Longitudinal Fracture Analysis of Inhomogeneous Beams with a Continuously Varying Height

Longitudinal fracture behavior of nonlinear elastic inhomogeneous beam configurations with a continuously varying height along its length is analyzed. The general solution of the strain energy release rate problem is obtained by considering the energy balance. Beam configurations with the longitudinal crack located arbitrarily along the height are analyzed. The beams exhibit smooth material inhomogeneity in the height direction. The solution derived is valid within the arbitrary law of continuous beam height variations. Longitudinal fracture in a simply supported nonlinear elastic inhomogeneous beam with a height that varies in a parabolic law is investigated by applying the general solution of the strain energy release rate problem. The J-integral approach is used to verify this solution. The effect of various geometrical and material parameters on the longitudinal fracture of the simply supported beam configuration is evaluated and discussed in detail.