A computational model and experimental validation of shielding and amplifying effects at a crack tip near perpendicular strength-mismatched interfaces

Abstract

The stress field around the crack tip near an elastically matched but strength-mismatched interface body in a bimetallic system is influenced when the crack tip yield or cohesive zone spreads to the interface body. The concept of crack tip stress intensity parameter, Ktip, is therefore employed in fracture analysis of the bimetallic body. A computational model to determine Ktip is reviewed in this paper. The model, based upon i) Westergaard's complex potentials coupled with Kolosov-Muskhelishvili's relations between a crack tip stress field and complex potentials and ii) Dugdale's representation of the cohesive zone clearly indicates shielding or amplifying effects of strength mismatch across the interface, depending upon the direction of the strength gradient, over the crack tip. The model is successfully validated by conducting series of high cycle fatigue tests over Mode I cracks advancing towards various strength-mismatched interfaces in bimetallic compact tension specimens prepared by electron beam welding of elastically identical weak ASTM 4340 alloy and strong MDN 250 maraging steels. List of symbols a Distance of crack tip from interface a ∗ Radial coordinate of point near crack tip A Parent body/parent steel containing crack B Interface body/back up steel b Length of cohesive zone across interface c Crack length cc Crack length ahead of load axis cmin Crack length required for linear elastic regime C Paris constant e, eav Percent difference between theoretical and experimental result, average of percent differences E Modulus of elasticity f (θ ) A function of angle w.r.t. crack axis F Applied load