Representative elementary volume

About: Representative elementary volume is a research topic. Over the lifetime, 4105 publications have been published within this topic receiving 86863 citations.

Fourier transforms and their application to the formation of textures and changes of morphology in solids.

Abstract: The presence of inhomogeneities in solids very frequently leads to the generation of eigenstresses and eigenstrains. One particular example is provided by ceramic materials reinforced with Zirconia particles which undergo phase transformations accompanied by a change in shape and volume (e.g., Stevens, 1986). Another example arises in Ni-base superalloys where a so-called forms in a matrix. The lattice parameters of both phases are different and, consequently, high internal stresses and strains occur near the coherent interface boundary (see, e.g., Hazotte et al., 1992, or Hazotte and Lacaze, 1994). Moreover, in both cases, externally superimposed mechanical stresses may locally trigger a phase transformation and, over time, lead to morphological changes of the microstructure. Fourier transforms, in particular in their discrete version, are an effective tool for the mathematical analysis of eigenstress problems in heterogeneous materials. In fact, Fourier transforms have been used before to determine microstresses and -strains around precipitates as well as to study their influence on the change of the local morphology in a solid (e.g., Khachaturyan, 1983, or Mura, 1987). In Section 2, the continuous and discrete versions of Fourier transforms (CFT and DFT) will be presented and applied to obtain a formal solution of linear-elastic eigenstress problems. Section 3 is devoted to various applications; in particular, an analytical, closed-form solution for the elastic fields inand outside of a cylindrical inclusion in a cubic matrix will be derived. Moreover, the stress/strain fields of heterogeneities of complex shape subjected to complex loading conditions will be studied numerically. It will be demonstrated that DFT is capable of assessing the influence of an arbitrary degree of anisotropy, thermal mismatch, ordering, lattice mismatch, particle interaction, as well as elastic mismatch in a solid. Section 4 concentrates on the modeling of the formation of textures and of the change in morphology observed in solids that are subjected to internal and external loads. To this end the stresses and strains obtained through application of CFT or DFT are used to compute and minimize stored energies in heterogeneous materials. In par-