Simulation of nonlinear Rayleigh wave propagation through minute surface crack

The second harmonic of a Rayleigh wave passing through a nearly closed surface crack which is inclined to the surface was numerically analyzed by semi-explicit FEM including special elements which consider a nonlinear stress-strain relation at crack surfaces. The nearly closed cracks were modeled by the contact elements. In simulation, it is assumed that the crack surfaces would transmit normal and shear stresses after crack closure while tensile and shear stresses are not transmitted through cracks that remain opened. This leads to marked nonlinear ultrasonic response. Calculation was performed for an aluminum sample having a inclined or normal surface crack of 1-8 nm in crack opening. Incident wave is burst wave of 10 cycles and 4 MHz. The simulated waveforms passing through the surface crack were processed by FFT and the fundamental and second harmonic amplitudes were calculated. The second harmonic amplitude ratio was found to be proportional to the crack length