Estimation of X-Ray Elastic Constants: An Alternative Approach

According to ASTM E1426, X-ray elastic constants (XEC) are measured using four-point bending fixtures on specimens with a length-to-width ratio of at least four (with a width sufficient enough for a strain gage to be mountable) and width-to-thickness ratio of greater than one. Typically, recommended sample dimensions for four-point fixtures are approximately 102 mm in length, 19 mm in width and 1.5 mm in thickness. However, the requirement of such larger dimensions limits sample extraction in engineering components with limited cross-section. Analytically, XECs can be estimated using either Voigt, Reuss, Kroner and modified Kroner models with single-crystal elastic constants (SCEC) of any material/alloy of interest as inputs. Even though several procedures for estimating SCECs are demonstrated in the literature, the lack of portability in them demands alternate approaches for measurement. Therefore, in this study, an alternate approach of estimating XEC constants from a cubic sample of Nickel-based super-alloy polycrystalline material was demonstrated. SCECs, C11, C12 and C44 were extracted by minimizing the difference between experimentally measured and analytically predicted ultrasonic parameters such as longitudinal velocity, shear velocity and attenuation coefficients. Further, using the predicted SCECs, the XECs were estimated using a modified Kroner approach. It was observed that the proposed approach predicted XECs within 3