The Static Stress Intensity Factor around the Antiplane Crack in an Infinite FGM Strip

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1. Introduction

Functionally gradient material is a new type of materials. The advent of functionally gradient material is in order to meet performance requirements of parts in all kinds of special environment. The sudden changes of the material composition and properties in a member often lead to obvious local stress concentration. If a material transition to another kind of material is the step by step, the stress concentration will greatly reduce. A new type of functional gradient materials (FGM) was developed in order to reduce the stress concentration of the material and improve the performance requirements of the material as discussed elsewhere [1–5]. Most previous studies about FGM in the past were focused on isotropic material as discussed elsewhere [6, 7]. However, a few FGMs were isotropic material. At present, the application of FGM has been expanded to space, energy, traffic, optics, chemistry, biomedical engineering, and so forth. However, due to the influence of the process conditions, FGM will produce some defects in manufacturing process. These defects will inevitably form crack due to stress action and crack expansion will affect the whole member. So, the research about crack and the crack expansion of FGM are very important as discussed elsewhere [8–11].

In the fracture mechanics study of FGM, most scholars use the power functions model as a material property parameter model. The model of μ(z)=μ0(1+c|z|) as discussed by Smith [1], the model of μ(z)=μ0(1+α|z|)2 as discussed by Smith [12], and the model of μ(z)=μ0(1+α|z|)k as discussed by Smith [13]. However, the models of double parameters index function were adopted...