Grain strain rate controlling

The case of constant density of steps modeled by Wakai is equivalent to the diffusion-controlled creep modeled by Raj and Chyung [80], and it is also consistent with terms of the stress, temperature and grain size dependence of the strain rate for interface-reactioncreep predicted by others [80]. However, in the two cases of bidimensional nucleation of step and spiral step, the creep parameters differ from those predicted by the authors cited above. In particular, for 2-D nucleation there is a divergence of the creep parameters which has been recently solved [81], considering in detail the precipitation or solution of the crystalline material at the step, which changes significantly the free enthalpy involved in the process. 

When using the creep model for duplex microstructure, as developed by French et al. [98], it is possible to fabricate a composite with a defined creep resistance that will control the grain size, the width of the layers, and the compression axis. In the case of isostrain, where the strain and strain rate are the same for each phase, and assuming the creep equation in a compact form as, e = Ajo the stress for this configuration, o, is given as ... 

In this equation, A is a constant, Q is the apparent activation energy, R is the gas constant, G is the shear modulus, and p and n are the inverse grain size and stress exponents, respectively. The values of n and Q, measured for the fibers considered here, are listed in Table VI. The high values of n suggest that creep deformation is rate controlled by an interface reaction-limited grain boundary diffusional process [78], Mullite fibers are more resistant to creep than a-alumina fibers. For example, the strain rate of the Nextel 480 mullite fiber at 1200 C is almost two orders of magnitude lower than that of the Nextel 610 a-alumina fiber [55]. 

For material produced in the 1970s with a mean, but strongly scattered, grain aspect ratio of around 35, dislocation creep dominated at stresses > 60 MPa (stress exponent = 25), as can be seen in Fig. 3.1-188. For material produced 20 years later with a similar grain aspect ratio of 31, a stress exponent of 1.2 was found in the stress regime from 30 to 80 MPa, indicating a diffusion-controlled creep process [1.214]. The evaluation of the strain rate/stress dependence of the values... 

Fig. 7.21. The stress-temperature history for a thin film of copper on a relatively thick substrate during a temperature excursion is shown. The dependence of plastic strain rate on stress includes (7.81) to represent obstacle controlled glide of dislocations and (7.86) to represent grain boundary diffusion. Results are shown for film thickness of 1 fim and grain sizes of 0.1 fxm, 1.0/

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