A criterion for plane strain, fully plastic, quasi-steady crack growth

Abstract

Plane strain fracture by hole growth in ordinary-sized parts of low-to-medium strength steels is essentially rigid-plastic, and may be approximated as non-hardening. Quasi-steady crack growth for such materials is predicted for crack-tip fields approximated by a pair of slip lines, such as unequally grooved specimens in tension and deep singly-face-cracked specimens under combined bending and tension. The crack growth increment Δa is given in terms of material parameters, far-field geometry, and loadings and their increments. For the rigid-plastic, non-hardening approximation, stress and strain increment fields for growing cracks are identical to those for stationary cracks. For fields with a pair of symmetric slip-lines, the flanks of the decohering zone turn out to be rigid, and the decohering zone does not affect the crack-tip opening angle (CTOA), which then depends only on the micromechanisms of hole nucleation, growth and linkage by flow localization or fine cracking. These mechanisms are in turn approximately controlled by the near-field plasticity parameters: the angle of the slip plane θs, and the normal stress and displacement increment across the slip plane σs and Δus. Note the three-parameter characterization of the near-tip fields, in contrast to the one- or two-parameter characterization in elastic or nonlinear elastic fracture mechanics. A sliding off and shear-cracking model for a growing crack, based on a hole growth equation, gives an approximate CTOA in terms of σs, θs, and material parameters. When hole nucleation strain is negligible, the estimated CTOA exhibits an inverse exponential dependence on σs and a higher order parabolic dependence on θs. For a given material, a series of fully plastic crack growth experiments is suggested to determine the approximate material parameters needed to characterize the dependence of CTOA on σs and θs, or from kinematics, of the shear strain behind the slip plane, γf, on σs.