A flexible numerical approach for non-destructive ultrasonic testing based on a time-domain spectral-element method: Ultrasonic modeling of Lamb waves in immersed defective structures and of bulk waves in damaged anisotropic materials

Abstract This paper deals with the introduction of a spectral-element method, in the time domain, to address problems of ultrasonic wave propagation in the field of the nondestructive ultrasonic testing and evaluation. Two kinds of problems are addressed. The first focuses on guided waves that are often used to control immersed layered defective structures. The second focuses on the use of bulk waves to inspect layered anisotropic media that may contain a defect. This full-wave technique allows for the use of significantly coarser meshes compared to other standard finite-element methods that can be used for non-flat defective or damaged models, as using one element per shortest wavelength is sufficient. It is thus well suited to the simulation of wave propagation phenomena in complex structures at high frequencies. With the goal of first validating our approach for simple cases, we begin by presenting results of simulations for a homogeneous plate. We compare the dispersion curves obtained with the analytical ones. The results are in excellent agreement, and the spectral-element method is fast enough to allow for simulations having a high level of accuracy. We then reproduce and analyze the transmission losses of a quasi plane wave across the immersed plate, and discuss the influence of the finite size of the ultrasonic beam in real physical experiments. We subsequently study the transmission of an ultrasonic wave through an immersed tri-layer composed of two aluminum plates glued together and with a defect, a model that is already not accessible to quasi-analytical calculation techniques. We again determine the dispersion curves, and then study transmission through the structure having a delamination defect compared to transmission through a healthy structure. We then compute the dispersion curves of the same tri-layer structure but with a varying glue thickness. These dispersion curves are compared to those of the healthy structure. We then perform a three-dimensional simulation of a pulse-echo experiment in an immersed medium composed of layers of transversely-isotropic austenitic steel, the axis of symmetry of each layer being tilted differently. This medium represents a very simple model of a weld, in which we include two kinds of defects: a gas bubble resulting from the welding process, and then a branching and crossing Y-shaped crack resulting e.g. from aging. We illustrate their effect on ultrasonic waves by computing the scattered field.