Quantitative biaxial stress measurement using ultrasonic LCR wave-based time-of-flight analysis

Ultrasonic stress measurement is a mature approach for uniaxial loading but lacks systematic validation under biaxial states. We develop an engineering-grade biaxial loading platform and a tridirectional integrated LCR probe that enables simultaneous three-direction TOF acquisition during single clamping. A 36-state in-plane stress matrix (0-250 MPa in 50-MPa steps; 10 uniaxial, 6 equibiaxial, and 20 asymmetric cases) is constructed. Based on Murnaghan acoustoelasticity, stress coefficients calibrated from X70 steel uniaxial tests are used for biaxial reconstruction with a controlled signal chain (5 MHz, DSO-X 2004A, 2 GSa/s, 0.5 ns, PDMS 1000 cSt). A categorywise evaluation reveals MAEs ≈ 7-8 MPa (∼3%FS), RMSEs ≈ 9 MPa (3.5-3.7%FS), and mean biases ≈ +0.3 MPa across the 0-250-MPa range; the maximum absolute error remains within ∼ 15 MPa (≤6%FS). These results provide a reproducible device-algorithm-data pipeline and quantitative evidence for acquiring ultrasonic LCR-based stress measurements under complex in-plane loading conditions, with direct relevance to health assessments of engineering structures.