The effect of reflected stress wave on crack speed in silicon crystal

Abstract

The effect of reflected stress wave on crack speed during dynamic crack propagation in brittle single crystal was investigated by cleavage fracture experiments and by cracks dynamics theory. The specimens in the experimental program were quasi-statically loaded using the Coefficients of Thermal Expansion Mismatch (CTEM) method. Silicon crystal served as a model material where the cracks were propagated on the (110)[11¯0] and (1 1 1)[1 1 2¯] low energy cleavage systems (LECSs) of the crystal.The effect of reflected stress wave was evaluated by comparing the experimental energy-speed relationship and the theoretical Freund equation of motion. The experimental quasi-static energy release rate (ERR) was calculated by Finite Element Analysis (FEA) and the crack speed was measured by Potential Drop Technique (PDT). Since Freund equation of motion does not take into account the effect of reflected stress wave, any deviation found in the experimental results from the theoretical energy-speed relationship, was identified as a possible effect of the reflected stress wave. We considered here the longitudinal wave, the horizontal shear wave, and the vertical shear wave.The time it takes for each wave to be reflected from the specimens' lateral boundaries back to the crack tip was calculated and the crack tip-wave front interaction was, accordingly, determined on the energy-speed plot. It was found that the effect of reflected stress waves on the crack speed in silicon is minor.Finally, we found that the effect of the reflected stress waves on the crack speed differed slightly for cracks with a different gradient of the driving force Θ = dG0/da which also affects the gradient of the crack speed, Φ = dV/da.