Thermoelastic effect

Let us consider an isotropic material whose temperature uniformly rises owing to external causes, for example heating, or the dissipation of energy produced in the body by the deformation. The cubic dilatation taking place in the material because of the effect of the change in temperature is given by 

The dilatation of the system in isothermal conditions obtained from Eq. (4.124) is given by 

By assuming superposition of effects, the dilatation of the system caused by both the stress applied on it and a change of temperature AT is 

Note that by using the relationships given between E and v and K and G indicated in Table 4.1, Eq. (4.129) also can be written as 

---

The SPATE technique is based on measurement of the thermoelastic effect. Within the elastic range, a body subjected to tensile or compressive stresses experiences a reversible conversion between mechanical and thermal energy. Provided adiabatic conditions are maintained, the relationship between the reversible temperature change and the corresponding change in the sum of the principal stresses is linear and indipendent of the load frequency. 

Most, if not all, microwave biological effects and potential medical appHcations are beheved to be the result of heating, ie, thermal effects. The phenomenon of microwave hearing, ie, the hearing of clicking sounds when exposed to an intense radar-like pulse, is generally beheved to be a thermoelastic effect (161). Excellent reviews of the field of microwave bioeffects are available (162,163). 

Thermoelastic Effect A mechanical phenomenon that involves the thermal expansion coefficient is the thermoelastic effect, in which a material is heated or cooled due to mechanical deformation. The thermoelastic effect is represented by the following relation ... 

The contribution of the thermoelastic effect to energy dissipation in solids under transient or cyclic deformation was first studied by Zener and shown to account for mechanical relaxation peaks in some metals. 

The general theory of thermoelasticity is well documented in the took by Nowacki43 which also gives solutions for some physical problems. In particular those for the quasistatic case in which inertia effects can be neglected are derived from the work of Biot. However, there does not appear to be any experimental work on the relation of internal friction to the thermoelastic effect other than that on metals (Zener42, Nowick and Berry44 ). 

In our own recent low temperature studies45 of ultra high drawn polyethylene, a change in the background level of tan 6 in tensile tests when the environmental gas is changed, is attributed to thermoelastic effects resulting from the different heat transfer characteristics of the gases used. 

As a first incursion into the thermomechanical analysis of the problem, we present recent results [57] in which only thermoplastic effects are accounted for. The related temperature variations appear larger than those from thermoelastic effects, and are expected to be of major importance in the competition between shear yielding and crazing. The influence of thermoelastic effects will be briefly discussed at the end of this section. 

The thermoelastic effect is the temperature change that results from stretching an elastic material or fiber. The work done on the material is aiven bv... 

FIGURE 18.10a Thermoelastic effects during directional solidification of a pure material showing (a) the physical system. 

FIGURE 18.10 (Continued) Thermoelastic effects during directional solidification of a pure material showing (b) perturbation in the metal-mold contact pressure versus time for different , and (c) perturbation of the solidification front for different sensitivities of the contact resistance to the contact pressure [56,57]. 

With respect to localized corrosion, various experiments with focused laser light were carried out. They show that the passive film may be destroyed by a laser pulse. The mechanism of destruction depends on the band gap of the oxide and the photon energy. In case of hv < g, photons generate a thermoelastic effect at the... 

FIGURE 47.10 Contributions of several relaxation mechanisms to the loss tangent of cortical bone, (a) Homogeneous thermoelastic effect, (b) Inhomogeneous thermoelastic effect, (c) Fluid flow effect, (d) Piezoelectric effect [Lakes and Katz, 1984]. (Courtesy CRC Press)... 

In many materials, the mechanical response can show both elastic and viscous types of behavior the combination is known as viscoelasticity. In elastic solids, the strain and stress are considered to occur simultaneously, whereas viscosity leads to time-dependent strain effects. Viscoelastic effects are exhibited in many different forms and for a variety of structural reasons. For example, the thermoelastic effect was shown earlier to give rise to a delayed strain, though recovery of the strain was complete on unloading. This delayed elasticity is termed anelastic-ity and can result from various time-dependent mechanisms (internal friction). Figure 5.9 shows an example of the behavior that occurs for a material that has a combination of elastic and anelastic behavior. The material is subjected to a constant stress for a time, t. The elastic strain occurs instantaneously but, then, an additional time-dependent strain appears. On unloading, the elastic strain is recovered immediately but the anelastic strain takes some time before it disappears. Viscoelasticity is also important in creep but, in this case, the time-dependent strain becomes permanent (Fig. 5.10). In other cases, a strain can be applied to a material and a viscous flow process allows stress relaxation (Fig. 5.11). 

The above equation describes the so-called thermoelastic effect . The amount of temperature change in a certain volume element depends on the change in the sum of the principal stresses, on its material factors and on the ambient temperature. For an isotropic material with a positive coefficient of thermal expansion, uniaxial tensile stresses lead to a decrease in temperature. 

C E Bakis and K L Reifsnider, The adiabatic thermoelastic effect in laminated fibre composites , J Compos Mater 1991 25 809-830. 

Modulated thermoreflectance and thermoelastic effect imaging have found important applications in the nondestructive inspection of semiconductors. 

Doust T.G., Parmar A. - Transient thermoelastic effects in a mechanical face seal , Proc. of the 14 International Conference on Fluid Sealing, BHRA, paper F4, pp. 407-422, Cannes, France. April 1987. 

Another thermoelastic effect that was mentioned earlier is the tendency of a rubber to become warm when stretched rapidly. This type of behaviour is illustrated in Fig. 5.19 for the adiabatic extension of a rubber. Some of the heating can be explained by crystallization which can also occur when a rubber is stretched (Section 4.4.5) but a temperature rise is found even in non-crystallizable rubbers. This can be explained by consideration of the thermodynamic equilibrium. The rise in temperature... 

---