Heterogeneous Internal Strain Evolution in Commercial Purity Titanium Due to Anisotropic Coefficients of Thermal Expansion

Heterogeneous internal elastic strain in polycrystalline hexagonal close-packed materials is found to originate from the intrinsic anisotropy in thermal expansivity. As most noncubic metals have anisotropic thermal expansivity, cooling from elevated temperature leads to internal stresses. To simulate the internal stresses present in a polycrystal prior to plastic deformation, the anisotropic coefficients of thermal expansion over a wide range of temperatures need to be known. One sample of strongly textured commercial purity titanium was probed using high-energy x-ray diffraction microscopy during in situ heating. From averages of the directional lattice strain as a function of temperature, the directional expansion of the material showed a crossover where the incremental c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ c $$\end{document}-axis expansion exceeded the a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ a $$\end{document}-axis expansion between 700°C and 800°C. Applying a three-dimensional crystal thermoelasticity model using a realistic microstructure based upon the experimental data, the anisotropic coefficients of thermal expansion were extracted by fitting to the average strain evolution identified from experiments.