13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Equation (7) may be employed to provide insight into the PLC effect in terms of the separated factor dependencies. For normal dislocation velocity description with thermally activated shear stress, τth, the first factor in Eq. (7), is negative and the second two factors are positive. The same equation is usefully applied to the analysis of the incremental PLC effect for τth. Note that when the third term is negative (as seen for PLC), then each of the first two terms must be positive. Thus a negative strain rate sensitivity of the flow stress for dynamic strain aging (PLC) is associated only with the stress rising to the peak of strain aging and not for an “over the top” régime of decreasing stress. Misunderstanding of this feature has led to some controversy in the literature about the analysis of the PLC activation energy. 5. Strain Concentration and Adiabatic Shear Banding Adiabatic shear banding refers in a formal sense to the case in which a localized shear band forms with no transfer of heat to or from the external environment (i.e. . The behaviour is favored in metals under conditions of low heat capacity and low thermal conductivity when deformed at high loading rates and/or low temperatures. The mechanical work associated with formation of the shear band is mainly transformed into heat and thereby manifested by an increase in temperature. Unlike the PLC effect which is self-exhausting, the formation of adiabatic shear bands (ASBs) is self amplifying and leads to localized failure. Recall that adiabatic shear banding was first observed by Tresca in a set of forging experiments on a Pt-Ir alloy [16]. When hammered just below the “red-hot” temperature, distinct X-type shear lines appeared on the longitudinal cross-section of the test specimen indicative of an exceptional temperature increase. Eshelby and Pratt [17] used the mathematical solution for the temperature increase associated with a moving source of energy provided by Carslaw and Yaeger [18] and modified it to rows of equally spaced dislocations passing by a fixed lattice point. The main result of their calculation was: (8) Where v is the dislocation velocity, K is the thermal conductivity, L is the length of the slip band and is an effective thermal a length given by: (9) where is the thermal diffusivity. Using reasonable values for Al, they showed that on the basis of this model, temperature increases of only 2o K was obtained from the model calculation. Furthermore, they examined other arrangements and concluded that no arrangement could be found which would give a large temperature increase. However, the very earliest work of Tresca proved that high temperature increases were occurring and thus the model of Eshelby and Pratt is a very useful step in developing a more complete understanding. This issue was re-examined by Coffey and Armstrong [19] on the basis of further accumulated evidence that appreciable temperature rises were being evidenced in shear banding experiments, A model favorable to shear banding was envisioned of isothermal stress build-up of stored energy in a dislocation pile-up, then leading to sudden obstacle collapse, and rapid dissipation of the stored energy by very localized plastic work in an earthquake-like dislocation avalanche. The model led, with employment of well-established slip band mechanics [20-21], to an expression for ΔT given by:
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