Nonlinear Acoustic Modeling and Measurements during the Fatigue Process in Metals.

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