Quasi-static crack advance under a range of constraints—Steady-state fields based on a characteristic length

Abstract A numerical investigation of a crack growing under steady-state, quasi-static conditions has been performed within the framework of a boundary layer formulation whereby the remote loading is fully specified by the first two terms in Williams' expansion, characterized by k 1 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 1 and T combinations. A length scale for the boundary layer problem is ( K 1 /σ 0 ) 2 , where σ 0 is the material's yield stress in tension. Rescaling physical coordinates by ( K 1 /σ 0 ) 2 results in a family of self-similar solutions parameterized by T /σ 0 . Moreover, these fields can be arranged into a one-parameter near-tip field based on a characteristic 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 rescaled by L g . Thus loading and crack geometry enter into the description of the near-tip field only through L g , which therefore scales the intensity of the near-tip fields. Consequently, a one-parameter crack growth criterion is rigorously valid for steady crack growth under well-contained yielding, when the oneparameter field dominates over microstructurally significant size scales, i.e. any postulated local fracture criterion can be expressed as the requirement that L g attains a critical value L gc . The latter provides a single, unified criterion to assess quantitatively loading and crack geometry effects on fracture toughness.