Shallow crack effect on evaluation of residual tensile strength: Harmless and stable cracks in finite-sized structure made of ductile metals

•Residual tensile strength may not be weakened by presece of shallow crack.•Plastic instability can dominate residual strength as pre-crack depth decreases.•Shallow cracks can strengthen pre-cracked cross-sections by hindering plastic instability.•Plastic strain localization of shallow crack has both positive and negative effects in cross-sectional load-carrying capacity.•Trend of residual strength can be anticipated from perspective of plastic strain localization after distinguishing physical meanings of residual strength. Residual tensile strength (hereinafter abbreviated as ‘residual strength’) is a critical fail-safe consideration but has rarely been reported in the case of shallow pre-cracked structures. When the pre-crack depth is shallower than a critical value, the residual strength of cylindrical specimens made of interstitial-free steel exhibits a plateau identical to the tensile strength of smooth specimens, and with a rupture occurred far away from the pre-cracked cross-section. According to the damage characteristics by microscopic observation and the plastic strain distribution by kernel average misorientation measurement, such a situation exists when the physical meaning of residual strength changes from fracture instability to plastic instability. The corresponding mechanism, with the assistance of finite element analysis, is ascribed to the following: 1. The plastic strain localization induced by shallow cracks preferentially hinders plastic instability in the pre-cracked cross-section rather than promotes fracture instability at the crack tip because the high fracture toughness makes shallow cracks remain non-propagating or stable-propagating at least until plastic instability occurs; 2. Whether a shallow crack strengthens or weakens the pre-cracked cross-section depends on the integrated factors of the effective area of cross-section for bearing load narrowed by the crack depth (negative effect), the strain hardening and damage initiation in near crack-tip region affected by gradient plasticity (positive or negative effect), and uniform plasticity in remote crack-tip region alleviated by plastic strain localized near the crack tip (positive effect). Then, the above features are defined as the ‘shallow crack effect’ in the residual strength issue. To incorporate this problem in design, a residual strength diagram considering physical meanings of residual strength and corresponding damage characteristics is suggested. It helps to estimate