Estimation of the stiffness tensor from Lamb wave velocity profiles measured on steel with different texture

Abstract

It is important that steel meets the designated material parameters after production. Ideally, relevant parameters should be measured inline to have the ability to control the process during production. This requires a method that determines material parameters, such as the texture and various stiffness matrix components. These material properties can be derived from ultrasonic Lamb wave velocity measurements for different angles relative to the rolling direction. Objectives A method for estimating relevant stiffness matrix components needs to be developed, tested on simulation results and applied on measurements. Work performed A set of 10 cold-rolled Interstitial Free (IF) steel samples is provided by Tata Steel. These samples have different microstructures and thus different elastic properties. The ultrasonic Lamb wave velocity is measured for each of those samples over 360°. For each sample, a digital representative volume element (RVE) is generated using periodic Voronoi diagrams with a very large number of grains (10,000 – 100,000), based on through-thickness microstructural characterization by Electron Backscatter Diffraction (EBSD). The set of 10 RVEs is used in 3D Finite Difference simulations where grains are included individually and modelled as single crystals with specific orientations. The wave propagation of the S0 and SH0 modes is simulated. An inversion scheme has been developed to estimate a large number of components of the stiffness matrix from a velocity profile. Results Velocity profiles obtained from simulations are compared with those from measurements. For each sample, the results are very similar. The inversion scheme has been tested on simulations and applied to measurements from the IF samples. Results indicate that an acceptable accuracy can be achieved, although not all components are resolved equally well in the measurements. Conclusions The proposed inversion scheme enables the estimation of all relevant stiffness tensor components from a Lamb wave velocity profile with sufficient accuracy.