Experimental and theoretical analysis of the correlation between cumulative plastic damage and SMFL of structural steel under low cycle fatigue

Evaluation of fatigue damage is critical for ensuring the safety and durability of steel structures. A newly developed non-destructive testing (NDT) method named magnetic memory method (MMM) is a valid approach to evaluate the ferromagnetic material stress and damage utilizing changes in the self-magnetic leakage (SMFL) field. However, because of the lack of accurate description of the SMFL changing mechanism under elastic and plastic cyclic loads, the application of MMM in the assessment of cumulative plastic damage D for structural steel under low cycle fatigue (LCF) is greatly limited. Hence, in this paper, based on J-A magneto-mechanical theory and J-A magnetic hysteresis theory, an improved theoretical model that described the variation of irreversible magnetization with plastic strain after cyclic loading was proposed and verified. Combining with magnetic charge theory and cumulative damage mechanics model further, the theoretical relationship between the gradient K of SMFL curves and cumulative plastic damage D was established, which indicated preliminarily K had a potential possibility to assess the D. Then, the tension–compression LCF tests on Q345B and Q345qC dog-bone steel sheet specimens were conducted and the surface SMFL of the specimens under cyclic load was measured. The experimental correlation between K and D was further given by the analysis of experimental data and clarified from the perspective of energy conversion for the first time. By the comparison between experimental and theoretical results, and the in-depth analysis of the microcosmic mechanism about the activity and multiplication of dislocation, the semi-quantitative correlation that K was related to D exponentially was presented. The accuracy of the established theoretical relationship was further verified. Thus, the established K-D theoretical relationship can be used for the theoretical analysis of the quantitative characterization of cumulative plastic damage. This work demonstrates that the cumulative plastic damage can be estimated semi-quantitatively via the variations of SMFL curve, which is beneficial for the fatigue damage assessment for structural steel under LCF.