Equivalence between shallow notch and shallow crack in structural failure caused by plastic instability

Introducing crack-like notches is essential for investigating the mechanical properties of pre-cracked structures because fatigue pre-cracking occasionally fails to ensure some rigorous investigation conditions. However, the results obtained by previous studies related to crack-like notches under small-scale yielding are invalid for shallow notches with extensive plasticity, particularly when plastic instability instead of unstable crack propagation governs the structural strength. This study focused on the plastic instability occurring under the plane strain condition without the assistance of pre-crack propagation. The boundary condition, geometric configuration, and elastoplastic fields dominating the overall work hardening in notched and cracked cross-sections were considered in finite element analyses. From the perspective of asymptotic and phenomenological analysis, this study proposes that a shallow crack-like notch should satisfy the following requirements: (1) the structural strength should be independent of the notch geometry, except for the notch depth; (2) the elastoplastic fields in the notched cross-section should be broadly convergent to those in the pre-cracked cross-section; (3) the failure mode characterized by damage pattern should be similar. The underlying reason for crack-like notches existing in extensive plasticity is that different elastoplastic field gradients close to the notch root or crack tip may still result in the same overall work hardening in notched and pre-cracked cross-sections. This concept was experimentally verified using interstitial-free steel, which is a typical strain-hardening ferrite steel with excellent ductility and simple metallurgical microstructure. The generality of the identification method and the significance of influential factors for shallow crack-like notches are discussed in this study.