Micromechanical models based on NTFA approach (Visco)-Plastic strain heterogeneity in composite and polycrystalline materials and the Nonuniform Transformation Field Analysis (NTFA)

Overview & Synopsis

Homogenization of composite or polycrystalline materials with nonlinear constituents is a long-standing problem. It is well recognized that the nonlinearity introduces a strong coupling between the different scales which, in full rigor, remain coupled. This observation has motivated the development of coupled, full-field, multi-scale methods (such as the FEM 2 method). However, the cost of these methods is still prohibitive for full-scale simulations of structural problems and has motivated the development of reduced order models (ROM) achieving a good compromise between accuracy and efficiency. A typical example of such a ROM is the Transformation Field Analysis (TFA). However, some of the characteristic features of the plastic strain fields are not well captured by the TFA, which assumes that the plastic strain field is uniform in individual phases or in subdomains of each individual phase. The Nonuniform Transformation Field Analysis (NTFA) extends on the TFA. It is not only motivated by the need of cutting down the costs of structural analyses at the macroscopic scale by working with a reduced-order model, but it also accounts in a more satisfactory way for the local characteristics of the microscopic strain fields observed in nonlinear composite and polycrystalline materials. Indeed, two striking features of these local fields, revealed either experimentally or through numerical simulations, are first their strong nonuniformity in space, even within individual constituents, and second a strong patterning effect (or selforganization) of the fields into zones where the plastic strain concentrates and zones which are left nearly undeformed. The NTFA is based on the decomposition of the (visco)plastic strain field on nonuniform (visco)plastic modes. NTFA is presented here in theoretical terms, in comparison with the TFA approach, and then applied to two typical examples: composite and polycrystalline materials used in the nuclear field, with non-linear behaviors.