Stress intensity factors for a moving cylindrical crack in a nonhomogeneous cylindrical layer in composite materials

Stresses are determined for a finite cylindrical crack that is propagating with a constant velocity in a nonhomogeneous cylindrical elastic layer, sandwiched between an infinite elastic medium and a circular elastic cylinder made from another material. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. An internal gas pressure is then applied to the crack surfaces. The solution is derived by dividing the nonhomogeneous interfacial layer into several homogeneous cylindrical layers with different material properties. The boundary conditions are reduced to two pairs of dual integral equations. These equations are solved by expanding the differences in the crack surface displacements into a series of functions that are equal to zero outside the crack. The Schmidt method is then used to solve for the unknown coefficients in the series. Numerical calculations for the stress intensity factors were performed for speeds and composite material combinations.     

Unstable crack motion is predictable

Yoffe's linear theory of dynamic brittle fracture suggests that crack motion will be unstable beyond ∼70% of the Rayleigh speed, a prediction that is not supported by experiment. We show by atomistic simulations that hyperelasticity, the elasticity of large strains, plays a governing role in the instability dynamics of brittle fracture. A simple, yet remarkable, scaling model based on an effective elastic modulus (the secant modulus at the stability limit) gives successful predictions for the onset speed of the crack instability.