Thermal and mechanical stresses in a functionally graded thick sphere

In this paper, a general solution for the one-dimensional steady-state thermal and mechanical stresses in a hollow thick sphere made of functionally graded material is presented. The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. The material properties, except Poisson's ratio, are assumed to vary along the radius r according to a power law function. The analytical solution of the heat conduction equation and the Navier equation lead to the temperature profile, radial displacement, radial stress, and hoop stress as a function of radial direction.     

Asymmetric mechanical and thermal stresses in 2D-FGPPMs hollow cylinder

The general solution of steady-state asymmetric mechanical and thermal stresses of a hollow thick cylinder made of fluid-saturated functionally graded porous piezoelectric materials based on two-dimensional equations of thermoelasticity is considered. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and the nonhomogeneous system of partial differential Navier equations, using the complex Fourier series and the power law functions method. The material properties are assumed to depend on the radial and circumferential variables and are expressed as power law functions along the radial and circumferential direction.     

Thermoelastic analysis of a cylindrical vessel of functionally graded materials

This paper presents a novel method for analyzing steady thermal stresses in a functionally graded hollow cylinder. The thermal and thermoelastic parameters are assumed to arbitrarily vary along the radial direction of the hollow cylinder. The boundary value problem associated with a thermoelastic problem is converted to a Fredholm integral equation. By numerically solving the resulting equation, the distribution of the thermal stresses and radial displacement is obtained. The numerical results obtained are presented graphically and the influence of the gradient variation of the material properties on thermal stresses is investigated. It is found that appropriate gradient can make the distribution of thermal stresses more gentle in the whole structure.     

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.     

Creep damage evaluation of 9Cr–1Mo–V–Nb steel welded joints showing Type IV fracture

By conducting long-term creep rupture tests for 9Cr–1Mo–V–Nb (P91) steel welded joints, creep rupture properties and microstructures were examined. Creep rupture tests were conducted at three temperatures of 823, 873 and 923 K, under applied stresses of 160–230, 80–130, and 40–80 MPa, respectively. The rupture locations were found to shift from the weld metal at the higher stress condition to the fine-grained HAZ adjacent to the base metal at lower stress conditions at 873 and 923 K. The relationship between microstructural changes and crack nucleation site and propagation path was clarified. A remarkable decrease of dislocation density and growth of precipitates of M₂₃C₆ and Laves phase during creep was observed in the vicinity of the fine-grained HAZ adjacent to the base metal for the Type IV fractured welded joint specimen. The stress–strain distribution in the welded joint was investigated by the finite element method (FEM) using creep data of the simulated HAZ specimen. It was found that the observed crack initiation site and crack growth path coincided better with the distribution of the stress triaxiality factor than that of the equivalent creep strain.     

High-temperature tensile and creep properties of a ferritic stainless steel for interconnect in solid oxide fuel cell

The purpose of this study is to investigate the high-temperature mechanical properties of a ferritic stainless steel (Crofer 22 APU) for use as an interconnect material in planar solid oxide fuel cells (pSOFCs). Tensile properties of the Crofer 22 APU steel are evaluated at temperatures of 25-800 °C. Creep properties are evaluated by constant-load tests at 650-800 °C. Several creep lifetime models are applied to correlate the creep rupture time with applied stress or minimum creep rate. Experimental results show the variation of yield strength with temperature can be described by a sigmoidal curve for different deformation mechanisms. The creep stress exponent, n, has a value of 5 or 6, indicating a power-law creep mechanism involving dislocation motion. The apparent activation energy for such a power-law creep mechanism is estimated as 393 kJ mol⁻¹ through some thermally activated relations. Creep rupture time of the Crofer 22 APU steel can be described by a Monkman-Grant relation with a time exponent, m = 1.11. The relation between creep rupture time and normalized stress is well fitted by a universal simple power law for all of the given testing temperatures. Larson-Miller relationship is also applied and shows good results in correlating the creep rupture time with applied stress and temperature for the Crofer 22 APU steel. Fractographic and microstructural observations indicate most of the creep cavities are nucleated along grain boundaries and a greater amount of cavities are formed under high stresses.     

Nonsymmetric thermomechanical analysis of a functionally graded cylinder subjected to mechanical,thermal, and magnetic loads

Thermoelastic analysis of a functionally graded cylinder under nonsymmetric thermal and mechanical loadings subjected to uniform magnetic field is presented in this article. All material properties are assumed to be variable along the thickness direction based on the power law. Due to nonsymmetric thermal and mechanical loadings and boundary conditions, a two-dimensional displacement field along the radial and circumferential directions is assumed for our analysis. The complex form of Fourier series is used as the method of solution. The nonsymmetric analysis of this problem for Lorentz force leads to radial and circumferential force components. The obtained results of this analysis indicate that the different parameters of material and loading have a considerable effect on the nonsymmetric behavior of cylinder.     

Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads

This paper considers the magnetothermoelastic problem of functionally graded material (FGM) hollow structures subjected to mechanical loads. Exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow cylinders and FGM hollow spheres are determined using the infinitesimal theory of magnetothermoelasticity. The material stiffness, thermal expansion coefficient and magnetic permeability are assumed to obey the same simple power-law variation through the structures’ wall thickness. The aim of this research is to understand the effect of composition on magneto- thermoelastic stresses and to design optimum FGM hollow cylinders and hollow spheres.     

Stress analysis of pierced regions for prestressed concrete reactor vessels

The analysis of prestressed concrete vessels for nuclear reactors and, in particular, the design of the perforated end-caps increasingly calls for better analytical techniques. A method is proposed by which the distribution of stress in the perforated end-caps may be defined, assuming constant elevated temperature and radial prestress. If required, more complex operating conditions can be incorporated. A special feature of the proposed analysis is the method by which an elastic solution can be modified to take account of the time-dependent effects such as creep and shrinkage at ambient and elevated temperatures. The elastic solution is based on a two-dimensional initial strain finite element displacement analysis using triangular plate elements. After obtaining the initial elastic state of stress, a complete elastic, thermoelastic creep and shrinkage solution is achieved in a step-by-step manner based on the ‘rate of creep’ approach and using small time intervals during which the stresses are assumed constant. The strains are known quantities or may be defined at the end of the interval considered.The technique was used to analyse slab models tested and the results have been reported elsewhere. It was shown that the proposed method estimates the deformational behaviour of the models with an acceptable degree of accuracy. The distribution of stress as a result of thermal creep predicted by the method also agreed well with the cracking pattern of the models.     

THERMO VISCOELASTIC STRESSES IN CYLINDERS DUE TO COOLING DOWN FROM HIGH TEMPERATURES

The stress problem in an infinite cylinder of temperature-dependent material properties may be treated by a quasi-linear approach based on radial subdivision and time step-wise integration. The temperature field during cooling is obtained as a multi-region eigenfunction series, while the stresses are obtained from the integration of the equilibrium displacement equation by taking into consideration thermoviscoelastic deformations. The particular case of a two-region formulation and its solutions are described in full. Numerical examples of induced stress predictions in optical glass fiber are given.     

Analysis of Thermoelastic Waves in Functionally Graded Hollow Spheres Based on the Green-Lindsay Theory

In this article, the Green–Lindsay theory of thermoelasticity is employed to study the thermoelastic response of functionally graded hollow spheres. This generalized coupled thermoelasticity theory admits the second sound phenomena and depicts a finite speed for temperature wave propagation. The materials of the hollow sphere are assumed to be graded through its thickness in the radial direction while a symmetric thermal shock load is applied to its boundary. The Galerkin finite element method via the Laplace transformation is used to solve the coupled form of governing equations. A numerical inversion of the Laplace transform is employed to obtain the results in time domain. Using the obtained solution, the temperature, displacement, radial stress, and hoop stress waves propagation are studied. Also the material distribution effects on temperature, displacement and stresses are investigated. Finally, the obtained results for the Green–Lindsay theory are compared with the results of classical thermoelasticity theory.     

Long-term evolution of mechanical performance of solid oxide fuel cell stack and the underlying mechanism

Mechanical performance analysis is important for ensuring the long-term reliability of solid oxide fuel cells (SOFCs). Thermal-mechanical models are constructed to conduct time-dependent mechanical performance analysis of SOFC stack with temperature field obtained by multiphysics modeling. The volume-averaged temperature field is used as comparison. The creep strains are examined with a time step of 10 h for 10,000 h. It reveals: (1) Uniform temperature significantly decreases the stresses, strains, failure probabilities of all stack components. (2) The failure probability of sealant reduced rapidly and the sealant becomes mechanically safer for long-term operation. (3) Creep strain is dominant for anode/sealant/interconnect, but negligible for electrolyte/cathode. All components are predictably safe against strain failure for 100,000 h (4) Creep strains of stack components interact with each other. Coupled analysis of creep strains of anode/sealant/interconnect is mandatory, but the creep strains of electrolyte/cathode may be neglected for studying mechanical evolutions.     

Creep crack growth in welded components — a numerical study and comparison with the R5 procedures

In the present study, creep crack growth (CCG) in a circumferentially welded low alloyed pipe is numerically investigated for a number of different combinations of weldment constituent material properties. A creep ductility based damage model describes the accumulation of creep damage ahead of the crack tip where a constraint parameter and the creep strain rate perpendicular to the crack plane are used as characterising parameters. It is assumed that a fully circumferential creep crack, located in the heat affected zone with a depth of one quarter of the pipe thickness, is growing at a constant rate from the outer surface towards the inside. The numerical results reveal that not only the properties of the zone containing the crack, but also the deformation properties of the surrounding material influence the CCG behaviour. This influence can be noted on the characterising parameters used for the CCG rate predictions as well as on the CCG rate itself. The mismatch influence on corresponding C^* values is, however, marginal. This indicates that determination of the CCG rate in weldments, based on the C^* value only, may result in uncertain estimates.The numerically investigated cases are also assessed by use of the R5 procedures for the sake of comparison. Considering the stress re-distribution, due to the mismatch effect, the CCG rate is determined for the different weldment configurations. The comparison shows that the assumption of plane strain or plane stress conditions in the R5 analysis is essential for the agreement of the results between R5 and the two-parameter approach. Assuming plane stress conditions at the crack tip results in a relatively good agreement for the axial stress dominated cases investigated. However, for the hoop stress dominated cases, the R5 procedures predict higher CCG rates by an order of magnitude.     

Three-dimensional thermoviscoelastic analysis of a FGM cylindrical panel using state space differential quadrature method

Mechanical behavior of a viscoelastic cylindrical panel with various edge boundary conditions, made up of functionally graded material (FGM) and subjected to thermal or mechanical load is investigated. For cases of simply supported boundary conditions, analytical solution is presented through Fourier series expansion along the axial and circumferential coordinates as well as state space method along the radial coordinate. For nonsimply supported conditions, semi-analytical solution is performed using differential quadrature method instead of Fourier series solution. Governing differential equations are transformed to Laplace transform domain and using inverse Laplace transform, obtained solutions are converted to time domain. In the present work, relaxation modulus of FGM is supposed to be according to the Prony series with power law variations along the radial direction. Numerical comparison was made with the available published results to assess the validity of present technique. Effect of relaxation time constant, thickness to mid-radius ratio, edges boundary condition and outer surface temperature on stress and displacement fields are discussed. Besides, time history of stresses for different relaxation time constant and for various boundary conditions is presented.     

The effect of filler metal thickness on residual stress and creep for stainless-steel plate–fin structure

Stainless-steel plate–fin heat exchanger (PFHE) has been used as a high-temperature recuperator in microturbine for its excellent qualities in compact structure, high-temperature and pressure resistance. Plate–fin structure, as the core of PFHE, is fabricated by vacuum brazing. The main component fins and the parting sheets are joined by fusion of a brazing alloy cladded to the surface of parting sheets. Owing to the material mismatching between the filler metal and the base metal, residual stresses can arise and decrease the structure strength greatly. The recuperator serves at high temperature and the creep would happen. The thickness of the filler metal plays an important role in the joint strength. Hence this paper presented a finite element (FE) analysis of the brazed residual stresses and creep for a counterflow stainless-steel plate–fin structure. The effect of the filler metal thickness on residual stress and creep was investigated, which provides a reference for strength design.     

Dual Phase Lag Model on Magneto-Thermoelasticity Infinite Non-Homogeneous Solid Having a Spherical Cavity

In this article, the induced displacement, temperature and stress fields in an infinite non-homogeneous elastic medium with a spherical cavity are obtained in the context dual-phase-lag model. The surface of the cavity is stress free and is subjected to a thermal shock. The material is assumed to be elastic and has an inhomogeneity in the radial direction. The type of non-homogeneity is such that the elastic constants, thermal conductivity and density are proportional to the n ^th power of the radial distance. The solutions are obtained analytically employing the Laplace transforms technique. The numerical inversion of the transforms is carried out using Fourier series expansions. The stresses components, temperature and displacement are computed numerically and presented graphically. A comparison of the results is made for different theories. If the magnetic field is neglected, the results obtained are deduced as a special case from this study.     

Creep strength of high chromium steel with ferrite matrix

Long-term creep strength of material in the low-stress regime below elastic limit is difficult to predict by an extrapolation of short-term creep strength in the high-stress regime above elastic limit. Long-term creep strength of fully annealed ferrite-pearlite microstructure of low alloy Cr–Mo steel is higher than that of martensite and bainite microstructures. It is explained by lower dislocation density of fully annealed microstructure. According to the above concept, creep strength of high chromium steel with ferrite matrix is investigated. Creep rupture life of 15Cr–Mo–W–Co steel with ferrite matrix which is longer than that of ASME Grade 92 steel is obtained at 650 °C by controlling the chemical composition and heat treatment condition.     

Evaluation of creep damage in heat affected zone of thick welded joint for Mod.9Cr–1Mo steel

Mod.9Cr–1Mo steel has been used for boiler components in ultra-supercritical (USC) thermal power plants. The creep strength of welded joint of this steel decreases due to the formation of Type IV cracking in heat affected zone (HAZ) at higher temperatures. The present paper aims to clarify the damage processes and mechanisms of the welded joint for Mod.9Cr–1Mo steel. Long-term creep tests of base metal, welded joint and simulated fine- grained HAZ were conducted at 550, 600 and 650 °C. Creep tests using thick plate welded joint specimen were interrupted at several time steps, and evolutions and distributions of creep damages were measured quantitatively using laser microscope. It is found that creep voids initiate at early stage of creep life (0.2 of life), the number of creep voids increases until 0.7 of life, and then voids coalesced into the macro crack at the later stage of life (0.8 of life). Creep damages concentrate mostly at a quarter depths of the plate thickness within the fine-grained HAZ of the present welded joint. The experimental creep damage distributions were compared with the computed results by using the FEM analysis. Both creep strain concentration and high stress triaxiality in fine-grained HAZ of welded joint are considered to accelerate the creep void formation and growth.     

Functionally graded hollow spheres under non-axisymmetric thermo-mechanical loads

An analytical method is developed to obtain the solution for the two-dimensional (r,θ)$(r,\theta )$ steady state thermal and mechanical stresses in a hollow thick sphere made of functionally graded material. The material properties are assumed to vary through the thickness according to the power law functions. The temperature profile is obtained solving the functionally graded energy equation. The Navier equations are solved analytically using the Legendre polynomials and the system of Euler differential equations. Temperature, displacement components and stresses distributions are obtained and plotted for different power law indices. The results are validated with the known data in literature.