Diffusional creep of three-dimensional polycrystals

10This duality has been recognized (e.g., Landau and Lifshitz [16] and Raj and Ashby [17]). 

The creep rate when boundary sliding is rate-limiting has been treated and discussed by Beere [13, 14]. If a viscous constitutive relation is used for grainboundary sliding (i.e., the sliding rate is proportional to the shear stress across the boundary), the macroscopic creep rate is proportional to the applied stress, and the bulk polycrystalline specimen behaves as a viscous material. An analysis of the sliding-controlled creep rate of the idealized model in Fig. 16.4 is taken up in Exercise 16.2. 

Variable boundary behavior complicates the results derived from the uniform equiaxed model presented above. Nonuniform boundary sliding rates may cause 

11 The functional forms of these relationships agree with those obtained by other investigators using a variety of approximations. However, the values of the constants Ai and A2 vary in some cases by factors as large as three. See Ashby [20], Burton [18], Arzt et al. [19], and Pilling and Ridley [15], 

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