QUASI-STATIC CRACK ADVANCE UNDER A RANGE OF CONSTRAINTS - STEADY-STATE FIELDS BASED ON A CHARACTERISTIC LENGTH

A NUMERICAL investigation of a crack growing under steady-state, quasi -static conditions has been performed within the framework of a bounda ry layer formulation whereby the remote loading is fully specified by the first two terms in Williams' expansion, characterized by K(I) and T. Mode I, plane strain crack tip fields have been obtained for strain -hardening and non-hardening materials over a wide range of K(I) and T combinations. A length scale for the boundary layer problem is (K(I)/ sigma0)2, where sigma0 is the material's yield stress in tension. Resc aling physical coordinates by (K(I)/sigma0)2 results in a family of se lf-similar solutions parameterized by T/sigma0. Moreover, these fields can be arranged into a one-parameter near-tip field based on a charac teristic length L(g), which scales with the smallest dimension of the plastic zone. Specifically, the numerically determined fields collapse into a single near-tip distribution when physical coordinates are res caled by L(g). Thus loading and crack geometry enter into the descript ion of the near-tip field only through L(g), which therefore scales th e intensity of the near-tip fields. Consequently, a one-parameter crac k growth criterion is rigorously valid for steady crack growth under w ell-contained yielding, when the one-parameter field dominates over mi crostructurally significant size scales, i.e. any postulated local fra cture criterion can be expressed as the requirement that L(g) attains a critical value L(gc). The latter provides a single, unified criterio n to assess quantitatively loading and crack geometry effects on fract ure toughness.