Stress-thermal coefficient

Here, Q are the elastic stiffness constants, are the thermal stress coefficients, and gkj and are the direct and converse piezoelectic stress coefficients, respectively. The superscript , on Pk, p k, and Xki indicates that these quantities are now defined under the conditions of constant strain. 

Concrete coefficient of thermal expansion affects the thermal stress significantly. Thus, for the calculation of concrete thermal stress, coefficient of thermal expansion is a key parameter. In the reference (Guanlin Shen, et al. 2006), a method to determine the equivalent coefficient of thermal expansion was proposed. Suppose that coefficients of thermal expansion of mortar and aggregate are known, the formula is... 

Thermal Stresses. When the wak of a cylindrical pressure vessel is subjected to a temperature gradient, every part expands in accordance with the thermal coefficient of linear expansion of the steel. Those parts of the cylinder at a lower temperature resist the expansion of those parts at a higher temperature, so setting up thermal stresses. To estimate the transient thermal stresses which arise during start-up or shutdown of continuous processes or as a result of process intermptions, it is necessary to know the temperature across the wak thickness as a function of radius and time. Techniques for evaluating transient thermal stresses are available (59) but here only steady-state thermal stresses are considered. The steady-state thermal stresses in the radial, tangential, and axial directions at a point sufficiently far away from the ends of the cylinder for there to be no end effects are as fokows ... 

Thermal Stresses and Properties. In general, ceramic reinforcements (fibers, whiskers, or particles) have a coefficient of thermal expansion greater than that of most metallic matrices. This means that when the composite is subjected to a temperature change, thermal stresses are generated in both components. 

Fig. 9. Residual stresses owing to thermal expansion mismatch between a particle with radius a and thermal expansion coefficient and a matrix with thermal expansion coefficient The stresses illustrated here are for and P is the interfacial pressure.

Values of thermal-expansion coefficients to be used in determining total displacement strains for computing the stress range are determined from Table 10-52 as the algebraic difference between the value at design maximum temperature and that at the design minimum temperature for the thermal cycle under analysis. 

The specific heats of polymers are large - typically 5 times more than those of metals when measured per kg. When measured per m, however, they are about the same because of the large differences in density. The coefficients of thermal expansion of polymers are enormous, 10 to 100 times larger than those of metals. This can lead to problems of thermal stress when polymers and metals are joined. And the thermal conductivities are small, 100 to 1000 times smaller than those of metals. This makes polymers attractive for thermal insulation, particularly when foamed. 

The restraint coefficient, K, in the thermal stress formula is very potent. It can be varied over a wider range than any of the other parameters. If a designer can build in flexibility, and thus substitute elastic deflection for plastic flow, he can achieve a major safety factor. 

Cathodoluminescence microscopy and spectroscopy techniques are powerful tools for analyzing the spatial uniformity of stresses in mismatched heterostructures, such as GaAs/Si and GaAs/InP. The stresses in such systems are due to the difference in thermal expansion coefficients between the epitaxial layer and the substrate. The presence of stress in the epitaxial layer leads to the modification of the band structure, and thus affects its electronic properties it also can cause the migration of dislocations, which may lead to the degradation of optoelectronic devices based on such mismatched heterostructures. This application employs low-temperature (preferably liquid-helium) CL microscopy and spectroscopy in conjunction with the known behavior of the optical transitions in the presence of stress to analyze the spatial uniformity of stress in GaAs epitaxial layers. This analysis can reveal,... 

By virtue of its chemical and thermal resistances, borosilicate glass has superior resistance to thermal stresses and shocks, and is used in the manufacture of a variety of items for process plants. Examples are pipe up to 60 cm in diameter and 300 cm long with wall tliicknesses of 2-10 mm, pipe fittings, valves, distillation column sections, spherical and cylindrical vessels up 400-liter capacity, centrifugal pumps with capacities up to 20,000 liters/hr, tubular heat exchangers with heat transfer areas up to 8 m, maximum working pressure up to 275 kN/m, and heat transfer coefficients of 270 kcal/hz/m C [48,49]. 

In both Equations (4.100) and (4.101), the six Oj are the coefficients of thermal deformation (expansion or contraction and distortion, I.e., shear), and AT is the temperature difference. In Equation (4.101), the terms CjjCXjAT are the thermal stresses if the total strain is zero. 

Figure 1. Thermal-expansion coefficients measured on cooling (300-77K and 4.2-2K) and heating (4.2-77K) along (OOl)e directions for In-26.5 at%Tl in the temperature range 2-3 OOK, with different external stress fields applied. (From reference 7)...

Under thermal cycling conditions, the principal source of stress within the oxide scale is the temperature change . Christl et have noted that, when cooling 2.25%Cr-l%Mo steel from 600°C in air, compressive stresses build up in the haematite, whilst tensile stresses build up in the magnetite and spinel layers. This arises because the thermal expansion coefficients of the individual oxide layers increase in the order a metal < a spinel < a magnetite < a haematite . ... 

Cyclic Oxidation In many industrial applications it is particularly important for the component to be resistant to thermal shock for example, resistance-heating wires or blading for gas turbines. Chromia, and especially alumina, scales that form on nickel-base alloys are prone to spalling when thermally cycled as a result of the stress build-up arising from the mismatch in the thermal expansion coefficients of the oxide and the alloy as well as that derived from the growth process. A very useful compilation of data on the cyclic oxidation of about 40 superalloys in the temperature range 1 000-1 I50°C has been made by Barrett et... 

When materials with different coefficients of linear thermal expansion (CLTE) are bolted, riveted, bonded, crimped, pressed, welded, or fastened together by any method that prevents relative movement between the products, there is the potential for thermal stress. Most plastics, such as the unfilled commodity TPs, may have ten times the expansion rates of many nonplastic materials. However there are plastics with practically no expansion. Details are reviewed in Chapter 2, THERMAL EXPANSION AND CONTRACTION. 

These technologies are very important since low-temperature structures experience large mechanical stresses due to temperature gradients and different thermal expansion coefficients of various materials. 

Fig. 18 Coefficient of fracture-resistance to thermal stress of several materials (Institute of Advanced Energy, Kyoto University, Japan Science and Technology Corporation)...

Polymer materials are frequently used under stress loadings and these may be concentrated at certain parts of the structure. Thermal stresses may be induced by non-uniform heating or by differential expansion coefficients the latter may be an important factor in the degradation of fibre-reinforced composites in the radiation environment of space. 

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