The nonlinear spring model combined with dislocation dipole theory was applied to\ndescribe the acoustic nonlinearity during the fatigue process in metals. The spring stiffness changes\nwith fatigue degree. For the early stage, spring stiffness approaches infinity, and the heavier\nnonlinearity mainly results from the increase of dislocation density. Further fatigue leads to the\noccurrence of micro-cracks, during which spring stiffness begins to decrease. Abundant micro-crack\nsprouting accelerates the crackâ??s expansion, and spring stiffness drops quickly, which causes the\nobvious decline in the transmitted harmonic amplitudes. Solutions obtained from the nonlinear wave\nequation with dislocation terms were added into the spring model. Varying spring stiffness was\nchosen for simulating the fatigue process. Then, nonlinear harmonic variation during this process\nwas observed, which was classified into three stages: (I) the early dislocation fatigue stage; (II) the\nmicro-crack sprouting stage; (III) the crack expansion stage. Nonlinear acoustic measurements were\ncarried out on an aluminum alloy specimen during its fatigue process until cracks could be seen\nclearly. Harmonic variations in experiments can also be classified into the same three stages as the\nnumerical results, which provides a theoretical and experimental reference for fatigue evaluation in\nmetals using the nonlinear acoustic method.
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