Effect of material nonhomogeneities on the HRR dominance

摘要: Abstract This work studies the asymptotic stress and displacement fields near tip of a stationary crack in an elastic–plastic nonhomogeneous material with emphasis on effect nonhomogeneities dominance field. While HRR singular field still prevails if properties are continuous piecewise continuously differentiable, simple analysis shows that size zone decreases increasing magnitude property gradients. The dominates at points satisfy |α −1 ∂ α/ x δ |≪1/r , 2 α/( γ )|≪1/r |n n/ |≪1/[r| ln (r/A)|] n/( )|≪1/[r | addition to other general requirements for solutions, where α is Ramberg–Osgood model, n strain hardening exponent, r distance from tip, xδ Cartesian coordinates, A length parameter. For linear materials, |E tan E / /( E/ E/( Etan tangent modulus Young’s modulus.