Transducer Effects in Ultrasonic Measurements of Material Stiffness

In recent years, ultrasonic methods have been developed that can be used to measure the mechanical stiffness of materials.1-5 In one such method, the velocity of a flexural plate wave, the lowest order antisymmetric Lamb mode, is measured as a function of frequency. Lamb waves arise from a coupling at the free boundaries between the shear waves and compressional waves in a plate structure.6 The modes are defined as symmetric or antisymmetric based on the symmetry of the wave about the mid-plane of the plate. These are dispersive waves, meaning waves at different frequencies will travel at different velocities. The shear modulus, G, and Young’s modulus, E, can be determined for isotropic materials from a reconstruction of the velocity dispersion curve. In a similar fashion, the bending and out-of-plane stiffness coefficients for composite laminates can be obtained. This technique provides new and advanced capabilities that allow process and material engineers to inexpensively map out material properties with higher resolution. Such a capability is particularly useful when there are variations in material properties across a given specimen, such as in the case of localized damage or variability caused by the manufacturing process. However, due to the highly dispersive nature of the flexural mode, accurate frequency and velocity measurements are required to correctly determine the material stiffnesses. This study demonstrates that errors in stiffness as large as 40% can result from inaccurate frequency measurements of only a few percent. A method to improve the accuracy in frequency measurements is discussed.