Dynamic Fracture Mechanics Model Of Functionally Graded Materials With Arbitrary Properties

Functionally graded materials (FGMs) are two or multi-phase particulate composites in which material composition and microstructure vary spatially. FGMs have many advantages in comparison with traditional materials . they have been widely introduced and applied to the development of thermal and structural components due to its ability not only to reduce the residual and thermal stresses but also to increase the bonding strength and toughness. Therefore, it necessary and important to analyze the influences of some stochastic factors (such as the volume fractions) on the effective properties and the crack-tip stress intensity factors (SIFs) in FGMs for its design, optimization and safety.The transient response of functionally graded materials of arbitrary properties with a crack vertical to the free surfaces is analyzed theoretically. The impact loading condition is considered. Based on the piecewise-exponential model (PE model), a new analytic method is developed. The functionally graded material is divided into some nonhomogeneous layers with exponentially properties along the gradient direction. Since the shear modulus has stronger influences than the mass density ratio on the dynamic stress intensity factors (DSIFs), the varying form of density ratio is assumed to be based on that of shear modulus. By using Laplace and Fourier integral transforms, singular integral equation methods and the theory of residues, the present problem can be reduced to a singular integral equation in the Laplace transform domain. Finally, the DSIFs can be calculated by applying the Laplace numerical inversion technique. Some representative samples with different kinds of nonhomogeneous properties are analyzed and the corresponding DSIFs are presented. It is shown that the properties varying forms have greatly influences on the DSIFs. The influences of the Young's modulus ratio, mass density on the DSIFs are also investigated.