Steady-state Thermal Stresses Research Articles

Finite element method with 3D polyhedron-octree for the analysis of heat conduction and thermal stresses in composite materials

Applying the hybrid flux finite element method(HF-FEM) and hybrid thermal stress finite element method (HTS-FEM) is not prevalent in analyzing heat conduction and thermal stresses in particle-reinforced composite materials. Most of the research on this technique is confined to two-dimensional problems. This paper proposes the HF-FEM and HTS-FEM, based on 3D polyhedron-octree, to calculate the steady-state heat conduction and thermal stress of particle-reinforced composites. In addition, this paper presents a method for partitioning spherical particle-reinforced materials into polyhedron-octree elements, each of which contains only one type of material. Each element is divided into multiple Delaunay tetrahedrons, and hammer integration is used to perform the integrals. Additionally, this paper presents a technique to construct the heat flux function for polyhedral elements, and the effectiveness of the above methods is demonstrated by comparing it to several numerical examples of traditional finite element methods.

Delamination analysis of a ductile phase-toughened environmental barrier coating for oxygen-rich turbopumps

The turbine in an oxygen-rich turbopump subjects materials to high-pressure gaseous oxygen environments, where the risk of metal fires presents a potentially catastrophic failure mode. A candidate approach for mitigating particle impact ignition, one key metal ignition mechanism, is to coat metallic components with an inert ceramic environmental barrier coating; however, such coatings are susceptible to delamination during the rapid thermal transients upon engine startup and shutdown. Here, we investigate the delamination risk of a ductile phase-toughened composite environmental barrier coating under a nominal flight cycle of a reusable boost-stage rocket engine. The coating of present interest comprises a borate-based glass-ceramic matrix reinforced with Ni and is applied as an aqueous slurry that bonds to the substrate upon firing. We first varied the Ni content in the coating and characterized its structure, finding that the Ni reinforcement sinters to the substrate and percolates through the brittle glass-ceramic when the Ni volume fraction exceeds 0.3, in excellent agreement with percolation theory. We also experimentally assessed the thermomechanical properties of the coating and used these measurements to compute its energy release rate under the thermal transients expected in service. Our analysis shows that thermal stresses and energy release rates are greatest during engine startup and shutdown, with energy release rates on the order of 100 J/m2 for a 100-μm thick coating on an IN718 substrate. Our analysis then highlights strategies for reducing the energy release rate, which include tailoring the thermal expansion coefficient to balance transient vs. steady-state thermal stresses and using active heating to promote film boiling upon exposure to cryogenic liquid oxygen, thus mitigating the severity of cold shocks. Most importantly with respect to materials design, we predict that interpenetrating composite coatings with Ni concentrations greater than 0.3 exhibit enhanced toughness via crack bridging, allowing them to resist delamination under even the most aggressive operating conditions. These results highlight the potential of high-toughness metal/ceramic interpenetrating composite coatings in thermal and environmental protection applications where extreme thermal transients delaminate conventional monolithic ceramic coatings.

Effect of Change in Startup Cycle Time on Transient Thermal Stresses in Steam Turbine Rotor

During the turbine start stop period, occuring at brief intervals , the temperature of the steam turbine rotor varies. Because of the significant temperature gradients, this shift in temperature causes transitory thermal stresses in the rotor. Changes in material parameters such as thermal expansion coefficient ,modulus of elasticity, thermal conductivity, specific heat, Poisson's ratio, and others cause transient stresses. Thermal and mechanical stresses are applied to the turbine rotor. Before designing the rotor, it is necessary to estimate transient thermal stresses. The finite element study of a 210 MW steam turbine rotor for transient thermal loading is investigated in this paper. 30Cr1Mo1V was used to make the rotor. CAD software (PRO-E) was used to create the high-pressure turbine model. Since the steam turbine shaft (rotor) was symmetric about the axis along which it rotates, the model was solved using a 1 Degree slice model. Ansys 11 was used to investigate the FE model for transient thermal stresses for reduced cold start up cycle. The analysis was carried out for start up cycles of 560, 440 and 320 minutes respectively. The comparative results were studied and it was observed thatalthough the transient thermal stresses in the reduced cold start up cycle of 440 minutes are higher as compared to the transient thermo-mechanical stress value for actual cold start up cycle (560 minutes) but are within safe limits of yield and tensile strength. The thermal stress values for the other reduced cold start up cycle (320 minutes) re quite higher than the allowable yield and tensile strength of the material and hence cannot be considered as feasible start up cycle. Thermal stresses in the transient state were found to be significantly higher than steady state thermal stresses.

Thermoelastic Analysis of Pressurized Hollow Spherical Vessels with Arbitrary Radial Non-Homogeneity

In this study, a general analysis of one dimensional steady-state thermal stresses of a functionally graded hollow spherical vessel with spherical isotropy and spherically transversely isotropy is presented with material properties of arbitrary radial non-homogeneity. The material properties may arbitrarily vary as continuous or piecewise functions. The boundary value problem associated with a thermo-elastic problem is converted to an integral equation. Radial and tangential thermal stress components distribution can be determined numerically by solving the resulting equation. The influence of the gradient variation of the material properties on the thermal stresses is investigated and the numerical results are presented graphically.

Development of the scaled boundary finite element method for crack propagation modeling of elastic solids subjected to coupled thermo-mechanical loads

This study presents the development of the scaled boundary finite element method to model discrete crack propagation induced by thermal loads. The SBFEM excels in modeling stress singularities at sharp crack tips with high accuracy. Polygon meshes are used so that a robust local re-meshing algorithm can be utilized to propagate the crack. The scaled boundary finite element formulation for steady-state thermal stress analysis is presented. Following a scaled boundary finite element analysis of a given thermal problem, the effect of initial strains due to temperature is taken into account semi-analytically in a subsequent stress analysis. Several numerical examples are presented to validate the technique and illustrate its salient features.

Thermal behaviour of annular hyperbolic fin with temperature dependent thermal conductivity by differential transformation method and Pade approximant

The current paper explores the steady-state heat transfer and thermal stress analysis of a hyperbolic annular fin with temperature dependent thermal conductivity. The framed equations are articulated in terms of non-linear ordinary differential equations. The domination of non-dimensional parameters on the thermal gradient of the fin has been analysed graphically by using Runge–Kutta Fehlberg fourth-fifth order (RKF-45) process and DTM-Pade approximant. Here, differential transformation method (DTM)-Pade approximant has been implemented to find the analytical solution for the non-linear ordinary differential equations. The RKF-45 method is used to obtain numerical outcomes for different non-dimensional parameters. Further, the obtained numerical results are compared with the results achieved from DTM-Pade approximant solution. This relation demonstrates that numerical outcome obtained by DTM-Pade approximant are nearer to that of numerical results. Outcome results exposes that, the escalating values of thermal conductivity parameter upsurges the thermal distribution. The growing values of the radius ratio elevate the thermal distribution in the fin. Further, the radial stress and tangential stress distribution varies for larger values of dimensionless parameters.

Exact solution for the thermo-elastic deformation and stress states of FG rotating spherical body

Abstract In this paper, a generalized solution for 1-D steady-state mechanical and thermal deformation and stresses in rotating hollow functionally graded spherical body is presented. Spherical shells are treated under mechanical and thermal loads in the form of rotational body force with heat generation. Temperature distribution is assumed to vary along the radial direction due to variable heat generation. General uniform mechanical boundary condition at inner and outer surfaces along with prescribed temperatures at both the ends are assumed as boundary conditions. In the present study, material properties are taken as power function of radius with grading parameter ranging between −2 to 3. Governing differential equation with variable coefficient is developed and solved to find deformation and stresses. The obtained results are verified with benchmark results and are found to be in good agreement. Results show that deformation and stresses decrease with an increase in the value of grading parameter and are less as compared to the homogeneous body.

A Magneto-Thermo-Static Study of a Magneto-Rheological Fluid Damper: A Finite Element Analysis

Nowadays, the automotive industry is oriented toward the production of new generation devices, such as magnetorheological fluid (MR fluid) dampers, which have a proven simplicity of design combined with reduced maintenance. Being devices powered by steady-state electric current, MR fluid dampers develop steady-state magnetic induction fields with associated steady-state thermal stresses and a consequent constant yield stress. In this work, an asymmetric MR damper has been studied using the finite-element method (FEM). Specifically, since steady-state electric current circulates in the coil of the device, a magneto-static analysis of the device and particularly of the strip of MR fluid contained therein is performed using the FEM. Furthermore, as the device is subject to heating during operation, a thermo-static analysis was also carried out using finite elements when different external temperatures were considered. Both analyses, performed by ANSYS ToolbBox, highlighted the areas of the device most subject to magnetic stress providing useful indications on the influence of temperature both on the magnetization of the magnetic particles and on the MR fluid as a whole.

Fracture behavior of tungsten-based composites exposed to steady-state/transient hydrogen plasma

The fracture behavior of plasma-facing components (PFCs) under extreme plasma-material interaction conditions is of great concern to ITER and future fusion reactors. This was explored in the current study by exposing pure tungsten (W), W-1%TiC and W-2%Y2O3 composites to a combined steady-state/transient hydrogen plasma up to a base surface temperature of ~2220 K, and up to 5000 transient pulses for 1000 s using the linear plasma generator Magnum-PSI. The applied heat loads were characterized by combining sheath physics, thermographic information and finite element analyses, with which the thermal stress was evaluated. Combining microstructural investigation and thermo-mechanical numerical analyses, a physical picture of fracture is developed. The transient heat loads drive surface crack initiation, whose depth can be estimated by a simple analytical model for pure tungsten, while the cooling period following the steady-state heat load induces tensile stresses, opening existing surface cracks deeper. The fracture process is mediated by the microstructure whereby the ceramic particles stabilize the microstructure but promote surface crack initiation due to suppressed plasticity at the grain boundaries and the particle-matrix interfaces. The surface cracks relieve the subsequent cycles of transient thermal stress but intensify the steady-state thermal stress, therefore, promoting deep crack propagation. These results help to understand failure mechanisms in PFCs under extreme operation conditions which are valuable for developing advanced PFCs.

Temperature and thermal stress distributions in a hollow circular cylinder composed of anisotropic and isotropic materials

In this article, an analytical solution is presented for the steady-state axisymmetric thermal stress distributions in a composite hollow cylinder. The cylinder is composed of two isotropic and anisotropic materials which is subjected to the thermal boundary conditions of convective as well as radiative heating and cooling on the inner and outer surfaces, respectively. The solution of the temperature is obtained by means of Bessel functions and the thermal stresses are developed using Potential functions of displacement. Numerical results are derived for a cylinder which is similar to a gas turbine combustor and showed that the maximum temperature and thermal stresses (radial, hoop, axial) occurred in the middle point of cylinder and the values of thermal stresses in anisotropic cylinder are more than the isotropic cylinder. It is worthy to note that the values of the thermal conditions which estimated in this research, not to be presented in any other papers but these values are very accurate in calculation.

Three-dimensional crack analyses under thermal stress field by XFEM using only the Heaviside step function

A three-dimensional crack analysis method based on XFEM using only the Heaviside step function was applied to heat transfer and subsequent thermal stress analyses of cracked structures. The proposed method employs tip elements to discretize the weak form governing equations using the approximation function with discontinuity. Two kinds of XFEM analysis software, which perform steady-state or transient heat transfer analysis and thermal stress analysis to evaluate J-integrals and stress intensity factors, were developed. As the XFEM model for the stress analysis is consistent with the heat transfer analysis model, nodal temperature data can be directly imported for stress analysis as thermal load data. The developed codes were verified by solving some benchmark crack problems, including both mechanical and thermal loading cases, and comparing the results with those of conventional methods and a reference. It was shown that the developed codes provide appropriate results for practical thermal stress analysis of cracked structures considering temperature-dependent material properties.

Novel Transient Liquid Phase Bonding for High-Temperature Automotive Power Electronics Systems

Abstract This paper demonstrates the concept and fabrication process for a novel (copper, nickel)–tin, (Cu, Ni)–Sn, transient liquid phase (TLP) high-temperature bond that exploits the addition of a pure aluminum (Al) core layer for die attachment in a power electronics power card structure. The bond quality and composition of the bond layer are characterized using confocal scanning acoustic microscopy (CSAM), scanning electron microscopy (SEM), and energy-dispersive X-ray (EDX). The experimental results indicate that the material composition and established fabrication process enable a crack-free bond that exhibits a void fraction of 2% or less. Compared to a traditional foil-based single-layer TLP bonding system, the proposed foil-based TLP/metal laminated structure displays ∼60% reduction in thermally induced mechanical stress built-in after fabrication, as verified through steady-state thermal stress simulations.

Control of steady-state thermal displacements and stresses in a plane-strained half-space

Inverse thermoelasticity problems, formulated as a result of reduction of two-dimensional steady-state control problems for a component of the displacement vector or the stress tensor (or their combinations) in a given cross-section of a plane-strained half-space, are analyzed. The intensity of the inner heat sources was selected to be the control function. Solutions to the mentioned inverse problems are obtained in the space of continuous functions. The finiteness conditions for the found integral intensity of the inner heat sources are derived and analyzed. The key features of the obtained solution are analyzed numerically for certain types of thermal loadings and characterizing parameters.

Evaluation of Separating Process for Different Materials by Thermal Stress Cleaving Technique

This paper aims to evaluate the separating process of brittle materials by thermal stress cleaving technique. This process is suitable for separating thin brittle materials such as sapphire and silicon wafer, which are sensitive to force. Both materials were used largely in microelectronics, solar cells and micro-mechanical industries that require precise machining. Finite element method was used to evaluate a steady state thermal stress by considering the temperature transient during laser irradiation process. The heat source was assigned according to the laser energy absorption characteristics of the materials. Stress intensity factor was analyzed to determine the starts of separation process. The results show that CO2 laser energy was absorbed on the surface of the sapphire material as compared proportionated absorption of Nd:YAG laser energy on silicon material. Due to thermal stress generated by the laser beam, material separation was start. Fracture begins at the bottom surface of sapphire wafer compared to fracture initiation at the prepared groove for silicon wafer. The material separation can be controlled when it begins at the groove. Hence, better surface finished can be achieved.

Steady state Thermal and Mechanical stresses in two-Dimensional functionally graded piezoelectric materials (2D-FGPMs) hollow cylinder

In this paper, the general analysis of two-dimensional steady-state thermal and mechanical stresses for a hollow thick cylinder made of functionally graded piezoelectric materials (2D-FGPMs) is developed.The general form of thermal ,mechanical and electrical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and the non-homogenous 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.

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

ABSTRACTThe 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.

Analytical investigation of thermomechanical stresses in graded interphase between the fiber and the matrix

ABSTRACTIn this article, the thermomechanical stresses in the graded interphase between the fiber and the matrix in fiber-reinforced composites are investigated. First, the general theoretical analysis of two-dimensional steady-state mechanical and thermal stresses in a graded cylinder along the radial direction with the Power Law and Exponential Law distribution of the material properties is developed. Then the theoretical solution is applied to investigate the mechanical stresses and the thermal stresses of the fiber-matrix interphase, and the effects of material graded constant on the mechanical stresses and thermal stresses are discussed. Finally, the stress transfer mechanisms in the graded interphase are investigated which indicates that the total stresses in the fiber-matrix interphase increased with the increasing of the interphase thickness if the material graded constant varied with the radius in Power Law, but decreased in Exponential Law.

Analytical solution for transient temperature and thermal stresses within convective multilayer disks with time-dependent internal heat generation, Part I: Methodology

ABSTRACTThis work deals with the exact solution for asymmetric transient problem of heat conduction and accordingly thermal stresses within multilayer hollow or solid disks which lose heat by convection to the surrounding ambient. The combination of the separation of variables method (SVM) and Duhamel's theorem is applied to the heat conduction problem which provides a versatile technique. The temperature distribution is obtained by the SVM which concerns the heat conduction problem with time-independent internal heat generation. Applying Duhamel's theorem on the previous solution, temperature distribution with time-dependent internal heat generation can be achieved. Accordingly, assuming plane stress condition, radial and tangential stresses are obtained which are incorporated into the equivalent tensile stress formulation to calculate von Mises stress. The comprehensive methodology described here can be useful addition for many new emerging fields in which both transient and steady-state temperature distributions and thermal stresses for composite disks are important.

A unified method for stresses in FGM sphere with exponentially-varying properties

Using the Complementary Functions Method (CFM), a general solution for the one-dimensional steady-state thermal and mechanical stresses in a hollow thick sphere made of functionally graded material (FGM) is presented. The mechanical properties are assumed to obey the exponential variations in the radial direction, and the Poisson's ratio is assumed to be constant, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. In the present paper, a semi-analytical iterative technique, one of the most efficient unified method, is employed to solve the heat conduction equation and the Navier equation. For different values of inhomogeneity constant, distributions of radial displacement, radial stress, circumferential stress, and effective stress, as a function of radial direction, are obtained. Various material models from the literature are used and corresponding temperature distributions and stress distributions are computed. Verification of the proposed method is done using benchmark solutions available in the literature for some special cases and virtually exact results are obtained.

An Investigation of Transient Thermal Analysis of 1st Stage Gas Turbine Blade Manufactured by Directional Solidification and Mechanically Alloyed Nickel-Based Superalloys

The turbine rotor blades of a gas turbine engine are designed for operation at elevated temperatures, particularly first stage gas turbine blades. During operation, the turbine blades are subjected to high temperatures and large centrifugal forces. In addition to these, the temperature variations occur at start-up and shutdown cycles of the engine. Due to sudden changes in temperature, transient thermal effects are sighted and time-dependent temperature gradients appear. The estimates of the thermal variations sighted on the turbine blade at various operational speeds of the gas turbine rotor are important in determining the fatigue life. The thermal condition during the startup sequence initiated is considered as a major factor in determining the rotor maintenance interval and individual rotor component life. This work has primarily focused on transient thermal stresses arising in the rotor blade by using Finite Element Analysis. Nowadays, the thermal stresses of the gas turbine parts are determined by user defined software’s that is based on numerical methods which are being used significantly. A typical turbine rotor blade has been modeled by using CATIA V5R21. Turbine blades are made of Nickel-based superalloys have been selected for transient thermal analysis by using ANSYS 15.0. Comparative analysis has also been carried out to determine the suitability and strength of turbine blade material under the same operating conditions. Two blade materials such as IN 792 DS and IN 754 MA have been selected for comparative analysis and these blades were manufactured by Directional solidification and mechanical alloying methods respectively. The physical and mechanical properties are updated to the model and appropriate boundary conditions are applied. Thermal stresses are evaluated for both materials and the results have been compared with IN 738 LC. Static analysis has also been carryout out to examine the structural performance of the alloys. It has been observed that maximum stress and strain are sighted near the root of the turbine blade. The temperature gradients sighted on the turbine blade during acceleration and decelerations are below the melting temperature of the blade materials. It has been noticed that the transient thermal stresses are higher than the steady state thermal stresses. It has been observed that IN 792 DS has better physical and thermo mechanical properties that can withstand higher turbine inlet temperatures and could be suitable material for the manufacturing of turbine blade at Marine and Related Environments.