Redefining stress triaxiality for ultra-low cycle fatigue of structural steels

TY - JOUR

T1 - Redefining stress triaxiality for ultra-low cycle fatigue of structural steels

AU - He, Qun

AU - Yam, Michael C.H.

AU - Lin, Xue-Mei

AU - Ho, H. C.

AU - Chung, Kwok Fai

N1 - Publisher Copyright: © 2026 Elsevier Ltd.

PY - 2026/1/28

Y1 - 2026/1/28

N2 - Stress triaxiality has been a cornerstone parameter for describing void growth and ductile fracture in metals for more than 60 years. Its classical definition, derived from J2 plasticity without accounting for backstress, becomes inadequate in ultra-low cycle fatigue conditions, where backstress evolution and load reversals significantly alter the stress state. In such cases, the conventional definition of stress triaxiality may even lead to singularities when the second invariant of deviatoric stress, i.e., J2, approaches zero. This study revisits the classical void growth problem and demonstrates that the definition of stress triaxiality is inherently dependent on the adopted plasticity model. Specifically, once backstress is included in cyclic plasticity, it must also be accounted for in the definition of stress triaxiality to maintain consistency. In this way, a new definition of stress triaxiality incorporating the effect of backstress is proposed, providing a physically meaningful measure of stress triaxiality under cyclic loading. The new definition is analytically derived and validated through ultra-low cycle fatigue (ULCF) experiments of high-strength steel Q690, supported by finite element simulations. Results show that the proposed definition reliably captures the stress state associated with void growth and accurately predicts ULCF crack initiation life, overcoming the limitations of the classical definition. These findings establish, for the first time, a consistent theoretical and experimental basis for extending void-based fracture models to cyclic loading, with direct implications for assessing the seismic safety of steel structures.

AB - Stress triaxiality has been a cornerstone parameter for describing void growth and ductile fracture in metals for more than 60 years. Its classical definition, derived from J2 plasticity without accounting for backstress, becomes inadequate in ultra-low cycle fatigue conditions, where backstress evolution and load reversals significantly alter the stress state. In such cases, the conventional definition of stress triaxiality may even lead to singularities when the second invariant of deviatoric stress, i.e., J2, approaches zero. This study revisits the classical void growth problem and demonstrates that the definition of stress triaxiality is inherently dependent on the adopted plasticity model. Specifically, once backstress is included in cyclic plasticity, it must also be accounted for in the definition of stress triaxiality to maintain consistency. In this way, a new definition of stress triaxiality incorporating the effect of backstress is proposed, providing a physically meaningful measure of stress triaxiality under cyclic loading. The new definition is analytically derived and validated through ultra-low cycle fatigue (ULCF) experiments of high-strength steel Q690, supported by finite element simulations. Results show that the proposed definition reliably captures the stress state associated with void growth and accurately predicts ULCF crack initiation life, overcoming the limitations of the classical definition. These findings establish, for the first time, a consistent theoretical and experimental basis for extending void-based fracture models to cyclic loading, with direct implications for assessing the seismic safety of steel structures.

KW - Backstress

KW - Cyclic plasticity

KW - Ductile fracture

KW - Stresstriaxiality

KW - Ultra-low cycle fatigue

UR - https://www.scopus.com/pages/publications/105029223577

U2 - 10.1016/j.ijfatigue.2026.109520

DO - 10.1016/j.ijfatigue.2026.109520

M3 - Article

AN - SCOPUS:105029223577

SN - 0142-1123

VL - 207

JO - International Journal of Fatigue

JF - International Journal of Fatigue

M1 - 109520

ER -