Constitutive and Fracture Models for Structural Steels

Localized plastic deformation followed by fracture is an important failure mode of steel structures， and its accurate prediction requires a full-range constitutive model together with a fracture model capable of accounting for complex stress states. Under static loading， methods for determining the true stress-true strain relationship over the full response of structural steels， from yielding and strain hardening up to fracture initiation， were systematically discussed. Before necking， the true stress-true strain relationship can be directly converted from the engineering stress-strain relationship. After necking， the Generalised Post-Necking （GPN） model was proposed， which ensures a continuously differentiable response at the onset of necking and allows the degree of reduction in the post-necking strain-hardening modulus with increasing plastic strain to be flexibly controlled. With only two parameters， it can describe the post-necking hardening behavior of various grades of steel. In addition， a direct method for determining the GPN model parameters was established. Under high strain rates， a pronounced strain-rate hardening effect was demonstrated over the full stress-strain response of structural steels， and this effect decreased as plastic strain developed. Accordingly， a Strain-Dependent Dynamic Increase Factor （SD-DIF） model was proposed. The model has a concise form and provides higher predictive accuracy than conventional models in which the strain-rate effect is decoupled from plastic strain. Regarding fracture initiation under complex stress states， stress triaxiality and the Lode angle parameter were adopted to characterize the stress state at a material point， and their effects on fracture strain were revealed. By incorporating the Lode angle effect into the Void Growth Model （VGM）， a Lode-angle Modified VGM （LMVGM） was developed， in which a three-parameter exponential formulation provides a unified description of the effects of stress triaxiality and the Lode angle parameter on fracture strain. Macroscopic tests and microstructural characterization under combined high strain rates and complex stress states revealed a pronounced coupled effect between strain rate and stress state， with both the magnitude and the trend of the strain-rate effect depending on the stress state. Based on this finding， a dynamic factor for fracture strain that simultaneously depends on strain rate， stress triaxiality， and the Lode angle parameter was introduced into the LMVGM， leading to a Coupled Dynamic LMVGM （CD-LMVGM）. The model can simultaneously capture the positive strain-rate effect under tension-dominated stress states and the negative strain-rate effect under shear-dominated stress states， while maintaining consistently high predictive accuracy for the fracture behavior of different materials.