Thermoelastic Stress Field Research Articles

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.

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.

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.

Thermo-mechanically coupled sliding contact shakedown analysis of functionally graded coating-substrate structures

The sliding contact shakedown map composed of elastic shakedown limit and elastic limit is significant to the further optimization of functionally graded (FG) coating parameters. The friction heat induced by the relative sliding velocity of contact pairs can cause thermal stress and changes in contact parameters. Nevertheless, the influence of thermo-mechanically coupled effect on the sliding contact shakedown map of FG coating-substrate structures keeps unrevealed. Therefore, a mathematical optimization model is proposed to draw the shakedown map considering the temperature-dependent friction coefficient and yield stress. Based on the thermo-elasto-perfectly plastic material model and multilayered approximation of FG coating, the required thermo-elastic stress field with the temperature-dependent friction coefficient is obtained by employing the conjugate gradient method and discrete convolution-fast Fourier transform algorithm. The results show that the friction heat can cause the decreases of elastic shakedown limit and elastic limit, and increasing the sliding velocity can enhance the decreases. Moreover, the friction heat can elevate the residual tensile stress near the surface and weaken the residual compressive stress at a large depth from the surface. Meanwhile, the temperature-dependence of friction coefficient can cause the increases of elastic shakedown limit and elastic limit, but the introduction of temperature-dependent yield stress brings no obvious change to the shakedown curves due to the slight thermally-induced change of yield stress. Additionally, decreasing the distribution gradient index can not only improve elastic limit and elastic shakedown limit at large friction coefficients, but also reduce the distribution of residual tensile stress near the surface.

Elastic shakedown analysis of two-dimensional thermo-elastic rolling/sliding contact for a functionally graded coating/substrate structure with arbitrarily varying thermo-elastic properties

The elastic shakedown analysis of rolling/sliding contact with friction heat is essential for the safety evaluation of tribological components with a functionally graded (FG) coating. However, the corresponding works are still lacking due to the complexity of thermo-elastic contact stress calculation and residual stress optimization induced by the non-homogeneity of material properties. An effective multi-layered model for the thermo-elastic rolling/sliding contact of two similar elastic cylinders with the FG coating involving arbitrarily distributed thermo-elastic properties is established, and the corresponding thermo-elastic stress field is obtained subsequently by using the conjugate gradient method and fast Fourier transform algorithm. Then, a specific bisection iteration procedure is applied to evaluate the elastic shakedown limit (ESL), and the effects of friction coefficient, rolling speed, distribution gradient indexes of various thermo-mechanical properties, and FG coating thickness on the ESL are discussed, respectively. The results show that the increases of friction coefficient and rolling speed can cause the decrease of ESL, the ESL can be improved significantly by adjusting the distribution gradients of shear modulus and yield stress appropriately, and the relations between the ESL and various heat conduction parameters show a strong dependence on the sliding velocity.

Simultaneous measurement of temperature, stress, and electric field in GaN HEMTs with micro-Raman spectroscopy.

As semiconductor devices based on silicon reach their intrinsic material limits, compound semiconductors, such as gallium nitride (GaN), are gaining increasing interest for high performance, solid-state transistor applications. Unfortunately, higher voltage, current, and/or power levels in GaN high electron mobility transistors (HEMTs) often result in elevated device temperatures, degraded performance, and shorter lifetimes. Although micro-Raman spectroscopy has become one of the most popular techniques for measuring localized temperature rise in GaN HEMTs for reliability assessment, decoupling the effects of temperature, mechanical stress, and electric field on the optical phonon frequencies measured by micro-Raman spectroscopy is challenging. In this work, we demonstrate the simultaneous measurement of temperature rise, inverse piezoelectric stress, thermoelastic stress, and vertical electric field via micro-Raman spectroscopy from the shifts of the E2 (high), A1 longitudinal optical (LO), and E2 (low) optical phonon frequencies in wurtzite GaN. We also validate experimentally that the pinched OFF state as the unpowered reference accurately measures the temperature rise by removing the effect of the vertical electric field on the Raman spectrum and that the vertical electric field is approximately the same whether the channel is open or closed. Our experimental results are in good quantitative agreement with a 3D electro-thermo-mechanical model of the HEMT we tested and indicate that the GaN buffer acts as a semi-insulating, p-type material due to the presence of deep acceptors in the lower half of the bandgap. This implementation of micro-Raman spectroscopy offers an exciting opportunity to simultaneously probe thermal, mechanical, and electrical phenomena in semiconductor devices under bias, providing unique insight into the complex physics that describes device behavior and reliability. Although GaN HEMTs have been specifically used in this study to demonstrate its viability, this technique is applicable to any solid-state material with a suitable Raman response and will likely enable new measurement capabilities in a wide variety of scientific and engineering applications.

Thermoelastic strain and stress fields due to a spherical inclusion in an elastic half-space

In this paper, closed form analytical expressions for thermoelastic strain and stress compo- nents due to a spherical inclusion in an elastic half-space are obtained. These expressions are derived in the context of steady-state uncoupled thermoelasticity using thermoelastic displacement potential functions. The thermal strain and stress fields are generated due to differences in the coefficients of linear thermal expansion between a subregion and the surrounding material. The strain and stress components for exterior points of the spheri- cal inclusion are same as those of the center of dilatation. Variations of strain and stress components for exterior and interior points of the spherical inclusion are shown graphically.

Heat Conduction and Thermo-Elastic Stress Field Disturbed by a Thermal-Medium Crack Propagating in Orthotropic Materials Characterized by Real or Complex Eigenvalues

A dynamic, partially permeable crack model for orthotropic materials is established with the crack full of thermal medium. Besides external thermal and elastic loadings, the heat flux generated by the crack interior full of a medium also contributes to the crack boundary conditions, which is dependent on the crack opening displacement. Thus, the heat conduction is dependent on elastic field. First, the heat conduction equation is solved exactly in terms of unknown heat flux of the crack interior. Then, the elastic field is presented for real or complex eigenvalue cases on the basis of the operator theory. Finally, the thermal and elastic fields are presented analytically, and the heat flux of the crack interior is determined explicitly. Numerical results are offered to show the influences of the thermal conductivity coefficient, normal and shear loadings and crack velocity on the distributions of the heat flux, temperature difference across the crack surfaces, and thermal stress intensity factor. Figures illustrate that increasing the crack velocity leads to a more thermally impermeable crack and produces a bigger temperature difference across the crack surfaces.

Inhibition of a curvilinear bridged crack by induced thermoelastic stress field

ABSTRACTTemperature changes near the end of a curvilinear crack in the presence of end areas with cohesive forces of the material are considered. It is assumed that these areas adjoin to the crack tip and their sizes are comparable with the crack size. The goal of local changes of temperature is to delay or inhibit the growth of a curvilinear crack. A boundary value problem on equilibrium of a bridged curvilinear crack under the action of external tensile loads, induced thermoelastic temperature field, and tractions in the bonds preventing its disclosure is reduced to the system of nonlinear singular differential equations with a Cauchy-type kernel. Normal and tangential tractions in the bonds are found from the solution of this system. The stress intensity factors are calculated. The condition of limit equilibrium of a curvilinear crack with an end area is formed based on two-parameter fracture criterion.

Analysis of the effective thermoelastic properties and stress fields in silicon nitride based on EBSD data

The present work focuses on the determination of the effective thermoelastic properties and the statistical characterization of stress fluctuations in silicon nitride's local phases. For that purpose, full field finite element solutions have been considered, based on 3D electron backscatter diffraction (EBSD) data of silicon nitride. A second-order mean field homogenization scheme, consisting in Hashin–Shtrikman bounds, has been also considered. Ab-initio simulations have been performed in order to determine the temperature-dependent elastic properties of the local phases. The isotropic material microstructure has been checked based on both experimental results and full field solutions. The effective thermoelastic properties have been assessed with the newly obtained experimental results. The stress fluctuations within silicon nitride's local phases have been examined under mechanical and thermal loadings. It has been shown that the amorphous phase is the most vulnerable to fracture and to micro-cracks initiation.

Partial closure of a curved crack in a plane using an induced thermoelastic stress field

On the basis of the methods of thermoelasticity, a mathematical description of the model of partial closure of a curved crack in a plane with the help of an induced temperature field was carried out. The determination of unknown contact stresses and the sizes of the contact zones in each approximation is reduced to the solution of a singular integral equation. Normal and tangential contact stresses and the values of the size of the tip zones where the faces of a curved crack close are found.

Numerical and experimental investigation of the influence of tumor size on laser-induced ultrasonics in soft tissue

The generation and propagation of laser-induced ultrasonic waves in soft tissue systems are investigated using the finite element method. Taking into account the effects of thermal diffusion, optical penetration, tumor elastic modulus and finite laser pulse duration, the transient temperature distribution is obtained. Using this temperature field as thermal loading in structural analysis, the thermoelastic stress field and laser-induced ultrasound waves in soft tissues are obtained. The results show that the intensity of the positive peak in the ultrasound wave increases and the arrival of the longitudinal wave takes place sooner as the tumor size becomes larger. It is also found that the duration of the laser ultrasound signal becomes shorter as the size of the tumor decreases. Meanwhile, the percentage of the received ultrasonic signal in the high-frequency region increases as the size of the tumor decreases, as has been proved by the experimental results.

Numerical simulation of the influence of the elastic modulus of a tumor on laser-induced ultrasonics in soft tissue

The influence of the elastic modulus of a tumor (EMT) on the laser-generated thermoelastic force source and ultrasound waves are investigated by using the finite element method. Taking into account the effects of thermal diffusion, optical penetration, and finite duration of laser pulse, the transient temperature distribution is obtained. Applying this temperature field to structure analyses as thermal loading, the thermoelastic stress field and laser-induced ultrasound wave in soft tissues are obtained. The results show that there is a linear correlation between the maximum compressive stress and the elastic modulus of tissues. It is also shown that the features and frequency regions of the laser-induced ultrasound waveform have a close relationship with the EMT, which has been further verified by a corresponding experiment.

A dual-reciprocity boundary element method for axisymmetric thermoelastostatic analysis of nonhomogeneous materials

Abstract The problem of determining the axisymmetric time-independent temperature and thermoelastic displacement and stress fields in a nonhomogeneous material is solved numerically by using a dual-reciprocity boundary element technique. Interpolating functions that are bounded in the solution domain but that are in relatively simple elementary forms for easy computation are constructed for treating the domain integrals in the dual-reciprocity boundary element formulation. The proposed numerical approach is successfully applied to solve several specific problems.

An analytical solution for thermal shock analysis of multiwall carbon nanotubes

Thermo-elastic stress field in shock-induced multiwall carbon nanotubes (MWCNTs) is analyzed using an analytical method. The linear model of van der Waals forces is applied between two adjacent tubes in the MWCNTs with finite length to simulate the force between layers. The presented method is based on a dynamic continuum model of 3D elasticity solution in cylindrical shells. In addition, to create realistic physical properties, the temperature dependence of material properties is considered for the problem. All governing equations are transferred to frequency domain using Laplace transform technique to solve analytically the time dependent governing equations. The results in Laplace domain are transferred to time domain using an inverse Laplace transformation method. The accuracy of solution is verified by comparison with those obtained from literature. The results are obtained for two types of MWCNTs with 4 and 13 layers. To access a proper design of MWCNTs under thermal shock, the effects of their sizes on dynamic behaviors of thermal stresses are studied in details. It is found that thermal shock has a significant effect on disturbance of thermo-elastic stress filed in time domain, which is studied for various types of MWCNTs in this paper.

Thermomechanical processes in an inertial thermonuclear fusion reactor blanket under cyclic exposure to neutron fluence

The thermomechanical processes occurring in the blanket of a heavy-ion inertial thermonuclear fusion reactor are analyzed. The heat-release density in the structural materials and the blanket coolant is calculated on the basis of prescribed characteristics of the neutron pulse from a ~1 GJ microexplosion of a target. Calculations of the nonstationary thermoelastic stress and pressure fields as well the temperature of the wall and blanket coolant are performed using simple one-dimensional models. The amplitude and frequency characteristics of the stress and pressure waves generated by the energy released in the microexplosion are obtained. The thermal relaxation processes occurring in the elements of the blanket between successive microexplosions are analyzed.

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.

Thermo-Mechanical Analysis of an Inhomogeneous Double-Layer Coating System under Hertz Pressure and Tangential Traction

The surface temperature distribution and thermo-elastic stress fields of an inhomogeneous coating system subjected to mixed Hertz pressure, tangential traction, and frictional heating are studied in this paper. The coating system consists of a surface coating and an intermediate functionally graded layer perfectly bonded to a substrate. The surface coating and the substrate are homogeneous materials with distinct physical properties while the intermediate layer is inhomogeneous with material properties changing exponentially along the thickness direction. It is assumed that the friction is of Coulomb type. Solutions for the temperature field and interfacial stresses are obtained using Fourier transform technique. The effects of total thickness, the graded layer thickness, Peclet number, and friction coefficient on the surface temperature field and interfacial stresses are investigated in detail. Direct comparisons with the results of a homogeneous single-layer coating system show that the use of the double-layer coating system can significantly reduce the surface temperature and interfacial normal stress.

Influence of transparent coating thickness on thermoelastic force source and laser-generated ultrasound waves

A numerical model is established to investigate the influence of transparent coating thickness on the laser-generated thermoelastic force source and ultrasound waves in the coating–substrate system by using the finite element method (FEM). Taking into account the effects of thermal diffusion, the finite width and duration of the laser source, as well as the temperature dependence of material properties, the transient temperature distributions are obtained firstly. Applying this temperature field to structure analyses as thermal loading, the thermoelastic stress field and laser-generated ultrasound wave in the specimen are obtained. The generation and propagation of the laser thermoelastically induced stress field and ultrasonic waves in coating–substrate system are presented in detail. The influence of transparent coating thickness on the transient temperature distribution, thermoelastic force source and the laser-generated ultrasound waveforms is investigated. The numerical results indicate that the thermoelastic force source and laser-generated ultrasound waveform are strongly affected by the coating thickness due to the constraint of coating. This method can provide insight into the generation and propagation of the laser-generated stress field in coating–substrate system consisting of a transparent coating and an opaque metallic substrate. It provides theoretical basics to optimize ultrasonic signal generation in particular applications and invert the physical and geometrical parameter of the coating–substrate system more accurately in the experiment.