Change in coefficient of thermal expansion

The increased volume of a material with increasing temperature is a result of the same atomic vibration phenomenon which stores thermal energy. Consequently, changes in coefficient of thermal expansion generally parallel changes in heat capacity. Both increase rapidly at low temperature and approach nearly constant values above the Debye temperature (section 3.7). 

According to the Frenkel equation, the abrupt change in coefficient of thermal expansion Of which is associated with an increase in number of microvoids (free volume) upon heating of glass can be determined merely by the fraction fgi... 

If a transient temperature field exists in the saturated rock, the difference in coefficient of thermal expansion of the pore fluid and the rock matrix can induce changes in pore pressure and stresses. This can lead to thermal-induced pore fluid flow and deformation of the rock around the borehole. 

For a press-fit joint, the effect of thermal cycling, stress relaxation, and environmental conditioning must be carefully evaluated. Testing of the factory assembled parts under expected temperature cycles, or under any condition that can cause changes to the dimensions or modulus of the parts, is obviously indicated. Differences in coefficient of thermal expansion can result in reduced interference due either to one material shrinking or expanding away from the other, or it can cause thermal stresses as the temperature changes. 

Dissimilar materials can be joined, e.g., aluminum-to-paper, iron-to-copper. When two metals are bonded, the adhesive separates them and prevents corrosion. When the two adher-ends are markedly different in coefficient of thermal expansion, a flexible adhesive lessens the stress due to temperature change. Laminates of dissimilar materials can give combinations superior to either adhered alone for example, a polyethylene-cellophane composite has the heat-sealability and water-resistance of the former plus the grease-resistance and print-ability of the latter. 

There is a subtle difference between the vertical temperature sensitivity and the horizontal temperature sensitivity of a seismometer. The vertical output of a seismometer is only sensitive to bulk temperature changes the horizontal outputs are sensitive to differences in temperature across the surface of some part of the enclosure or differences in coefficient of thermal expansion combined with bulk changes in temperature. 

This table lists values of /3, the cubical coefficient of thermal expansion, taken from Essentials of Quantitative Analysis, by Benedetti-Pichler, and from various other sources. The value of /3 represents the relative increases in volume for a change in temperature of 1°C at temperatures in the vicinity of 25°C, and is equal to 3 a, where a is the linear coefficient of thermal expansion. Data are given for the types of glass from which volumetic apparatus is most commonly made, and also for some other materials which have been or may be used in the fabrication of apparatus employed in analytical work. 

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. 

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). 

Fig. 11. Neutron irradiation-induced changes in the coefficient of thermal expansion of GraphNOL N3M at irradiation temperatures of 600 and 875 C [61].

The change in shape of a material when it is subjected to a change in temperature is determined by the coefficient of thermal expansion, aj- Normally for isotropic materials the value of aj will be the same in all directions. For convenience this is often taken to be the case in plastics but one always needs... 

There are standard procedures for determining aj (e.g. ASTM 696) and typical values for plastics are given in Table 1.2. It may be observed that the coefficients of thermal expansion for plastics are higher than those for metals. Thus if 50 mm lengths of polypropylene and stainless steel are each heated up by 60°C the changes in length would be... 

The factors that cause a gear to mesh tightly are (1) tolerance on concentricity of shaft hole with pitch diameter, (2) tolerance on center distance, (3) tolerance on quality, (4) coefficient of thermal expansion, and (5) change in dimensions due to moisture absorption, which is a consideration/detriment in some materials. The first three apply to gears of any material. Item 4, and in some cases Item 5, for plastic gears deserves special consideration. 

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