Nonlinear ultrasonic phased-array imaging method for closed cracks based on conjugate delay-multiply-and-sum and fixed-voltage fundamental wave amplitude difference.

Conventional linear ultrasonic phased-array imaging is often limited by crack closure and propagation direction, making stable, high-contrast imaging of closed fatigue cracks difficult. To address residual linear artifacts in odd-even fundamental wave amplitude difference (OE-FAD) imaging associated with system nonlinearity in some conventional phased-array instruments, this study investigates a nonlinear ultrasonic phased-array imaging method based on complex-valued correction-factor-enhanced OE-FAD. The method is combined with conjugate delay-multiply-and-sum (conj-DMAS) post-processing and a conventional matrix-scanning physical focusing strategy to visualize randomly oriented closed fatigue cracks and evaluate crack-tip localization. Experiments were conducted on five 6061 aluminum alloy specimens containing closed fatigue cracks with different propagation directions. The results show that the proposed method effectively compensates for amplitude and phase mismatch between different imaging responses and markedly suppresses residual linear artifacts induced by system nonlinearity. After conj-DMAS post-processing, the nonlinear responses in the crack region become more concentrated, leading to improved crack-tip localization and characterization of crack propagation direction. The proposed method provides a practical approach for nonlinear detection of closed fatigue cracks using conventional phased-array equipment.