Unified parameter of in-plane and out-of-plane constraint effects and its correlation with brittle fracture toughness of steel

Abstract

In this work, the equivalent plastic strain $$\varepsilon _{p}$$ distributions ahead of crack tips for the experimental specimens with combined in-plane and out-of-plane constraints under brittle fracture condition in the literature were calculated by three-dimensional finite element. The constraint parameter $$A_{p}$$ based on the areas surrounded by $$\varepsilon _{p}$$ isolines ahead of crack tips has been comparatively analyzed with several constraint parameters ( $$T$$ -stress, $$A_{2}$$ , $$Q$$ and stress triaxiality $$h$$ ) based on the crack-tip stress fields, and the capability of parameter $$A_{p}$$ for characterizing in-plane and out-of-plane crack-tip constraint effects for brittle fracture has been identified. The results show that the parameter $$A_{p}$$ has a good correlation with brittle fracture toughness $$K_{Jc}$$ and $$J_{c}$$ of various specimens with different constraint levels, and it is a unified measure parameter of in-plane and out-of-plane constraint for brittle fracture. The unified correlation lines and formulae of the normalized brittle fracture toughness $$K_{Jc}/K_{ref}$$ and $$J_{Ic}/J_{ref}$$ with $$\sqrt{A_p}$$ have been obtained for the steel, and they may be used to determine constraint-dependent or structurally relevant fracture toughness of specimens or cracked components with any constraint levels. The application methodology of the constraint parameter $$A_{p}$$ for structural integrity assessments needs to be further investigated by numerical calculations and experiments.