Interface behaviors of elastic-plastic waves and its impact on uncertainties in vibro-acoustic modulation (VAM) for structural health monitoring (SHM) of bolt loosening

The non-monotonic relationship between nonlinear VAM features and the residual torque of bolted joints has been experimentally observed in previous studies. Such non-monotonicity leads to the misjudgment in the quantitative SHM of bolt loosening. However, the causes leading to the non-monotonic behavior are unclear and an effective theoretical explanation is still lacking. To circumvent this deficiency, the interface behaviors of elastic–plastic waves are investigated in this study via theoretical modelling, simulation and experiment. A new exponential theoretical stiffness model is proposed to quantitively consider the effect of both surface roughness and interfacial pressure on the plastic asperity softening, in which roughness-related parameters are also incorporated in the exponent. The non-monotonic nonlinear VAM features are then predicted by both single-degree-of-freedom and multi-degree-of-freedom wave-surface interaction models. The effect of initial surface roughness and its variations caused by repeated loading on VAM features are validated by comparative experiment involving tightening tests of the aluminum-aluminum joint and the CFRP-CFRP joint, and retightening tests of the latter, respectively. The results show that the non-monotonicity of nonlinear VAM features is primarily influenced by the distribution of rough asperities on joint surfaces, and the different patterns of such non-monotonicity can be described by the proposed model. Higher model parameters indicate a rougher interface and result in more significant non-monotonic nonlinear VAM features. Retightening of rough joints can smoothen the contact surface. Following this guidance, the monotonic monitoring range of the CFRP-CFRP joint (Sa = 5.362) has been improved from 11 N·m to 20 N·m after 16th bolt retight.