Measurement of the single crystal elasticity matrix of polycrystalline materials

Abstract

Many engineering metals are polycrystalline, as such the elasticity, crystalline orientation and grain distribution are cardinal factors in determining the physical properties of the material. The grain distribution can be measured using a number of different techniques and the orientation by a subset of these (electron back scatter diffraction, spatially resolved acoustic spectroscopy). These measurements are routinely deployed in materials development. However, the elasticity remains a more difficult parameter to measure and is rarely measured because the existing techniques are slow and cumbersome, with most current techniques requiring the laborious growth or destructive isolation of single crystals. In this work we present a technique that can determine the elasticity, crystalline orientation and grain distribution in a fast and easy measurement. The technique utilises SRAS imaging to provide the raw measurement of single grain velocity surfaces, this is input to a novel inverse solver that mitigates the problem of the inversion being very ill-conditioned, by simultaneously solving for multiple uniquely orientated grains at once in a brute-force approach. This allows simultaneous determination of the elastic constants and crystallographic orientation. Furthermore, this technique has the potential to work on polycrystalline materials with minimal preparation and is capable of high accuracy, with the potential to realise errors in the determination of elastic constants values of less than 1 GPa (∼1). In this work we demonstrate good agreement with EBSD (<6∘ disagreement on average for all Euler angles) and determine elastic constants in line with existing single-crystal values, with an expected accuracy of better than 4 GPa. Experimental results are presented for pure α-Ti (hexagonal), Ni and the more exotic Ni-base alloy CMSX-4 (both cubic). With the proposed method, once the initial measurement has been made, subsequent measurements of the elasticity on the same sample can be made rapidly so that the elasticity can be measured in real time, opening the possibility that on-line measurement of elasticity can be used to monitor processes and enable high-throughput materials screening. The current instrumentation approach is applicable to materials with grain sizes down to 50 µm, with the possibility of improving this to grain sizes of ∼5 µm. Further modifications to instrumentation and acoustic velocity calculation will facilitate greater accuracy in the determination of elastic constants.