Ratcheting assessment of steel alloys under uniaxial loading: a parametric model versus hardening rule of Bower

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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,

Section: Materials Testing and Multiaxial Ratcheting Datasupporting

confidence: 59%

Ratcheting of 304 Stainless Steel Alloys subjected to Stress‐Controlled and mixed Stress‐ and Strain‐Controlled Conditions evaluated by Kinematic Hardening Rules

Hamidinejad

Noban

Varvani‐Farahani

2015

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“…The well‐known Armstrong–Frederick kinematic hardening model (A–F), which is based on strain hardening and dynamic recovery of back stress, was reported to overestimate the ratcheting strain . Subsequently, the models based on the A–F with modification of the dynamic recovery term have been proposed to improve the prediction, for example, Chaboche, Ohno and Wang, Abedl and Karim, Hassan and Kyriakides, Kang et al ., Jiang and Sehitoglu, Zakavi, Jiao, Dahlberg, Liang, Adibi‐Asl, Chen, Zhang and Ahmadzadeh . Among these models, the nonlinear kinematic hardening rule with the critical state for dynamic recovery developed by Ohno and Wang is considered to be the most successful.…”

Section: Introductionmentioning

confidence: 99%

A plastic shakedown constitutive curve based on uniaxial ratcheting behavior of 304 stainless steel at room temperature

Jiang

Sun

Liu

et al. 2013

On the basis of the Bauschinger effect, a relationship between the elastic space defined in this study and the accumulated plastic strain is measured in uniaxial ratcheting tests of 304 stainless steel at room temperature. According to this relationship, a new model of uniaxial ratcheting is established and used to simulate uniaxial ratcheting behavior. The results of simulation agree well with the experimental results. These results demonstrate that the relationship between the elastic space and the accumulated plastic strain plays an important role in uniaxial ratcheting simulation. Furthermore, by taking into account the interaction of ratcheting and viscoplasticity, the relationships among elastic space, accumulated plastic strain and loading cases are discussed. It can be seen that, when the stress ratio R of valley stress versus peak stress is not less than zero, the accumulated plastic strain is a function of the peak stress. So, a constitutive curve is obtained to describe the stable states of plastic shakedown for 304 stainless steel material under the stress ratio R ≥ 0. It can be used to determine the accumulated plastic strain of engineering structures under cyclic loading only by an elastic–plastic analysis.

“…A constitutive model has been introduced by Chaboche 16 in the form of superposition of the series of decomposed A-F nonlinear hardening rules. 30 The present study further develops the modified A-F hardening rule of Bower by involving new ratcheting rate coefficients. Chaboche 17 further improved the capability of A-F rule in predicting ratcheting strain by introducing a dynamic recovery term in the form of a power function and a threshold.…”

Section: Introductionmentioning

confidence: 91%

Ratcheting assessment of materials based on the modified Armstrong–Frederick hardening rule at various uniaxial stress levels

Ahmadzadeh

Varvani‐Farahani

2013

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The present study evaluates ratcheting response of materials by means of the Armstrong–Frederick (A–F) hardening rule, the modified A–F rule (Bower's model), and further modifications of the hardening rule based on new introduced coefficients. The implemented modifications on the A–F‐based hardening rule aims to address stages of ratcheting over stress cycles. The modified hardening rule predicts the ratcheting strain rate decay over stage I and the constant rate of strain accumulation during stage II. The modified hardening rule consisted of the coefficients of the hardening rule controlling stress–strain hysteresis loops generated over stress cycles during ratcheting process (Bower's modification on A–F rule) plus the coefficients controlling rates over stages of materials ratcheting deformation. Stress–strain‐dependent coefficients in the modified rule are responsible to compromise overprediction of ratcheting of A–F during stage I and the premature plastic shakedown beyond stage I induced by Bower's model. Ratcheting strain rate coefficients improved the hardening rule capability to calibrate and control the rate of ratcheting in stages I and II and enabled the modified hardening rule to predict ratcheting strain over a prolonged domain of stress cycles. The modified hardening rule was employed to assess ratcheting response of 304, 42CrMo, 316L steel and copper samples under uniaxial loading conditions. The predicted ratcheting values based on the modified hardening rule and the experimental ratcheting strains were found in good agreements.