Nonlinear ultrasonic characterization method for early-stage damage state detection in welded pressure vessels

To address the weak detectability and poor traceability of early-stage degradation and micro-damage in welded pressure vessels during service, a nonlinear ultrasonics (NLU) detection strategy based on harmonic features is proposed, in which Equivalent nonlinear parameters of fundamental amplitude A1 and second harmonic amplitude A2 the parameter β′ = A₂/A₁² is adopted as a unified, trend-oriented metric for state characterization. An explicit finite element model incorporating material elastic response nonlinearity and closed microcrack/micro-interface contact acoustic nonlinearity is first established to systematically analyze the effects and coupling characteristics of multiple nonlinear mechanisms on harmonic generation and parameter responses. The investigation shows that contact acoustic nonlinearity can exhibit stronger nonlinear effect characteristics; under the fixed ultrasonic propagation path and excitation condition, β′ is more appropriately extended and interpreted as an equivalent indicator of the coupled intensity of multi-source nonlinear mechanisms, so as to clarify its physical meaning and applicability boundary. Subsequently, an NLU detection chain platform is constructed and calibrated, and repeated coupling measurements are conducted on specimens subjected to gradient fatigue loading. The experimental results show that β′ exhibits a reproducible double-peak evolution trend with The ratio of fatigue life N to the fatigue life at failure Fatigue process (N₀ = N/N_f), providing higher sensitivity and discriminability to early-stage material state variations than linear acoustic indicators. This study establishes an interpretable parametric feature baseline for periodic inspection and trend-based condition assessment of welded pressure vessel structures, and lays a foundation for subsequent data-driven and intelligent structural health evaluation.