Ultrasonic phased array combined with modified delay multiply and sum beamforming for nonlinear imaging of closed microcracks

Traditional phased array ultrasonic (PAU) non-destructive testing technology is not prone to generating echo response when detecting closed microcracks, making it difficult to perform quantitative detection. In this paper, a nonlinear PAU modified delay-multiply-and-sum (PAU-MDMAS) imaging method is proposed to achieve the accurate detection of closed microcracks. In order to effectively collect nonlinear signals, full array elements, odd array elements, and even array elements are used to adjust the amplitude of incident waves at the focal point, and the fixed voltage fundamental amplitude difference (FAD) method is used to obtain nonlinear signals. On this basis, the signal processing removes clutter interference and effectively improves the signal-to-noise ratio of nonlinear signals. In addition, the MDMAS adaptive beamforming algorithm is proposed for post-processing imaging. By utilizing the spatial coherence between signals, the delay signals are adaptively paired and multiplied to highlight the nonlinear response from closed microcracks, and the coherence factor (CF) is calculated for adaptive beamforming to improve the nonlinear imaging accuracy of ultrasonic phased array. The experimental results show that the nonlinear PAU-MDMAS imaging method not only achieves high-precision localisation imaging of closed microcracks but also quantitatively characterises their length and better detects their expansion trends.