Subject linear thermal expansion

When the wall of a cylindrical pressure vessel is subjected to a temperature gradient, every part expands depending on the coefficient of linear thermal expansion of the steel. The parts at lower temperature impede the expansion of those parts with higher temperature, and induce additional thermal stresses. To estimate the transient thermal stresses which regularly appear e.g. during start-up or shut-down of process components or as well as a result of process interruptions and in the case of pulsating temperature conditions during operation. Informations about the temperature distribution across the vessel wall as a function of radius and time [12]... 

The composite material of Example 6.4 is subjected to a temperature rise of 100 K. Calculate its free thermal expansion in the direction inclined at 30° to the fibres. Take the coefficients of linear thermal expansion to be 5 X 10 K and 60 X 10" K for glass and epoxy, respectively. 

For linear thermal expansivity, a variety of other terms is in common use, including thermal expansion, coefficient of expansion, and coefficient of thermal expansion, among others. Frequently it is difficult to know whether linear or volume expansivity is the subject, even when units are given. To further complicate the picture, the temperature coefficient of specific volume is often referred to as thermal expansion or thermal expansion coefficient, although the units usually imply this distinction. 

MCLCPs absorb very low levels of moisture (typically less than 0 2% on immersion in water) and therefore the change in dimension of mouldings of MCLCPs due to moisture absorption is very low. The coefficients of linear thermal expansion of MCLCPs are much lower than those for conventional polymers (even when glass-fibre reinforced) and are comparable to those for metals, as shown in Fig. 8.20. This similarity in thermal expansion for metals and MCLCPs is expected to result in good component integrity and minimal strain when components containing metals (e.g. solder) and MCLCPs are in contact and are subjected to thermal cycling or shock. With conventional... 

Dimensional Stability. Plastics, ia general, are subject to dimensional change at elevated temperature. One important change is the expansion of plastics with increa sing temperature, a process that is also reversible. However, the coefficient of thermal expansion (GTE), measured according to ASTM E831, frequendy is not linear with temperature and may vary depending on the direction in which the sample is tested, that is, samples may not be isotropic (Eig. 7). 

Automated soldering operations can subject the mol ding to considerable heating, and adequate heat deflection characteristics ate an important property of the plastics that ate used. Flame retardants (qv) also ate often incorporated as additives. When service is to be in a humid environment, it is important that plastics having low moisture absorbance be used. Mol ding precision and dimensional stabiUty, which requites low linear coefficients of thermal expansion and high modulus values, ate key parameters in high density fine-pitch interconnect devices. 

In this example it has been assumed that the service temperature is 20 °C. If this is not the case, then curves for the appropriate temperature should be used. If these are not available then a linear extrapolation between temperatures which are available is usually sufficiently accurate for most purposes. If the beam in the above example had been built-in at both ends at 20 °C, and subjected to service conditions at some other temperature, then allowance would need to be made for the thermal strains set up in the beam. These could be obtained from a knowledge of the coefficient of thermal expansion of the beam material. This type of situation is illustrated later. 

A side effect of the use of a second phase with markedly different linear coefficients of thermal expansion (CTEs) is the residual stresses that are generated during cooling from the processing temperature. Residual stresses in composite materials, and how they impact mechanical properties, have become an increasingly important subject in materials research in recent years." As researchers continue to push materials closer to their property limits, it has become mote important to understand and control failure. Residual stresses are important because, vriien combined with applied stresses, they can lead to premature structural failure. Thus, the ability to limit residual stresses could improve the thermo-structural capabilities of a material. These stresses in multi-phase materials such as ZrB2-SiC, arise from the difference in the CTE of the phases (for ZrB2 CTE = 6.7 x lO" K for SiC CTE = 4.7x 10- K- ). 

We can show that the linear coefficient of thermal expansion is equal to one-third of the coefficient of thermal expansion. Subject a cubical object of length L to an infinitesimal change in temperature, dT. The new length of the object is... 

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