Simulation of ductile fracture propagation using the elastoplastic phase-field damage method calibrated by ultrasonic wave velocity measurement

The phase-field damage theory has become a powerful approach to estimate crack propagation via the finite element method (FEM). The sharp crack is smeared into a diffusive fracture propagation zone within a length scale parameter (l). However, the calibration of the phase-field damage model is still difficult, especially for the length scale parameter, which is difficult to directly observe and accurately measure in laboratory testing. In most numerical studies, the length scale parameter is arbitrarily determined as the minimum element size in FEM. However, the selection of the length scale parameter may largely affect the accuracy of the phase-field model. Also, most current phase-field models only consider elasticity and few studies further consider the ductile (plastic) fracture propagation, since the plastic recoverable energy does not have a convincing form. In this study, we aim to calibrate the elastoplastic phase-field damage model based on the traditional continuum damage mechanics, with the assistance of ultrasonic wave velocity measurement. The traditional damage var-iable can be back-calculated from the drop of P wave velocity, following the energy equivalence hypothesis. This traditional damage variable is shown to be consistent with the phase-field damage variable as calculated in our proposed elastoplastic phase-field damage model. Therefore, the length scale parameter can be determined from fitting the rock damage evolution. The plastic flow and its corresponding plastic-free energy are considered, using a phenomenological function obeying preliminary thermodynamic assumptions. The proposed model shows good consistency with laboratory observations. Numerical implementation of the proposed model was achieved by inserting it into COMSOL Multiphysics using a weak form formulation. This paper introduces a pragmatic approach to calibrate the phase-field damage model based on laboratory testing results.