Abstract
The self-consistent (SC) theory is the most commonly used mean-field homogenization method to estimate the mechanical response behavior of polycrystals based on the knowledge of the properties and orientation distribution of constituent single-crystal grains. The original elastic SC method can be extended to thermo-elasticity by adding a stress-free strain to an elastic constitutive relation that expresses stress as a linear function of strain. With the addition of this independent term, the problem remains linear. Although the thermo-elastic self-consistent (TESC) model has important theoretical implications for the development of self-consistent homogenization of non-linear polycrystals, in this paper, we focus on TESC applications to actual thermo-elastic problems involving non-cubic (i.e. thermally anisotropic) materials. To achieve this aim, we provide a thorough description of the TESC theory, which is followed by illustrative examples involving cooling of polycrystalline non-cubic metals. The TESC model allows studying the effect of crystallographic texture and single-crystal elastic and thermal anisotropy on the effective thermo-elastic response of the aggregate and on the internal stresses that develop at the local level.
Highlights
The self-consistent (SC) theory is the most commonly used mean-field homogenization method for estimating the mechanical response behavior of polycrystals based on the knowledge of the properties and orientation distribution of constituent single-crystal grains
The thermo-elastic self-consistent (TESC) formulation is presented in detail and applied to the cooling of polycrystalline single-phase non-cubic metals
The TESC model captures the effect of crystallographic texture and single-crystal elastic and thermal anisotropy on effective and local thermo-elastic responses
Summary
The self-consistent (SC) theory is the most commonly used mean-field homogenization method for estimating the mechanical response behavior of polycrystals based on the knowledge of the properties and orientation distribution of constituent single-crystal grains. The solution of a thermo-elastic self-consistent (TESC) problem for composites, consisting of a phase made of inclusions embedded in a matrix phase with different mechanical properties, was introduced by Walpole [6] and further reformulated and extended by, for example, Willis [7], Buryachenko [8], and Milton [9] These works identified and, in some cases, tackled the case of polycrystals as a special composite made of many mechanical phases, with distinct properties associated with different single-crystal orientations, with no matrix phase. Tomé et al [10] presented the TESC formulation specialized for polycrystals to predict the thermo-mechanical response of hexagonal close packed (hcp) Zr aggregates, which, as almost every non-cubic material, has anisotropic thermal properties at the single-crystal level. Deformation is based on anisotropic crystal elasticity and thermal expansion, which in the case of non-cubic crystals is anisotropic
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
