The Yield Condition of Crystalline Solids
A brief account of some results pertaining to the yield are presented. Accordingly to thermostatics an equilibrium state is stable when the second variation of the energy is positive definite (δ 2 u> O) and unstable when it is indefinite (δ 2 u can take negative values for one or more variables). The onset of material instability occurs when the second variation is positive -semidefinite (δ 2 u⩾ O). Crystal plasticity is caused by instabilities in the dislocation structure. The situation is analyzed whereby dislocation segments bow out circularly as is the usual assumption made for the Frank-Read source; but equally other situations as extended screw pile-ups can be considered. Applying thermodynamic formalism proves that the onset of instability is governed by calculations to be performed at constant temperature and applied stress. The resulting yield stress depends only weakly on temperature via the temperature dependence of the elastic constants. However classical thermostatics and dynamics deals only with average values of state variables. The temperature dependence of the static yield stress is explained by considering the fluctuations in the dislocation state induced by thermal agitations. This makes that a state which has a relative energy minimum and is therefore stable accordingly to classical theory may actually be unstable. Although the presented results are not new the author is not aware that the underlying assumptions made in their derivation have been proved.
KeywordsSlip System Yield Condition Dislocation Segment Thermal Agitation Static Yield Stress
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