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.     

A THERMOELASTOPLASTIC SOLUTION FOR A CIRCULAR SOLID CYLINDER SUBJECTED TO HEATING AND COOLING

Abstract

This paper presents a theoretical study of the stresses in an infinite circular solid cylinder subjected to rapid surface heating and cooling. A quasistatic, uncoupled, thermoelastoplastic analysis based on the incremental theory of plasticity is formulated, and a numerical procedure is developed for a method of successive elastic solutions. The material of the cylinder is assumed to have temperature-dependent properties and to be characterized by the Romberg-Osgood stress-strain relation. The transient and residual stress distributions are discussed in detail, along with variations of the equivalent stress and plastic strain with time.     

COMBINED MACROSCOPIC AND MICROSCOPIC ANALYSIS OF THERMOELASTOPLASTIC STRESSES OF A FUNCTIONALLY GRADED MATERIAL PLATE

This article discusses the elastoplastic thermal stresses induced in a ceramic-metal functionally graded material plate (FGP) subjected to a thermal load taking the fabrication process into consideration. The FGP is divided into three regions. The first region near the cooling, metal, surface of the FGP is produced by ceramic particle-reinforced metal; while the second region near the heat-resistant, ceramic, surface is the opposite; and the third middle region is perfectly mixed by the metal and the ceramic. The first and second regions are governed by the particle-reinforced thermoelastoplastic constitutive equation, while the third region is expressed by the macroscopic analysis. Three cases of the temperature condition are studied: cooling from the fabricated temperature to room temperature, heating from the room temperature, and heating after cooling from the fabricated temperature. The temperature-dependent material properties are considered, and the particle volume fraction is assumed to vary according to a power function along the thickness direction of the FGP. The effect of the distribution parameter of the composition on the macroscopic stress, the stress in the matrix, and the stress in the particle in the FGP are discussed and illustrated in figures. Also, the effect of the fabricated temperature on the maximum tensile matrix stress is discussed.     

THERMOELASTOPLASTIC STRESS ANALYSIS DURING PHASE TRANSFORMATIONS

Numerical results obtained from the thermoelastoplastic analysis of low carbon steel under heating and cooling are presented using the procedure of Mendelson's method of successive elastic solutions. A₁ and A₃ transformations on heating, and martensitic or pearlitic transformation on cooling, are reasonably taken into account as the typical models of phase transformations. Mechanical and thermal properties of steel are considered to be temperature dependent.

From stresses and strains calculated with consideration of phase transformations, it is found that phase transformations during rapid cooling have the greater effect on stresses and strains than those during slow cooling.     

3D modelling of a multi pass dissimilar tube welding and post weld heat treatment of nickel based alloy and chromium steel

A dissimilar tube welding is performed between the nickel based Alloy617 and creep resistant steel VM12 using the former as the weld material. SYSWELD welding software is used to model the thermal and mechanical analysis. A readily available thermal history is used to calibrate the heat source input for the thermal analysis to generate the adequate thermal cycle by fitting the welding velocity, heat intensity factor of the GOLDAK heat source and the length of molten zone. The transient temperature field is then incorporated as the input for the mechanical analysis to obtain the residual stresses in which the phase transformation of the materials during welding is taken into account. Subsequently, the weld materials are characterized by using the Norton’s creep law to determine the Norton parameters based on relaxation experiments. The residual stresses generated after the multi pass welding by SYSWELD is transferred into ABAQUS as the initial condition for the post weld heat treatment (PWHT) simulation. The simulations show that the residual stresses reduce in magnitude but still present even after PWHT.     

THERMOELASTO-PLASTIC STRESSES AND THERMAL DISTORTIONS IN A BRAKE DRUM

Most analyses of thermal stresses generated in a brake drum are studies within either an elastic or a plastic region with constant yield strength. As a matter of fact, however, a severe brake application will create a thermal environment on the friction surface with an excessively high surface temperature. At a high temperature, the degradation of yield strength of a drum material may become significant and an important factor to be taken into account in the analysis. This article deals with the thermoelasto-plastic stresses and the thermal distortions produced in a brake drum during a severe braking condition, taking account of the temperature dependence of the yield strength of a drum material. It is found that high compressive thermoelastoplastic stresses are created during a brake application but eventually residual tensile stresses are developed in the vicinity of the rubbing surface in the course of cooling. These residual tensile stresses are strongly presumed to be one of the significant factors causing the heat crack in a brake drum. In addition, the thermal distortions of the drum suggest a loss of the contact area between the drum fictional surface and the brake shoe linings during braking.     

锅炉过热器蒸汽侧氧化膜瞬态应力的有限元分析

采用有限元方法,计算并分析了过热器管基体及氧化膜内的温度和应力情况,通过稳态分析得到了稳定工况下的温度和应力分布;在此基础上又进行了瞬态分析,分别考虑了蒸汽侧温度和烟气侧温度两种情况下的扰动,得到了扰动后温度和应力的响应曲线.结果发现:蒸汽侧扰动时,氧化膜内温度和应力的变化都很大,更易于造成氧化膜的剥落.     

ANALYSIS OF TRANSIENT THERMAL BENDING MOMENTS AND STRESSES OF THE WORKPIECE DURING SURFACE GRINDING

Geometrical inaccuracy is often induced by heat generated during grinding. Furthermore, the transient thermal process is the main cause for the residual stresses on theground surface. The objective of this article is to investigate the three-dimensional transient temperature distribution of the workpiece using the finite difference method,and based on the acquired temperature and beam theory, the thermal moment and thermoelastic stress as calculated using Simpson's multiple numerical integral method. The energypartition is the key factor in accurately predicting the temperature distribution, on which the solution of the thermal moment and stress rely. As the heat conductivity of the workpiece decreases, the stress and moment increase near the wheel-workpiece contact zone and the peaks move closer to the contact position. A smaller thickness results in higher thermal stress and lower thermal moment. Enhancing cooling in grinding effectively reduces temperature and the induced stress.     

NUMERICAL SIMULATION OF THE THERMAL CONTROL OF HEAT EXCHANGERS

The temperature control of outlet air by changing the water flow rate in a single-pass waterto-air cross-flow heat exchanger is investigated. The conservation laws are applied to finite control volumes and an implicit formulation is used for transient numerical solutions. Conjugate forced convection heat transfer from the tube is solved to calculate the temperatures of the air and water coming out of the heat exchanger. In the simulations the outlet air temperature is controlled by changing the water flow rate entering the heat exchanger using a proportional-integral (PI) controller. The range of controllability of the heat exchanger was studied first. Then disturbances in the form of step changes in the inlet air temperature, the air flow rate, and the set point temperature were separately introduced. The effects of the limiting-condition constraints and different control parameters on controlling the outlet air temperature are presented. The results show that the control behavior can be simulated numerically and that this control methodology is effective within limits.     

固体吸附式制冷系统中吸附床内传热过程的数值模拟

对一简化吸附床模型中传热过程进行理论分析,对吸附床内的热传导方程和换热管内流体的能量控制方程进行离散并利用控制容积法进行模拟数值计算,在计算模型中加入随时间变化的边界条件,得到吸附床内吸附剂和换热管内流体的两种互相耦合的温度分布,为吸附床的实际优化设计提供理论依据。     

TRANSIENT ANALYSIS OF THERMOELASTIC CONTACT BEHAVIORS IN COMPOSITE MULTIDISK BRAKES

The transient analyses of the thermoelastic contact problem are performed for carbon–carbon composite multidisk brakes subject to mechanical and frictionally excited thermal loads. The finite element method, based on the coupled theory in which displacement and temperature fields are mutually affected, is applied for the numerical simulations. In the present study, to improve the accuracy of computations and stabilize the algorithm, the implicit transient scheme is used for the thermoelastic analysis. The law of action and reaction, Signorini's law of contact, Coulomb's law of friction, and Archard's law of wear are applied to be valid locally at each point for friction surfaces. The computation results are obtained for the antiskid brake conditions and presented for the transient evolution of contact pressure, temperature on each friction surface between the bodies, and thermoelastic deformations. It is also found that the high thermal stresses due to considerable temperature difference during the landing process occur in multidisk brakes.     

MEASUREMENT OF TRANSIENT THERMAL STRESSES USING THE 5-ELEMENT STRAIN GAGE

The transient thermal stresses on the 5-element strain gage are measured both for the disk and the circular plate with holes, and under a partial heating by molten metal on one face. The results are in good agreement with the theoretical solutions. The effects of the disk thickness and the interference with holes on the thermal stresses have been investigated.     

Thermal stresses in radiant tubes due to axial,circumferential and radial temperature distributions

This paper presents an analysis of the thermal stresses in radiant tubes. The analytical analysis is verified using a finite element model. It was found that axial temperature gradients are not a source of thermal stresses as long as the temperature distribution is linear. Spikes in the axial temperature gradient are a source of high thermal stresses. Symmetric circumferential gradients generate thermal stresses, which are low as compared to the stress rupture value of radiant tubes. Radial temperature gradients create bi-axial stresses and can be a major source of thermal stress in radiant tubes. A local hot spot generates stresses, which can lead to failure of the tube.     

Thermal stress analysis of eccentric tube receiver using concentrated solar radiation

In the parabolic trough concentrator with tube receiver system, the heat transfer fluid flowing through the tube receiver can induce high thermal stress and deflection. In this study, the eccentric tube receiver is introduced with the aim to reduce the thermal stresses of tube receiver. The ray-thermal-structural sequential coupled numerical analyses are adopted to obtain the concentrated heat flux distributions, temperature distributions and thermal stress fields of both the eccentric and concentric tube receivers. During the sequential coupled numerical analyses, the concentrated heat flux distribution on the bottom half periphery of tube receiver is obtained by Monte-Carlo ray tracing method, and the fitting function method is introduced for the calculated heat flux distribution transformation from the Monte-Carlo ray tracing model to the CFD analysis model. The temperature distributions and thermal stress fields are obtained by the CFD and FEA analyses, respectively. The effects of eccentricity and oriented angle variation on the thermal stresses of eccentric tube receiver are also investigated. It is recommended to adopt the eccentric tube receiver with optimum eccentricity and 90° oriented angle as tube receiver for the parabolic trough concentrator system to reduce the thermal stresses.     

Transient Thermal Stresses in an Orthotropic Cylinder under the Hyperbolic Heat Conduction Model

An important consideration in design involving high temperature variation is the determination of the thermal stresses developed. The numerical solution for thermoelastic transient response of orthotropic cylinder subjected to a constant temperature at the surface is presented. The thermoelastic equations with one relaxation time developed by Lord and Shulman with uncoupled thermoelasticity assumption are used in the present work. The hyperbolic heat conduction model is used for the prediction of the temperature history. Thermally induced displacement and stresses are determined. A numerical method based on implicit finite difference scheme is used to calculate the temperature, displacement, and stress distributions within the cylinder. Numerical examples for orthotropic, transverse isotropic, and isotropic cylinders were carried out for the stresses. Furthermore, the results of the numerical solution and the exact solution at the steady state condition are compared.     

Transient Thermo-Mechanical Analysis of Functionally Graded Hollow Circular Cylinders

Thermo-mechanical analysis of functionally graded hollow circular cylinders subjected to axisymmetric mechanical and transient thermal loads is carried out in this study. Thermo-mechanical properties of functionally graded materials (FGM) are assumed to be temperature independent and vary continuously in the radial direction of the cylinder. Employing the Laplace transform, the Galerkin method and series method for ordinary differential equations, solutions for the time-dependent temperature and transient thermo-mechanical stresses are obtained. As an example, a molybdenum/mullite FGM with material properties obeying the exponential law is considered. Effects of heat transfer coefficients and gradient parameters of FGM on the time-dependent temperature and transient thermal stresses are discussed in detail.     

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.     

NUMERICAL SOLUTION OF FORCED CONVECTION HEAT TRANSFER IN He II

A theoretical investigation of one-dimensional forced convection heat transfer in He II is conducted. The problem of interest involves a flow tube containing He II, which is heated at its midpoint along its length. Two modes of heating are analyzed: step function and square pulse. The one-dimensional He II energy equation is used to find the temperature distribution along the tube for both steady-state and transient situations. For the steady-state case, a numerical integration routine is used to obtain a solution, whereas for the solution of the transient case, a finite-difference scheme is developed. The numerical temperature profiles are then shown to compare well with the results of an experiment.     

Effect of the history term on the transient energy equation for a sphere

This paper addresses the importance of the history term on the transient energy equation of particles. The physical origin of this term is the diffusion of the transient temperature gradients around the sphere. The history term accounts for the effect of all the previous temperature changes of the sphere to the current temperature change. The derivation and analysis of the transient energy equation of rigid particles are presented. In order to solve numerically the transient energy equation, three different fluid temperature fields (step, ramp and sinusoidal) are applied and the temperature of the sphere is computed with and without the history term. The evaluation of the maximum deviation between these two computations allows us to determine for each case the effect of the history term and, especially, when the history term may be neglected. The final results of these computations allow several conclusions and recommendations on the appearance, importance and significance of the history term.     

FRACTURE OF THICK-WALLED CYLINDERS SUBJECTED TO TRANSIENT THERMAL STRESSES

In this paper, the fracture problem of a thick cylinder subjected to transient thermal stresses is considered. The problem has practical significance in the conventional and nuclear power industries where the structural integrity of components may be damaged due to sudden temperature changes. Neglecting the inertia effects, the thermal fracture problem is uncoupled. First the thermal stresses in a thick cylinder due to a sudden change in temperature are computed separately as a function of time. Then, these stresses are used as external loads in analyzing the fracture of a thick cylinder. The assumed crack, may be an inner edge crack, outer edge crack or an embedded crack. Extensive results are obtained by varying the parameters of the problems. The main parameters affecting fracture are identified and the results are discussed in some detail.