A study of frictional contact in dynamic fracture along bimaterial interfaces

Abstract

We investigate numerically the dynamic in-plane propagation of a centered crack along bimaterial interfaces using a spectral formulation of the elastodynamic boundary integral equations. Particular attention is given to the effect of contact zones at the subsonic/intersonic transition. In a single set-up, we simulate and describe the different phenomenon observed experimentally (distinct natures of contact zones, unfavorable velocity range, asymmetric crack propagation). We show that different behaviors are observed as function of the crack propagation direction, i.e., with respect to the particle displacements of the compliant material. When the crack propagates in the same direction, the propagation velocities between $c_\mathrm{R}$ and $c_\mathrm{s}$ are forbidden and the subsonic/intersonic transition occurs with the nucleation of a daughter crack in front of the main rupture. The intersonic stress field at the crack front is compressive due to the material mismatch and a contact zone appears behind the tip. In the opposite direction, a smooth subsonic/intersonic transition occurs although crack face closure (in normal direction) is observed for speeds between $c_\mathrm{s}$ and $\sqrt{2}c_\mathrm{s}$. In this regime, a Rayleigh disturbance is generated at the crack surface causing a contact zone which detaches from the tip. Using a contact model governed by a regularized Coulomb law, we provide a quantitative evaluation of the influence of friction on the effective fracture toughness. Finally, we show the applicability of our analysis to the description of different bimaterial situations as well as the single-material set-up.