Theoretical approach of characterizing the crack-tip constraint effects associated with material’s fracture toughness

The conversion problem of plane strain fracture toughness (\(K_\mathrm{IC}\)) which is necessarily measured according to ASTM standards, to lower constraint applications generally existing in engineering structures, has led to extensive material and labor costs. The present paper explores and quantifies the crack-tip constraint effects by the crack-tip plastic zone to serve the prediction of material’s fracture toughness. Firstly, the approximate three-dimensional crack front displacement fields are obtained by using the variable separation method. The three-dimensional stress field is then used to predict the shape and size of the crack-tip plastic zone. Secondly, the two-dimensional in-plane and the three-dimensional out-of-plane geometric constraint effects are quantified separately, and two constraint factors, i.e., \(\alpha _\mathrm{in}\) and \(\alpha _\mathrm{out}\) are proposed. A series of configurations of the two-dimensional and three-dimensional crack-tip plastic zones that vary with the specimen’s geometric size (plate width, thickness, etc.) are presented, which will facilitate a better understanding of the crack-tip constraint effect. Finally, the present method is applied to elucidate the significant “thickness effect” of the X70 pipeline steel’s fracture toughness by using the out-of-plane constraint factor \(\alpha _\mathrm{out}\). The corresponding results are compared with the experimentally measured and FEM-predicted fracture toughness \(K_\mathrm{C}\). It is concluded that the parameters \(\alpha _\mathrm{out}\) and the fracture toughness \(K_\mathrm{C}\) can be correlated with each other, which will be beneficial to the prediction of material’s fracture toughness and the avoidance of experimental costs.