Diffusion creep

Wanderung,/. migration creeping diffusion traveling, travels, walking, walking trip. 

Arrhenius Law. A logarithmic relationship between reaction rate and temperature which applies to creep, diffusion and solid state phase transformations (among many other chemical and physical reactions), log V = A - q/kT... 

A. Lakki, R. Herzog, M. Weller, H. Schubert, C.Reetz, O. Gdrke, M. Kilo, G. Borchardt, Mechanical loss, creep, diffusion and ionic conductivity of Zr02-8 mol% Y2O3 polycrystals. J. Eur. Ceram. Soc. 20(3), 285-296 (2000)... 

On the other hand, the reliability of the product improves, too, if each state of the plasticity deformation, the creep deformation, and the diffusion joint in the solid phase diffusion bonding as the bonding process, is accurately understood, and the bonding process is controlled properly. 

An account of the mechanism for creep in solids placed under a compressive hydrostatic suess which involves atom-vacancy diffusion only is considered in Nabano and Hemirg s (1950) volume diffusion model. The counter-movement of atoms and vacancies tends to relieve the effects of applied pressure, causing extension normal to the applied sU ess, and sluinkage in the direction of the applied sU ess, as might be anticipated from Le Chatelier s principle. The opposite movement occurs in the case of a tensile sU ess. The analysis yields the relationship... 

In this chapter we discuss the origin of Arrhenius s Law and its application to diffusion. In the next, we examine how it is that the rate of diffusion determines that of creep. 

This method of writing D emphasises its exponential dependence on temperature, and gives a conveniently sized activation energy (expressed per mole of diffusing atoms rather than per atom). Thinking again of creep, the thing about eqn. (18.12) is that the exponential dependence of D on temperature has exactly the same form as the dependence of on temperature that we seek to explain. 

But what about creep In the next chapter we shall see how diffusion can explain creep. 

There are two mechanisms of creep dislocation creep (which gives power-law behaviour) and diffusiona creep (which gives linear-viscous creep). The rate of both is usually limited by diffusion, so both follow Arrhenius s Law. Creep fracture, too, depends on diffusion. Diffusion becomes appreciable at about 0.37 - that is why materials start to creep above this temperature. 

As we saw in Chapter 10, the stress required to make a crystalline material deform plastically is that needed to make the dislocations in it move. Their movement is resisted by (a) the intrinsic lattice resistance and (b) the obstructing effect of obstacles (e.g. dissolved solute atoms, precipitates formed with undissolved solute atoms, or other dislocations). Diffusion of atoms can unlock dislocations from obstacles in their path, and the movement of these unlocked dislocations under the applied stress is what leads to dislocation creep. 

Climb unlocks dislocations from the precipitates which pin them and further slip (or glide ) can then take place (Fig. 19.3). Similar behaviour takes place for pinning by solute, and by other dislocations. After a little glide, of course, the unlocked dislocations bump into the next obstacles, and the whole cycle repeats itself. This explains the progressive, continuous, nature of creep, and the role of diffusion, with diffusion coefficient... 

Diffusion creep (giving linear-viscous creep)... 

As the stress is reduced, the rate of power-law creep (eqn. (19.1)) falls quickly (remember n is between 3 and 8). But creep does not stop instead, an alternative mechanism takes over. As Fig. 19.4 shows, a polycrystal can extend in response to the applied stress, ct, by grain elongation here, cr acts again as a mechanical driving force but, this time atoms diffuse from one set of the grain faces to the other, and dislocations are not involved. At high T/Tm, this diffusion takes place through the crystal itself, that... 

Viscous flow is a sort of creep. Like diffusion creep, its rate increases linearly with stress and exponentially with temperature, with... 

Fig. 20.4. Investment casting of turbine blades. This produces a fine-grained material which may undergo a fair amount of diffusion creep, and which may fail rather soon by cavity formation.

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