Three dimensional K-Tz stress fields around the embedded center elliptical crack front in elastic plates

摘要

Through detailed three-dimensional(3D)finite element(FE)calculations,the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied.The distributions of Tz 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.Tz decreases from an approximate value of Poisson ratio ν at the crack tip to zero with increasing normalized radialdistances (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 sanle r/a.with a/c rising to 1.0,Tz is getting nearly independent of φ and is only related to r/a.Based on the present FE calculations for Tz,empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0.These Tz 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-Tz principle is proposed.