A Multiaxial Low Cycle Fatigue Life Prediction Model for Both Proportional and Non-proportional Loading Conditions (original) (raw)

It is generally accepted that the additional hardening of materials could largely shorten multi-axis fatigue life of engineering components. To consider the effects of additional hardening under multi-axial loading, this paper summarizes a new multi-axial low-cycle fatigue life prediction model based on the critical plane approach. In the new model, while critical plane is adopted to calculate principal equivalent strain, a new plane, subcritical plane, is also defined to calculate a correction parameter due to the effects of additional hardening. The proposed fatigue damage parameter of the new model combines the material properties and the angle of the loading orientation with respect to the principal axis and can be established with Coffin-Manson equation directly. According to experimental verification and comparison with other traditional models, it is clear that the new model has satisfactory reliability and accuracy in multi-axial fatigue life prediction. KEYWORDS additional hardening, critical plane approach, fatigue life prediction, multi-axial fatigue, nonproportional loading NOMENCLATURE: α max , direction angle of critical plane; Δα t , deviation of the plane with maximum shear strain from critical plane; Γ t , statistical parameter considering additional hardening at time t; Γ T , statistical parameter considering additional hardening in 1 cycle; γ, applied shear strain; γ −1 , shear strain fatigue limit; γ' f , torsional fatigue ductility coefficient; γ αmax , maximum shear strain on critical plane; γ t,α , shear strain on the plane with angle α and at the time t; Δγ, Δγ e , Δγ eq , shear strain, shear elastic strain, and equivalent shear strain range; ε, applied normal strain; ε −1 , normal strain fatigue limit; ε' f , axial fatigue ductility coefficient; ε n * , normal strain excursion; ε αmax , normal strain amplitude on critical plane; ε t,αt , normal strain on the plane with angle α t and at the time t; Δε, Δε e , Δε eq , normal strain, normal elastic strain, and equivalent normal strain range; U, error index; μ(U), Δμ(U), σ(U), average values, relative average value, and standard deviations of U; ν e , ν p , ν eff , elastic, plastic, and effective Poisson's ratio; σ y , yield strength; σ n,max , maximum normal stress; Φ, non-proportionality factor; L, non-proportional hardening coefficient; φ, phase angle between the applied tension and torsion strain; b, b γ , axial and torsional fatigue strength exponent; c, c γ , axial and torsional fatigue ductility coefficient; E, E * , G, elastic modulus, secant modulus, and shear modulus; E s , stacking fault energy; K′, cyclic strength coefficient; N f , number of cycles to failure; N E , N P , experimental life and predicted life; n′, cyclic strain hardening exponent; t, T, loading time and cycle