Naotake Noda

THERMAL STRESSES IN FUNCTIONALLY GRADED MATERIALS

The thermal stress problems of functionally graded materials (FGMs), as one of the advanced high-temperature materials capable of withstanding the extreme temperature environments, are discussed. The FGMs consist of the continuously changing composi tion of two different materials. For example, one is an engineering ceramic to resist the severe thermal loading from the high-temperature environment, and the other is a light metal to maintain the structural rigidity. When the FGMs are subjected to extremely severe thermal loading, large thermal stresses are produced in the FGMs. Therefore, one of the most important problems of FGMs is how to decrease thermal stresses and how to increase heat resistance. The optimal composition profile problems of the FGMs in decreasing thermal stresses are discussed in detail. When FGMs are subjected to extremely severe thermal loading, the FGMs are damaged. The crack initiates on the ceramic surface and propagates in the FGMs. It is important to discuss the thermal stresse...

Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material

This paper considers the steady thermal stresses in a hollow circular cylinder and a hollow sphere made of a functionally gradient material (FGM). The aim of this research is to understand the effect of the composition on stresses and to design the optimum FGM hollow circular cylinder and hollow sphere. We discuss the influence of inside radius size on stresses and the available temperature regions. We also compare these results with those of a FGM plate.

Thermo-elasto-plastic stresses in functionally graded materials subjected to thermal loading taking residual stresses of the fabrication process into consideration

Functionally graded materials (FGMs) have recently been received with considerable interest, primarily as high temperature resistant materials for space vehicles subjected to high temperature environment. FGMs are one of the composite materials and consist of continuous change of composition of different material components from one surface to the other. FGMs usually fabricated at high temperature at which the FGMs have stress free condition. After the FGMs cooled from the fabrication temperature to the room temperature residual thermal stresses produced. In this paper, elasto-plastic thermal stresses in a rectangular plate (FGP) of a particle reinforced composite FGM are treated by finite element method due to the microscopic combination law when the FGP is subjected to three kinds of temperature conditions, first is cooling from the fabricated temperature to the room temperature, second is heating and last is heating after cooling from the fabricated temperature. In the analysis, the thermal stress constitutive equation of a particle-reinforced composite taking temperature change and damage process into consideration is used. The effects of the particle volume fraction and the three kinds of temperature conditions on the stresses in the matrix, stresses in the particle and macroscopic stress are discussed.

Optimum material design for functionally gradient material plate

SummarySteady thermal stresses in a plate made of a functionally gradient material (FGM) are analyzed theoretically and calculated numerically. An FGM plate composed of PSZ and Ti-6Al-4V is examined, and the temperature dependence of the material properties is considered. A local safety factor is used for evaluation of the FGMs strength. It is assumed that top and bottom surfaces of the plate are heated and kept at constant thermal boundary conditions. The pairs of the surface temperatures, for which the minimum local safety factor can be of more than one, are obtained as available temperature regions. The temperature dependence of the material properties diminishes, available temperature region as compared with that for an FGM plate without it. The available temperature region of the FGM plate is wider than that of the two-layered plate, especially for the surface temperatures which are high at the ceramic surface and low at the metal side. The influence of different mechanical boundary conditions is examined, and available temperature regions are found to be different, depending on the mechanical boundary conditions. The influence of the intermediate composition on the thermal stress reduction is also investigated in detail for the surface temperatures which are kept at 1300 K at the ceramic surface and 300K at the metal side. Appropriate intermediate composition of the FGM plate can yield the local safety factor of one or more for the four mechanical boundary conditions at once. For the two-layered plate there does not exist, however, any appropriate pair of metal and ceramic thicknesses which would yield the local safety factor of one or more for the four mechanical boundary conditions at once. The influence of the intermediate composition on the maximization of the minimum stress ratio depends on the mechanical boundary conditions. Finally, the optimal FGM plates are determined.

EDGE CRACK IN A NONHOMOGENEOUS HALF PLANE UNDER THERMAL LOADING

This paper deals with the problem of an edge crack in a semi-infinite nonhomogeneous plate under steady heat flux loading conditions. The objective of the study is to assess the effect of material nonhomogeneity on the thermal stress intensity factor. All material properties are supposed to be exponentially dependent on the distance from the boundary of the plate. By using the Fourier transform, the problem is reduced to a singular integral equation that is solved numerically. The thermal stress intensity factors for various material constants are calculated. The results show that by selecting the material constants appropriately the stress intensity factor can be reduced.

Mixed mode crack initiation in piezoelectric ceramic strip

Abstract When piezoelectric ceramics are subjected to mechanical and electrical load, they can fracture prematurely due to their brittle behavior. Hence, it is important to know the electro–elastic interaction and fracture behavior of piezoelectric materials. The problem of a through crack in a piezoelectric strip of finite thickness is studied in this paper. Fourier transforms are used to reduce the problem to the solution of singular integral equations. The model technique can solve for polarization in an arbitrary direction and material anisotropy. Numerical values of the crack-tip field amplification for a piezoelectric strip under in-plane electromechanical loading are obtained. Energy density factor criterion is applied to obtain the maximum of the minimum energy density and direction of crack initiation. The influence of crack length and crack position on stress intensity and energy density factors is discussed.

A crack in functionally gradient materials under thermal shock

SummaryThis paper deals with the problem of two bonded semi-infinite functionally gradient material plates with a crack at the interface under thermal shock loading conditions. All material properties are supposed to be exponentially dependent on the distance from the crack line. By using both the Laplace transform and the Fourier transform, the problem is reduced to a singular integral equation which is solved numerically. The stress intensity factor versus time for various material constants is calculated. The results show that by selecting the material constants appropriately, the stress intensity factor can be lowered substantially.ÜbersichtDie Arbeit behandelt das Problem zweier beschichteter Platten aus einem Funktionalgradientenmaterial mit einem Riß entlang der Verbindungsfläche unter einer thermischen Schockbeanspruchung. Die Materialeigenschaften hängen exponentiell vom Abstand von der Bruchlinie ab. Durch kombinierte Anwendung der Laplace- und der Fourier-Transformation wird das Problem auf eine singuläre Integralgleichung reduziert, die numerisch gelöst wird. Daraufhin wird der Spannungsintensitätsfaktor als Funktion der Zeit für mehrere Sätze von Materialkonstanten berechnet. Es zeigt sich, daß der Spannungsintensitätsfaktor durch eine geeignete Wahl der Materialkonstanten beträchtlich reduziert werden kann.

Transient thermoelastic responses of functionally graded materials containing collinear cracks

A generalized method to treat the collinear cracks in functionally graded materials (FGMs) subjected to thermal loads is established. The integral transform technique is used to reduce the problem to a set of singular integral equations which is solved numerically. A metal/ceramic FGM plate and a metal layer/ceramic layer bonded plate are analyzed as examples. Numerical results are obtained to show the influence of crack spacing on field intensity factors ahead of the crack-tips. It is observed that thermal stress intensity factors can increase or decrease with the crack spacing. Through the introduction of the FGM, the thermal stress intensity factors can be reduced.

ELASTO-PLASTIC THERMAL STRESSES IN FUNCTIONALLY GRADED MATERIALS CONSIDERING MICROSTRUCTURE EFFECTS

Functionally graded materials (FGMs) have been developed as ultrahigh temperature resistant materials for aircraft, space vehicles and other engineering applications. Most of FGMs are particle reinforced FGMs and their compositions depend on position. In the heat-resistant FGMs which contain particles (ceramics) in the matrix (metal), the matrix will be subjected to plastic deformation, particles will be debonded, and finally cracks will be generated. In the past many studies of FGMs, a macroscopic combination law has been adopted to express the material properties. However in order to obtain more correct thermal stresses in the FGMs, it is necessary to analyze thermal stresses by use of the microscopic combination law. In this paper, we use the thermal stress constitutive equation of a particle-reinforced composite taking temperature changes and damage process into consideration. The volume fraction of the ceramic and the metal are evaluated using the power law distribution. Elastoplasticity is considered in the formulation and a finite element model of the formulation is developed. The effect of the particle volume fraction and the initial temperature condition on the stress variations are discussed in the manufacturing process.