A Preliminary Numerical Study on the Interactions Between Nonlinear Ultrasonic Guided Waves and a Single Crack in Bone Materials With Motivation to the Evaluation of Micro Cracks in Long Bones

Fatigue damage in a bone occurs in the form of micro-scale cracks with the lengths as small as to a few microns. The evaluation of cracks in bones has recently been a hot topic. However, the current most frequently used method is based on traditional linear ultrasound, which is just sensitive to gross damages rather than micro cracks. Nonlinear ultrasonic technique, which is capable of detecting micro-scale damages, has been widely used in metallic structures. However, few study has been directed to employing second harmonic generation of nonlinear ultrasound to evaluate fatigue damages in bones. In this study, a preliminary study is conducted on the interactions between nonlinear guided waves and a single crack in bone materials motivating to the evaluation of micro cracks in long bones. Considering the symmetry, asymmetry, location, orientation, length and width of the crack in bone materials, their influences on second harmonic responses are discussed in detail. Our results are presented as follows. Firstly, not only the primary S0 but also A0 mode Lamb wave generates the second harmonic component of S0 mode after interacting with a symmetric crack. Secondly, along the thickness direction, the primary S0 mode Lamb wave possesses almost the same detection sensitivity, no matter where the crack is located. Thirdly, the amplitudes of S0 mode second harmonic component are increased slightly when the oblique angle of the crack is set from 0°to 45°, while the amplitudes increase dramatically when the oblique angle changes to 67.5° and 90°. Lastly, the second harmonic amplitude and the relative acoustical nonlinear parameter are increased with the length of the crack, while they possess a monotonically decreasing relationship with the width of the crack. Our preliminary studies will provide priori knowledge when using nonlinear ultrasonic guided waves for detecting micro-scale cracks in long bones in future clinical inspections.