13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Figure 5. Arrhenius plot of deformation behaviour of IN 100 showing the boundary between PLC behaviour and non-PLC behaviour which gives an activation energy of 1.14 eV [5]. its slip plane the same process would operate. However, based on this model, the second slip plane to activate would do so at a higher stress because of the higher unlocking stress and the back stress due to the piled up dislocations in the first slip plane. Similarly the next source to operate would follow the same process but at an increased stress. Such a model would account for an accompanying Hall-Petch dependence that is known to apply for PLC behaviour. The pile-up mechanism implicitly accounts for ending the behaviour when all of the locked dislocations having relatively low unlocking stresses have been mobilized after which point deformation continues by normal flow processes. Thus this model description appears to account for: • Temperature and strain rate effects through the initial unlocking of the initial dislocations on each slip plane. • Macroscopic strain localization through local stress intensification at locked dislocations by the mobile dislocations. • Exhaustion of the phenomenon through strain hardening due to the distribution of unlocking stresses, and activating normal flow processes at some stress level. • An increasing mean stress (cyclically increasing flow stress) due to interactions from piled up dislocations and a generally increasing for each slip plane. Extension of the Cottrell-Bilby model to the PLC effect has an interesting connection to the modern thermally activated strain rate analysis (TASRA) for dislocation plasticity. A positive or negative strain rate sensitivity (SRS) may occur according to whether one is on the upside or downside of the added PLC thermal activation curve [1]. Given that the PLC process is thermally activated, the following functional dependence is implied: ,ln f T th (6) Here the symbols on the right have their usual meaning. However, some attention must be paid to the meaning of th which is that component of the flow stress above long range internal stresses. There are examples in the literature in which it is mistakenly taken as the total stress which results in some errors in activation energies and over-all understanding. From calculus, Eq. (6) may be used to give the result: 1 ln ln ln th T th th T T (7)
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