Influence of density variation on the arbitrarily propagating crack tip fields in functionally graded materials

The stress and displacement fields for an arbitrarily propagating crack tip in functionally graded materials (FGMs) with exponential variation of density and shear modulus are obtained. Nonhomogeneous parameters of density and shear modulus are different from each other. The solutions for higher order terms in the dynamic equilibriums are obtained by transforming the general differential equations to the scaled Laplace's equations. Using the stress fields, the effects of the nonhomogeneous density on stress components is investigated. In addition, the contours of the constant maximum shear stress at a propagating crack tip are generated and the effects of the nonhomogeneous density on the isochromatics are discussed.