Abstract: Assuming small strain condition, perturbation method is used to resolve one dimensional wave equation. The nonlinear wave rule is studied when ultrasonic wave propagates in solid medium. When tension stresses change in metal materials, the variation trends of the nonlinear coefficients β and δ are studied. The nonlinear ultrasonic testing system is set up to detect the harmonic wave amplitudes. The variation trends of the nonlinear coefficients with stresses are acquired. The results show that the nonlinear coefficients increase with the tension stress. For 2024 aluminum alloy, the second order nonlinear coefficient β is approximately linear with the tension stress when the tension stress is smaller than 84.6% of the yield strength, and it increases slowly with tension stress when the tension stress is bigger than 84.6% of the yield strength. For 45 steel, the second order nonlinear coefficient β increases linearly with the stress when the tress is smaller than 84.5% of strength stress, and it increases quickly with stress when the stress is bigger than 84.5% of the yield strength. The third nonlinear coefficients δ have change points in 76.9% and 78.9% of yield strength for 2024 aluminum alloy and 45 steel, respectively. The second nonlinear coefficients β and the third nonlinear coefficients have different sensitivities to the stress. The third nonlinear coefficients δ have higher sensitivity than the second nonlinear coefficients β.

Key words: high order nonlinear coefficients, nonlinear ultrasonic, tension stress