Unified characterisation of in‐plane and out‐of‐plane constraint based on crack‐tip equivalent plastic strain

Abstract

Constraint can be divided into two conditions of in‐plane and out‐of‐plane, and each of them has its own parameter to characterize. However, in most cases, there exists a compound change of both in‐plane and out‐of‐plane constraint in structures, a unified measure that can reflect both of them is needed. In this paper, the finite element method (FEM) was used to calculate the equivalent plastic strain (ɛp) distribution ahead of crack tips for specimens with different in‐plane and out‐of‐plane constraints, and the FEM simulations based on Gurson–Tvergaard–Needleman (GTN) damage model and a small number of tests were used to obtain fracture toughness for the specimens with different constraints. Unified measure and characterisation parameter of in‐plane and out‐of‐plane constraints based on crack‐tip equivalent plastic strain has been investigated. The results show that the area APEEQ surrounded by the ɛp isoline ahead of crack tips can characterize both in‐plane and out‐of‐plane constraints. Based on the area APEEQ, a unified constraint characterisation parameter Ap was defined. It was found that there exists a sole linear relation between the normalised fracture toughness JIC/Jref and regardless of the in‐plane constraint, out‐of‐plane constraint and the selection of the ɛp isolines. The unified JIC/Jref−reference line can be used to determine constraint‐dependent fracture toughness of materials. The FEM simulations with the GTN damage model (local approach) can be used in obtaining the unified JIC/Jref−reference line for materials with ductile fracture.

The matching of crack-tip constraint between standard and non-standard specimen

“…[27][28][29][30] Mostafavi et al 27,28 have defined a new constraint parameter u which can quantify the both constraints. And then, a modified unified parameter A p was defined by Yang et al 29 Thus, in this article, different SENB specimens were selected, and the matching of crack-tip constraint between different specimens was systematically studied based on the unified constraint parameter A p .…”

“…29 Thus, in this article, the areas surrounded by the e p = 0.2 isoline at the crack tip at different J-integrals were calculated.…”

Unified characterization of in-plane and out-of-plane creep constraint based on crack-tip equivalent creep strain

“…It has been identified that both the constraint parameter Q and stress triaxiality factor h are not a good unified representative of constraint, and a monotonic trend curve does not exist between the parameters (Q and h) and fracture toughness for various specimens with different in-plane and out-of-plane constraints under elastic-plastic fracture conditions [12,15,16,18,60]. The reason for this is that the two parameters are not equally sensitive to both in-plane and out-of-plane constraints.…”

“…They argued that there is no significant difference in the plastic zone sizes at fracture between in-plane and out-of-plane constraints, and the parameter u is equally sensitive to in-plane and out-of-plane constraints. However, finite element method (FEM) calculations by Yang et al [15,16] show that the constraint parameter u has its limitation in characterizing constraint at higher J-integral for the ductile material with higher fracture toughness due to the extension of the plastic zone size to the specimen boundaries. Thus, they defined a new unified constraint parameter A p by modifying the parameter u as follows [15,16]:…”

“…It has been shown that the parameter A p can characterize both in-plane and out-of-plane constraint for ductile materials with higher fracture toughness, and based on the A p the unified correlation of in-plane and out-of-plane constraint with ductile fracture toughness of A508 steel [15,16] and a dissimilar metal welded joint [17] were obtained. In a recent study of authors [18], it has been shown that the parameter A p also can characterize both in-plane and out-of-plane crack-tip constraint under brittle fracture conditions.…”