (FE) calculations, the out-of-plane constraints T z along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of T z are obtained near the crack front with aspect ratios (a/c) of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. T z decreases from an approximate value of Poisson ratio ν at the crack tip to zero with increasing normalized radial distances (r/a) in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle ϕ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, T z is getting nearly independent of ϕ and is only related to r/a. Based on the present FE calculations for T z , empirical formulas for T z are obtained to describe the 3D distribution of T z for embedded center-elliptical cracks using the least squares method in the range of 0.2≤a/c≤1.0. These T z results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded center-elliptical crack front field, and a two-parameter K-T z principle is proposed.
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