Numerical Analysis of FG and TBC Systems Based on Thermo-Elasto-Plastic-Damage Model

The model of thermo-elasto-plastic damage functionally graded material is developed and the numerical simulation of the material behaviour under complex thermomechanical loading conditions is performed. Sensitivity of the model response to variation of the basic mechanical moduli is examined for a graphite cast iron characterized by a changing volume fraction of graphite particles. The capability of the model to predict response of the complex (thermal barrier/functionally graded material/substrate material) system under thermal loading is checked by the use of two constituents: cast iron and ceramic, and the spatially changing temperature-dependent properties are governed by the appropriate rule of mixture. The response of the three-layer TBC/FGM/S system is compared to the reference metallic structure to show the benefits of the three-layer system.     

Investigation of Aerothermoelastic Behaviors of Functionally Graded Panels in Supersonic Flows

Considering the potentials of Functionally Graded Panels (FGPs) in aerospace field, it is necessary to study the aerothermoelastic behaviors of FGPs in supersonic flows. In this study, Piston Theory Aerodynamics (PTA) and Eckert reference enthalpy method are used to model aerodynamic force and heating, respectively. The 2-D heat conduction equation is solved and the impact of elevated temperature on the mechanical properties of FGPs is considered to build an aerothermoelastic two-way coupling model of FGPs, and Finite Element Method (FEM) is used to approach the solution. As the results, it is found that there exist three different regions in the bifurcation diagram, namely, thermal buckling region, critical region and flutter region. Due to the inhomogeneous distribution of thermal expansion coefficient, the panel buckles up first and then buckles down via vibration, as thermal buckling happens. Also, irregular vibrations are observed in the critical region of bifurcation diagram. In the flutter region, the dynamic behavior of FGPs is discontinuous and very sensitive to initial conditions. With the impact of aerothermoelastic two-way coupling, different FGPs behaviors lead to the differences in temperature distribution. In particular, the final buckling position and vibration center move to lower positions, and lower temperature region near leading edge is left in the FGPs, because of thermal moment. Also, regular vibrations, rather than irregular vibrations, are easy to extract more principal and regular POD (Proper Orthogonal Decomposition) modes. The results presented could be applied to the analysis and design of Functionally Graded Panels in supersonic flows.     

Thermo-Mechanical Bending of Functionally Graded Plates

In this work the deformations of a simply supported, functionally graded, rectangular plate subjected to thermo-mechanical loadings are analysed, extending Unified Formulation by Carrera. The governing equations are derived from the Principle of Virtual Displacements accounting for the temperature as an external load only. The required temperature field is not assumed a priori, but determined separately by solving Fourier's equation. Numerical results for temperature, displacement and stress distributions are provided for different volume fractions of the metallic and ceramic constituent as well as for different plate thickness ratios. They correlate very well with three-dimensional solutions given in the literature.     

Transient Thermomechanical Analysis of a Layered Cylinder by the Parametric Finite-Volume Theory

The recently developed parametric finite-volume theory for functionally graded materials is employed to investigate the response of a layered cylinder under transient thermal loading that simulates a cyclic thermal shock durability test. The results reveal a potential for the occurance of two distinct failure modes that may be activated due to two different stress components reaching critical values during different portions of the thermal cycle at different locations. These are delamination of the ceramic top coat from the bond coat, and radial cracking of the top coat that potentially initiates at the outer surface subjected to concentrated transient thermal load. Steady-state analysis substantially underestimates the magnitude of the radial and hoop stresses and, moreover, does not predict the stress reversals during cooldown that likely initiate radial cracks at the outer surface. The fidelity with which local stress fields are captured provides a convincing evidence that the parametric finite-volume theory is an attractive alternative to the finite-element analysis for this class of problems.     

Effects of Thermal Loading on the Buckling and Vibration of Ring-Stiffened Functionally Graded Shell

A theoretical method is developed to investigate the effects of thermal load and ring stiffeners on buckling and vibration characteristics of the functionally graded cylindrical shells, based on the first-order shear deformation theory (FSDT) considering rotary inertia. Heat conduction equation across the shell thickness is used to determine the temperature distribution. Material properties are assumed to be graded across the shell wall thickness of according to a power-law, in terms of the volume fractions of the constituents. The Rayleigh–Ritz procedure is applied to obtain the frequency equation. The effects of stiffener's number and size on natural frequency of functionally graded cylindrical shells are investigated. Moreover, the influences of material composition, thermal loading and shell geometry parameters on buckling and vibration are studied. The obtained results have been compared with the analytical results of other researchers, which showed good agreement. The new features of thermal vibration and buckling of ring-stiffened functionally graded cylindrical shells and some meaningful and interesting results obtained in this article are helpful for the application and the design of functionally graded structures under thermal and mechanical loads.     

Analysis of Thermal Stress in a Functionally Graded Coating on a Parabolic Substrate

The thermal stress field in a functionally graded coating on a parabolic substrate, where the material properties vary along the thickness direction, is considered. The closed-form solutions of thermal stresses related to compositional gradient, coating thickness and substrate curvature were obtained based on force and moment balances, and then numerical results are presented for several special examples. It is found that the magnitude and distribution of thermal stress in the functionally graded coating system with general geometrical shape can be designed properly by controlling the compositional gradient, coating thickness and substrate curvature.     

Effects of Crack Surface Conductance on Intensity Factors for a Functionally Graded Piezoelectric Material Under Thermal Load

Effects of crack surface conductance on intensity factors for a functionally graded piezoelectric material under thermal load are investigated. The heat flux through the crack is assumed to be proportional to the local temperature difference. Moreover, two models for more realistic crack face electric boundary conditions are proposed. By using the Fourier transform, the thermal and electromechanical problems are reduced to a singular integral equation and a system of singular integral equations, respectively, which are solved numerically. Detailed results are presented to illustrate the influence of the thermal and electric conductance on the stress and electric displacement intensity factors.     

Axisymmetric and One-Dimensional Thermoelastic Fields of Radially Graded Bodies

In this paper, both Young's modulus and Poisson's ratio along with thermal expansion coefficient are allowed to vary across the radius in a solid ring and a curved beam. Effects of non-constant Poisson's ratio on the thermoelastic field in these graded axisymmetric and one-dimensional problems are studied. A governing differential equation in terms of stress function is obtained for general axisymmetric and one-dimensional problems. Two linearly independent solutions in terms of hypergeometric functions are then attained to calculate the stresses and the strains. Using Green's function method, a form of a solution for the stress functions in terms of integral equations for a curved beam and a solid ring are obtained. Specifically, closed form solutions for the stress functions, when Young's modulus and Poisson's ratio are expressed as power law functions across the radius, are calculated. The results show that the effect of varying Poisson's ratio upon the thermal stresses is considerable for the solid ring. In addition, a non-constant Poisson's ratio has significant influences on the thermal strain field in solid rings. The effect of varying Poisson's ratio upon the thermal stresses is negligible for the curved beam. However, non-constant Poisson's ratios have substantial effects on the thermal strain field in curved beams. Finally, the effects of varying Poisson's ratio on the thermal stresses in thick solid rings and curved beams are also investigated.     

Conditions of Single-Valuedness of Rotation and Displacements for Non-Homogeneous Materials in Plane Thermoelasticity

The conditions of single-valuedness of rotation and displacements in the multiply connected regions for non-homogeneous materials are discussed theoretically by using the stress function. As an example of a multiply connected region, we have considered the steady thermal stresses in a functionally graded hollow circular body with an eccentric outer circular boundary. The material properties are expressed by the power law of the radius of the inner circle. The inner boundary conditions are satisfied strictly, whereas the outer boundary conditions are satisfied numerically using a point-matching method. Steady thermal stresses in the body are shown for ZrO₂/Ti-6Al-4 V functionally graded materials (FGMs). The results were verified by comparing with those of a functionally graded hollow circular cylinder.     

Thermal Buckling Response of Functionally Graded Plates with Clamped Boundary Conditions

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The material properties of FGM plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations are solved analytically for a plate with simply supported boundary conditions. Resulting equations are employed to obtain the closed-form solution for the thermal force resultant for each loading case. Numerical examples covering the effects of the plate aspect ratio, side-to-thickness ratio and gradient index on thermal force resultant are discussed.     

Exact Solution for Thermal Buckling of Functionally Graded Plates Resting on Elastic Foundations with Various Boundary Conditions

In this article, we investigate the buckling analysis of plates that are made of functionally graded materials (FGMs) resting on two-parameter Pasternak's foundations under thermal loads. Three different thermal loads were considered, i.e., uniform temperature rise (UTR), linear and non-linear temperature distributions (LTD and NTD) through the thickness. The mechanical and thermal properties of functionally graded material (FGM) vary continuously along the plate thickness according to a simple power law distribution. Employing an analytical approach, the five coupled governing stability equations, which are derived based on first-order shear deformation plate theory, are converted into two uncoupled partial differential equations (PDEs). Considering the Levy-type solution, these two PDEs are reduced to two ordinary differential equations (ODEs) with variable coefficients. Then, the ODEs are solved using an exact analytical solution, which is called the power series Frobenius method. The appropriate convergence study and comparison with previously published related articles was employed to verify the accuracy of the proposed method. After such verifications, the effects of parameters such as the plate aspect ratio, side-to-thickness ratio, gradient index, and elastic foundation stiffnesses on the critical buckling temperature difference are illustrated and explained. The critical buckling temperatures of functionally graded rectangular plates with six various boundary conditions are reported for the first time and can serve as benchmark results for researchers to validate their numerical and analytical methods in the future.     

Thermal Effects on Stress Analysis in Large Amplitude Vibration of a Thick Annular Functionally Graded Plate

This paper deals with the nonlinear free and forced vibration of thick annular functionally graded material plates. The temperature field considered is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction. The formulations are based on the first-order shear deformation plate theory and von Kármán-type equation. The numerical illustrations concern with nonlinear vibration characteristics of functional graded plates with two constituent materials in thermal environments. Effects of material compositions and thermal loads on the vibration characteristics and stresses are examined.     

Numerical Analysis of Transient Stress Field of a Functionally Graded Nickel-Zirconia Profile under Thermal Loading

One-dimensional analysis of the thermomechanical response of a 3-layered nickel-functionally graded material-zirconia composite configuration under thermal loading, is the aim of this contribution. A Finite Element code is developed for the analysis. The thickness of the lower layer (nickel) is considered to be “infinite,” when compared to the thickness of the first two layers. The influence of the thickness of the functionally graded layer on the thermomechanical response of the composite material is analysed. Several distributions of the properties inside the functionally graded layer are also examined.     

Corrosion resistance of functionally graded TiN/Ti coatings for proton exchange membrane fuel cells

Bipolar Plates (BPP) are important components of proton exchange membrane fuel cell (PEMFC) stacks. In the development of innovative fuel cell designs, it is advantageous to use aluminum for these applications, however, this material lacks the necessary corrosion resistance. Since the performance of PEMFC stacks depends on BPP properties, in particular, corrosion resistance, depositing titanium nitride (TiN) thin films onto aluminum substrates may improve their efficiency and durability. The present work focuses on improving corrosion resistance and hydrophobicity of TiN/Ti by using N graded films deposited onto aluminum substrates (AA-1100) by grid-assisted magnetron sputtering (GAMS). Electrochemical impedance spectroscopy (EIS) and potentiodynamic and potentiostatic polarization are used to investigate the performance of the substrate/film system at room temperature and 70 °C, thus simulating a prototypic PEMFC electrolyte environment. Electrochemical test results showed that graded TiN films improved corrosion resistance when compared with both the homogeneous films and the AA1100 uncoated substrate. Furthermore, contact angle results reveal improved hydrophobicity for both homogeneous and graded TiN coatings when compared with the AA1100 substrate.     

Size-Dependent Thermal Buckling and Postbuckling of Functionally Graded Annular Microplates Based on the Modified Strain Gradient Theory

This article reports on the thermal instability of functionally graded (FG) annular microplates with different boundary conditions. The modified strain gradient elasticity theory is employed to capture size effects. The non-linear governing equations and boundary conditions are derived based on the first-order shear deformation theory (FSDT) and virtual displacements principle. The generalized differential quadrature technique is implemented so as to discretize. To obtain the critical buckling temperature, the set of linear discretized governing equations is solved as an eigenvalue problem. Also, the non-linear problem of thermal postbuckling is solved by the pseudo arc-length continuation method. The effects of boundary conditions, length scale parameter, and the variation of material through the thickness and geometrical properties on both critical buckling temperature and thermal postbuckling behavior are studied.     

Computation of Thermal Fracture Parameters for Inclined Cracks in Functionally Graded Materials Using J k -Integral

This article describes the formulation and implementation of the J _k -integral for the analysis of inclined cracks located in functionally graded materials (FGMs) that are subjected to thermal stresses. The generalized definition of the J _k -integral over a vanishingly small curve at the tip of an inclined crack is converted to a domain independent form that consists of area and line integrals defined over finite domains. A numerical procedure based on the finite element method is then developed, which allows the evaluation of the components of the J _k -integral, the modes I and II stress intensity factors and the T-stresses at the crack tips. The developed procedure is validated and the domain independence is demonstrated by providing comparisons to the results obtained by means of the displacement correlation technique (DCT). Detailed parametric analyses are conducted by considering an inclined crack in an FGM layer that is subjected to steady-state thermal stresses. Numerical results show the influences of the thermal conductivity and thermal expansion coefficient variation profiles and the crack inclination angle on the mixed-mode fracture parameters.     

Effects of homogeneous and inhomogeneous heating on rotating shrink fits with annular inclusion and functionally graded hub

Abstract

For given geometrical properties of a shrink fit, the interface pressure is decisive for reliable operation and should stay as large as possible during operation. Using an appropriate functionally graded material for the hub facilitates a less decreasing interface pressure with increasing angular speed and, moreover, substantial weight-reduction. However, temperature cycles may influence the interface pressure considerably, and if partial plastification occurs, even a permanent decrease may result. These issues are discussed by analytical means, and both homogeneous and inhomogeneous temperature fields in an initially elastic shrink fit with hollow steel inclusion and steel-aluminum FGM-hub are considered.     

The Influence of Graded Coatings on the Thermal Stress Intensity Factors of an Oblique Crack in a Semi-Infinite Substrate Subjected to Local Heating on the Boundary

Thermally induced singular behavior of an arbitrarily oriented crack in a homogeneous substrate overlaid with a functionally graded coating is considered, within the framework of linear plane thermoelasticity. It is assumed that the graded coating/substrate system is subjected to steady-state thermal loading applied over a finite region at the coating surface and the crack in the substrate is thermally insulated, disturbing the prescribed heat flow. Based on the method of Fourier integral transform and the coordinate transformations of basic field variables in thermoelasticity equations, formulation of the crack problem is reduced to two sets of Cauchy-type singular integral equations for temperature and thermal stresses in the coated medium. In the numerical results, the main emphasis is placed on the investigation of influences of loading, geometric, and material parameters of the coated system on the variations of mixed-mode thermal stress intensity factors. Further addressed are the probable cleavage angles for the incipient growth of the original crack and the corresponding values of effective tensile-mode stress intensity factors.     

Effects of Magnetic Fields on Morphology and Nanostructure Evolution of Incipient Soot Particles from n-heptane/2,5-dimethylfuran Inverse Diffusion Flames

Differences of the morphology and nanostructure evolution of incipient soot particles generated in n-heptane/2,5-dimethylfuran(DMF) inverse diffusion flames(IDFs) with/without magnetic fields were investigated. Utilizing a high resolution transmission electron spectroscopy, the morphology and nanostructures of soot sampled from spatial locations at different heights in IDFs were analyzed. The graphitization and the oxidation reactivity of soot were tested by an X-ray diffraction and a thermograv...