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 stresses in the FGMs with various types of cracks. The thermal stress intensity factors in the FGMs with various types of crack are treated analytically and numerically. The optimal composition profile problems of the FGMs in decreasing thermal stress intensity factor are studied. Finally, the crack propagation paths due to thermal shock are discussed.     

RELATIONSHIP BETWEEN THERMAL SHOCK STRENGTH BY LASER IRRADIATION TECHNIQUE AND FRACTURE TOUGHNESS FOR CERAMICS

The traditional water quenching technique used to evaluate the thermal shock resistance of ceramics is accompanied by an unstable heat transfer coefficient in the quenching process. This leads to an unreliable result of the value of the thermal shock strength of ceramics. Our purpose is to establish a new method using the laser irradiation technique by which the thermal shock strength of ceramics could be evaluated. Defining the laser power density, the so-called critical power density P L at which the ceramic specimen fractures, the method was evaluated both theoretically and experimentally for several structural ceramic materials. Since thermal shock fractures are caused by the induced thermal stress, the thermal shock strength must be correlated to the fracture toughness of ceramics. This study presents a relationship between the thermal shock strength P L , which corresponds to the critical powerdensity, by laser irradiation and the fracture toughness K IC by the indentation fracture technique for ceramics as a means to investigate their fracture mechanism. The thermal shock strength P L can be used as a fracture criterion corresponding to the critical temperature difference in the quenching method. The thermal shock strength for several ceramics was obtained by the irradiations with CO 2 lasers. On the other hand, their fracture toughness was measured by the indentation technique using a micro Vickers hardness tester. It was concluded that these two quantities, the thermal shock strength and the fracture toughness, were closely correlated; a linear relation was shown in a semi-log plane.     

ON INERTIA EFFECTS IN THERMOELASTICITY AND THERMAL SHOCK PARAMETERS

A material parameter R_d is presented, called the “dynamic thermal shock resistance,” which measures the resistance to thermal stress waves induced by very rapid body heating, e.g. by radiation, of both slender and massive bodies. This dynamic parameter is the complementing counterpart to the well-known “quasi-static thermal shock resistance” R_s, which is the classical measure for the resistance to thermal stresses due to temperature gradients induced by ordinary contact (or surface) heating when inertia effects may be neglected. The two material parameters. R_d and R_s, give a very different ranking of materials. Both parameters have an important physical significance: they place a restriction, solely defined in terms of material properties, on the maximum value of the product of a characteristic structural dimension and the specific thermal power or heating.     

CYCLIC LOADING OF THERMAL STRESSES

The isotropic and kinematic hardening theories of plasticity are used to evaluate the cyclic loading behavior of structures under thermal stresses. The material of the structures used in this article is assumed to follow nonlinear strain hardening property. The material's strain hardening curve in tension and compression is assumed to be both identical for isotropic material and different for anisotropic material. The method of successive approximation is used to calculate the stresses and plastic strains in the structure due to cyclic loadings. The results of the analysis are checked with the known experimental test. The thermal stresses are categorized into load- and deformation-controlled stresses. It is concluded that the isotropic hardening theory, excluding creep, will always result in structural shakedown. The kinematic hardening theory under deformation-controlled conditions, excluding creep, will result in reversed plasticity. The load-controlled cyclic loading under kinematic hardening theory with isotropy assumption results in reversed plasticity. Under the anisotropy assumption of tension/compression curve, the load-controlled stress based on kinematic hardening theory predicts ratcheting behavior. When creep deformation is considered, the load-controlled thermal stresses results in ratcheting, and the deformation-controlled thermal stresses result in shakedown behavior, regardless of the material's isotropic and anisotropic properties or the hardening theories.     

DQM-Based Thermal Stresses Analysis of a Functionally Graded Cylindrical Shell Under Thermal Shock

The transient thermal stresses of a functionally graded (FG) cylindrical shell subjected to a thermal shock are investigated. The dynamic temperature fields of FG shells are obtained by using the Laplace transform and power series method. The differential quadrature method is developed to obtain the transient thermal stresses by solving dynamic governing equations in terms of displacements. The effects of the material constitutions on the transient temperature and the thermal stresses are analyzed in the cases of obverse thermal shock and reverse thermal shock. It turns out that the thermal stresses could be alleviated by means of changing the volume fractions of the constituents.     

TRANSIENT THERMAL STRESS ANALYSIS AND BENDING BEHAVIOR OF AN ANGLE-PLY LAMINATED SLAB

Abstract

This paper is concerned with a theoretical treatment of thermal stress and bending behavior in a transient state of a multilayered, nonisotropic, laminated slab. As an analytical model, we consider an infinitely long, laminated slab, which consists of obliquely directed layers with orthotropic material properties; the model corresponds to the so-called angle-ply laminate. We solve the thermoelastic problem for the slab under the condition of uniformly distributed heat supply from its one surface. Introducing a method of Laplace transforms to the temperature field, we obtain the temperature solution using the residue theorem, and we evaluate the thermal stresses in a transient state by using the elementary plate theory. As an example, we carry out numerical calculations for the five-layered angle-ply laminate, evaluate the thermal stress distributions and the bending behavior, and examine the influence of the ply angle on the thermal stress distribution.     

THERMAL STRESSES AND DISPLACEMENTS INDUCED IN A FINITE,ORTHOTROPIC, CYLINDRICAL,THIN SHELL BY AN INSTANTANEOUS THERMAL SHOCK

The thermal responses in a thin cylindrical shell of graphite material with finite length, subjected to an instantaneous thermal shock, are investigated. Closed-form solutions for the thermal stresses and displacements caused by a line source along the circumferential direction are obtained by integrating the fundamental solutions for a point heat source acting on a finite, orthotropic, cylindrical, thin shell. Grade ZTA graphite is used in the numerical examples. As expected, orthotropic thermal and mechanical properties significantly affect the induced displacements and thermal stresses in the shell due to the thermal shocks.     

TWO CRACK GROWTHS IN A FUNCTIONALLY GRADED PLATE UNDER THERMAL SHOCK

This article examines the problem of two thermal cracks under a transient temperature field in a ceramic/metal functionally graded plate. When the functionally graded plate is subjected to thermal shock, multiple cracks often occur on the ceramic surface. It is shown that the crack paths are influenced by interaction between multiple cracks and a compositional profile of the functionally graded plate. Transient thermal stresses are treated as a linear quasi-static thermoelastic problem for a plane strain state. The crack paths of two cracks are obtained using the finite element method with mode I and mode II stress intensity factors.     

CRACK ARREST ANALYSIS UNDER CYCLIC THERMAL SHOCK FOR AN INNER-SURFACE CIRCUMFERENTIAL CRACK IN A FINITE-LENGTH THICK-WALLED CYLINDER

This article presents a crack arrest depth analysis under cyclic thermal shock for an inner-surface circumferential crack in a finite-length thick-walled cylinder with rotation-restrained edges. The inside of the cylinder is cooled from a uniform temperature distribution. The effects of heat transfer conditions on the maximum transient stress intensity factor for the problem were investigated with systematical evaluation methods formerly developed. Then, under an assumption of a tentative threshold stress intensity range j K th together with the Paris law, the crack arrest depth under cyclic thermal stress was evaluated. The results suggested the existence of an upper limit for the normalized crack arrest depth, independent of the cylinder material in an engineering sense. Finally, the validity of applying j K max h j K th as a crack arrest criterion under cyclic thermal shock was confirmed by fatigue tests under mechanical loads equivalent to those induced by cyclic thermal shock.     

ANALYSIS ON TRANSIENT THERMAL STRESSES IN AN ANNULAR FIN

Transient thermal stresses are an important consideration in production processes involving large temperature changes. Recently, thermal stresses have also become significant in design problems related to microelectronic devices through their effects on material properties and system parameters. To calculate the thermal stresses, three kinds of methods are available. The first is the analytical method, in which the elastic theory is used to find the exact solution. The second approach consists of some kind of approximate technique, such as a perturbation procedure. The third method is the use of a numerical process, such as a finite-difference or a finite-element method.

This article investigates the transient thermal stresses in an annular fin with its base subjected to a heat flux of a decayed exponential function of time. In order to obtain the solution of the governing equation, which is a partial differential equation, the following procedures of analysis are used.

1. Normalize the governing partial differential equation subject to appropriate initial and boundary conditions.

2. Take the Laplace transform of the resulting equation with respect to time.

3. Utilize the exponential-like solutions introduced by Keller and Keller to solve the transformed system.

4. Achieve the inverse Laplace transform by means of complex contour integration and the residue theorem.

5. Substitute the temperature distribution function into the governing equation of thermal stresses. Then use Simpson's rule to obtain the thermal stress distribution as a function of time and position of the fin.     

THERMAL STRESS ANALYSIS IN THERMOPIEZOELASTIC STRIP WITH AN EDGE CRACK

The analysis of thermal stresses becomes important when the piezoelectric material has to be operated in either extremely cold or hot temperature environments. Hence, it is essential to know the interaction of mechanical defects with temperature changes. This investigation is concerned with a strip problem of transversely isotropic thermopiezoelastic material containing an edge crack under partial thermal and electric loading conditions. Thermopiezoelastic stresses are analyzed by introducing potential functions and Fourier transforms. The problem reduces to solving a singular integral equation, and the singular integral equation is solved. Numerical calculations of the thermal stress intensity factors are carried out for a cadmium selenide material.     

A Study on Coupled Thermo-Elasto-Plastic-Damage Dissipative Phenomena: Models and Application to Some Innovative Materials

This is a review paper on some irreversible thermodynamics-based constitutive models capable of capturing complex dissipative physical bahaviour in multifunctional innovative materials. The thermomechanical response of such materials accounts for two basic sources of material nonlinearity, plasticity and damage, which may result in various failure mechanisms. A number of couplings, such as thermo-elastic-damage, elastic-plastic hardening, plastic-damage hardening, thermo-elastic-plastic-damage, etc., are discussed. Various material symmetry classes, including anisotropy, orthotropy, transverse isotropy, are referred to some innovative materials, such as composite materials, functionally graded structures, thermal or wear resistant coatings, etc. Examples of implementation of chosen models for simulation of some initial boundary problems are presented.     

ELASTOPLASTIC ANALYSIS OF W-Cu FUNCTIONALLY GRADED MATERIALS SUBJECTED TO A THERMAL SHOCK BY MICROMECHANICAL MODEL

We consider the transient elastoplastic behavior of the functionally graded divertor plate due to a thermal shock with temperature-dependent properties. The development of a micromechanical model for functionally graded materials is presented, and its application to thermoelastoplastic analysis is discussed for the case of the W-Cu functionally graded material for the international thermonuclear experimental reactor divertor plate. The divertor plate consists of a graded layer bonded between a homogeneous substrate and a homogeneous coating, and it is subjected to a cycle of heating and cooling on the coating surface of the material. The material properties of the divertor plate are dependent on the temperature and the position. Numerical results presented include the transient elastoplastic stresses.     

3D Study of Thermal Stresses in Lead-Free Surface Mount Devices

The paper presents the study of non-uniform temperature distributions in a flip chip electronic assembly, and the use of these temperature distributions to analyse the thermal stresses in lead-free solder joints in surface mount devices. The thermal stresses in the solder joints are mainly due to the mismatch in the coefficients of thermal expansions between the component and substrate materials, and temperature gradient in the electronic assembly. The thermo-elasto-visco-plastic finite element analysis is carried out to investigate the extent of thermal stresses induced in solder joints between a surface mount component and a FR4 circuit board (substrate) under conditions of thermal cycling with the chip resistor operating at its full power condition. Three different cases of spatial temperature distributions are considered including one with an experimentally obtained non-uniform temperature distribution. A comparative study of thermal stresses is performed using a near-eutectic SnAgCu solder material for three different thermal cases.     

THERMALLY INDUCED BENDING VIBRATION OF COMPOSITE SPACECRAFT BOOMS SUBJECTED TO SOLAR HEATING

Thermally induced bending vibration of spacecraft booms modeled as circular thin-walled beams of closed cross section and subjected to thermal radiation is investigated. One assumes that the boom is built up of composite material systems, and in this context, the constituent materials of the beam include nonclassical effects such as anisotropy and transverse shear. In addition, in order to induce beneficial elasticcouplings, a special ply-angle distribution achieved via the usual helically wounding fiber-reinforced technology is implemented. Both the dynamic governing equations involving the temperature effects and the related boundary conditions are obtained via the application of the extended Hamilton principle. The case of the spacecraft boom equipped with a concentrated mass at its free end, fixed at the other end, and exposed to solar radiant heating is studied from both the induced-vibration and stability points of view. The numerical simulations display deflection time history of bending displacements as a function of the fiber orientation of the composite materials, damping factor, and angle of incidence of heat radiation. The obtained results are likely to fill a gap in the specialized literature and to play a good role toward a better understanding of the factors that contribute not only to the occurrence of the thermal flutter instability, but also to its avoidance.     

THERMOELASTIC INTERACTIONS WITHOUT ENERGY DISSIPATION IN AN UNBOUNDED MEDIUM WITH A SPHERICAL CAVITY DUE TO A THERMAL SHOCK AT THE BOUNDARY

Thermoelastic interactions without energy dissipation in an unbounded elastic medium with a spherical cavity have been investigated. The cavity surface is assumed to be stress free and is subjected to a thermal shock. The solutions for displacement, temperature, and stresses are obtained using the Laplace transform procedure. The discontinuities of the distributions of the physical quantities are determined and compared with earlier findings. The inversions are also carried out with a numerical method based on Fourier series expansions of functions. The results are compared with the corresponding results obtained in cases of conventional thermoelasticity theory and the generalized theories of thermoelasticity with thermal relaxation time parameters.     

Simple determination of the thermal conductivity of the solid phase of particulate materials

It is often desirable to predict the thermal conductivity of a heterogeneous or composite material based on its composition, particularly where variations in composition are expected. In the case of particulate materials such as sand and soil the volume fraction of the solid phase is often known, while it's thermal conductivity is not (and vice versa for the fluid phases). It is proposed that the thermal conductivity of the solid phase of granular materials may be determined simply by measuring the thermal conductivities of the material in both the bone-dry and water-saturated states and making use of a modified form of Maxwell's conductivity model. The method was illustrated using beach sand.     

THERMAL EFFECTS ON FLOW PROPERTIES OF ALUMINUM ALLOYS

The flow properties of aluminum alloys under hot working conditions can be studied by hot torsion testing. However, the properties obtained may be severely affected by the thermal effects generated during testing. In this paper thermal analysis is made by a finite element analysis (FEA) to evaluate the temperature distribution over the test specimen, and the predictions of the flow stresses of an aluminum alloy AA5252 are modified by taking into account the temperature changes. It has been shown that the further flow softening at high strain rates, as a result of heat accumulation during testing can be predicted by the method presented.     

Vibration Control of Composite Spacecraft Booms Subjected to Solar Heating

In this paper, piezoelectric feedback control of vibration and instability of spacecraft booms modeled as circular thin-walled cross-section beams and subjected to solar radiant heating is investigated. Having in view that composite material systems are likely to play a great role in the design of these devices, the beam constituent materials encompass non-classical effects such as anisotropy and transverse shear. In addition, in order to induce beneficial elastic couplings, a special ply-angle distribution achieved via the usual helically wounding fiber-reinforced technology, the so called filament winding, is implemented. The dynamic governing equations including the temperature effects and the related boundary conditions are obtained via the application of Hamilton's principle. Toward the end of controlling the oscillations and prevent the occurrence of the thermal dynamic instability, a feedback control capability based on the use of the piezoelectric induced strain actuation is implemented. The performance of its implementation considered in conjunction with that of the structural tailoring are highlighted and pertinent conclusions are derived.     

Experimental investigations of the coupled conductive and radiative heat transfer in metallic/ceramic foams

Due to their interesting thermal, mechanical and exchange properties, solid metal or ceramic foams have shown a strong development in numerous technological fields for which the knowledge of their thermal properties is of primary importance. In order to investigate the coupled conductive/radiative heat transfer in this kind of materials, we propose an identification method using thermograms obtained from laser-FLASH measurements. This permits us to evaluate, at ambient and high temperatures, the effective thermal conductivity and two global radiative properties of various metal or ceramic foams, describing the thermal behavior of their equivalent homogeneous semi-transparent materials. This new method of characterization of solid foams is promising since conduction and radiation contributions to heat transfer can be evaluated from a unique experiment.