(1) A 1 = E s 1 + Q 1. If we isothermally anneal the accumulated defects and return the system to the initial state with the initial dislocation density ρ 0 along the path 1→3, the energy stored by plastic deformation in state 3 will be zero while the residual plastic strain will be ε 1.
The stored energy reflects all the microstructural changes occurring in the course of strain hardening, and the non-dissipated energy is stored mainly in the elastic stress fields of dislocations .
The Eq. (18) relating the stored energy to the dislocation density allows for a transparent physical interpretation: the stored energy refers to the difference between the energies of the crystal deformed and the initial state characterised solely by the dislocation densities ρ and ρ 0, respectively.
The internal energy can be stored in the system in a variety of ways. Generally speaking, heat and work cannot be conserved independently since they both depend on the process (this is reflected symbolically by δ underlying that the increments of heat and work are not perfect differentials in contrast to the internal energy U).
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