Thermal Stresses and Cracks During the Growth of Large-sized Sapphire with SAPMAC Method

The finite-element method has been used to study the thermal stress distribution in large-sized sapphire crystals grown with the sapphire growth technique with micro-pulling and shoulder-expanding at cooled center （SAPMAC） method. A critical defect model has been established to explain the growth and propagation of cracks during the sapphire growing process. It is demonstrated that the stress field depends on the growth rate, the ambient temperature and the crystallizing direction. High stresses always exist near the growth interfaces, at the shoulder-expanding locations, the tailing locations and the sites where the diameters undergo sharp changes. The maximum stresses always occur at the interface of seeds and crystals. Cracks often form in the critical defect region and spread in the m-planes and a-planes under applied tensile stresses during crystal growth. The experimental results have verified that with the improved system of crystal growth and well-controlled techniques, the large-sized sapphire crystals of high quality can be grown due to absence of cracks.

Stochastic transient analysis of thermal stresses in solids by explicit time-domain method

Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years.The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses.Therefore,it is reasonable to consider the variability of thermal environments while conducting thermal analysis.However,for ambient thermal excitations,only stationary random processes have been investigated thus far.In this study,the highly efficient explicit time-domain method(ETDM)is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems.The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body.Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses.A numerical example involving non-stationary stochastic internal heat generation rate is investigated.The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.

A MIXED METHOD OF DETERMINING THETHERMAL STRESS FOR COLD ROLLER

A mixed method which combines the recent developed finite analytical method and the boundary fitting coordinate transformation method was used first to calculate the temperature field and thermal stress field of the cold roller in this paper. The following results are obtained by the calculation: thermal stresses σr=0, σθ=σz are maximum tension stress on the inner surface of the cold roller and σr=0, |σθ|=|σz| are maximum compression stress on the outer surface of the cold roller in the steady and unsteady case. Effectiveness and validity of the mixed method are checked with steady coil roller problems having theoretical solutions. The results show that good agreement is achived between the calculated value and theoretical solution,and the mixed method used in the paper is very workable. The mixed method is also useful in solving the steady and unsteady thermal stress field proplems of the hot -rolled for the reversing rolling mill and the continous rolling mill.

Techniques for improving computational speed in numerical simulation of casting thermal stress based on finite difference method

Finite difference method (FDM) was applied to simulate thermal stress recently, which normally needs a long computational time and big computer storage. This study presents two techniques for improving computational speed in numerical simulation of casting thermal stress based on FDM, one for handling of nonconstant material properties and the other for dealing with the various coefficients in discretization equations. The use of the two techniques has been discussed and an application in wave-guide casting is given. The results show that the computational speed is almost tripled and the computer storage needed is reduced nearly half compared with those of the original method without the new technologies. The stress results for the casting domain obtained by both methods that set the temperature steps to 0.1 ℃ and 10 ℃, respectively are nearly the same and in good agreement with actual casting situation. It can be concluded that both handling the material properties as an assumption of stepwise profile and eliminating the repeated calculation are reliable and effective to improve computational speed, and applicable in heat transfer and fluid flow simulation.

Thermal stress analysis method considering geometric effect of risers in sand mold casting process

Solidif ication and f luid f low analysis using computer simulation is a current common practice. There is also a high demand for thermal stress analysis in the casting process because casting engineers want to control the defects related to thermal stresses, such as large deformation and crack generation during casting. The riser system is an essential part of preventing the shrinkage defects in the casting process, and it has a great inf luence on thermal phenomena. The analysis domain is dramatically expanded by attaching the riser system to a casting product due to its large volume, and it makes FEM mesh generation diff icult. However, it is diff icult to study and solve the above proposed problem caused by riser system using traditional analysis methods which use single numerical method such as FEM or FDM. In this paper, some research information is presented on the effects of the riser system on thermal stress analysis using a FDM/FEM hybrid method in the casting process simulation. The results show the optimal conditions for stress analysis of the riser model in order to save computation time and memory resources.

Numerical Simulation of Temperature Field and Thermal Stress Field of Work Roll During Hot Strip Rolling

Based on the thermal conduction equations, the three-dimensional （3D） temperature field of a work roll was investigated using finite element method （FEM）. The variations in the surface temperature of the work roll during hot strip rolling were described, and the thermal stress field of the work roll was also analyzed. The results showed that the highest roll surface temperature is 593 ℃, and the difference between the minimum and maximum values of thermal stress of the work roll surface is 145.7 MPa. Furthermore, the results of this analysis indicate that temperature and thermal stress are useful parameters for the investigation of roll thermal fatigue and also for improving the quality of strip during rolling.

Dynamic thermal stress distribution in surface of two-dimensional cavity

Although we have had the problem of dynamic thermal stress distribution solved in the surface of a cavity in some special shapes, a general solution to this problem for an arbitrary shaped cavity was still not obtained. Using the complex function method, the present paper analyzed the dynamic thermal stress distribution in the surface of an arbitrary shaped cavity subjected to a steady temperature field. Actually, not only is a general solution of this problem represented by Hankle function obtained for an arbitrary shaped cavity, but also a process to calculate the coefficient of the dynamic thermal stress distribution in the surface of an arbitrary shaped cavity is derived. For illustration, some numerical results of a circular cavity, an elliptic cavity, a lining horseshoe cavity and a square cavity are given.

Calculation of Thermal Stress and Fatigue Life of 1000 MW Steam Turbine Rotor

The paper calculated the temperature and stress fields of 1000 MW ultra-supercritical steam turbine rotors which start in cold condition using the finite element calculation program (ANSYS). After getting rotor stress field, the paper use the general slope method to estimate the low cycle fatigue life loss, the rest of the conditions can be calculated in this method.

Thermal residual stresses and stress distributions under tensile and compressive loadings of short fiber reinforced metal matrix composites

The thermal residual stresses and the stress distributions of short fiber reinforced metal matrix composite under tensile and compressive loadings were studied using large strain axisymmetric elasto plastic finite element method. It is demonstrated that the thermal residual stresses can result in asymmetrical stress distributions and matrix plasticity. The thermal residual stresses decrease the stress transfer in tension and enhance the stress transfer in compression. The fiber volume fraction has more important effects on the thermal residual stresses and the stress distributions under tensile and compressive loadings than the fiber aspect ratio and the fiber end distance. [

THERMAL STRESS MEASUREMENT OF QUARTZ OSCILLATOR MODULE PACKAGING

The thermal stress of the quartz oscillator module packaging isinvestigated using digital-im- age correlation method (DICM), and theexperimental results are given. Under the quartz oscillator modulepackaging, the quartz oscillator and the Fe-Sn-Cu alloy frame arejoined together with the electroconductive adhesive (PI), and theelectroconductive adhesive needs to be cured twice at 150 deg. C and275 deg. C respective- ly.

ANALYSIS OF THERMAL-ELASTIC STRESS OF WHEEL-RAIL IN ROLLING-SLIDING CONTACT

A coupling thermo-mechanical model of wheel/rail in rolling-sliding contact is put forward using finite element method. The normal contact pressure is idealized as the Hertzian distribution, and the tangential force presented by Carter is used. In order to obtain thermal-elastic stress, the ther-mal-elastic plane stress problem is transformed to an elastic plane stress problem with equivalent fictitious thermal body force and fictitious boundary distributed force. The temperature rise and ther-mal-elastic stress of wheel and rail in rolling-sliding are analyzed. The non-steady state heat transfer between the contact surfaces of wheel and rail, heat-convection and radiation between the wheel/rail and the ambient are taken into consideration. The influences of the wheel rolling speed and wear rate on friction temperature and thermal-elastic stress are investigated. The results show the following： ① For rolling-sliding case, the thermal stress in the thin layer near the contact patch due to the friction temperature rise is severe. The higher rolling speed leads to the lower friction temperature rise and thermal stress in the wheel; ② For sliding case, the friction temperature and thermal stress of the wheel rise quickly in the initial sliding stage, and then get into a steady state gradually. The expansion of the contact patch, due to material wear, can affect the friction temperature rise and the thermal stress during wear process. The higher wear rate generates lower stress. The results can help under-stand the influence of friction temperature and thermal-elastic stress on wheel and rail damage.

Residual stress evolution regularity in thermal barrier coatings under thermal shock loading

Residual stress evolution regularity in thermal barrier ceramic coatings （TBCs） under different cycles of thermal shock loading of 1 100℃ was investi- gated by the microscopic digital image correlation （DIC） and micro-Raman spec- troscopy, respectively. The obtained results showed that, as the cycle number of the thermal shock loading increases, the evolution of the residual stress under- goes three distinct stages： a sharp increase, a gradual change, and a reduction. The extension stress near the TBC surface is fast transformed to compressive one through just one thermal cycle. After different thermal shock cycles with peak temperature of 1 100℃, phase transformation in TBC does not happen, whereas the generation, development, evolution of the thermally grown oxide （TGO） layer and micro-cracks are the main reasons causing the evolution regularity of the residual stress.

Effect of fiber distribution on residual thermal stress in titanium matrix composite

Residual thermal stresses (RTS) of SCS-6 SiC/Ti-24Al-11Nb composite were analyzed by using finite element method (FEM). Three models of fiber array in the composite and the effect of fiber distance on the RTS were discussed. In all the three models compressive stress was found in the radial direction and tensile stress in the tangential direction. It is pointed out that, in real composite system, hexagonal fiber geometry is superior because the distribution and the magnitude of the residual stress are similar to those in single fiber model. In square fiber geometry, it is easier to make the matrix crack due to the larger residual tangential stress. RTS becomes very large and changes violently when the fiber distance is less than 15 μm or so, therefore too high fiber volume is apt to result in matrix crack.

Finite Element Analysis on Thermal Stress of SEN

Thermal stress of SEN was studied by using finit element analysis（ FEA）. The results disclose：（ 1） fo the tapered zone of SEN,the thermal stress reaches it peak after casting for about 30 s,at this moment,th axial stress is the largest,the circumferential stress come the second and the radial stress is the smallest;（ 2）when SEN suffers the thermal stress,the inner wall suf fers the pressure stress,and the shorter the distance from the inner wall is,the larger the pressure stress is; th outer wall suffers the tensile stress and the shorter the dis tance from the outer wall is,the larger the tensile stres is; the axial stress holds a dominant position in the ta pered zone,while the circumferential stress takes the lead in the cylindrical zone;（ 3） as angle α of SEN’s taper ed zone increases, the thermal stress grows obviousl when α is larger than 110°; while the thermal stress re duces obviously,when α is larger than 140°; thus,fo SEN design,it is essential to avoid the interval of α =110°- 140°.

An analytical model of thermal mechanical stress induced by through silicon via

We present an accurate through silicon via （TSV） thermal mechanical stress analytical model which is verified by using finite element method （FEM）. The results show only a very small error. By using the proposed analytical model, we also study the impacts of the TSV radius size, the thickness, the material of Cu diffusion barrier, and liner on the stress. It is found that the liner can absorb the stress effectively induced by coefficient of thermal expansion mismatch. The stress decreases with the increase of liner thickness. Benzocyclobutene （BCB） as a liner material is better than SiO2. However, the Cu diffusion barrier has little effect on the stress. The stress with a smaller TSV has a smaller value. Based on the analytical model, we explore and validate the linear superposition principle of stress tensors and demonstrate the accuracy of this method against detailed FEM simulations. The analytic solutions of stress of two TSVs and three TSVs have high precision against the finite element result.

Thermal stress and fracture temperature prediction for flexible pavement

Analytical solutions of thermal stresses in multilayered elastic system whose materials characteristics are dependent on temperature are derived by a transfer matrix and integral transformation method.The resulting formulation is used to calculate thermal stresses in the low temperature cracking problem of asphalt pavement.Numerical simulations and analyses are performed using different structural combinations and material characteristics of base course.And fracture temperatures are predicted for a given flexible pavement constructed with three types of asphalt mixtures based on the calculated results and experimental data.This approach serves as a better model for real pavement structure as it takes into account the relationships between the material characteristics and temperature in the pavement system.

Experimental research on the residual stress of polycrystalline diamond compacts for oil drilling

Practical experiences gained in the past several years show that the thermal residual stress(TRS) is a main cause leading polycrystalline diamond compacts(PDC) to premature failure.It is the very important to measure the TRS accurately for optimizing the interface and improving the service performance of PDC.In this paper,the TRS in 1913 flat-interface PDC was measured using improved stress-release method(ISRM). The TRS on the surface of polycrystalline diamond(PCD) table was obtained,which can be used to calculate the radial thermal residual stress(RTRS) at the interface of PCD table via a refutation process.The obtained results show that there are compressive residual stress at the PCD table interface and in the most region of PCD table surface.The exception occurs near the outer diameter of the PCD table,where the PDC begins to bend and put the PCD table surface into a tension state,an undesirable state for a brittle material.The ISRM has covered the shortage existing in traditional stress-release method,in which only finite points on the surface of PCD table can be tested for one specimen and one time.Simple as the experimental procedures are,the test results are also very accurate and reliable.This method provides the theoretical and experimental basis for testing TRS of PDC accurately.

MD simulation of a copper rod under thermal shock

In this paper, thermoelastic problem of onedimensional copper rod under thermal shock is simulated using molecular dynamics method by adopting embedded atom method potential. The rod is on axis x, the left outermost surface of which is traction free and the right outermost surface is fixed. Free boundary condition is imposed on the outermost surfaces in direction y and z. The left and right ends of the rod are subjected to hot and cold baths, respectively. Temperature, displacement and stress distributions are obtained along the rod at different moments, which are shown to be limited in the mobile region, indicating that the heat propagation speed is limited rather than infinite. This is consistent with the prediction given by generalized thermoelastic theory. From simulation results we find that the speed of heat conduction is the same as the speed of thermal stress wave. In the present paper, the simulations are conducted using the large-scale atomic/molecular massively parallel simulator and completed visualization software.

Investigation of temperature effect on stress of flexspline

The effect of temperature loading on the stress of a flexspline is investigated. Based on the geometric and mechanical characteristics of the harmonic gear flexspline, a circular thin shell model is presented in this paper. The theoretical solution for the flexspline under different displacement loads and different temperature fields is derived. Meanwhile, an impact factor formula, which reflects the effect of the temperatures of the inner and outer surfaces of the flexspline on the stress of the flexspline, is presented. Finally, numerical calculations by the finite element method （FEM） are adopted to verify the corresponding conclusions.

Adaptive nodeless variable finite elements with flux-based formulation for thermal-structural analysis

A nodeless variable element method with the fluxbased formulation is developed to analyze two-dimensional thermal-structural problems. The nodeless variable formula- tion provides accurate temperature distributions to yield more accurate thermal stress solutions. The flux-based formulation is used to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element meshes that can adapt and move along with the transient solution behavior. A version of a nearly optimal element size determination is proposed to provide high convergence rate of the predicted solutions. The combined procedure is evaluated by solving several thermal, structural, and thermal stress problems.