Analysis of a transiently propagating crack in functionally graded materials under mode I and II

Abstract

Crack tip stress and displacement fields for a transiently propagating crack along gradient in functionally graded materials (FGMs) with a linear variation of shear modulus are developed. The higher order terms of the transient stress and displacement fields at crack tip were obtained by transforming the general partial differential equations of the dynamic equilibrium into Laplace’s equations whose solutions have harmonic functions. Thus, the fields can be expressed very simply. Using these stress components, isochromatics and the first invariant at crack tip are generated. The results show that the isochromatics (constant maximum shear stress) for mode I crack tilt backward around the crack tip with an increase of crack tip acceleration c ˙ ( d c / d t ) , and tilt forward around the crack tip with an increase of rate of change of dynamic mode I stress intensity factor K ˙ I ( d K I / d t ) . The isochromatics for mixed mode crack move to upper direction with an increases of K ˙ I and K ˙ II , and lower direction with an increase of c ˙ . Contours of the first stress invariant for mode I crack enlarge around the crack tip with an increase of c ˙ , and decrease around the crack tip with an increase of K ˙ I . As K ˙ I ( II ) decreases at crack initiation, the predicted kinking angles increase. As c ˙ increases, the predicted kinking angles also increase.