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.