A set of strain-controlled biaxial proportional and non-proportional tests were conducted on solid and tubular specimens of 30CrNiMo8HH steel. The effect of the phase angle on fatigue life was studied. This effect becomes noticeable when applying a 90° out-of-phase loading, reducing the fatigue life by a factor up to 5. It has been shown that the material has no additional hardening due to out-of-phase loading. To account for this severe path dependency, a material dependent non-proportionality modification factor is proposed. This path dependent sensitivity factor is applied to six different fatigue parameters including maximum equivalent total strain, maximum equivalent stress, Smith-Watson-Topper, Fatemi-Socie, plastic strain energy density and total strain energy density to correlate the fatigue results. The predicted fatigue lives are compared with the experiments. The cyclic plasticity models of Mroz and Chaboche were successfully employed to model the cyclic behavior of 30CrNiMo8HH steel. It has been shown that estimations based on the proposed non-proportionality modification factor agree well with the experimental results.
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A B S T R A C T The present study predicts ratcheting response of SS304 tubular stainless steel samples using kinematic hardening rules of Ohno-Wang (O-W), Chen-Jiao-Kim (C-J-K) and a newly modified hardening rule under various stress-controlled, and combined stress-and strain-controlled histories. The O-W hardening rule was developed based on the critical state of dynamic recovery of backstress. The C-J-K hardening rule further developed the O-W rule to include the effect of non-proportionality in ratcheting assessment of materials. The modified rule involved terms dε p Áa= a j j , and n: a= a j j h i 1=2 in the dynamic recovery of the Ahmadzadeh-Varvani (A-V) model to respectively track different directions under multiaxial loading, account for nonproportionality and prevent plastic shakedown of ratcheting data over multiaxial stress cycles.The O-W model persistently overestimated ratcheting strain over the multiaxial loading paths. The C-J-K model further lowered this overprediction and improved the predicted ratcheting curves. The predicted ratcheting curves based on the modified model closely agreed with experimental data under various loading paths.Keywords hardening; non-proportionality; loading paths; rule ratcheting strain; stress/ strain-controlled.
N O M E N C L A T U R Eā = Total backstress tensor b = Second kinematic variable in the A-V and the modified hardening rules C = Material constant in the A-V and the modified hardening rules d ā = Increments backstress tensor dp = Increment of accumulated plastic strain ds = Deviatoric stress increment dε = Total strain increment dε p = Plastic strain increment dε e = Elastic strain increment dε t xy = Incremental strain tensor dσ xy = Incremental stress tensor E = Young's modulus f = Yield surface function G = Shear modulus H p = Plastic modulus function Ī = Unit tensor n = Unity exterior normal to the present yield surface at the stress state γ 1 = Material constant in the A-V and the modified hardening rules γ 2 , δ = Stress level dependent constants in the A-V hardening rule γ 2 = Calibrating coefficient in the modified hardening rule ε r = Ratcheting strain υ = Poisson's ratio Correspondence: S. M. Hamidinejad,
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