Hybrid phase-field modeling of crack propagation in a sigmoid functionally graded blades under cyclic thermomechanical loading: A comparison of adaptive implicit and explicit cyclic jump schemes

This work, for the first time, presents a comparison of an adaptive implicit and explicit cycle-jump schemes with an unaccelerated scheme under the frame work of hybrid phase-field modeling for simulating crack propagation and for calculation of time under varying parameters like cyclic thermomechanical load, crack angle, pure thermal load and porosity coefficient in a sigmoid functionally graded material (S-FGM) blade. The S-FGM blade is graded through-the-thickness from pure ceramic (front surface) to pure metal (back surface). Temperature-dependent material properties are described by a power law relation, and the ceramic volume fraction follows a sigmoid distribution. A hybrid phase-field damage model is used to treat the crack as a continuous domain. Two different adaptive cyclic jump schemes, viz., adaptive implicit cycle-jump and explicit cycle-jump, have been implemented to accelerate the crack simulation and calculation times in the present unaccelerated scheme. From the present investigation, it is observed that for achieving a given crack length, the implicit adaptive cycle-jump scheme requires the least number of cycles and calculation time, followed by the explicit adaptive cycle-jump scheme, and the same is observed to be highest for an unaccelerated scheme.