Effect of material inhomogeneity under creep and plastic to creep transition of cracks

Abstract

The driving force of a crack in a non-linear elastic material is described by the conventional J-integral, J (Rice 1968). For elastic−plastic materials, J does not describe the crack driving force. However, it describes the intensity of the crack tip field and can be, therefore, used to quantify the fracture toughness (Rice 1968). For the high-temperature behaviour of materials where creep deformation dominated, analogous parameter to J-integral were deduced, the C*-integral and a similar parameter, the Ct-integral (Landes and Begley 1976). C* has been proven to have a good correlation with the creep crack growth rate for many materials, mostly under extensive creep conditions. However, it does not describe the crack driving force.

Based on the concept of configurational forces, a J -integral for elastic–plastic materials, Jep, was derived, which is able to quantify the true crack driving force in accordance with incremental theory of plasticity [4]. Hereby, the plastic strain is treated as an eigen-strain. Jep can be applied also in cases of non-proportional loading, e.g. for a growing crack (Simha et al. 2008) or for cyclic loading conditions (Ochensberger and Kolednik 2015). In this work, the concept of configurational force is applied to evaluate the crack driving force under small, medium and extensive creep conditions. Hereby, the creep strain is treated as a time dependent eigenstrain. A case study is performed where the path dependences of the elastic–plastic J-integral, Jep, and the conventional parameters Ct and C* are studied for materials which undergo elastic+creep deformation, with material inhomogeneity.

It has been confirmed in the recent studies (Kolednik et al. 2014, Tiwari et al. 2020) that the material inhomogeneity term affects the crack depending on the nature of material inhomogeneity. This effect is unknown for creep deformation and the same has been studies on idealized fracture specimen under creep deformation using configurational forces and finite element method simulating real situations of dissimilar metals used at high temperatures in nuclear power plants and jet engines.