Driving force for creep

Multiply both sides by atomic volume, Q, and rearrange them  

N is the number of atoms. 9A/9N is the excess chemical potential per atom, and is given by Equation 15.10 where is the standard chemical potential of atoms in a stress-free solid. 

The applied stress p produces a stress o, let us say. The excess chemical potential is due to this stress. Thus, substituting p by o in Equation 15.9, then putting the value of 9A/9N in Equation 15.10 and writing this equation in terms of the chemical potential of the stressed solid, we get  

This equation gives the extent of driving force available for an atom to diffuse from a region under a compressive stress to that under a tensile stress. 

at atomistic level, let us discuss the mechanism of creep. We have seen that under the action of a stress, atoms migrate to vacancies. Hence, vacancy concentration affects creep. Vacancy concentration, C, under a flat and stress-free surface is given by Equation 15.14 

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It is useful to define a parameter that describes the direction and magnitude of the driving force for stress redistribution. Rather than use the difference in creep rates, it is more convenient to define this parameter as the ratio between the constituent creep rates. For this purpose, a time-dependent... 

The in situ creep mismatch ratio CMR, can provide a quantitative estimate of the driving force for load transfer between constituents. However, it is a rather complicated function of the stress redistribution processes. In order to indicate the basic characteristics of stress redistribution, it is convenient to directly compare the intrinsic (unconstrained) creep rates using the initial elastic stress experienced by the constituents. From Eqn. (12),... 

DeutroD scattering [henceforth SANS] measurements of the two kinds of aluminas (illustrated in the above examples of cavitation) are given in Fig. 6.72 in terms of cavity radius as a function of creep time. Though, at present, there is no conclusive data proving that GBS is the driving force for the nucieation and growth of creep cavities, a nmnber of studies have concluded that cavity nucieation is, in fact, induced by GBS. 

Interface stability in co-extrusion has been the subject of extensive analysis. There is an elastic driving force for encapsulation caused by the second normal stress difference (56), but this is probably not an important mechanism in most coprocessing instabilities. Linear growth of interfacial disturbances followed by dramatic breaking wave patterns is observed experimentally. Interfacial instabilities in creeping multilayer flows have been studied for several simple constitutive equations (57-59). Instability modes can be traced to differences in viscosity and normal stresses across the interface, and relative layer thickness is important. 

These equations have been solved for rigid (Nl) and circulating spheres (Jl, K6, W3, W4) in creeping flow. Since the dimensionless velocities within the particle are proportional to (1 + k) (see Eq. (3-8)), F is a function only of Tp and PCp/(l + k). In presenting the results, it is instructive to consider the instantaneous overall Sherwood number, Shp, as well as F. The driving force is taken as the difference between the concentration inside the interface, and the mixed mean particle concentration, Cp, giving... 

Abstract When subjected to a mechanical loading, the solid phase of a saturated porous medium undergoes a dissolution due to strain-stress concentration effects along the fluid-solid interface. Through a micromechanical analysis, the mechanical affinity is shown to be the driving force of the local dissolution. For cracked porous media, the elastic free energy is a dominant component of this driving force. This allows to predict dissolution-induced creep in such materials. 

Although Eqs. (12.4) to (12.6) elucidate the nature of the driving force operative during creep, they do not shed any light on how the process occurs at the atomic level. To do that, one has to go one step further and explore the effect of applied stresses on vacancy concentrations. For the sake of simplicity, the following discussion assumes creep is occurring in a pure elemental solid. The complications that arise from ambipolar diffusion in ionic compounds are discussed later. The equilibrium concentration of vacancies Cq under a flat and stress-free surface is given by (Chap. 6)... 

When the flow of gas is induced by a driving force of total pressure gradient, the flow is called the viscous flow. For typical size of most capillaries, we can ignore the inertial terms in the equation of motion, and turbulence can be ignored. The flow is due to the viscosity of the fluid (laminar flow or creeping flow) and the assumption of no slip at the surface of the wall. 

Models for hot pressing by diffusional mass transport under the driving forces of surface curvature and applied stress were formulated by Coble (39,40). In one approach, the analytical models for sintering were adapted to include the effects of an applied sdess, while in a second approach, hot pressing is viewed in a manner analogous to that of creep in dense solids and the creep equations... 

The basic concepts embodied in describing densification in terms of creep kinetics were adapted to the case of pure sintering by Palmour and Johnson ( ). They proposed substituting the product of surface energy per unit area, y, and the surface area per unit volume, 0, for a as the driving force in Eq. (2)... 

In the Fe-rich phases and in FeAl, however, no subgrain formation has been observed even after long creep times. The dislocation density remains high (about 10 cm, and the stress exponent varies between 3 and 3.6. This indicates class I behaviour, i.e. here the creep is controUed by the viscous glide of dislocations. In both cases only <100) dislocations have been observed. Obviously the driving force and the atomic mobility that are necessary for subgrain formation are sufficient only in the Ni-rich phases. 

For creep to take place, there should be atom movement. Also, there should be some driving force. 

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