Quasi-static Thermal Stresses Research Articles

Boundary Element and Sensitivity Analysis of Anisotropic Thermoelastic Metal and Alloy Discs with Holes.

The main aim of this paper was to develop an advanced processing method for analyzing of anisotropic thermoelastic metal and alloy discs with holes. In the boundary element method (BEM), the heat impact is expressed as an additional volume integral in the corresponding boundary integral equation. Any attempt to integrate it directly will necessitate domain discretization, which will eliminate the BEM’s most distinguishing feature of boundary discretization. This additional volume integral can be transformed into the boundary by using branch-cut redefinitions to avoid the use of additional line integrals. The numerical results obtained are presented graphically to show the effects of the transient and steady-state heat conduction on the quasi-static thermal stresses of isotropic, orthotropic, and anisotropic metal and alloy discs with holes. The validity of the proposed technique is examined for one-dimensional sensitivity, and excellent agreement with finite element method and experimental results is obtained.

Behaviour of Quasi Static Thermal Stresses on Account of Internal Moving Heat Generation in Solid Sphere

Behaviour of Quasi Static Thermal Stresses on Account of Internal Moving Heat Generation in Solid Sphere

Efficiently controlling crystallization and magnetic properties of nanostructured Nd-Ce-Fe-B ribbons via electron beam exposure

Electron beam exposure (EBE) has been implemented to synthesize Nd-Ce-Fe-B-based nanostructured magnetic materials with controllable morphology and tunable magnetic properties. Greatly reduced crystallization time of amorphous ribbons to about 0.1 s is achieved, which is by far the most effective method due to the effect of an extremely high heating rate. The extremely high heating rate gives rise to a huge temperature gradient in the annealed ribbons leading to platelet-like grains due to the oriented nucleation and growth under quasi-static thermal stress. It was found that the size and shape of the grains can be finely controlled by the beam current intensity. A coercivity as high as 12.9 kOe, and a maximum energy product as high as 15.4 MGOe are obtained in pure (Nd0.8Ce0.2)12.2Fe81.6B6.2 ribbons exposed to a beam current of 0.4 mA, without doping any other heavy rare earth or coercivity enhancement elements. A single magnetic domain covering many grains was observed by the Lorentz transmission microscope (LTEM). It was found that the improvement of the magnetic performance has a deep correlation with the achievement of a single domain structure. Our results demonstrate that EBE shows great advantages in preparing the high coercivity Ce-substituted Nd2Fe14B magnets due to higher efficiency and higher controllability than conventional furnace annealing.

Formation of a Double-Layer Ultrafine Crystal Structure for High-Current Pulsed Electron Beam-Treated Al–20Si–5Mg Alloy

In this paper, the effect of high-current pulsed electron beam (HCPEB) on the microstructure refinement of an Al–20Si–5Mg alloy in the cross-section modified zone was studied, and a double-layer ultrafine crystal structure of the Al–20Si–5Mg alloy was formed. It was found that the cross-section modified zone was divided into three zones, namely, the remelted layer, the heat-affected zone, and the thermal stress wave-affected zone after HCPEB treatment. For the remelted layer, metastable structures were formed due to the rapid heating and cooling rates. For the heat-affected zone, the grain of the aluminum phase was refined due to the cooperative effects of shock wave (formed during an eruption event of the brittle phase), thermal-stress wave (formed during thermal expansion of the alloy surface), and quasi-static thermal stress (formed as a result of an unevenly distributed temperature gradient in the inner material) at high temperatures. For the thermal stress wave-affected zone, the grain refinement was not obvious due to the decreasing energy of the shock wave and the thermal-stress wave at low temperatures. In addition, firm evidence for the tracing of shock waves in the heat-affected zone was demonstrated for the first time and verified for the founding of the broken acicular eutectic silicon. Through this experiment, the mechanical properties of Al–20Si–5Mg alloy materials in both the remelted layer and heat-affected zone were significantly improved after HCPEB treatment.

The applicability of model order reduction based on proper orthogonal decomposition to problems in dynamic thermoelasticity with multiple subdomains

A robust proper orthogonal decomposition technique is applied to develop reduced-order models (ROMs) for time-dependent thermal stress problems that are arbitrarily discretized with multiple sub-domains to provide flexibility and generality in the sense that different spatial methods and different time integration algorithms can be employed in a single analysis. This approach enables large computational savings for model problems with either/both transient thermal and dynamic structural effects by reducing the degrees of freedom with minimal losses to accuracy. The method of snapshots is used to construct a reduced-order basis from a short training simulation of the full-order model (FOM) which selectively preserves only the relevant physical characteristics of the solution. The approach is described in detail for both first- and second-order ordinary differential equations and differential algebraic equations, such as arising from problems with multiple sub-domains, and the solution of the FOM and ROM by the state-of-the-art GSSSS framework of algorithms is described. Numerical examples in thermal transport, quasi-static thermal stresses, and thermally-induced vibrations for single domains and multiple domains via the finite element method (other methods within each sub-domain can also be integrated with FEM but are not discussed here) illustrate the robustness and utility of the proposed methodology.

A unified computational methodology for dynamic thermoelasticity with multiple subdomains under the GSSSS framework involving differential algebraic equation systems

A novel and general computational methodology for thermal stress problems with multiple subdomains is presented under the unified generalized single-step single-solve (GSSSS) framework for first- and second-order differential algebraic equations. It enables arbitrary number of subdomains and the coupling of different but compatible time-stepping algorithms ensuring second-order time accuracy in all differential and algebraic variables. The framework permits implicit/explicit coupling and subcycling; however, only selected coupling of algorithms in different subdomains is focused upon. Numerical examples encompassing transient heat conduction with quasi-static thermal stresses, and thermally-induced vibrations are illustrated.

Analytical model for investigation of the effect of friction power on the thermal stresses in friction elements of brakes

The influence of the change with time of friction power on thermal stresses in a friction element of a brake system is investigated. For this purpose, a list of ten different temporal profiles of specific friction power is used, which has been experimentally established for a single braking process. The corresponding profiles of transient temperature fields in the considered element are applied as input parameters to find quasi-static thermal stresses. Numerical analysis concerned with spatio-temporal distributions of the stresses and their evolutions on the heated surface is presented.

Frictional heating of the brake disc with essential nonlinearity thermal barrier coating

A mathematical model to investigate temperature field distributions in a brake disc with thermal barrier coating (TBC) was proposed. For this purpose, a one-dimensional boundary-value heat conduction problem was formulated for the coating (TBC) - substrate (disc) system. It was assumed that the materials of both the coating and the substrate are thermally sensitive and characterized by essential thermal nonlinearity. The surface of the coating was heated by a heat flux with intensity proportional to the friction power during single braking. Thermal contact between the coating and substrate is perfect. The solution to the problem was obtained by means of an integro-interpolation variant of the method of lines and the DIFSUB package for numerical solving of systems of ordinary differential equations. Quasi-static thermal stresses in the strip with taking into account change in temperature mechanical properties, were determined, too. Numerical analysis was conducted for a coating made from Yttria-Stabilized Zirconium ZrO2–3Y2O3 (YSZ) deposited on an AISI 1040 steel disc.

Quasi-Static Transient Thermal Stresses in an Elliptical Plate due to Sectional Heat Supply on the Curved Surfaces over the Upper Face

This paper is an attempt to determine quasi-static thermal stresses in a thin elliptical plate which is subjected to transient temperature on the top face with zero temperature on the lower face and the homogeneous boundary condition of the third kind on the fixed elliptical curved surface. The solution to conductivity equation is elucidated by employing a classical method. The solution of stress components is achieved by using Goodier’s and Airy’s potential function involving the Mathieu and modified functions and their derivatives. The obtained numerical results are accurate enough for practical purposes, better understanding of the underlying elliptic object, and better estimates of the thermal effect on the thermoelastic problem. The conclusions emphasize the importance of better understanding of the underlying elliptic structure, improved understanding of its relationship to circular object profile, and better estimates of the thermal effect on the thermoelastic problem.

Influence of thermal sensitivity of the materials on temperature and thermal stresses of the brake disc with thermal barrier coating

The time-dependent frictional heating of a disc with applied thermal barrier coating (TBC) on its working surface was investigated. To determine the temperature fields in the coating and the disc a one-dimensional friction heat problem during braking was formulated, with taking into account the dependence of thermal properties of materials from temperature. A model was adopted for materials with a simple non-linearity, i.e. materials whose thermal conductivity and specific heat are temperature dependent, and their ratio – thermal diffusivity is constant. The linearization of the corresponding boundary-value heat conduction problem was made by the Kirchhoff transformation and the linearizing multipliers method. A numerical-analytical solution to the obtained problem was found by Laplace transform method. Knowing the temperature distributions, quasi-static thermal stresses in the strip (TBC) with taking into account change in temperature mechanical properties, were determined. The distribution of temperature and thermal stresses in the strip made from ZrO2 deposited on the UNS G51400 steel disc, was investigated.

Finite element analysis of the 3-D thermal stress state in a brake disk

The quasi-static thermal stress state within the linear uncoupled elasticity is studied. The calculations were performed using the finite element method (MSC.Patran/MSC.Nastran). In order to examine smooth stress changes in a brake disk during braking, based on the temperature fields at particular time steps, additionally the script using Python programming language was developed. The numerical three-dimensional FE model of the brake disk for calculation of the transient temperature field was adopted from the previous author’s study. A single braking process at linear deceleration and constant contact pressure was simulated. The evolutions and the contours of the components of the stress tensor as well as the equivalent Huber-Mises stress were examined. The most important aspects of the stress state during braking were discussed.

Quasi-static thermal stresses due to a concentrated moving heat source in a thin plate

Temperature and thermal stress distributions in a two-dimensional infinite thin plate subjected to a moving heat source with variable power and velocity are obtained by solving quasi-static thermoelasticity equations analytically with the aid of a thermoelastic displacement potential. The results show good agreement with experimental data for a stationary source with constant power and with a steady-state analytical solution in the open literature. It is shown that the quasi-static solution can predict changes of the thermal stress field during the movement of the heat source, and can give the effect of changes of power and velocity of the heat source on the thermal stress field during its movement.

Microstructural Modification of Brush-Plated Nanocrystalline Cr by High Current Pulsed Electron Beam Irradiation

Cr layer was fabricated on 40Cr steel by electric brush plating process and then treated by high current pulsed electron beam irradiation technique. Surface microstructures of specimens before and after the irradiation were investigated. Results show that Cr surface is composed of uniformly distributed small nodule units which are composed of fine Cr particles smaller than 100nm. After high current pulsed electron beam treatment, many cracks are found on surface. The main reason is possibly due to the quasi-static thermal stresses accumulated along the surface of the specimens during the electron beam treatment. The surface grain grow from Cr particles because of heating by electron beam, and their size is less than 200nm.

Surface modification of Cu–25Cr alloy induced by high current pulsed electron beam

A Cu–25Cr alloy prepared by vacuum induction melting method was treated by the high current pulsed electron beam (HCPEB) with pulse numbers ranging from 1 to 100. Surface morphologies and microstructures of the alloy before and after the treatment were investigated by scanning electron microscopy and X-ray diffraction. The results show that significant surface modification can be induced by HCPEB with the pulse number reaching 10. Craters with typical morphologies on the Cu–25Cr alloy surface are formed due to the dynamic thermal field induced by the HCPEB. Micro-cracks, as a unique feature, are well revealed in the irradiated Cu–25Cr specimens and attributed to quasi-static thermal stresses accumulated along the specimen surface. The amount of cracks is found to increase with the pulse number and a preference of these cracks to Cr phases rather than Cu phases is also noted. Another characteristic produced by the HCPEB is the fine Cr spheroids, which are determined to be due to occurrence of liquid phase separation in the Cu–25Cr alloy. In addition, an examination on surface roughness of all specimens reveals that more pulses will produce a roughened surface, as a result of compromising the above features.

Evolution of surface microstructure of Cu-50Cr alloy treated by high current pulsed electron beam

A Cu-50Cr alloy was treated by the high current pulsed electron beam (HCPEB) at 20 and 30 keV with pulse numbers ranging from 1 to 100. Surface morphologies and microstructures of specimens before and after the treatments were investigated by employing scanning electron microscopy and X-ray diffraction. Results show that the HCPEB technique is able to induce remarkable surface modifications for the Cu-50Cr alloy. Cracks in Cr phases appear even after one-pulse treatment and their density always increases with the pulse number. Formation reason for these cracks is attributed to quasi-static thermal stresses accumulated along the specimen surface. Craters with typical morphologies are formed due to the dynamic thermal field induced by the HCPEB and they are found to prefer the sites near cracks or boundaries between neighboring Cr phases. Another microstructural characteristic produced by the HCPEB is the fine Cr spheroids, which are determined to be due to occurrence of liquid phase separation in the Cu-50Cr alloy. Finally, a general microstructural evolution profile that incorporates various HCPEB-induced surface features is tentatively outlined.

Study on Unsteady Temperature Field of Diesel Engine Piston

The paper took the piston of 620 single-cylinder engine as an example,a finite element model of piston was built with the help of ANSYS software. Than to calculate temperature field and and quick cold start conditions respectively[1]. Through the periodic transient thermal analysis, temperature fluctuations on the surface of the piston were derived, which indicated that the surface contacted with gas was the main temperature fluctuation area. The max temperature fluctuation can be up to 20 ° C and the wild fluctuation occurred in a distance of 2 mm from the surface of the piston. Temperatures of the piston went up according to exponential rule during the course of quick cold start, Extreme temperature fluctuations will generate huge quasi-static thermal stress.

Quasistatic thermal stresses in a thermosensitive layer under convective heat exchange with media of time-varying temperature

We have tested the method of linearizing parameters for the determination of temperature fields in thermosensitive structural elements by the example of the determination of a temperature field in a thermosensitive layer through the surfaces of which convective heat exchange with an environment of timevarying temperature occurs. The components of the stress-strain state caused by the found temperature distribution have been determined and investigated.

Thermal stresses induced by a point heat source in a circular plate by quasi-static approach

The present paper deals with the determination of quasi-static thermal stresses due to an instantaneous point heat source of strength gpi situated at certain circle along the radial direction of the circular plate and releasing its heat spontaneously at time t = τ. A circular plate is considered having arbitrary initial temperature and subjected to time dependent heat flux at the fixed circular boundary of r = b. The governing heat conduction equation is solved by using the integral transform method, and results are obtained in series form in terms of Bessel functions. The mathematical model has been constructed for copper material and the thermal stresses are discussed graphically.

Mechanisms of hardening, wear and corrosion improvement of 316 L stainless steel by low energy high current pulsed electron beam surface treatment

The mechanisms of corrosion and wear improvements by low energy high current pulsed electron beam (LEHCPEB) have been investigated for an AISI 316 L steel. Selective purification followed by epitaxial growth occurred in the top surface melted layer (2–3 μm thick) that was softened by tensile stresses and, to a much lower extent, by lower efficiency of MnS precipitation hardening. Electrochemical impedance spectroscopy and potentiodynamic polarization analyses used to model the corrosion behavior revealed that, while craters initiated at MnS inclusions initially served as pitting sites, the resistance was increased by 3 orders of magnitude after sufficient number of pulses by the formation of a homogeneous covering layer. The wear resistance was effectively improved by sub-surface (over 100 μm) work hardening associated with the combine effect of the quasi-static thermal stress and the thermal stress waves. The overall results demonstrate the potential of the LEHCPEB technique for improving concomitantly the corrosion and wear performances of metallic materials.

QUASI-STATIC THERMOELASTIC PROBLEM OF AN INFINITELY LONG CIRCULAR CYLINDER

The aim of this work is to determine the quasi-static thermal stresses of an in- finitely long circular cylinder having constant initial temperature under steady-state field. The arbitrary heat flux is applied on the lower surface and the upper surface of the cylinder is at initial temperature. The fixed circular edge is thermally insulated. The results are obtained in series form in terms of Bessel's functions. These have been computed numerically and illus- trated graphically.