Three-level modeling of fcc polycrystalline inelastic deformation: grain boundary sliding description

Multilevel model of polycrystalline materials: grain boundary sliding description

“…Spin tensor Ω of moving coordinate system (relation (12)) and elastic modulus tensor П (relation (13)) are transmitted from mesolevel to macrolevel using the averaging operation over a representative macrovolume. Tensors in s Z (relation (14)) and th Z (relation (15)) are defined from mesolevel model with consistency conditions [12], the following notations are used: as in relations (12) and (13) (16) is defined due to averaging of internal heat source capacity q over a representative macrovolume, k is heat capacity (generally temperature and temperature rate are defined from boundary value problem for temperature). We will have more to say below about inclusion of GBS mechanism in structure of performed two-level statistical model and description of inelastic component in gb Z due to realization of this mechanism.…”

“…Relative displacements of crystallites (grains, subgrains) along the common boundary during GBS are observed in bicrystals and polycrystals [13]. In polycrystalline materials GBS is limited by neighboring crystallites, which is modeled in grain boundary hardening law [12]. It is assumed that grain boundary of each crystallite is a set of flat facets with zero thickness, each pair of neighboring crystallites in a representative macrovolume has a common boundary facet, and relative displacements of crystallites occur along a common facet by moving grain boundary dislocations (however the last one is not modeled in explicit form).…”