A Proposal of a Constitutive Model Considering Ultra-Low Cycle Fatigue Damage Accumulation Under Tension–Compression Cyclic Loading

The cyclic material properties are crucial for accurate assessment of structural response; however, conventional numerical methods often fail to replicate the mechanical degradation caused by ultra-low cycle fatigue (ULCF) damage accumulation. This paper focuses on a novel constitutive model characterizing the continuous degradation in yield stress and stiffness under large-strain tension–compression cyclic loads. A series of 32 cyclic tests on circular notched specimens covering a range of stress triaxialities are first revisited to systematically identify the cyclic softening behavior. The corresponding limitations of the widely applied classical Chaboche theory are examined, and an enhanced elastoplastic constitutive framework is proposed accordingly. On this basis, the stress-weighted ductile fracture model (SWDFM), which is developed from micro-damage mechanics, is then employed as the internal damage criterion of the proposed constitutive model. Explicit functional relationships linking the evolved yield stress and Young’s modulus to the imposed damage index are established and calibrated against the test data. Based on these findings, a new cyclic ductile constitutive model is developed, which is programmed into the UMAT subroutine compatible with ABAQUS/Standard. Numerical validations against the experimental cyclic responses exhibit good agreement, as indicated by the considerably low average errors of 5% for both strength and stiffness, demonstrating its validity in terms of the hysteretic behavior simulation for metals subjected to progressive ULCF damage.