Plasticity of crystals and interfaces: From discrete dislocations to size-dependent continuum theory

In this communication, we summarize the current advances in size-dependent continuum plasticity of crystals, specifically, the rate-independent (quasistatic) formulation, on the basis of dislocation mechanics. A particular emphasis is placed on relaxation of slip at interfaces. This unsolved problem is the current frontier of research in plasticity of crystalline materials. We outline a framework for further investigation, based on the developed theory for the bulk crystal. The bulk theory is based on the concept of geometrically necessary dislocations, specifically, on configurations where dislocations pile-up against interfaces. The average spacing of slip planes provides a characteristic length for the theory. The physical interpretation of the free energy includes the error in elastic interaction energies resulting from coarse representation of dislocation density fields. Continuum kinematics is determined by the fact that dislocation pile-ups have singular distribution, which allows us to represent the dense dislocation field at the boundary as a superdislocation, i.e., the jump in the slip filed. Associated with this jump is a slip-dependent interface energy, which in turn, makes this formulation suitable for analysis of interface relaxation mechanisms. Prikazani su nedavni istrazivacki rezultati u kontinualnoj plasticnosti kristala (kvazistaticka formulacija nezavisna od brzine) na osnovu mehanike dislokacija. Poseban naglasak je stavljen na relaksaciju klizanja na medjupovrsi. Ovaj nereseni problem je na sadasnjem frontu istrazivanja u plasticnosti kristalnih materijala. Postavljamo ovde okvir za sledeca istrazivanja zasnovana na teoriji razvijenoj za trodimenzioni kristal. Ova teorija je zasnovana na konceptu geometrijski potrebnih dislokacija, posebno, na konfiguracijama gde dislokacije se nagomilavaju nasuprot medjupovrsi. Prosecno rastojanje izmedju ravni klizanja obezbedjuje karakteristicnu duzinu teorije. Fizicka interpretacija slobodne energije ukljucuje gresku u energijama elasticne relaksacije koje rezultiraju iz grube reprezentacije polja dislokacione gustine. Kinematika kontinuuma je odredjena cinjenicom da dislokaciona nagomilavanja imaju singularni raspored koji nam dozvoljava da prikazemo gusto dislokaciono polje na granici kao jednu superdislokaciju, to jest, skok u polju klizanja. Pridruzena ovom skoku je energija medjupovrsi koja zavisi od klizanja, sto opet cini ovu formulaciju podesnom za analizu mehanizama relaksacije na medjupo