Thermoelastic Stress Distributions Research Articles

Comprehensive stress-driven multi-material problem for heat-sinking heterogeneous structures

In the realm of designing thermoelastic structures, particularly within aerospace and broader engineering fields, complex challenges arise from the diverse behaviors of heterogeneous materials and the intricate requirements of stress-based systems in coupled thermomechanical considerations. This study addresses these challenges by proposing a comprehensive methodology with two main contributions: (i) the development of an effective unified solution for stress-driven designs that tackle heat-sinking problems by accommodating a wide range of materials, from homogeneous to heterogeneous and (ii) the introduction of a robust stress-based optimization approach for multi-material problems within coupled thermomechanical systems. The methodology employs the well-established P-norm approach to consolidate heterogeneous stresses into a unified global metric. Additionally, it integrates effective material interpolation with the generalized Solid Isotropic Material with Penalization (SIMP) framework, resulting in comprehensive multi-material models that include the constitutive matrix, thermal conductivity, thermal stress coefficient, and thermoelastic stress distributions. To further enhance adaptability and flexibility, the methodology incorporates a polygonal discretization technique. Detailed sensitivity analyses, using the adjoint variable technique, are conducted to improve computational efficiency in gradient-based mathematical programming algorithms. The efficiency, robustness, and practicality of the proposed methodology are validated through numerical examples, demonstrating its effectiveness and reliability in real-world applications.

The mathematical model of thermoelastic stresses in the Carpathian region

The two-dimensional thermoelastic model of the Carpathian region is constructed using the finite element method. The physical-mathematical model is as close as possible to the real environment. A~high-precision detailed distribution of temperatures, heat flow, thermoelastic stresses and displacements is obtained. It is shown that inhomogeneous heating of rocks and structural heterogeneities lead to significant changes in stress and displacement fields in the Carpathian region.

Fractional Order Transient Thermoelastic Stress Analysis of a Thin Circular Sector Disk

Analysis of transient thermoelastic stress distribution of a thin circular sector disk with a time-fractional derivative of order α is proposed. The Neumann types of boundary conditions are used and the integral transform method and Caputo fractional derivative are used to obtain the analytical solutions of the temperature, displacement, and stresses. Numerical values of temperature, displacement, and stresses are computed for an Aluminum (pure) material and presented graphically with help of Mathcad software.

Study on the Effect of Load Frequency on Temperature and Stress States Measured by Infrared Thermoelastic Method

We investigated the effect of load frequency using thermoelastic finite element (FE) analysis on a gusset welded joint specimen commonly used in welded structures. To simulate the thermoelastic effect, we developed a stress field-temperature field thermoelastic FE analysis technique that calculates the heat transfer of heat generation and heat absorption according to compression and tensile stress. The calculated stress distribution showed a good agreement with thermoelastic stress distribution measured using an infrared ray method. The result implies that the developed technique is effective in reproducing the thermoelastic effect. In the case of a load frequency of 1 Hz, a small gradient of temperature distribution appeared. Therefore, when applying the thermoelastic method to the stress concentration field, it is important to consider the influence of the load frequency.

Influence upon temperature field distribution with straight grooves parameters of clutch friction disk

The instability of the temperature field distribution in clutch friction pair tends to increase exponentially with time when the relative velocity is greater than a certain critical value, which indicates the system enters a state of thermoelastic instability. During high-speed frictional sliding at a high temperature and high pressure, thermoelastic instability will generate local high temperature on friction pair and then cause high-frequency vibration, warping, fatigue fracture, and so on. With the aim of studying the problems arising from local hot spots and the mechanism behind the characteristics of temperature field in friction pair, a thermoelastic finite element analysis model was established for friction pair of heavy-duty vehicle clutch in this paper. The characteristics of thermoelastic stress and temperature distribution under different conditions were obtained by simulation analysis where different values were applied to groove distribution parameters such as number, angle, depth, and width. Experiments were carried out on a friction pair to test its thermoelastic instability. Results show that as the value of each groove distribution parameter increases, the fitting curves of the average temperature, range, and the temperature inhomogeneity coefficient of the temperature field are in forms of oscillation. The average temperature and range have the same trends. The paper concludes that the average temperature range and inhomogeneity coefficient of the temperature field distribute in order, so that the optimized structural parameters were obtained.

STRESSES IN ANVILS OF VARIOUS CONSTRUCTION OF CONTINUOUS CASTING AND DEFORMATION PLANT AT PRODUCTION OF SHEETS FROM STEEL FOR WELDED PIPES

A comparative assessment of strenuous state of the anvils with and without channels has been carried out for the installation of combined continuous casting and deformation process in the production of steel sheets for welded pipes. The conditions of operation and loading of the anvils of combined continuous casting and deformation process are described. The design of anvil with channels for water cooling and the nature of its loading are given. Using the algorithm for solving problems in the elasticity theory by finite element method, the laws governing the distribution of axial stresses in anvils from the slab reduction force are determined. Effect of the channels for anvils cooling with water on the magnitude and nature of stresses distribution in them from the stress of the slab reduction was estimated. The calculation results of temperature fields and axial and equivalent thermoelastic stresses in anvils with channels are presented for the production process of steel sheets for welded pipes in a combined continuous casting and deformation unit. The article considers regularities of total stresses distribution in anvils with channels. To assess the effect of anvils structure on their stress state, regularities of distribution of thermoelastic and total stresses in strands without channels have been determined. The graph of dependence of thermoelastic stresses in the anvil on temperature of its contact surface is given. Recommendations for choosing the material of the fighters are given. The advantages and disadvantages of the anvils with channels for the unit for combined continuous casting and deformation are described. The parameters of such a pilot installation are presented. The authors also describe the results of an experimental study of the parameters of a combined process at the manufacture installation for continuous casting and deformation of JSC Ural Pipe Plant.

Thermo-stressed state of a single-crystal cooled blade taking into account the axial orientation of the crystallographic axes

The thermo-stressed state of a single-crystal blade with vortex and partially film cooling systems is studied. The problem is solved in a three-dimensional formulation using the finite element method. It is known that the orientation of the crystallographic axes exerts a significant influence on the distribution of the stress fields. When the orientation of crystallographic axes changes, the redistribution all of stress is occur and changing the whole picture of stress-strain state of the blade. This work is a continuation of a series of papers by the authors in which the effect of the deviation of the azimuth orientation of the crystallographic axes on the thermo-stressed state of a single-crystal cooled blade is considered. Therefore, in this paper the influence of the axial orientation of the crystallographic axes on the distribution of thermoelastic stresses in the volume of the blade is investigated. Numerical studies have made it possible to show the change in the maximum temperature stresses during the rotation of the crystallographic axes in the yz plane around the x axis and in the xz plane around the y axis. For reasons of ensuring the strength of the blade, it is advisable to limit the spatial rotation of the crystallographic axis [001] within 12 - 15. These limitations are similar to the need to ensure the spread of the natural frequencies of the blade in the range of 8 to 10%. The study made it possible to reveal the effect of a change in the axial orientation of the crystallographic axes on the stress-strain state of the blade. A generalization of the results of previous studies to the limitations of the deviations of the crystallographic axes is performed. The general picture of a stress-strain state is cyclically repeated when the crystallographic axes are rotated by 90. Places of localization of thermoelastic stresses often coincide with places of localization of vibration stresses, which creates an additional danger.

Global simulation of an RF Czochralski furnace during different stages of germanium single crystal growth, part II: to investigate the effect of the crucible's relative position against the RF coil on the isotherms, flow fields and thermo-elastic stresses

By changing the vertical relative position of the crucible against the induction coil, the flow and thermal fields in the melt are seriously affected. The distribution of heat generation along the crucible vertical inner wall is assumed in three cases. A downward shift of the crucible leads to an increase in the heat generation rate near the crucible rim and its reduction near the bottom, while the temperature distribution along the crucible bottom wall varies monotonically with the transmission of the crucible. With downward movement of the crucible and relocation of the hottest region from bottom to top, a reduction in the maximum temperature of 17 degrees can be seen and the freezing amount of liquid on the floor rapidly increased. In contrast, if the crucible is pulled upward, the crucible vertical wall's temperature decreases from bottom to top, due to heat generation by the induced electromagnetic field, and some melt was frozen at the melt free surface. Also, there were two eddy currents in opposite directions within the melt which improve the heat transfer to the crystal–melt interface and the convexity of the germanium crystal decreased. Changes in the manner of thermo-elastic stress distribution against the crucible's relative movement have also been reported.

The Influence of Azimuth Orientation of Crystallographic Axes on Thermoelastic State of a Gte Blade with a Vortex Cooling System

The paper addresses the temperature and thermoelastic states of a single-crystal blade with a complex vortex cooling system and passages for cooling air outflow. The problem of determination of stress-strain state of the blade at hand under the action of temperature fields and centrifugal forces is solved by the finite element method. The authors study the influence of azimuth orientation of crystallographic axes on the distribution and magnitude of thermoelastic stresses in the blade volume.

A thermo-visco-elastic shear-lag model for the prediction of residual stresses in photovoltaic modules after lamination

The distribution of residual thermo-elastic stresses in encapsulated solar cells arising from lamination is relevant for the characterization of the long term performance of photovoltaic (PV) modules during service. Accurate modelling of the structural response of the laminate in the transient regime during cooling after lamination is a challenging task from the computational point of view. In this work we propose a semi-analytic model based on the Kirchhoff plate theory and the shear-lag approach for the treatment of the polymeric encapsulant layers and accounting for their time and temperature dependency according to a rheological model derived from fractional calculus considerations. Spatially uniform and non-uniform temperature distributions are compared to accurately assess the amount of the residual compressive stresses raised in the Silicon cells after lamination. The use of more realistic non-uniform temperature distributions leads to lower residual compressive stresses in Silicon as compared to the uniform case.

逆問題解析を援用したコーティング下の応力計測に関する研究

赤外線サーモグラフィを用いた熱弾性応力測定法によって鋼構造物の作用応力を計測する際,塗膜外面温度変動から鋼材表面の温度変動を逆解析的に推定することで塗膜を除去せずにき裂周辺の応力評価を行うことを検討した.

Effect of 6H-SiC crystal growth shapes on thermo-elastic stress in the growing crystal

The effect of 6H-SiC crystal growth shapes on the thermo-elastic stress distribution in the growing crystal was systematically investigated by using a finite element method. The thermo-elastic stress distribution in the crystal with a flat growth shape was more homogeneous than that in the crystals with concave and convex growth shapes, and the value of thermo-elasticity in the crystal with a flat growth shape was also smaller than that in the two other types of crystals. The maximum values of thermo-elastic stress appeared at interfaces between the crystal and the graphite lid. If the lid was of the same properties as 6H-SiC, the thermo-elastic stress would decrease in two orders of magnitude. Thus, to grow 6H-SiC single crystals of high quality, a transition layer of SiC formed by deposition or reaction is suggested; meanwhile the thermal field in the growth chamber should be adjusted to maintain the crystals with flat growth shapes.

Finite Deformation Thermoelasticity of Thick-Walled Cylindrical Vessels Based on the Multiplicative Decomposition of Deformation Gradient

In this article, a brief review of the multiplicative decomposition of the deformation gradient into mechanical and thermal parts is given up. To model the mechanical behavior of thermoelastic continua in the stress-producing process of nonisothermal deformation, an isothermal effective stress-strain equation based on the logarithmic strain measure is considered for implementation in the governing equations of finite deformation thermoelasticity. Using this constitutive law and assuming the so-called mechanically incompressible material, the thermoelastic stress distribution in the thick-walled cylindrical vessels under steady-state thermal loading and internal/external pressures is determined analytically in the cases of small and finite deformations.

825 赤外線応力分布計測データに基づく応力拡大係数評価の高精度化(GS-3 き裂検出,固定)

825 赤外線応力分布計測データに基づく応力拡大係数評価の高精度化(GS-3 き裂検出,固定)

Time-dependent thermoelastic creep analysis of rotating disk made of Al–SiC composite

Time-dependent creep stress redistribution analysis of rotating disk made of Al–SiC composite is investigated using Mendelson’s method of successive elastic solution. All mechanical and thermal properties except Poisson’s ratio are radial dependent based on volume fraction percent of SiC reinforcement. The material creep behavior is described by Sherby’s constitutive model using Pandey’s experimental results on Al–SiC composite. Loading is an inertia body force due to rotation and a distributed temperature field due to steady-state heat conduction from inner to outer surface of the disk. Using equations of equilibrium, stress strain, and strain displacement, a differential equation, containing creep strains, for displacement is obtained. History of stresses and deformations are calculated using method of successive elastic solution. It is concluded that the uniform distribution of SiC reinforcement does not considerably influence on stresses. However, the minimum and most uniform distribution of circumferential and effective thermoelastic stresses belongs to composite disk of aluminum with 0% SiC at inner surface and 40% SiC at outer surface. It has also been found that the stresses, displacement, and creep strains are changing with time at a decreasing rate so that after almost 50 years the solution approaches the steady-state condition.

Limiting thermal regimes of active disk elements under steady-state pumping and two-dimensional temperature distribution inside the disk

An analytic expression describing the stationary two-dimensional axially symmetric temperature distribution in a disk active element (AE) is derived upon pumping the entire disk whose thickness is 0.01 cm ≤ h ≤ 0.3 cm and the diameter-to-thickness ratio is 1 ≤ d/h ≤ 100. Thermomechanical stresses are calculated. It is shown that from the point of view of the disk damage, the tangential stress on the disk side face constitutes the major threat. For different scaling parameters x =d/h, the limiting lasing powers Plas are estimated in multimode approximation, which can be obtainedusing a disk AE in the case of end and side cooling for different heat exchange coefficients a (by the example of an Nd : YAG crystal). It is found that the side cooling can decrease Plas in some situations. The priority regions are established in the space of the parameters h, x, and a which, while increasing the pump intensity, are accompanied by one of the three events violating the normal operation of the laser: deterioration of spectral and luminescent AE parameters due to heating, malfunctioning of the cooling regime, or thermomechanical damage of the disk. It is shown that an increase in thescaling parameter x smoothes the radial temperature profile and the thermoelastic stress distribution profile.

Thermoelastic model of carpathian region

The two-dimensional thermoelastic model of Carpathian region on the basis of a numerical finite elements method is constructed. The physical and mathematical model is as much as possible approached to the real environment. Detailed high-precision distribution of thermoelastic stresses and dislocations is received. The mountainous rocks non-uniform heating and structural non-uniforms leads to considerable changes of stress fields and dislocations in Carpathian region.

Thermoelastic Stress Field Investigation of GaN Material for Laser Lift-off Technique based on Finite Element Method

The transient thermoelastic stress fields of GaN films is analyzed by the finite element method for the laser lift-off (LLO) technique. Stress distributions in GaN films irradiated by pulse laser with different energy densities as functions of time and depth are simulated. The results show that the high thermoelastic stress distributions in GaN films localize within about 1 μm below the GaN/Al2O3 interface using proper laser parameters. It is also found that GaN films can avoid the thermal deformation because the maximum thermoelastic stress 4.28 GPa is much smaller than the yield strength of GaN 15GPa. The effects of laser beam dimension and the thickness of GaN films on stress distribution are also analyzed. The variation range of laser beam dimension as a function of the thickness of GaN films is simulated to keep the GaN films free of thermal deformation. LLO experiments are also carried out. GaN-based light-emitting diodes (LEDs) are separated from sapphire substrates using the parameters obtained from the simulation. Compared with devices before LLO, P–I–V measurements of GaN-based LEDs after LLO show that the electrical and optical characteristics improve greatly, indicating that no stress damage is brought to GaN films using proper parameters obtained by calculation during LLO.

The planar contact problem of interaction between a rigid heat-conductive cylindrical die and an elastic layer in frictional heat emission

The paper presents discussion of a new planar problem of contact interaction between a rigid heat-conductive die of circular cross section and an elastic layer. The apparatus of integral transformation is used to obtain a precise solution of the nonstationary equations of heat conductivity for the layer and the cylindrical die. This method makes it possible to reduce the formulated problem to a system of integral equations with time-variable limits of integration; the structure of the equations is governed by the type of thermophysical conditions on the interaction surface. An algorithm is advanced for solving this type of integral equation; the variations in time of the contact pressure and the interaction area boundaries are explored. Thus, it is possible to make the problem’s mathematical formulation closer to the real distribution of thermoelastic stresses and to estimate more accurately the effect of temperature fields on the value and pattern of the contact-pressure distribution.

Plane contact problem of interaction between a rigid heat-conducting wedge and an elastic layer under nonstationary friction heat release

We consider a solution to the new plane problem of contact interaction with an elastic layer of a rigid, heat-conducting cross-sectional die in the form of a bounded or unbounded wedge. Using the apparatus of integral transformations, we have obtained an exact solution of the heat-conduction equations for the die and the layer, which permits reducing the problem stated to a system of integral equations whose structure is determined by the kind of thermophysical conditions on the interaction surface. This enables us to make the mathematical statement of the problem more realistic in terms of the distribution of thermoelastic stresses and adequately estimate the influence of thermal fields on the value of the contact pressure and the character of its distribution.