Numerical study on geometric constraint effects on ductile fracture toughness of thin advanced high-strength steel sheet

Abstract The total fracture energy arises from the energy dissipated within the fracture process zone, comprising the work of necking and the work of fracture, and the energy dissipated in the surrounding plastic zone, referred to as plastic work. The essential work of fracture methodology expresses the fracture toughness in terms of these energy contributions. Although the influence of the geometric parameters, namely thickness and ligament length, on the cracking resistance is well established in the literature, their effect on the different energy contributions are less understood. This work investigates how the different energy contributions evolve with sheet thickness and ligament length, using existing theoretical framework. The ligament length effect was studied experimentally and numerically under the scope of the essential work of fracture, covering both conventional and small ligament regimes, whereas the effect of the thickness was investigated numerically. A new local quantity was introduced to quantify the energy dissipated within the fracture process zone, at a distance from the crack plane, allowing the estimation of necking height. The results show that the necking work per unit area increases with thickness up to a critical value, beyond which it decreases. While thinner specimens undergo more severe necking, thicker specimens dissipate greater necking energy before the critical thickness. Furthermore, the linear extrapolation of the essential work of fracture in the small-ligament regime yields a fracture energy whose value depends on the sheet thickness.