Octahedral strain rate

The scalar strain rate is defined as the octahedral strain rate, which for small strains is given by... 

Sharma (90) has examined the fracture behavior of aluminum-filled elastomers using the biaxial hollow cylinder test mentioned earlier (Figure 26). Biaxial tension and tension-compression tests showed considerable stress-induced anisotropy, and comparison of fracture data with various failure theories showed no generally applicable criterion at the strain rates and stress ratios studied. Sharma and Lim (91) conducted fracture studies of an unfilled binder material for five uniaxial and biaxial stress fields at four values of stress rate. Fracture behavior was characterized by a failure envelope obtained by plotting the octahedral shear stress against octahedral shear strain at fracture. This material exhibited neo-Hookean behavior in uniaxial tension, but it is highly unlikely that such behavior would carry over into filled systems. 

Strain rate of 5x10" s , while the strain rates within the epoxy surface layer are in the order of 10 s under fretting conditions. Accordingly, the values of the octahedral shear stress at the onset of yield are probably underestimated. In addition to the limited viscoelastic response of the epoxy material at the considered frequency and temperature (tan 8 = 0.005 at 25°C and 1 Hz, table I), this analysis supports the validity of a global elastic description of the contact stress environment. 

Figure 11.20 The strain rate dependence of the octahedral shear stress Toct at atmospheric pressure using data from torsion (o), tension (A) and compression ( ). (Reproduced with permission from Duckett et al., Br. Polym. J., 10, 11 (1978))...

Equations (12.17) and (12.18) can be used in three-dimensional stress analyses on the basis that they give scalar rates of plastic strain, which can be converted to tensor strain rate components via the use of a flow rule. The shear stress r is defined as the octahedral shear stress in terms of the principal stresses... 

Rate equations of this type are normally associated with the formation of associative intermediates or the involvement of deprotonated ligand forms in reactions with two (or more) competitive pathways. However, in the case of octahedral metal complexes of ligands such as 2,2 -bipyridine or 1,10-phenanthroline, such mechanisms do not appear to be likely. Associative mechanisms would involve seven-co-ordinate intermediates, which are likely to be sterically strained and electronically disfavoured on ligand field grounds. Furthermore, this type of ligand does not appear to contain any strongly acidic protons which are likely to be involved in reactions with aqueous hydroxide ion (but see later). 

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