The thermodynamical theory of elasto-viscoplasticity for description of nanocrystalline metals

The main objective of the present paper is the development of thermodynamical elastoviscoplastic constitutive model describing the behaviour of nanocrystalline metals. Only fcc, bcc and hcp metals will be covered in this description, because they are the classes of metals for which systematic experimental observation data sets are available. Investigation of the deformation mechanisms is important for understanding, controlling and optimizing of the mechanical properties of nanocrystalline metals. Strengthening with grain size refinement in metals and alloys, with an average grain size of 100 nm or larger, has been well characterized by the Hall-Petch (H-P) relationship, where dislocation pile-up against grain boundaries, along with other transgranular dislocations mechanisms, are the dominant strength-controlling processes. When the average, and entire range of grain sizes is reduced to less than 100 nm, the dislocation operation becomes increasingly more difficult and grain boundary-mediated processes become increasingly more important. The principal short-range barrier, the Peierls-Nabarro stress, is important for ultrafine crystalline bcc metals, whereas in ultrafine crystalline fcc and hcp metals, forest dislocations are the primary short-range barriers at lower temperatures. Experimental observations have shown that nanosized grains rotate during plastic deformation and can coalesce along directions of shear, creating larger paths for dislocation movement. The model is developed within the thermodynamic framework of the rate-type covariance constitutive structure with a finite set of the internal state variables. The thermodynamic restrictions have been satisfied and the rate-type constitutive equations have been determined. Fracture criterion based on the evolution of the anisotropic intrinsic microdamage is formulated. The fundamental features of the proposed constitutive theory have been carefully discussed.