Special Colloquium
Department of Physics, NCU
Phase-field modeling of crack front instabilities
Speaker
Dr. Chih-Hung Chen陳志鴻)
Research Center for Applied Sciences, Academia Sinica
Date 2018.01.9 (Tue)
Time 11:00
Place S4-625
Abstract: This talk discusses two types of fracture instabilities: crack front segmentation in mixed-mode fracture and oscillatory instability in fast fracture. Applying simultaneously tension and a shear stress parallel to crack front is universally observed to produce arrays of daughter cracks shaped as tilted facets. We investigate facet propagation and coarsening using in situ microscopy observations of fracture surfaces at different stages of quasi-static mixed-mode crack propagation and phase-field simulations. The results demonstrate that the bifurcation previous theoretical predictions of linear stability analysis with experimental observations.
Besides, experiments in thin brittle gels have shown that cracks can attain extreme speeds approaching the shear wave speed when micro-branching, which limits propagation to smaller speeds in thick samples, is suppressed. Furthermore, these studies revealed the existence of an oscillatory instability with an intrinsic system-size-independent wavelength above a threshold speed. We investigate this oscillatory instability using a phase-field model of two-dimensional dynamic brittle fracture that includes elastic nonlinearity and has unique capability to describe experimentally observed ultra-high-speed cracks that accelerate above 90% of their sonic velocity. Our simulation results demonstrate that cracks undergo a dynamic oscillatory instability controlled by small-scale elastic nonlinearity near the crack tip. This instability occurs above an ultra-high critical velocity and features an intrinsic wave-length that increases proportionally to the ratio of the fracture energy to an elastic modulus, in quantitative agreement with experiments. This ratio emerges as a fundamental scaling length for nonlinear effects assumed to play no role in the classical theory of cracks, but shown by our computations to strongly influence crack dynamics.