The dynamic cleavage energy of brittle single crystals

Abstract

Crack initiation in brittle materials is usually dictated by the energy required to create two new surfaces. This energy is known as Griffith barrier and equals twice the free and relaxed surface energy, 2γs. This value is usually taken as the cleavage energy for crack propagation as well. We investigated, experimentally, the fundamentals of cracks dynamics in brittle single crystals, with emphasis on the cleavage energy at initiation and during propagation. Silicon single crystal, which has a diamond cubic symmetry, served as a model material. The experiments were performed using the Coefficient of Thermal Expansion Mismatch method (CTEM), developed in our laboratory in recent years. The CTEM method possesses the advantage of controlling the quasi-static energy release rate (ERR) gradient to the crack front, dG0/da, denoted here Θ.The cleavage energies at initiation and propagation of dynamic cracks on two Low-Energy Cleavage Systems (LECSs) of brittle silicon crystal, (110)[11¯0] and (111)[112¯], were evaluated by comparing the experimental energy–speed relationship with the theoretical one, manifested by Freund theory for cracks dynamics, known as Freund equation of motion. The ERR, G0, was evaluated using quasi-static, anisotropic Finite Element Analysis (FEA), and the crack speed was measured using Potential Drop Technique (PDT).The experiments revealed that the energy required to initiate and propagate a crack is governed by Θ. When Θ > 0.7 J/m2mm, the cleavage energy at initiation is higher than 2γs and linearly increase with increasing Θ for both LECSs of silicon. Surprisingly, the cleavage energy for initiation and propagation remain constant during the event of fracture for a prescribed Θ, meaning, it is not crack speed dependent. Moreover, we show that all the variables participating dynamic cleavage are linearly dependent on Θ, which provides the evidences that the ERR gradient is the controlling variable governs cracks dynamics.Finally, we suggest that the physics of the above fundamental behavior is laying on the way crack initiate and propagate at the atomistic scale, i.e., the bond breaking mechanisms in form of kinks.