Dislocation 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. 

Two types of basic creep mechanisms have been identified in models for dislocation creep. (1) In glide-controlled creep, the obstacles to dislocation motion are on the scale of the dislocation core the obstacles are overcome by... 

First, volatiles exert an important control on the physical properties of the mantle. For example, the presence of water reduces the strength of olivine aggregates and seriously alters the viscosity of the mantle. Experimental studies show that at 300 MPa, in the presence of water, the viscosity of olivine aggregates deformed in the dislocation creep regime is reduced by up to a factor of 140. Thus a wet mantle is a low viscosity mantle. Conversely a mantle that is dried out by partial melting will be stiffer and more refractory, as is the case for the lithospheric "lid" to modern oceanic mantle. Thus, if it is possible to estimate the volatile content of the mantle both now and in the Archaean, it will be possible to set some physical constraints on models of mantle evolution over time. 

Over a dozen mechanisms have been proposed to explain the functional dependence described by Eq. (12.1), but in general they fall into one of three categories diffusion, viscous, or dislocation creep. To cover even a fraction of these models in any detail is clearly beyond the scope of this book. Instead, diffusion creep is dealt with in some detail below, followed by a brief mention of the other two important, but less well-understood and more difficult to model, mechanisms. For more comprehensive reviews, consult the references at the end of this chapter. 

The creep strength of AljNb is comparatively low - a stress of 10 MN/m produces 1 % strain in only 500 h and fracture in 2300 h - whereas the yield stress compares favorably with the superalloys. This illustrates the fact that the difference between the yield stress and the creep strength is much more pronounced for intermetallics than for conventional alloys. Creep of Al3Nb is controlled by dislocation climb which is accompanied by subgrain formation. The observed creep behavior corresponds to that of conventional disordered alloys and the creep rates are described by the known constitutive equations. This will be discussed in more detail with respect to NiAl (Sec. 4.3). The secondary creep rate follows the power law, i.e. Dorn equation for dislocation creep... 

The creep behavior of the ternary B2 phase (Ni,Fe)Al was studied in detail as a function of stress, temperature, composition, and grain size (Rudy and Sauthoff, 1985 Rudy, 1986 Jung etal., 1987). At high temperatures, e.g. 60% of the melting temperature or higher, the secondary creep at rates between about 10" s" and 10" s exhibits power law behavior, i.e. the observed secondary creep rates are described by the familiar Dorn equation for dislocation creep [Eq. (2)] (Mukherjee etal., 1969). 

Dislocation creep of conventional disordered alloys is produced by gliding and... 

These findings show that the dislocation creep of such intermetallic alloys and... 

This threshold stress is proportional to the Orowan stress, as was shown theoretically for various climb processes (Arzt and Rosier, 1988), and thus is proportional to the reciprocal particle distance, in agreement with the experiments (Jung and Sauthoff, 1987,1989 a). The observed, secondary dislocation creep can be described by Eq. (4) and deformation maps can be calculated on the basis of the experimental data (Jung and Sauthoff, 1989 a). 

In tension, Emin is a weak function of grain size, with grain size exponents <1. The same is true in compression, but only at low stresses, which implies the dominant creep mechanism is most likely dislocation creep, despite the fact that n is less than the exponents (3-7) typically associated with dislocation creep [163, 165]. 

In the absence of cavitation, creep in vitreous-bonded materials would occur by S-P, wherein material dissolves from one side of the grain and deposits on another [48, 49]. No definitive studies have been made to date that support the dislocation creep models in which the grains of silicon nitride deform by dislocation motion. Studies of deformed silicon nitride grains have provided no evidence of the types of dislocation pileup that should be present in order for this type of mechanism to be active [50]. 

---