Compensating Couplant Effects in Phased-Array Ultrasonic ToF Sensing for Residual Stress

Residual stress (RS) is a key integrity parameter after welding and additive manufacturing, motivating portable sensing methods for in-situ assessment. Phased Array Ultrasonics for Residual Stress (PAURS) treats a phased-array probe as a time-of-flight (ToF) sensor and infers RS from ToF changes of the longitudinal critically refracted (LCR) wave propagating near the surface. In practical deployments, however, the ToF sensing chain can be susceptible to systematic bias from sensor–specimen interface variability (couplant layer thickness) which can dominate the inferred stress uncertainty if not quantified and corrected. This study combines numerical modelling with experimental validation to (i) characterise couplant-induced sensitivity in LCR ToF sensing, (ii) propagate this effect into RS error/uncertainty, and (iii) demonstrate a model-informed compensation strategy suitable for practical calibration workflows. Simulations show that couplant thickness variations can introduce RS errors of ~36 MPa (~13% of yield strength). The proposed compensation reduces ToF bias to 0 ns under idealised simulated conditions and to ~0.3 ns in experiments, corresponding to ~1.1 MPa RS error (~0.4% of yield strength). These results provide configuration-specific guidance for sensor calibration and uncertainty reporting in phased-array ultrasonic RS sensing, and establish a foundation for future in-process sensing of residual stress and microstructure evolution.