Determination of mode-II critical energy release rate using mixed-mode phase-field model

To overcome the harsh experimental conditions of obtaining the mode-II critical energy release rate GIIC, an easy and flexible method for determining GIIC is proposed based upon the mixed-mode fracture experiments and corresponding simulations using the mixed-mode phase-field model. In details, a mixed-mode fracture experiment is first conducted to determine the initial crack deflection angle. Subsequently, a range of phase-field numerical simulations are conducted through adjusting the value of GIC/GIIC to reproduce the experimental results so as to determine the value of GIIC with a known GIC. Three mixed-mode fracture tests (single edge cracked circular test, central crack rectangular tension test and compact tension shear test) of PMMA indicate that the determined GIIC is a stable material parameter independent of test and loading conditions. Meanwhile, the determined prediction of GIIC is compared with those in other references with a deviation of about 3.5%, which demonstrates that the proposed method can quantitatively and qualitatively obtain GIIC. Furthermore, the determined parameter GIIC is used to develop the mixed-mode phase-field model through using the mode-mixity factor (GIC/GIIC) to regular the relative proportions of volumetric and distortional crack driving energy, which results in better numerical results than the classical phase-field model (with relative deviation < 1.0%). Without the harsh conditions of the pure mode-II fracture experiment, the proposed method is of significant practice in the determination of GIIC.