A Stress Function Formulation and Approximate Solution of the Unsymmetric Deformation Problem for Cracks in Non-Uniform Materials,

摘要

Relative stress and strain distributions are presented for the near-tip deformation field corresponding to a homogeneous cracked plate with spatially variable mechanical properties. Using a nonlinear (strain-hardening) stress-strain relationship and deformation plasticity, a first approximation asymptotic stress function solution was determined which shows that unsymmetric deformation fields develop in homogeneous materials with non-uniform properties. The amplitude of the stress singularity at the tip is also found to be dependent upon the non-uniformity. Experimental verification is presented showing extreme unsymmetry for an SEN specimen with a one-dimensional off-angle yield strength gradient. The engineering significance of the effect is discussed. (Author)