The combination of several materials in one component offers, in many cases, significant improvements to its functional
performance. Optimally, material properties throughout a component should be tailored to its specific application, often requiring
combinations of properties that are unattainable with a single homogeneous material. Functionally graded materials (FGMs) can offer an
advantageous means of combining materials, providing a spatial variation in composition and material properties, as an alternative to homogeneous
materials and conventional composite materials.
In general, the highest temperature on the surface of future space planes has been estimated to reach 2100K. Hence, materials at the surface must withstand temperature as high as 2100K and temperature differences of 1600K. The concept of FGMs was proposed in 1984 by Niino of the National Aerospace Laboratory and his colleagues in Sendai, Japan, as a means of preparing thermal barrier materials usable in space plane systems. FGMs had been introduced primarily to take advantage of the heat and corrosion resistance of ceramics and the mechanical strength of metals, and at the same times, to reduce the magnitude of thermal stresses. Although the original purpose of FGMs was the development of super-resistant materials for population systems and airframe of the space planes in decreasing thermal stresses and increasing the effect of protection from heat, subsequent investigations have addressed a wide variety of application. These include the potential use of FGMs in nuclear fusion and fast breeder reactors as first-wall composite materials; in electric and magnetic applications as piezoelectric and thermoelectric devices; in thermionic applications, e.g. thermionic converters: in biomaterials, e.g. dental and other implants.
The applications of FGMs in various branches of engineering and technological necessitate identifying the probable failure modes and
designing them against those failures. In the design of FGMs, an important aspect is the problem of mechanical failure, specifically the
fracture. Although the absence of sharp interfaces in FGMs does largely reduce materials properties mismatch, cracks may occur when they are subjected to external loading. Very often the process begins with the formation of microcracks at the locations of corrosion pits, surface flaws, or severe stress concentrations. Generally a number of microcrakcs coalesce and form a local dominant crack, which would then propagate substantially under or sustained loading. The loads or stresses acting on the medium may be mechanically or thermally induced. These are also uncertainties arising from voids and defects that are introduced in FGMs during manufacturing. Even a small quantity of mechanical imperfections can cause a marked influence on their fracture strength. Therefore, the study of the fracture mechanics of these materials appears to be an utmost necessary to understand, quantify and improve their fracture strength.
An important aspect of FGM bodies still remaining to be dealt with is the inverse problems in which the improved characteristics of FGM bodies under mechanical and thermal loadings can be prescribed and the corresponding material composition profiles via the material properties can be obtained by optimization method. This approach appears to be quite effective and efficient tool in designing with FGM bodies for obtaining a desired behavior for an application. Obviously, the inverse problems cannot be restricted to certain assumed functions for the material property distributions. These assumed properties distributions may be not physically realizable for certain material composition profiles which may be obtained by the inverse problems. Therefore, to solve the optimization problem for improving fracture strength, it is necessary to develop a method to obtain the stress intensity factors for the cracks in FGMs that have arbitrary variation of material properties.
There are two distinct fracture criteria to deal with the optimization problem of material distributions for improving the fracture strength in FGMs. The first is the strength criterion based on the strength of materials. Many studies dealt with the optimization problems of material distribution profiles for minimizing the thermal stresses in FGMs under steady and unsteady state. The alternative one is the strength criterion based on the theory of fracture mechanics for ensuring the structural integrity of FGMs against fracture formation from the viewpoint of damage tolerant design. However, the studies by employing the optimization problems of material distributions for improving the fracture strength, which is determined using the strength criterion based on the theory of fracture mechanics, have been very few up to date.
The main objective of this study is to improve the fracture strength of the thick-walled FGM circular pipes by choosing optimum materials distribution profiles. First, homogenizing the FGM circular pipes by simulating the nonhomogeneity of thermal conductivity by a distribution of equivalent eigentemperature gradient and the nonhomogeneities of Young's modulus and Poisson's ratio by a distribution of equivalent eigenstrain, we present an approximate method to obtain the stress intensity factor in the FGM circular pipes with arbitrarily varied material properties. This method is applied to optimization problem of material distribution profiles.
edited by Kimiaki YOSHIDA