Finite element analyses of deformation around holes near a crack tip and their implications to the J-resistance curve

Abstract

The initiation phase of ductile crack growth is investigated in a detailed finite element analysis. The process is modelled by the growth and coalescence of a series of holes in front of a blunted crack tip, representing the growth of holes separated from large inclusions. The reductions of each ligament between neighbouring holes due to hole growth are calculated as well as crack-tip opening displacements (CTOD). All the ligaments except the first and last show similar behaviour of reduction, with the reduction curves separated in an equal CTOD increment. The CTOD increment as a function of effective crack extension due to hole growth defines crack-tip opening angle, a measure of crack-growth resistance for a given condition. As the CTOD increment changes substantially due to crack extension in small-scale yielding, crack initiation is defined at the point of deviation from the linear increment of CTOD against F for a stationary crack. The effective crack tip is defined at each hole with the ligament reduction of crack initiation. Therefore, the F-resistance curve may be derived from the hole growth model, and hence the effects of specimen geometry, crack length and specimen size on the R-curve are discussed. The calculations for a hole spacing 10 times of the initial hole diameter are in agreement with the experimental R-curve of 2024-T351 aluminium alloy.