The strain-rate expression

The crystallographie shear-strain-rate expression of erystal plasticity is (Kocks et al. 1975) 

In all three modes of nucleation the mean-free-path length is close to A, and the attempt frequency vq = vd/20, where vd, the lattice shear vibration frequency on the (100) plane in the [001] direction, is estimated to be close to 6.0 x 10 s and the factor 1/20 comes from the expected characteristic saddle-point half-loop diameter of 20h. Thus, with these considerations we have 

the shear-strain-rate expression of eq. (9.18) gives 

In determining the temperature dependence of the plastic resistances in uniaxial deformation the temperature dependence of the shear modulus fj. = C55 is needed. Karasawa et al. (1991) provide such information derived from theoretical force-field methods. Their calculated results for C55 appear as the upper curve in Fig. 9.20. However, for a variety of reasons discussed by Argon et al. (2005), including the defected nature of the usual HDPE, the C55 modulus needs to be attenuated by a factor of 0.635. This attenuated modulus is also shown in Fig. 9.20, as the lower curve. 

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