Modeling method for a crack problem of functionally graded materials with arbitrary properties—piecewise-exponential model

Abstract

A new model, piecewise-exponential model (PE model), is developed to investigate the crack problem of the functionally graded materials (FGMs) with arbitrary properties. In the PE model, the functionally graded material is divided into some nonhomogeneous layers along the gradient direction of the properties, with each layer's properties varying exponentially. By this way, the real material properties can be approached by a series of exponential functions. Since the real material properties are used on both surfaces of each nonhomogeneous layer, the nature of continuously varying properties of FGMs can be approached accurately. The influences of the local nonhomogeneity on the crack-tip fields can be fully considered. By using the new model, the fracture problem of a functionally graded strip with arbitrary properties and a crack vertical to the free surfaces is studied. The integral transform method, the theory of residues and the theory of singular integral equation are applied. Some representative samples with different kinds of nonhomogeneous properties are analyzed and the corresponding stress intensity factors (SIFs) are presented. It is shown that the PE mode is effective for investigating the crack problems of the FGMs with arbitrary properties.

A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

“…finite-element model) for the crack problems of FGMs with stochastic properties so that the probabilistic characteristic of the SIFs can be calculated efficiently with a small sample size. Therefore, different from Guo & Noda (2007), the present method should be able to not only deal with stochastic mechanical properties, but also obtain the stable probabilistic characteristics of the SIFs with high efficiency. (2) To realize the aim in paragraph (1) above, a micromechanics-based method is developed to obtain the explicit probabilistic characteristics of the effective properties of the FGMs so that the stochastic mechanical properties can be applied in the analytical model to obtain the SIFs.…”

“…For each sample of the shear modulus G(x), the crack problem of the FGM plate in figure 3 can be studied by using the PE model (Guo & Noda 2007). Figure 4 shows the schematic of the layers in the PE model in which the FGM strip is divided into M layers, with each layer denoted by a subscript 'n' (n = 1, 2, .…”

Multiple Parallel Symmetric Mode-III Cracks in a Functionally Graded Material Plane

“…In the practice, the piecewise-exponential model can be used to approach the practical arbitrary distributing properties of FGMs as discussed in Ref. [9].…”

Three-dimensional thermal weight function method for the interface crack problems in bimaterial structures under a transient thermal loading

“…The analytical solutions are available only for very limited cases [1][2][3][4][5][6][7][8][9][10][11][12][13][14], wherein the cracked bodies are assumed to be in nite and subjected to special thermal loading conditions. It is di cult to derive the exact solutions for cracked bodies of nite dimension.…”