Nonlinear ultrasonic characterization of fatigue microstructures

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Abstract

Dislocation dipole substructures formed during metal fatigue are shown to produce a substantial distortion of ultrasonic waves propagating through the fatigued material. A model of ultrasonic wave–dislocation dipole interactions is developed that quantifies the wave distortion by means of a material nonlinearity parameter β. Application of the model to AA2024-T4 predicts a value of β approximately 300% larger in material cyclically loaded for 100 kcycles in stress-control at 276 MPa and R=0 than that measured for virgin material. Experimental measurements show a monotonic increase in β as a function of the number of fatigue cycles that closely approaches the predicted increase. The experiments also suggest that the relevant dislocation substructures are localized in the material.

Introduction

Elastic and plastic nonlinearities in a material lead to ultrasonic wave distortion along the wave propagation path and the generation of harmonics of the initial waveform. A quantitative measure of the wave distortion is the ‘acoustic’ nonlinearity parameter. The magnitude of the nonlinearity parameter is highly dependent on the crystalline structure of the solid [1] and on the presence of defect structures [2], [3], [4]. Such dependence has made measurements of the acoustic nonlinearity parameter a useful materials characterization tool [5]. Cyclic loading in metal fatigue promotes the formation of dislocation dipoles as the result of the mutual trapping of dislocations moving to-and-fro in response to the cyclic stresses. To assess the potential of acoustic nonlinearity measurements as a characterization tool for metal fatigue, a generic model is developed of the interaction of ultrasonic waves with arrays of dislocation dipoles. The model predictions are compared to experimental measurements of polycrystalline aluminum alloy 2024-T4.

Section snippets

Interaction of ultrasonic waves with dislocation dipoles

A longitudinal stress perturbation σ associated with a propagating ultrasonic wave produces a longitudinal strain in the material. It is assumed that the total longitudinal strain ε is the sum of an elastic component εe and a plastic component εpl associated with the motion of dislocations in the dipole configuration. Thus,ε=εeplThe relation between the stress perturbation and elastic strain may be written in the nonlinear Hooke's law formσ=Ae2εe+12Ae3ε2e+⋯where Ae2 and Ae3 are the Huang

Experiments

Three ASTM standard ‘dogbone’ specimens of AA2024-T4 were fatigued at a rate of 10 Hz under uniaxial, stress-controlled load at 276 MPa and R=0. Each specimen was fatigued for a different number of cycles: 3 cycles, 10 kcycles, and 100 kcycles. A fourth specimen was unfatigued. Three cylindrical samples each of length 1.9 cm were cut from the 2.53 cm diameter gauge section of each of the four specimens. Optical microscopical examination of the end surfaces of the samples revealed no cracks

Conclusion

The ultrasonic measurements taken of AA2024-T4 show a substantial monotonic increase of the material nonlinearity parameter with an increasing number of fatigue cycles. Similarly dramatic increases in β have been observed in fatigued Ti–6Al–4V [17] and in 410Cb stainless steel specimens [18]. Good agreement is obtained between the value of the nonlinearity parameter measured at 100 kcycles of fatigue in AA2024-T4 and that predicted from the generic ultrasonic wave–dislocation dipole interaction

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