Thermoelastic component

The overall residual stress in the film is equal to the sum of the thermoelastic component and intrinsic component. In the case of low deposition temperatures, the intrinsic stress is still the main contributing factor to the overall residual stress. In contrast, in the case of high deposition temperatures, the thermoelastic stress predominates. Therefore, while the signs of these stresses are identical, there is an intermediate deposition temperature for which the residual stress is minimised (Figure 2). 

Force-temperature ("thermoelastic") relations lead to a quantitative assessment of the relative amounts of entropic and energetic components of the elasticity of the network. 

Shen 391 has considered the thermoelastic behaviour of the materials described by the Mooney-Rivlin equation and has shown that the energetic component is given... 

Kilian 103) has used the van der Waals approach for treating the thermoelastic results on bimodal networks. He came to a conclusion that thermoelasticity of bimodal networks could satisfactorily be described adopting the thermomechanical autonomy of the rubbery matrix and the rigid short segments. The decrease of fu/f was supposed to be related to the dependence of the total thermal expansion coefficient on extension of the rigid short segment component. He has also emphasized that calorimetric energy balance measurements are necessary for a direct proof of the proposed hypothesis. 

Using poly(oxytetramethylene)glycol as diol component, the subsequent polymerization of styrene led to a thermoplastic elastomer with properties similar to commercial thermoelastics . 

For most particulate composites the mismatch between the particles and the matrix is more important than the anisotropy of either component (though alumina/aluminium titanate composites provide a notable exception and are described below). The main features of the stresses can therefore be understood in terms of a simple elastic model assuming thermoelastic isotropy and consisting of a spherical particle in a concentric spherical shell of matrix with dimensions chosen to give the appropriate volume fractions. The particles are predicted to be under a uniform hydrostatic stress, ap after cooling. If the particles have a larger thermal expansion coefficient than the matrix, this stress is tensile, and vice versa. For small particle volume fractions the stress... 

Leaving aside the special case of epitaxial stresses resulting from parameter differences between two monocrystalUne media, the residual stresses in a film/substrate system have two components, one thermoelastic and the other intrinsic. 

The effect of different types of interlayer on thermoelastic residual stresses can be analyzed from finite-element calculations for a two-dimensional geometry, assuming perfect adherence and without taking into account any reactivity between the components. 

The nondiagonal components of the stress and strain tensors are also null. For the thermoelastic case, the stress-strain relationship is... 

Most micromechanical theories treat composites where the thermoelastic properties of the matrix and of each filler particle are assumed to be homogeneous and isotropic within each phase domain. Under this simplifying assumption, the elastic properties of the matrix phase and of the filler particles are each described by two independent quantities, usually the Young s modulus E and Poisson s ratio v. The thermal expansion behavior of each constituent of the composite is described by its linear thermal expansion coefficient (3. It is far more complicated to treat composites where the properties of some of the individual components (such as high-modulus aromatic polyamide fibers) are themselves inhomogeneous and/or anisotropic within the individual phase domains, at a level of theory that accounts for the internal inhomogeneities and/or anisotropies of these phase domains. Consequently, there are very few analytical models that can treat such very complicated but not uncommon systems truly adequately. 

A general procedure developed by Tucker et al [3,6] can be used to predict the thermoelastic properties of multiphase systems containing any number of components, of any shape, in any type of average orientation state, and of any number of layers ... 

As was noted above, local nonuniform heating of the crystal in the pore region should give rise to stresses around the pore. In the framework of the theory of thermoelasticity, an expression relating the stresses to the temperature distribution can be obtained. For this purpose, using the methods described in Gatewood [36] a relationship can be derived for the radial component of the elastic stress tensor at the pore boundary ... 

Analytical solutions for thermoelastic stress distributions within moving material, irradiated with two-dimensional CW Gaussian beams (P 1 = 0), have also been obtained [24], For a material characterized by k = 50.2 W/mK, p = 7880 kg/m3, c = 502 J/kgK, PI2r = 105 W/m, 7 = 4 mm/s, P = 10 5 K-1, v = 0.3, and p = 105 MPa (the material shear modulus), the dimensionless surface stress component varies with Pe as shown in Fig. 18.9. Here, Pe was varied by changing the beam radius, and the beam moves relative to the surface in the positive x direction. At large Pe, stresses are relatively uniform, while, at extremely small Pe, stress gradients... 

Figure 3.13. Thermoelastic response of an LCE prepared from Components lOa-c. a mechanical field L length of the network in the nematic state iiso length of the network in the isotropic state Tred reduced temperature. Source Wermter and Finkelmann, 2001.

Figure 5.7. Thermoelasticity experiments to estimate the entropic component of elastic force in pure water (curves B) and in the solvent mixture of 30% ethylene glycol 70% water (curves A). On increasing ethylene to 30%, the heat of the transition approaches zero, which means that the solvent entropy change approaches zero. The purpose of the experiment is to see if solvent entropy change contributes to the force developed on raising the temperature. Interestingly, the 90% entropic elastic force...

Kerner [104] made the first sophisticated analysis of thermoelastic properties of composite media using a model which had been considered earlier by van der Poel for calculation of the mechanical properties of composite materials. Here the dispersed phase has been assumed for spherical particles. Kemer s model accounts for both the shear and isotactic stresses developed in the component phases and gives for the composite ... 

This problem can be overcome with the combined use of established probabilistic design methods developed for brittle structural components, good thermoelastic and thetmomechanical databases of the candidate oxide material comprising the TE device, and iteratively applied design sensitivity analysis. Therefore, the objective of this work is to demonstrate the use of a probabilistic... 

The energetic and entropic components of the elastic force, fe and fs, respectively, are obtained from thermoelastic experiments using the following equations ... 

The component p (l) is dne to the electrostiictive effect (the movement of molecules under intense electric field) it is proportional to y and is characterized by the Brillouin relaxation constant and frequency Q. From Equations (9.9) and (9.19) one can see that this component gives rise to a propagating wave. On the other hand, the component p (f) is due to the thermoelastic contribution (proportional to p ) and is characterized by the thermal decay constant it is nonprop-agative. 

Stresses and strains are generated in the part as a function of time and temperature based on the mechanical and thermal stresses that develop during the welding process. These can be established with the aid of the thermoelasticity and plasticity theory [4]. This theory works on the basis of elastic-plastic material deformation, with the overall strain Sau made up of an elastic component a thermal component e and a plastic component d K When the load is removed, the plastic component remains [4] ... 

---