Numerical investigation of creep crack growth in plastically graded materials using C(t) and XFEM

In this work, a numerical methodology is proposed to predict the creep response and creep crack growth for functionally graded material/plastically graded material in the extended finite element method framework. The stress relaxation and redistribution as a result of creep are incorporated into the analysis of graded material. The C(t)-integral (which includes all creep stages from small-scale creep to extensive creep) based relation analogous to Paris Law is employed to calculate the creep crack growth rate. The numerical difficulties faced at the time of simulation, such as strain-energy rate density derivative and maintaining plastic/creep irreversibility during crack growth are well addressed in this paper. The strain-energy rate density derivative is evaluated by the surface approximation. The plastic/creep irreversibility is maintained by the appropriate data transfer and null step analysis scheme. The crack growth direction is decided by the maximum circumferential stress criterion. The proposed methodology is first validated with the experimental results for homogeneous material and later on, it is implemented to calculate the crack growth for various cases of gradation. The capabilities of the present scheme are demonstrated by performing the mixed-mode crack growth simulations at the specimen and component level.