Thermoelastic Fields Research Articles

Application and comparison of several adaptive sampling algorithms in reduced order modeling

Model Order Reduction (MOR) techniques have extensive applications across scientific and engineering disciplines, such as neutron field reconstruction of nuclear reactor cores, thermoelastic field reconstruction, fluid, and solid mechanics. In the process of building a Reduced Order Model (ROM), the selection of the basis functions in the offline stage is crucial and directly depends on the parameter space sampling strategy. This problem has always been a challenge in MOR. Research into adaptive sampling algorithms has become a hot topic in recent years. To better understand the application of these algorithms to MOR, this paper focuses on three prevalent adaptive sampling algorithms: pseudo-gradient sampling, adaptive sparse grid sampling, adaptive training set extension. These have been successfully applied in various applications, including nuclear reactor cores, molten salt reactor system, power system for convection problems. We systematically assess and compare their performance, finding that adaptive sampling algorithms excel in sampling divergent and oscillating areas and are generally better than the standard sampling strategy. Specifically, the pseudo-gradient sampling algorithm is effective for small-scale scenarios, while the other two algorithms are designed for large-scale sampling. Their practicality is confirmed through successful applications in nuclear reactor cores.

Finite element analysis of a generalized rotating FGM vessel subjected to thermo-mechanical loadings: Effect of Poisson ratio and inhomogeneity parameters

Cylinders and thick walled cylindrical shells are commonly utilized in several industries to transport and store fluids under certain pressure and temperature conditions. In the present paper, a numerical solution is developed in order to investigate displacement, temperature and stress fields in a rotating pressure vessel made of generalized functionally graded material (FGM) subjected to different thermo-mechanical boundary conditions. The aim is to investigate the effect of Poisson ratio, internal pressure and temperature and inhomogeneity parameters on the stress and deformation distributions of the rotating pressure vessel. The material is considered isotropic nonhomogeneous and linearly elastic with its properties varying along the radial direction. Additionally, certain conditions, such as exterior or interior problems where r → ∞ or r → 0, respectively, are impossible to resolve using the variation of attributes as a power-law distribution. An approach to the spatial Young modulus distribution that is more broad has been suggested in the literature which can be applied to such physical challenges. The rotation of the pressure vessel is considered in the analysis, and the temperature distribution is assumed to be non-uniform. Since an analytical solution to the differential equation is not accessible, the conventional Galerkin discretization approach of the Finite Element Method (FEM) is applied, nowadays is considered one of the main numerical tools for solving Boundary Value Problems (BVP). It is addressed how stress, strain, and displacement are affected by the inhomogeneity parameter, rotation speed, pressure, temperature, and Poisson ratio. The examination of the various findings indicates that changes in the temperature profile, rotation, and inhomogeneity parameter on the thermoelastic field have a substantial impact on the stress and strain in the FGM cylinder. The findings indicate that the Poisson ratio and inhomogeneity parameters have a significant impact on the stress and deformation distributions. According to the results, the above-mentioned parameters can be adapted to control the thermoelastic filed in a FGM cylinder. The present research offers significant perspectives on the development and enhancement of rotating FGM pressure vessels intended for high-temperature applications.

A mechanism for spontaneous thermal fragmentation with coolant entrainment during the molten fuel–sodium interaction

Experimental investigation of two interactions between metallic corium jets and sodium, pertaining to severe accidents in a sodium-cooled fast reactor, have been undertaken at the MELT facility. X-ray imaging and debris analysis reveal rapid formation of a crust at the melt coolant-interface, instigating thermal fragmentation events. Heat transfer calculations at the jet-coolant interface, supported by particle tracking velocimetry characterisation of the jet velocity, imply the formation of a solid crust within milliseconds of contact with the coolant. A mechanism for enhanced thermal fragmentation is proposed, inspired by observations from the X-ray imaging of coolant entrainment into the jet. Elevated pressures at the internal crust wall compete with densification and contraction of the crust, resulting in significant stress in the crust. Modelling of the thermoelastic stress field indicates that fracture is dictated by the tangential stress at the outer crust wall, consistent with 200–300 μm long fractures observed during SEM imaging of the outer crust surface. The elevated pressure at the internal crust wall appears to dominate on short timescales, imparting tensile stress at the outer crust wall which may initiate fracture. On longer cooling times, the densification and contraction of the jet dominate resulting in tangential compression. Thus, coolant entrainment and vaporisation within the jet appears to impart competing stresses in the crust which may influence the mode of jet rupture.

Thermal effect induced by viscous dissipation on characteristics of aerodynamic foil journal bearing with aero-thermo-elastic coupling

In aero–thermo–elastic analysis, aerodynamic foil bearings are one of the most representative components that involve strong coupling among microscale shear flow, aerodynamic heating, and elastic foil deformation. Researches on the role of aerodynamic heating in bearings are really inadequate. This study clarifies the effect of thermal behavior induced by viscous dissipation on the characteristic of an aerodynamic foil journal bearing (AFJB) with a rotational speed of 4 × 104–8.0 × 104r/min and an eccentricity ratio of 0.4–0.8. The results indicate that the thermal effect induced by viscous dissipation significantly affects the aerodynamics of shear flow and the dynamic response of elastic foils in the AFJB. The inherent thermal effect induced by viscous dissipation strengthens the inherent viscosity-temperature effect and weakens the pulsation of static pressure while intensifying the temperature increase of the shear flow. The dynamic response of the elastic foils in the solid domain is closely associated with the behavior of shear flow in the fluid domain. The static pressure and temperature elevation increase with the rotational speed and eccentricity ratio owing to strengthened hydrodynamic effects. The effect of thermal behavior induced by viscous dissipation on the aerodynamic and thermal characteristics of the shear flow becomes significant at high rotational speeds and eccentricity ratios. The load capacity and peak temperature elevation increase with the rotational speed and eccentricity ratio. In the solid domain, the thermal effect induced by viscous dissipation negligibly affects the deformation of the elastic foils because the variation in the temperature increase is insignificant, thus resulting in insignificant variations in the properties of the gas film. This study elucidates the impact of aerodynamic heating, especially the thermal effect induced by viscous dissipation, on the aero–thermo–elastic field in bearings and the performance of the bearings. The results of this study serve as basic design guidelines for AFJBs and can be used to optimize the operation security.

An isoparametric inclusion model for determining the thermo-elastic fields produced by varying Eigen-temperature gradients

The existence of inclusions or inhomogeneities may disrupt heat flow, resulting in increased stresses and temperature fluctuations at the material interface. Analyzing the thermo-elastic fields surrounding such microstructures is crucial for unveiling the intricate failure mechanisms within materials. Based on the method of Green's function and contour integral, this work presents a complete set of explicit analytical solutions for thermal and elastic fields of an arbitrary polygonal inclusion subjected to linearly varying eigen-temperature gradients or thermal eigenstrains. In contrast to the previous studies on potentials showing analogy with anti-plane elasticity, a mathematical analogy of Green's functions between steady-state heat conduction and thermal inclusion for plane elasticity is accordingly established. By employing the linear interpolation of the nodal eigen-temperature gradients or eigenstrains, the work further extends the traditional isoparametric element idea to the thermos-elastic inclusions, and proposes a novel isoparametric inclusion model to solve arbitrarily shaped inclusions with any distributed eigen-temperature gradients. Unlike the finite element method, which requires meshing for both the matrix and inclusion, the present model exhibits efficiency, flexibility, and versatility with the mesh discretization only conducted inside the inclusion domain. The inclusion based isoparametric method may have potential applications in mechanical engineering and material science for analyzing the thermo-structural behavior of various microstructures.

Magnetoelastic effect of kimberlite host rocks (Yakutsk diamondiferous province)

The purpose of the research is to conduct petro- and paleomagnetic studies of Early Paleozoic rocks of the carbonate basement of a number of diamond deposits in the Yakutsk diamondiferous province in order to study the changes in petrophysical parameter values in the dynamic influence zone of a kimberlite pipe. It is shown that the formation of kimberlite diatremes accompanied by pulsating explosions shifting upwards brings about thermoelastic stress fields in the kimberlite-bearing medium, which are characterized by epigenetic changes and associated petrophysical heterogeneities (petrophysical anomalies). Petromagnetic heterogeneities of burning and stress are, therefore, some of these petrophysical anomalies, within which kimberlite-bearing rocks have contrastingly changed their original magnetic characteristics under the action of thermodynamic processes. Primarily, petromagnetic anomalies are reflected in the changed nature of the anisotropy of magnetic susceptibility: from sedimentary to dyke geotype. In addition, petromagnetic anomalies of magnetic susceptibility can be accompanied by the formation of metachronous natural residual magnetization vectors in kimberlite host rocks. The dimensions of petromagnetic anomalies (petromagnetic heterogeneities) may significantly exceed the size of the kimberlite pipe itself, which facilitates identification and delineation of the most promising areas. Besides, the magnetoelastic effect can create zones close to the kimberlite bodies that are hardly permeable for relatively viscous, protocrystal-rich mafic magmas. This is the reason for their wedging out along petrophysical barriers that is presented by splitting into thin tongues, formation of trap-free windows and corridors, toroidal shafts with sharply increasing thickness in intrusions, etc. Having relatively elevated values of magnetic and density parameters, such forms of igneous formations will be reflected in the observed geophysical fields. Thus, it is reasonable to consider petromagnetic anomalies as an important petrophysical search criterion for the detection of bedrock kimberlite bodies.

Thermomechanical modeling of dissimilar-material interfaces in composite structures

Due to the heterogeneities in material properties of strongly-bonded multi-material composite structures, there exist singularities of the stress fields at the material interface as well as the interface corners on the bounding surfaces. The finite-element method is probably the only plausible option to analyze the stress around such interfaces between dissimilar materials subjected to combined thermo-mechanical loading. In this article, we propose a novel mathematical model for the computational analysis of coupled thermo-elastic fields with perfectly bonded interfaces of dissimilar isotropic/orthotropic composite-material structures. A scalar function of the spatial variables, namely, the displacement function, is used to integrate the temperature field and the associated displacement-function field to obtain two nonhomogeneous partial-differential equations of equilibrium that govern two thermo-mechanical sub-problems defined in terms of the appropriate conditions of orthogonal temperature gradients. For a specific temperature field, obtained as a steady-state solution of the given thermal problem, the two thermo-mechanical sub-problems are solved independently to obtain the full-field solution of the thermo-elastic problem using the method of superposition. As an alternative to the conventional computational approach, we employed a single variable semi-analytical method of solution to determine the thermo-mechanical response of the multi-material composite structures. The continuity of the temperature and the heat flux in the thermal field problem and the continuity of the displacement and the traction vectors are utilized in the elastic field problem to determine the appropriate algebraic equations suitable for nodal application at the interfaces as well as interface corners on the boundaries of the respective problems. The quantitative comparison of the present displacement-function solutions to several mixed-boundary-value problems with those obtained by the conventional finite-element method verifies the high accuracy and effectiveness of the present method. This computational model has potential applications in identifying near-interface high-stress locations as well as possible critical regions of the physical boundary of composite structures subjected to mixed modes of thermal and mechanical loadings.

Analytical solutions for the plane thermoelastic problem of a nano-open crack in one-dimensional hexagonal quasicrystal non-periodic plane

As a stable material at high temperatures, the presence of cracks and other defects greatly reduces the performance of quasicrystals (QCs). The plane thermoelastic problem of one-dimensional hexagonal quasicrystals (1DHQ) non-periodic plane containing a nano-open crack is analyzed using surface elasticity theory. The closed form solutions are obtained to describe the thermoelastic field corresponding to the nano-crack by the Fourier integral transformation technique. The analytical solutions of the thermal stress intensity factors (TSIFs) and the strain energy density factor (SEDF) at the crack tip are derived explicitly. The influence of the applied loads, the surface effects and the multi-field coupling effects on the TSIFs and SEDF are discussed. The numerical results reveal that the surface effects have an obvious impact on TSIFs with small applied loads, and the surface effects will inhibit the propagation of nano-open cracks. The research results of this study provide some reliable theoretical references for the development of nano-QCs.

Traps of the Morkoka River Basin and their morphology as response to the possible presence of kimberlites

The traps in outcrops of the middle course of the Morkoka River were formed in three stages and implementation phases. Each subsequent introduction phase of the basite melt was distinguished by its petrogeochemical features, degree of crystallization of the magmatic melt, and density. An unusual form of intrusion introduction in the second phase (crushing of the sill and the introduction of an early intrusion into the rocks) was revealed. During the formation of kimberlite diatremes, the carbonate rocks containing them became denser and thermoelastic stress fields associated with the magnetoelastic Villari effect arose. As a result, the so-called “protective shield” was formed around the kimberlites. A comparison of the trap sill behavior of the Morkoka River with the similar behavior of traps near kimberlites (Komsomolskaya and Morkoka tubes) suggests the presence of an unknown kimberlite body under traps in this area.

Morphology of trap sills near kimberlites

Research subject. Trap sills of the Daldin-Alakit diamond-bearing region of western Yakutia. Aim. To establish the reason for the influence of sedimentary rocks containing kimberlite diatremes on the introduction of basite magma that forms trap sills and the possibility of using the morphology of sills as a search signs for kimberlites. Materials and methods. Sections of trap sills near kimberlites, their structure, petrographic and petrochemical composition of dolerites performing sills were studied. Results. During the formation of kimberlite diatremes, accompanied by pulsating explosions shifting to the top, a significant compaction of the sedimentary rocks containing kimberlites occurs, associated with thermoelastic stress fields. This process leads to the formation of zones near kimberlites, which are difficult to penetrate for relatively viscous, protocrystalline-enriched basite magmas. When such magmas are introduced, the latter before kimberlites form torus-shaped shafts with a sharply increasing power in intrusions. Sometimes magma, flowing around kimberlites, creates “trappless windows”, occasionally splitting into low-power “tongues”. Quite frequently, before kimberlites, sills crumple, acquiring a wave-like shape. Conclusion. All the listed morphological features of traps arise during the introduction of magma, thus providing an indirect method of searching for kimberlites, particularly during the areal drilling of territories covered by continuous trap fields conducted by ALROSA in Western Yakutia.

Analytical solution of the temperature-dependent thermoelastic problem induced by Joule heating and the presence of an elliptic cavity

Joule heat induced by electric current may well lead to thermal stress and contribute to structural failure and crack evolution in a range of modern materials. In this paper, we use complex variable methods to obtain the thermoelastic fields around an elliptic cavity in a plate subjected to remote electric and thermal loads. Of particular interest is the fact that we consider the temperature dependency of the corresponding thermoelastic coefficients. We introduce an analytical method which is verified by the fact that it leads to results which reduce to the classical analytical results in the literature when the thermoelastic coefficients are taken to be temperature-independent. We find that when the elliptic cavity is reduced to the representation of a linear crack, the corresponding stress intensity factor increases to a greater extent under the temperature-dependent assumption versus the corresponding classical results. Our findings are significant in forming the basis for the analysis of the evolution of crack growth under severe temperature gradients such as those occurring as a result of Joule heat loading.

Memory effects on the thermal fracture behavior of cracked plates via fractional heat conduction models

Studies have shown that fractional derivatives have important memory effect on the thermal shock fracture of structures. In the present work, four generalized fractional models are applied to investigate the thermal fracture problem of cracked plates. Laplace transform and finite sine transform are employed to obtain transient temperature and thermal stresses. Stress intensity factors around the crack tips are evaluated through the weight function method for edge and center cracks. Numerical results show that memory effects on the thermoelastic fields are different with different fractional derivative definition and fractional orders, and the effects will vary accordingly with crack geometry parameters.

Effective medium method in solution of the elastic and thermo-elastic homogenization problems for polycrystals with spheroidal transverse isotropic grains

Self-consistent effective medium method is used for determination of the effective elastic and thermo-elastic properties of polycrystalline materials with spheroidal transverse isotropic grains. The grains with arbitrary aspect ratios including very oblate (disks) and very prolate (fibers) spheroids are considered. The function of the Owens-March type is used for description of distribution of grains over orientations. The equations for the effective elastic stiffness tensor and the tensor of effective coefficients of thermo-expansion of polycrystals are derived using integral equations for elastic and thermo-elastic fields in heterogeneous media and the hypotheses of the effective medium method. The numerical algorithm of the method is described in detail. Numerical examples are presented for polycrystalline clay rock materials with strongly anisotropic grains and for polycrystalline zinc. Graphs of the dependences of the effective elastic constants and effective coefficients of thermo-expansion of the polycrystals on the parameters of the orientation distribution function and aspect ratios of grains are presented.

Fatigue of short carbon fiber reinforced PEEK under compression: Influence of the load ratio and predictions from heat buildup measurements

AbstractFew works investigate the fatigue of short fiber reinforced thermoplastics under cyclic compression. Furthermore, the heat buildup approach to quickly predict the fatigue lifetime of these materials has not yet been investigated for compression–compression loadings. This paper first describes an experimental protocol to perform well‐controlled cyclic compression tests without anti‐buckling device that may induced bias. The uniaxiality of the global loading is checked during the test based on kinematic and thermoelastic coupling field measurements. Then, the paper compares the results from fatigue and heat buildup tests performed on polyetheretherketone reinforced with 30 wt% of short carbon fibers for several load ratios. It is shown that the fatigue lifetime is higher in compression than in tension and depends on the compression load ratio. The heat buildup approach appears to be relevant to quickly predict the fatigue lifetime of the material for the different loading ratios studied, including compression–compression.

Thermoelastic contact responses of transversely isotropic coating considering heat partition

Transverse isotropy is typical material property of coating, which affects thermoelastic contact characteristics of coated materials a lot, without due attention. A thermoelastic contact model between a sliding ball and transversely isotropic coating considering heat partition is thus established with a semi-analytical method (SAM) in this investigation to reveal its effects. In the proposed model, general solution of thermoelastic field of transversely isotropic material is derived and transformed to the Fourier frequency domain; explicit analytical expressions of frequency response functions (FRFs) for thermoelastic field of transversely isotropic coating are newly derived following the surface and interface boundary conditions. Employing the proposed model, effects of material thermal properties, coating thickness and sliding velocity on thermoelastic contact characteristics of transversely isotropic coating are explored, as well as sensitivity of the maximum temperature rise on system parameters. Simulation results indicate that contact pressure, heat partition coefficient and temperature rise increase with the sliding velocity; location of the peak temperature rise moves away from the contact center to a fixed value x = −0.45r as the sliding velocity increases; ratio of thermal conductivity of the coating to that of the substrate has significant effect on contact pressure, temperature rise distribution and heat partition coefficient, while ratio of thermal expansion coefficient of the coating to that of the substrate has slight influence; thermoelastic responses are dominant by the coating-substrate system when the coating thickness changes from about 0.01 to 4 times contact radius; sensitivity of the maximum temperature rise on the six system parameters in a descending order is V >K331 >K111 > h >α331 >α111. This investigation may provide potential application in thermal-related contact failure analysis and guidance for coating optimal design.

Stress analysis of rotating thick-walled nonhomogeneous sphere under thermomechanical loadings

In this work, a rotating thick-walled spherical vessel made of nonhomogeneous materials subjected to internal and/or external pressure under thermal loading was analyzed within the context of three-dimensional elasticity theory. An analytical formulation was established for computing the displacement and stress fields. It has been assumed that the mechanical and thermal properties are varying through thickness of the functionally graded material (FGM) according to a power-law nonlinear expression, while Poisson's ratio is considered as constant. Based on equilibrium equation, Hooke's law, stress-strain relationship in the spheres and other theories from mechanics a second-order ordinary differential equation well-known as Navier equation is obtained that represents the thermoelastic field in hollow FGM sphere. Navier equation derived from the mechanical equilibrium equation was solved to obtain the exact solution of the displacement and stress distributions. Different results of thermoelastic field are presented across the thickness of the sphere. The analysis of the different results reveals that stress and strain in the FGM sphere are significantly depend upon variation made in temperature profile, rotation and inhomogeneity parameter on the thermoelastic field. Thus, the inhomogeneity in material properties can be exploited to optimize the distribution of displacement and stress fields.

Thermoelastic fields for a heat exchanger of arbitrary shape in a bi-material infinite plane

When a bi-material with two jointed dissimilar half-planes containing an arbitrarily shaped polygonal inclusion is subjected to heat flow, the thermoelastic fields, including temperature and displacement, can be derived by the Green’s function technique with the integral of the source over the inclusion. Using Hadamard’s regularization, the two-dimensional (2D) thermal, elastic, and thermoelastic Green’s functions of two-jointed dissimilar half-planes are firstly derived from the 3D Green’s functions as the corresponding fundamental solutions. The fundamental solutions for semi-infinite and infinite domains can be recovered by adjusting the material constants. Eshelby’s tensors are derived in terms of the biharmonic, harmonic, and two Boussinesq’s displacement potential functions. When a heat exchanger of arbitrary shape is embedded in a matrix with different thermal and mechanical properties, combining a continuously distributed eigen-temperature gradient and eigenstrain field, the dual equivalent inclusion method (DEIM) is applied to handle the material mismatch of thermal conductivity, stiffness, and thermal expansion coefficient, respectively. Therefore, the full thermoelastic fields can be obtained by the integral over the heat exchanger only. The eigen-fields are expanded in the Taylor series referred to the center of the particle, which exhibits tailorable accuracy with uniform, linear or quadratic terms in comparison with the analytical solution for a circular inhomogeneity in the infinite domain. An exact thermoelastic solution of a circular inhomogeneity embedded within the infinite domain is present. The case study of an electric heat cable in the concrete block demonstrates the capability and exactness of the model. The method can be used for a thin film containing a heat exchanger of arbitrary shape as either a heat sink or source.

The Green’s function based thermoelastic analysis of spherical geothermal tanks in a semi-infinite domain

When an underground heat exchanger is subjected to a surface load on the ground and temperature change inside, the stress transfer between the thermal tank and the earth may cause the deformation and destruction of the tank. The bi-material thermoelastic fundamental solution of two-jointed dissimilar half-spaces is applied to elastic and thermal analysis of spherical heat storage tanks, where the continuity equations at the bi-material interface are satisfied. Using Hadamard’s regularization in the x3 direction, the two-dimensional bi-material thermoelastic fundamental solution can be obtained. By changing the material constants, the fundamental solution for a semi-infinite domain or an infinite domain with a single material can be recovered. In general, the storage tanks and soil exhibits different thermal and mechanical properties. A dual equivalent inclusion method (DEIM) is proposed to simulate the material mismatch of thermal conductivity and elasticity with continuously distributed eigen-temperature-gradients and inelastic eigenstrains on the tanks, respectively. Using the analytical domain integrals, no mesh is required for inhomogeneities. Due to the boundary effects and inhomogeneity interactions, the eigen-fields are expanded at the center of each inhomogeneity using the Taylor series with tailorable accuracy. The DEIM is verified by the finite element method and demonstrated by the geothermal applications using uniform, linear, or quadratic orders of eigen-fields. For a spherical heat exchanger in an infinite homogeneous domain, DEIM provides the exact solutions of the thermoelastic fields for a uniform heat source and a uniform far-field heat flux field.

An elliptical inhomogeneity under nonuniform heat flux

We use complex variable techniques to study the decoupled two-dimensional steady-state heat conduction and thermoelastic problems associated with an elliptical elastic inhomogeneity perfectly bonded to an infinite matrix subjected to a nonuniform heat flux at infinity. Specifically, the nonuniform remote heat flux takes the form of a linear distribution. It is found that the internal temperature and thermal stresses inside the elliptical inhomogeneity are quadratic functions of the two in-plane coordinates. Explicit closed-form expressions of the analytic functions characterizing the temperature and thermoelastic field in the matrix are derived.

Frictional contact of one-dimensional hexagonal quasicrystal coating considering thermal effects

In this paper, the contact behavior of a one-dimensional hexagonal quasicrystal coating fully bonded to a rigid substrate under the action of a spherical indenter rotating around its own axis is investigated. The frictional heat generation and heat transfer are considered. Using the general solutions of thermoelastic fields combined with thermal–mechanical boundary conditions followed by the double Fourier transforms, the frequency response functions of the basic solutions of the thermoelastic contact problem are obtained. The basic solutions in spatial domain are calculated by the discrete convolution-fast Fourier transform (DC-FFT) algorithm and the inverse fast Fourier transform (IFFT) algorithm. The results show that the asymmetry of responses of phonon normal stress, phason normal displacement and phason normal stress are mainly caused by friction behaviors. The increase of friction coefficient does not change the phonon normal displacement, but makes the phason normal displacement and the normal stresses of phonon and phason field opposite change trends on both sides of the contact center.