Mathematical Modeling and Computer-Aided Simulation of the Acoustic Response for Cracked Steel Specimens

Photoacoustic imaging (PAI) is an emerging nondestructive testing technique to evaluate ever-growing steel products and structures for safety and reliability. In this study, we have analyzed steel material with inbuilt cracks using computer-aided numerical simulations, imitating the PAI methodology. Cracks are introduced in a steel cylinder along three axes at different locations, and then a finite element method simulation in Abaqus software is performed to generate an acoustic wave and read it back at sensing locations after passing through the crack. The data are observed, analyzed, and modeled using the composite sine wave data fitting modeling technique. Afterwards, the Nelder–Mead simplex method is used to optimize the parameters of the model. It is concluded that with the change in the crack location, there is a change in the model parameters such as amplitude and frequencies. Results for cracks at seven different locations along each of the three axes are added, and listed in tabular form to present an analysis and comparison of the changes in the modeled parameters with respect to these crack locations.