Thermoelastic Displacement Research Articles

Instantaneous thermal fracture behaviors of a bimaterial with a penny-shaped interface crack via generalized fractional heat transfer

In the high-temperature environment, a larger thermal expansion mismatch of a bimaterial leads to pronounced thermal stresses and interface crack growth. In this paper, a generalized fractional heat conduction model is used to determine the instantaneous thermal fracture behaviors of a bimaterial interface crack. An axisymmetric thermoelastic problem is solved with the aid of Goodier's thermoelastic displacement potential and Love's potential functions. A mixed initial-boundary value problem is then converted to a singular integral equation of second kind by using the Hankel and Laplace integral transforms. Numerical results of the intensity factors of heat flux and thermal stresses are evaluated using Stehfest's Laplace inversion scheme. The influence of fractional kernel functions with power and exponential law are analyzed, respectively, for aluminum-steel and steel-epoxy, respectively. The thermal stress intensity factors exhibit more wave-like behaviors based on Riemann-Liouville and Atangana-Baleanu models which is different from Caputo-Fabrizio and the complete diffusion model.

Calculations of Temperature and Thermo-Elastic Displacement Distributions Generated by Laser-Ultrasonic Inspection System

Calculations of temperature and thermo-elastic displacement distributions generated by laser-ultrasonic inspection system are performed. The goal is to determine temperature distributions created in the test objects by generation laser and the respective thermo-elastic displacement distributions causing the ultrasonic waves propagating within the test objects during laser-ultrasonic inspection of parts. The respective heat propagation equation and thermo-elastic equation of motion are solved analytically for 1D and 3D test objects with different geometries.

Probe beam deflection technique with liquid immersion for fast mapping of thermal conductance

Frequency-domain probe beam deflection (FD-PBD) is an experimental technique for measuring thermal properties that combines heating by a modulated pump laser and measurement of the temperature field via thermoelastic displacement of the sample surface. In the conventional implementation of FD-PBD, the data are mostly sensitive to the in-plane thermal diffusivity. We describe an extension of FD-PBD that introduces sensitivity to through-plane thermal conductance by immersing the sample in a dielectric liquid and measuring the beam deflection created by the temperature field of the liquid. We demonstrate the accuracy of the method by measuring (1) the thermal conductivity of a 310 nm thick thermally grown oxide on Si, (2) the thermal boundary conductance of bonded interface between a 3C-SiC film and a single crystal diamond substrate, and (3) the thermal conductivities of several bulk materials. We map the thermal boundary conductance of a 3C-SiC/diamond interface with a precision of 1% using a lock-in time constant of 3 ms and dwell time of 15 ms. The spatial resolution and maximum probing depth are proportional to the radius of the focused laser beams and can be varied over the range of 1–20 μm and 4–80 μm, respectively, by varying the 1/e2 intensity radius of the focused laser beams from 2 to 40 μm. FD-PBD with liquid immersion thus enables fast mapping of spatial variations in thermal boundary conductance of deeply buried interfaces.

Understanding the spatio-temporal evolution of fractures in pillow basalt

We investigated the origin and spatio-temporal evolution of cooling fractures in pillow basalt which undergo thermal contraction after their eruption in an aqueous environment. Through a computer-based simulation using Fourier transformation, the thermo elastic stress displacement profiles within individual pillow units are determined. The scaled model (pillow diameter - 1 meter) generated radial, linear fractures perpendicular to pillow margin and irregular discrete flaws in the pillow interior like the ones observed in natural examples. Radial linear fractures of 3–5 centimetre in length have been measured in pillows of average one-metre diameter from the Maradihalli region, in the Chitradurga Schist Belt, India. An estimated time of 94–118 minutes was required to get radial fractures of similar length in the simulation. Our model efficiently replicated the generation and distribution of thermal fractures and allowed an estimation of cooling time for the peripheral glassy zone but has limitations in deciphering the formation of fracture networks in progressively crystalline inner zone of pillows.

Thermoelastic Analysis For A Thick Plate Under The Radiation Boundary Conditions

A fractional Cattaneo model for studying the thermoelastic response for a finite thick circular plate with source function is considered. The thick plate is subjected to radiation-type boundary conditions on the upper and lower surfaces, and its curved surface is kept at zero temperature. The theory of integral transformations is used to solve the generalized fractional Cattaneo-type, classical Cattaneo-Vernotte and Fourier heat conduction model. The analytical expressions of displacement components using thermoelastic displacement potentials; and thermal-stress distribution are computed and depicted graphically. The effects of the fractional-order parameter and the relaxation time on the temperature fields and their thermal stresses are investigated. The findings show that the higher the fractional-order parameter, the higher the thermal response. The greater the relaxation period, the longer the heat flux propagates on thick structures.

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.

"THERMOELASTIC DISPLACEMENT AND TEMPERATURE RISE IN A HALF-SPACE DUE TO A STEADY-STATE HEAT FLUX "

Due to model complexity, classical contact mechanics theory assumes isothermal contact processes, involving bodies with uniform temperatures and no heat transmitted or generated through or near the contact interface. This paper addresses the problem of frictional heating in non-conforming or rough contacts by investigating the thermoelastic behaviour of asperities. The heat generated in a sliding contact by interfacial friction leads to thermoelastic distortion of the contact surface, further modifying contact parameters such as pressure, gap or temperature. The thermal expansion of the contacting bodies must therefore be accounted for when solving the contact problem. The thermoelastic displacement is computed with the aid of the half-space theory and of fundamental solutions for point sources of heat located at the free surface, derived in the literature of heat conduction in solids. The linearity of conduction equations encourages the use of superposition principle in the same way as for the elastic displacement. As the thermoelastic displacement is expressed mathematically as a convolution product, methods derived in contact mechanics for elastic displacement calculation are adapted to the heat conduction equations. The influence coefficients needed to efficiently compute the convolution products are derived, and the Discrete Convolution Fast Fourier Transform technique is applied to improve the algorithm computational efficiency. A similar method is then advanced for the temperature rise on the contact interface due to arbitrary heat input. The predictions of the newly advanced computer programs are tested against existing closed-form solutions for uniform circular or ring heat sources, and a good agreement is found.

"A NUMERICAL SOLUTION FOR THE ELASTIC SLIDING CONTACT WITH FRICTIONAL HEATING "

A thermoelastic contact model for non-conforming smooth or rough surfaces is proposed in this paper, based on a method for thermoelastic displacement computation. A classical contact model for the contact of rough surfaces is enhanced by integrating the thermal component of displacement. In the sliding contact model, heat is generated by friction at the contact surface, at a rate proportional to the sliding velocity, the frictional coefficient and the contact pressure. The latter, in its turn, is influenced by the initial clearance, the rigid body approach and the normal displacement, which comprises contributions from (1) the elastic displacement due to pressure, (2) the elastic displacement due to the shear tractions, assumed proportional to pressure according to Coulomb law of friction, and (3) the thermoelastic displacement due to the liberated heat, also proportional to pressure. These dependencies suggest that the geometric contact equation can be reduced to an equation in pressure, whose solution is obtained numerically based on an iterative search of the contact area and of the pressure distribution as in the case of isothermal contacts. A spherical contact is simulated with the newly advanced computer program, by including the thermoelastic effects. It is found that the contact area predicted by the isothermal contact model is larger than for the thermoelastic contact, and the pressure in the central contact region is underestimated when the thermal distortion is neglected. The advanced method is expected to provide base for the study of transient contact processes with consideration of thermal parameters.

"THERMOELASTIC DISPLACEMENT DUE TO TRANSIENT SURFACE HEATING "

The starting point in the calculation of normal displacement due to transient heating is the Green’s function for the elastic half-space. Superposition principle leads to a triple integral (double integral over surface and simple integral over time) that can be formally re-written as a three-dimensional convolution product. Given the singularities of the Green’s function in the time/space domain, it is more convenient to employ its spectral counterpart, i.e. the frequency response function (FRF), in the convolution calculation. A special technique for the calculation of the 3D convolution product based on the FRF is advanced in this paper. The resulting algorithm is very efficient from a computational point of view, as the transfers to and from the time/space domain to the frequency domain are handled by the fast Fourier transform. A simulation example is presented, involving the transient thermoelastic displacement due to a uniform heat source that vanishes everywhere except for a square surface domain, and which is applied continuously only in a limited time window. The numerical results predict that the displacement increases with time as long as heat is supplied, and is gradually recovered once the heat is removed. The loaded half-space patch undergoes a growth-release process that is accurately captured by the simulation method. The developed framework anticipates the solution of the contact process with transient heating.

3D Displacement and Stress Fields of Compacting Reservoir: Alternative Solutions

ABSTRACT. We have presented alternative solutions for the displacement and stress fields outside and inside of a 3D right rectangular prism under constant pressure. These solutions are obtained by integrating the well-known nucleus-of-strain solution over the volume of the prism. They are based on the similarity between the gravitational potential yielded by a volume source under a density variation and the thermoelastic displacement potential yielded by a volume source in a half-space under a pressure variation. This similarity enables the use of closed expressions of the gravitational potential and its derivatives. We use our solution for approximating the displacement and stress fields due to a reservoir with arbitrary shape and under arbitrary pressure changes. We discretized the reservoir as a grid of 3D right rectangular prisms juxtaposed in the horizontal and vertical directions. Each prism has homogeneous pressure; however, pressure variations among different prisms are allowed. This parametrization of the reservoir yields a piecewise constant distribution of pressure in the subsurface. We validate the resultant displacement and stress fields due to the reservoir by numerical simulations including a reservoir with arbitrary geometry and under arbitrary pressure distribution, based on a production oil field in offshore Brazil.

A novel hybrid technique to decompose in-plane thermoelastic displacement fields into thermal and structural displacement fields

A novel hybrid technique to decompose in-plane thermoelastic displacement fields into thermal and structural displacement fields

Hollow Cylinder with Thermoelastic Modelling by Reduced Differential Transform

The term thermal stresses are related to mechanics of materials. The thermal stress is formed due to any changes in temperature of a material. The large change in temperature concludes to higher the thermal stresses. Also, there is an effect of thermal expansion coefficient on thermal stresses. The thermal expansion coefficient is different for different materials. In the present paper, the design of a mathematical model concerning the thermal stresses in hollow cylinder subject to the heat conduction with initial and boundary conditions have developed. The basic aim of this work is related to calculations of thermal stresses and thermoelastic displacement in the hollow cylinder by using the reduced differential transform method. The analytical solution is satisfied with the aim of special cases for the copper material properties. The numerical results are illustrated graphically by using mathematical software SCILAB.

Spectroscopic thermo-elastic optical coherence tomography for tissue characterization

Optical imaging techniques that provide free space, label free imaging are powerful tools in obtaining structural and biochemical information in biological samples. To date, most of the optical imaging technologies create images with a specific contrast and require multimodality integration to add additional contrast. In this study, we demonstrate spectroscopic Thermo-elastic Optical Coherence Tomography (TE-OCT) as a potential tool in tissue identification. TE-OCT creates images based on two different forms of contrast: optical reflectance and thermo-elastic deformation. TE-OCT uses short laser pulses to induce thermo-elastic tissue deformation and measures the resulting surface displacement using phase-sensitive OCT. In this work we characterized the relation between thermo-elastic displacement and optical absorption, excitation, fluence and illumination area. The experimental results were validated with a 2-dimensional analytical model. Using spectroscopic TE-OCT, the thermo-elastic spectra of elastic phantoms and tissue components in coronary arteries were extracted. Specific tissue components, particularly lipid, an important biomarker for identifying atherosclerotic lesions, can be identified in the TE-OCT spectral response. As a label-free, free-space, dual-contrast, all-optical imaging technique, spectroscopic TE-OCT holds promise for biomedical research and clinical pathology diagnosis.

Influence of non-irradiated surface optical absorber on temperature gradient induced by photothermal effect in a thin film

This paper presents the model of surface temperature variations, resulting from the photothermal effect induced in a ?thin film ? highly absorbing surface layer? structure, where the thin film is irradiated. The influence of the optical absorption coefficient and sample thickness on the induced temperature gradient is analyzed. It is shown that, depending on the product of these parameters (optical absorbance) in the described structure, the phenomenon of inverse temperature gradient can occur, further influencing the direction and the magnitude of thermoelastic displacement.

Modeling of thermal stresses during hardening the product surface by thermal pulse

A particular solution of a linear variant of the dynamic thermal elasticity problem is considered in application to modeling the conditions of surface hardening of metal products by an energy pulse. The authors determined the equation of medium motion with the model of temperature pulse tested earlier for compatibility with special cases of the equations of parabolic and hyperbolic thermal conductivity. The problem of loading a flat plane of a short circular cylinder (disk) with a temperature pulse is presented. Pulse is a consequence of adopted structure of the volumetric power density of the heat flux, the time multiplier of which has the form of a single wave of the Heaviside function. Classical thermoelastic displacement potential and the method of its division into the product of independent variables functions were used to construct the thermal stress tensor. Differential equations for multiplier functions and their general solutions were found. Natural boundary conditions were set for the components of thermal stress tensor, and their tasks were solved. The obtained solutions are in the form of segments of functional series (the Bessel function in radial coordinate and the exponential function in axial coordinate). The article considers a numerical example of loading a disk made of 40KhN steel which has the mechanical properties sensitive to temperature treatment. Maple computer mathematics package was used in the calculations. Approximate solutions take into account the first 24 terms of the functional series. Estimation of the example makes it possible to explain the presence of stress peaks and stress intensity as a consequence of mutually inverse processes of temperature stress growth and reduction of elasticity coefficients with temperature rise. The numerical example warns against relying only on estimates of solutions to thermoelasticity problems without taking into account the plastic and viscous properties of the material.

All-optical noncontact phase-domain photoacoustic elastography.

Mechanical properties such as elasticity are important indicators of tissue functions that can be used for clinical diagnosis and disease monitoring. However, most current elastography techniques are limited in their ability to distinguish localized microstructural mechanical variations due to employing elastic wave velocity measurement. In addition, their contact-based measurement manner is not favored and may even be prohibited in many applications. In this Letter, we propose all-optical noncontact phase-domain photoacoustic elastography (NPD-PAE), leveraging the temporal response characteristics of laser-induced thermoelastic displacement using optical interferometric detection to calculate the elastic modulus. The all-optical pump-probe method allows the capture of the initial displacement profiles generated at the origin, thus enabling the extraction of in situ elasticity. The feasibility of the method was verified using a tissue-mimicking phantom. The capability to map the mechanical contrast was demonstrated on an ex vivo biological tissue. NPD-PAE opens a new avenue for development of a noncontact elastography technique, holding great potential in the biomedical field and materials science.

UNIDIRECTIONAL COUPLED FINITE ELEMENT SIMULATION OF THERMOELASTIC TCP-DISPLACEMENT THROUGH MILLING PROCESS CAUSED HEAT LOAD

The paper presents a numerical simulation of thermal induced tool displacement during milling oper-ation. An unidirectional finite element model is developed which consists of two sections. A CFX model and a thermal transient model. With the aid of CFX module, the conjugated heat transfer be-tween milling tool and coolant fluid is described. The result of these efforts is the body temperature field of the end mill cutter due to thermal load, which is the thermal fingerprint of the cutting process. Subsequently the calculated body temperature field is linked with a transient-structural module to cal-culate the resulting thermal elastic displacement of the milling cutter. The thermo-elastic displace-ment of the tool is determined by examining a pilot node at the tip of the end mill, whose displace-ment is calculated in relation to the global coordinate system of the model.

CONTROL APPROACHES FOR TEMPERING MACHINE TOOL FRAMES WITH MULTIPLE FLUID CHANNELS AND LIMITED, JOINTLY USED ACTUATING VARIABLE

Nowadays, the thermo-energetic design of a machine tool also includes the thermal stabilization of its machine components. In the past, thermal stability was irrefutable connected to minimizing the temperature gradient of machine tools by air conditioning the entire machine or even the factory hall. Today, thermal stability also defines minimal inhomogeneities in the temperature field of the machine tool due to higher energy efficiency requirements. Fluidic tempering systems of machine components offer considerable potential concerning the minimization of thermo-elastic displacements with acceptable energy demand. Hence, intelligent algorithms are required to combine tolerable geometric deviations with minimal energy effort. The scope of this paper is the integration of a demand-oriented fluidic temperature control system into a machine bed. The resulting multi-input-multi-output (MIMO) systems and varying boundary conditions are challenges, which are addressed. Therefore the paper compares two control approaches, a decentralized single-loop control and a multi-loop control by decoupling the control loops and especially focus on the distribution of the jointly used actuating variable, combined with the variation of different boundary conditions.

Analytical Solution of the Problem of Symmetric Thermally Stressed State of Thick Plates Based on the 3D Elasticity Theory

An important place among thermoelasticity problems is occupied by the plane elasticity problem obtained from the general three-dimensional problem after using plane stress state hypotheses for thin plates. In the two-dimensional formulation, this problem has become widespread in the study of the effect of temperature loads on the stress state of thin thermosensitive plates. The article proposes a general three-dimensional solution of the static problem of thermoelasticity in a form convenient for practical application. To construct it, a particular solution of the inhomogeneous equation, the thermoelastic displacement potential, was added by us to the general solution of Lamé's equations, the latter solution having been previously found by us in terms of three harmonic functions. It is shown that the use of the proposed solution allows one to satisfy the relation between the static three-dimensional theory of thermoelasticity and boundary conditions, and also to construct a closed system of partial differential equations for the introduced two-dimensional functions without using hypotheses about the plane stress state of a plate. The thermoelastic stress state of a thick or thin plate is divided into two parts. The first part takes into account the thermal effects caused by external heating and internal heat sources, while the second one is determined by a symmetrical force load. The thermoelastic stresses are expressed in terms of deformations and known temperature. A three-dimensional thermoelastic stress-strain state representation is used and the zero boundary conditions on the outer flat surfaces of the plate are precisely satisfied. This allows us to show that the introduced two-dimensional functions will be harmonic. After integrating along the thickness of the plate along the normal to the median surface, normal and shear efforts are expressed in terms of three unknown two-dimensional functions. The three-dimensional stress state of a symmetrically loaded thermosensitive plate was simplified to the two-dimensional state. For this purpose, we used only the hypothesis that the normal stresses perpendicular to the median surface are insignificant in comparison with the longitudinal and transverse ones. Displacements and stresses in the plate are expressed in terms of two two-dimensional harmonic functions and a particular solution, which is determined by a given temperature on the surfaces of the plate. The introduced harmonic functions are determined from the boundary conditions on the side surface of the thick plate. The proposed technique allows the solution of three-dimensional boundary value problems for thick thermosensitive plates to be reduced to a two-dimensional case.

Thermoelastic damping in a thin circular transversely isotropic Kirchhoff–Love plate due to GN theory of type III

This research deals with the study of thermoelastic damping in transversely isotropic thin circular Kirchhoff–Love plate. Mathematical model is formed for time-harmonic displacement and temperature fields due to the GN theory of thermoelasticity of type III. The model is solved to obtain the expressions for thermoelastic damping, displacement, and temperature fields for circumferential surface wave modes for simply supported and clamped plate resonators. The numerical results for both the simply supported and clamped boundary conditions for an axisymmetric circular plate are illustrated. It is observed that the damping of vibrations is considerably influenced by surface wave modes. The thickness of the plate also has major effects on the vibrations of resonators. The computer-simulated results to illustrate the effect of circumferential surface wave modes on thermoelastic damping for the GN III theory of thermoelasticity have been depicted graphically.