Theoretical Investigation In A Functionally Gradient Material With Finite Width Under Anti-plane Fracture Analysis

In recent years, the concept of functionally grated materials( FGM) has been introduced and applied to engineering structures. The advantages of FGM are that the materials could resist corrosion, radiation and high temperatures effectively and, at the same time, the residual and thermal stresses could be relaxed significantly. People pay more and more attention to research FGM. It is expected that FGM have promising applications in aerospace engineering, nuclear power plants, electronics, optics, chemical engineering, biomedicine and so on.From the viewpoint of applied mechanics ,FGM are nonhomogeneous solid. The nonhomogeneous of FGM has a great influence on their mechanical behavior. To provide technical support for material scientists and design and manufacturing engineering engineers, significant attention has been paid to various theoretical and practical aspects of the mechanical behavior of FGM. However, the studies on FGM dynamic fracture mechanics are not enough, especially for the problems on moving and expanding cracks and waves striking cracks. In this paper, first the development and introduction of FGM are expounded .The static state crack problem of mode III crack in a finite isothotropic FGM anti-plane loaded and the static state and motorial crack problem of mode III crack in a finite orthotropic FGM anti-plane loaded are studied by using of integral transforms-dual integral equations method .The material parameter is assumed to hyperbolic function .By using with Matlab soft ware a series of results are obtained. The main study process and production are as follows:1. Mode III static state crack anti-plane fracture problem of finite strip isotropic FGM was studied. The results display that with the fixed width of the strip if the crack is located near the middle part of the strip the range of variation of the stress intensity factor is small, when the crack is located on the verge of the strip the stress intensity factor is very sensitive to the variety of the crack location.2. Mode III static state crack anti-plane fracture problem of finite strip orthotropic FGM was studied. The results display that with the increasing of coefficient of inhomogenous material ,the value of stress intensity factor decreases. With the increasing of length of the crack, the value of stress intensity factor increases. So by increasing shear moduli's gradient parallel crack surface of FGM can restrain the driving force of crack expanding.3. Mode III static state crack anti-plane fracture problem of finite strip orthotropic FGM was studied when the location of the crack moves parallelly. The results display that the influence of crack location on the stress intensity factor is more like to the condition of mode III static state crack anti-plane fracture problem of finite strip orthotropic FGM. We can also know that with the increasing of gradient parameter ,the value of stress intensity factor decreases, With the increasing of length of the crack, the value of stress intensity factor increases, also the influence of gradient parameter on the stress intensity factor is larger. So by increasing shear moduli's gradient parallel crack surface of FGM can restrain the driving force of crack expanding.4. The dynamic problem of Yoffe type III mode crack was studied subjected to anti-plane shear impact in finite orthotropic FGM. The dynamic stress intensity factor will increase with the increase of the speed ,it will decrease with the increase of material inhomogenous coefficient. So by increasing shear moduli's gradient parallel crack surface of FGM can restrain the driving force of crack expanding.