Estimating single-crystal elastic constants of polycrystalline β metastable titanium alloy: A Bayesian inference analysis based on high energy X-ray diffraction and micromechanical modeling

Abstract

A two-phase near- beta titanium alloy (Ti–10V–2Fe–3Al, or Ti-1023) in its as-forged state is employed to illustrate the feasibility of a Bayesian framework to identify single-crystal elastic constants (SEC). High Energy X-ray diffraction (HE-XRD) obtained at the Diamond synchrotron source are used to character- ize the evolution of lattice strains for various grain orientations during in situ specimen loading in the elastic regime. On the other hand, specimen behavior and grain deformation are estimated using the elastic self-consistent (ELSC) homogenization scheme. The XRD data and micromechanical modelling are revisited with a Bayesian framework. The effect of different material parameters (crystallographic and morphological textures, phase volume fraction) of the micromechanical model and the biases intro- duced by the XRD data on the identification of the SEC of the βphase are systematically investigated. In this respect, all the three cubic elastic constants of the βphase ( C11(beta) , C12(beta) , C44(beta) ) in the Ti-1023 alloy have been derived with their uncertainties. The grain aspect ratio in the ELSC model, which is often not considered in the literature, is found to be an important parameter in affecting the identified SEC. The Bayesian inference suggests a high probability for non-spherical grains (aspect ratio of ∼3 . 8+/-0 . 8 ) : C11(beta) = 92 . 6+/-19 . 1 GPa , C12(beta) = 82 . 5+/-16 . 3 GPa , C44(beta) = 43 . 5+/-7 . 1 GPa . The uncertainty obtained by Bayesian approach lies in the range of ~1-3 GPa for the shear modulus mu’ = (C11(beta) −C12(beta) )/2 , and ~7 GPa for the shear modulus mu’’ = C44(beta) , while it is significantly larger in the case of the bulk modulus (C11(beta) +2C12(beta))/3 (~17-24 GPa).