Abstract: The nonlinear ultrasonic wave rule is studied.The relationships of second or third order relative nonlinear ultrasonic coefficients versus fundamental and harmonic amplitudes are determined.The nonlinear spring model of micro-crack is set up.The relationships of Second Order Relative Nonlinear Ultrasonic Coefficients (SORNC) versus dimensions of micro-cracks are determined.The SORNC increase with the length of micro-crack and the SORNC decrease with the width of micro-crack.The data predicted by the model is consisted with the experimental data.The Third Order Relative Nonlinear Ultrasonic Coefficients (TORNC) increase with the length of micro-crack and the TORNC decrease with the width of micro-crack.

Key words: nonlinear ultrasonics, third order relative nonlinear ultrasonic coefficient, micro-crack, nonlinear spring model