Thermal Stress Relaxation Research Articles

Approximate method for solving relaxation problems in terms of material's damagability under creep

The technology of thermoforming under creep and superplasticity conditions is finding increasing application in machine building for producing articles of a preset shape. After a part is made there are residual stresses in it, which lead to its warping. To remove residual stresses, moulded articles are usually exposed to thermal fixation, i.e., the part is held in compressed state at a certain temperature. Thermal fixation is simply the process of residual stress relaxation, following by accumulation of total creep in the material. Therefore the necessity to develop engineering methods for calculating the time of thermal fixation and relaxation of residual stresses to a safe level, not resulting in warping, becomes evident. The authors present an approximate method of calculation of stress-strain rate of a body during relaxation. They use a system of equations which describes a material`s creep, simultaneously taking into account accumulation of damages in it.

Reactive melt infiltration of silicon-niobium alloys in microporous carbons

Studies of the reactive melt infiltration of silicon-niobium alloys in microporous carbon preforms prepared by the pyrolysis of a polymer precursor have been carried out using modeling, DTA, and melt infiltration. Mercury porosimetry results indicate a very narrow pore size distribution with virtually all the porosity within the carbon preforms open to infiltrants. The morphology and amount of the residual phases (niobium disilicide and silicon) in the infiltrated material can be tailored according to requirements by careful control of the properties (pore size and pore volume) of the porous carbon preforms and alloy composition. The average room temperature four-point fiexural strength of a reaction-formed silicon carbide material (made by the infiltration of medium pore size carbon preform with Si–5 at. % Nb alloy) is 290 ± 40 MPa (42 ± 6 ksi) and the fracture toughness is 3.7 ± 0.3 . The fiexural strength decreases at high temperatures due to relaxation of residual thermal stresses and the presence of free silicon in the material.

Thermoviscoelastic theory of freezing of stress and strain in a symmetrically cooled infinite glass plate

Abstract The Gardon and Narayanaswami theory of annealing and tempering of glass is rederived in a unifying way using the framework of the theory of thermoviscoelasticity. It is extended by including the effect of isothermal pressure relaxation in addition to the relaxation of shear stress. In the new theory, relaxation of shear stress, isotropic stress (pressure) and thermal stress, which causes thermal expansion, are treated on the same level. The thermal expansion coefficient, a frequency-dependent quantity like bulk and shear modulus, has high- and low-frequency limits identified with the thermal expansion coefficients of glass and liquid. The results of numerical calculation of stresses and strains in a symmetrically cooled infinite plate for the extended theory illustrate the decisive importance of the dispersion of the thermal expansion coefficient.

Piezospectroscopic Determination of Residual Stresses in Polycrystalline Alumina

The residual stresses created in polycrystalline aluminum oxide as a result of its constrained anisotropic thermal contraction are measured with the technique of piezospectroscopy using the fluorescence from trace Cr3+ impurities. The average residual stresses in the crystallographic a and c directions are determined as a function of grain size for a high‐purity alumina, as is the width of the stress distribution (assuming it to be Gaussian). Over the range of grain sizes investigated, from 2 to 16 μm, the residual stresses exhibit a dependence on grain size consistent with the prediction of the Evans‐Clarke model of thermal stress relaxation by grain boundary diffusion.

Line width Dependence of Stress Relaxation and Yield Behavior of Passivated Al(Cu) Lines

ABSTRACTStress relaxation behavior of thermally induced stresses in passivated line structures is strongly influenced by the metal yield strength. For some line geometries, stress relaxation can lead to void formation. In this study, bending beam measurements have been carried out to measure the thermal stress and stress relaxation behavior of passivated Al(l wt.% Cu) line structures with 3, 1, and 0.5 µm line widths. Our results reveal that stress relaxation in Al(Cu) films and lines shows log(time) kinetics consistent with a thermally activated dislocation glide mechanism. The kinetics of stress relaxation depend on line geometry and temperature, which can be explained by a combined effect of temperature (mass transport) and shear stress (driving force).

Thermal Stress Relaxation due to Plastic Flow in the Fiber Coating of a Continuous Fiber Reinforced Composite

An analytical solution is obtained for the elastic response of a three coax ial cylinder model of a composite to thermal and mechanical loading. Calculations of the thermal stresses for various fiber coatings reveal certain relationships between the coating stresses that make it possible to solve for the plastic flow of the coating. In the case of a high expansivity coating, the elastic solution indicates that the radial and hoop stresses are the extreme stresses which satisfy the conditions for Tresca flow in the r-θ plane. However, as the temperature changes, plastic flow is shown to relax the hoop stress to the extent that it becomes less than the axial stress which violates the condition for Tresca flow. In order to obtain solutions for plastic flow in the coating it is then necessary to consider plastic flow in more than a single plane. The Prandtl-Reuss flow rule can be used to solve for flow in three planes but because of the mathematical complexity it is necessary to use numeri cal techniques for the calculations. As an alternative, analytical solutions are developed for flow in two planes using an approximation for the Prandtl-Reuss flow. Three different solutions are obtained to include flow in the r-θ r-z, z-r z-θ, and θ-r θ-z planes. Each of these is applied for a different expansivity value of the fiber coating with various linear work hardening coefficients of the coating.

Measurement of thermal stress and stress relaxation in confined metal lines. I. Stresses during thermal cycling

A method based on the bending beam technique has been developed to measure the thermal stresses of fine lines confined by a dielectric layer. This method has been employed to determine the thermal stress of Al (2 at. % Cu) lines passivated by a SiO2 overlayer between room temperature and 400 °C. The effect of quartz confinement was analyzed by matching the thermal displacement at the metal/passivation interfaces and by imposing a mechanical equilibrium condition on the structure. The analysis enables us to deduce the triaxial stress components of metal and passivation from measurements of the substrate bending parallel and perpendicular to the length direction of the lines. Results of the measurements show a substantial stress enhancement as a result of the confinement, with the stress level significantly higher than that of a passivated blanket film. Parameters that influence the magnitude of the stress components are line geometry, layer deposition conditions, and the extent of plastic deformation during thermal cycling. Results of the measurements are consistent with those determined using x-ray techniques.

Measurement of thermal stress and stress relaxation in confined metal lines. II. Stress relaxation study

The bending beam technique and stress analysis developed for stress measurements of fine line structures have been applied to investigate stress relaxation in confined Al (2 at. % Cu) line structures on a Si substrate. The observed relaxation of the line structure is compared with corresponding unpassivated and passivated layered film structures. The overall behavior of all structure is similar, showing an initial plastic deformation, then a fast relaxation in sequence with a log(time) slow relaxation. The kinetics of these relaxation processes are found to decrease due to the presence of the passivation and a higher degree of dielectric layer confinement. In addition, the relaxation behavior of the principal stress components of the line structure is anisotropic and does not vary monotonically with the annealing temperature. The results are attributed to the relaxation mechanism and interaction at the metal/dielectric interface.

Creep-fatigue life prediction based on crack growth of 2.25CrMo steel castings: Kadoya, Y., Goto, T., Kaneko, H. and Sakon, T. J. Soc. Mater. Sci. Jpn May 1992 41, (464), 648–653 (in Japanes)

An experimental investigation was made on the effect of fatigue on the change of interface shear friction stress in SiC (SCS-6) fiber-reinforced Ti-15-3 composite. An unnotched composite was subjected to a tension-tension fatigue test (R = 0.1, f = 2 Hz) with applied stresses of 450 and 670 MPa. Thin specimen push-out and push-back tests were carried out for both pristine and fatigued composites to examine the change of interface shear friction stress. A change of morphology and roughness of the extracted fiber surface were observed by AFM. The surface roughness became smoother as the fatigue progressed while the shear frictional stress decreased. The number of cycles loaded and stress applied significantly affected the shear friction stress, respectively. Increasing the number of cyclic loading and applied stress, respectively, resulted in a reduction in the shear friction resistance. The dominant mechanisms for the reduction in interface shear friction stress were: (i) asperity wear of the SCS coating layer, and (ii) relaxation of radial residual thermal stress in the matrix. A model prediction was made incorporating both factors and the result explained the reduction of the interface shear friction stress by the fatigue test.

Thermal stress relaxation behavior in thin films under transient laser-pulse heating

Transient laser pulse has been used to generate nonsynchronous change of temperature rise and thermal expansion in thin films. The transient process of thermal expansion is recorded by a photoelectric high-speed acquisition system. By comparison of the calculated temperature rise and thermal expansion, thermal stress relaxation processes in Al films of 20–50 μm thickness is obtained. This result shows that, for transient heating, thermal stress exists even in the case of uniform temperature distribution and free expansion. And also there is a transient high stress in thin films under high-speed heating.

The effects of water fluid at temperatures up to 850°C and pressure of 300 MPa on porosity and permeability of amphibolite

Compressional wave velocities were measured in amphibolite under gas and water fluid pressure of 300 MPa and at temperatures up to 850°C. Fluid and confining pressures were equal during the experiments. The data obtained under water pressure differ from those for gas pressure by the reversion of the V p temperature trend: on heating under gas pressure V p decreases throughout the temperature range, whereas on heating under water pressure V p decreases at first, reaches a minimum value at approximately 650°C and then increases. A similar V p trend was determined for quenched samples. For initial and quenched amphibolite samples, porosity, permeability and pore size distribution were measured and the microstructure was examined. It was found that changes in the elastic properties of rock with temperature rise are determined by the transformation of its microstructure. The temperature trends of porosity and permeability are in negative correlation with the V p temperature trends. The increase of effective porosity is caused by initiation of new microcracks and the opening of pre-existing microcracks. The decrease of effective porosity is caused by the sealing of microcracks (mostly thin ones). Two types of processes are responsible for the transformation of pore structure: phase transitions within a narrow temperature range (the high-low quartz transition at T ≈ 650° C, P = 300 MPa, and the partial melting of amphibolite at T = 740–760° C, P = 300 MPa) and processes that take place throughout the temperature range. These latter processes are caused by thermal stress accumulation and relaxation. Under gas pressure, thermally induced microcracking leads to porosity increase and V p decrease. Under water pressure, the processes of microcrack generation and sealing develop simultaneously. At temperatures below 650°C the processes leading to microcrack generation and porosity increase prevail and, as a result, V p decreases. At temperatures over 650°C the processes leading to microcrack sealing and porosity decrease prevail, with a concomitant V p increase.

Relaxation of Thermal Stresses by Varying the Edge Shape of Ceramics-Metal Bonded Structure.

Relaxation of Thermal Stresses by Varying the Edge Shape of Ceramics-Metal Bonded Structure.

Fibre-matrix interphases and interfaces in ceramic matrix composites processed by CVI

The fibre-matrix (FM) interfacial zone plays a key role in the mechanical behaviour of Si-C(O)/SiC inverse composites fabricated by chemical vapour infiltration (CVI) from ex-polycarbosilane Si-C(O) fibres precoated with pyrocarbon or boron nitride. It consists not only of the C (or BN) main interphase, but also of very thin secondary interphases (i.e. carbon and silica) resulting from the decomposition of the metastable Si-C(O) fibres thought to occur during the fabrication of the fibres and/or the composites. The FM interfacial zone may play two complementary roles: (i) it provides low-energy microcrack propagation paths parallel to the fibre axis, and (ii) it may act as a compliant buffer for the relaxation of the residual thermal compression stresses on the interface. The FM bond strength is low or moderate when a quasi-continuous thin layer of anisotropic carbon is present between the fibre and the main interphase and when the fibre surface remains smooth. The mechanical behaviour in tension is non-b...

An FEM study of the plastic deformation process of whisker reinforced SiC/Al composites

The finite element method (FEM) was employed to investigate the matrix plastic flow in a whisker reinforced SiC/Al composite under external tensile load. It was found that the plastic zone induced by the plastic relaxation of thermal stresses expands under the external tensile load. The overall matrix plastic flow was characterized by the expansion and interconnection of the plastic zones around whiskers. This process can be divided into several characteristi stages, and related to the global stress-strain relationship. It also indicated that the strengthening was due mainly to the thermally induced matrix work hardening at the tip of the whisker. Finally, the initiation of plastic flow in an inhomogeneously reinforced composite was governed by the redistribution of the average stress and strength in the reinforcement clusters.

Use of quenching media with different cooling capacity in heat treating the grooved rolls of cold rolling pipe mills

The effect of quenching media with different cooling capacity on the quench hardness, hardenability, and the level of residual stresses in the grooved rolls of cold rolling pipe mills is studied. The cooling capacity of an oil spray, a 6% aqueous solution of potassium permanganate, a water spray, and a water-air mixture is determined. It is shown that with an increase in grooved roll weight the maximum cooling capacity of a water spray and a water-air mixture shifts into a higher temperature region. As a result of this, relaxation of thermal stresses which arise occurs at higher temperatures, and this leads to a reduction in residual stresses. It is established that the most suitable cooling medium in hardening grooved rolls is a water-air mixture.

The Influence of the Real Structure on the Deformations in Layer Systems

ABSTRACTThe relaxation of thermal stresses during the Czochralsky growth leads to frozen in deformations in the boules. These deformations lead to a nonintentional inhomogeneous miscut of the wafers. From the X-ray double crystal measurement of frozen in deformations in GaAs bulk crystals a nonintentional miscut of about 10−4 may be estimated. The measurement of the misorientation distribution over a LEC GaAs wafer yielded even higher inhomogeneities which are believed to be due to local curvature of the lcm2 samples. The relaxation of GaAs/AlAs Braggreflectors of 3μm overall thickness depends on the density of threading dislocations i.e. of the type of substrate (LEC or HB). The inhomogeneous strain field of misfit dislocations in InGaAs/GaAs multilayer systems and their inhomogeneous distribution leads to deformations in epitaxial layers limiting the dimensions of coherently scattering domains. The resulting mosaic spread in the epitaxial layer systems has been obtained using triple crystal measurements. The experimentally determined mosaic spread has to be taken into account to simulate the the diffraction pattern more correctly.

Thermal expansion and stress relaxation of metal-matrix composites

The coefficient of thermal expansion (CTE) of a series of Al-6%Si matrix samples, with reinforcements of carbon, SiC, Al 2O 3, or boron fibres, cloths, or ceramic particles was measured in the range 60°–220°C with a dilatometer. The anisotropy of the CTE was measured and found to be very large for specimens unidirectionally reinforced with carbon fibre. Relaxation of stresses due to the different thermal expansion of matrix and reinforcement was studied by using the bending of asymmetrically reinforced samples and the magnitude of the stresses evaluated using bending beam theory.

粉末冶金法による傾斜機能材料の開発

Powder Metallurgical (P/M) processing of thermal-stress relief type of functionally gradient materials (FGM) was reviewed on the basis of the work achieved by the authors' laboratory of Tohoku University. The role of thermal stress relaxation function in thermal barrier performance was emphasized. The processing routes of FGM were briefly summarized, in which the sintering balance for different mixing conditions of metals and ceramics and the fineness of compositional profile were mentioned. Spray deposition technique and differential temperature sintering have been developed of material species. The characteristic microstructural transition in a graded materials and the accompanying property transion were demonstrated. Two aspects in designing an optimum compositional profiles were described for the reduction of the thermal stress generated during processing ( during cooling from sintering temperature) and in a temperature gradient of thermal barrier situation. Two kinds of thermal loading tests were applied for the evaluation of thermal barrier performance of P/M FGM; a thermal shock test and a differential thermal loading test. The thermal stress conditions during the testing were discussed.

Thermal residual stress relaxation at surface of SiC/Al composite

Thermal residual stresses in the bulk and near the surface of a SiC/Al composite are calculated through the two-dimensional finite-element method (FEM). With regards to material constitutive relations, a thermal elastic-plastic isotropic material and isotropic thermal-elastic models are selected for Al and SiC, respectively. A close correlation in the thermal residual stress between FEM calculations and X-ray diffraction measurements is indicated, and the effect of thermal residual stress relaxation near the surface on bulk residual stresses in the composite is discussed. 9 refs.

State of the art of material design projects for severe service applications

An outline of research and development (R&D) projects to advanced materials under elevated-temperature conditions is reviewed. The paper describes a national research project on functionally gradient materials for relaxation of thermal stress and gives highlights of research concerning development of advanced materials for severe service applications. Included are composite materials, crystal structure controlled alloys and intermetallic compounds. Finally, a brief description of R&D projects on a ceramics gas turbine is given.