Decoupling fatigue micro-crack orientation and length via one-way collinear bulk-wave mixing with a linear receiver array

Quantitative characterisation of closed fatigue micro-cracks under single-sided inspection constraints remains challenging due to the signal coupling between micro-crack orientation and length. To resolve this, this paper proposes a one-way collinear bulk-wave mixing method assisted by a linear receiver array. Finite element (FE) simulations first determine a critical transmission-side collinearity offset between the two transmitting transducers, establishing a geometric constraint that strictly preserves the monotonicity of the summed difference-frequency (DF) amplitude. Subsequently, a dual-metric identification framework is developed, integrating a mirror-asymmetry coefficient to characterise the spatial distribution of the DF response, and a normalised summed DF amplitude to evaluate its overall intensity. This strategy effectively decouples orientation information from micro-crack length. Experimental validation demonstrates that the proposed method accurately estimates geometric parameters, limiting orientation errors to within ±8° and length errors to below 19%, confirming its reliability for precise in-service non-destructive evaluation.