Ratcheting of 304 stainless steel under multiaxial step-loading conditions

Nayebi

2018

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The current study has attempted to comprehensively review ratcheting response of materials involving various influential parameters such as loading spectra, thermal cycles, stress levels, stress raisers, strain rate, and visco‐plasticity and material types with a focus on pressurized pipes and equipment. The mechanism of deformation, types, and the rate of progress over stages of ratcheting were discussed. Safety design codes and procedures were highlighted for reliable design of pressurized pipes against progressive ratcheting and to safeguard the system against catastrophic failure at which both mechanical and thermal ratcheting were integrated. Boundaries and demarcation of ratcheting‐shakedown zones developed based on Bree's diagram were employed to assess plastic deformation accumulation over stress cycles. Shakedown and ratcheting boundaries were discussed through methods developed on the basis of Melan's theorem over last few decades. Ratcheting response of materials was reviewed through descriptions of parametric models and kinematic hardening rules involving various variables and parameters. Interaction of ratcheting with creep and low‐cycle fatigue has promoted progressive damage in materials. Pressurized pipes subjected to thermal cycles and external bending cycles were evaluated by numerical solutions along with kinematic hardening rules to assess ratcheting over stress cycles.

Section: Kinematic Hardening Models Using Von Mises Yield Surfacementioning

confidence: 99%

Ratcheting in pressurized pipes and equipment: A review on affecting parameters, modelling, safety codes, and challenges

Nayebi

2018

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“…Coefficient δ was defined through product of

{⟨\overset{true¯}{n} . \overset{true¯}{a} / |\overset{a}{true}|⟩}^{1 true/ 2}

and internal variable

\overset{b}{true}

to control ratcheting rate and to prevent plastic shakedown over multiaxial stress cycles. Introducing terms in the dynamic recovery of the A–V hardening rule, the model is rewritten as

d \overset{a}{true} = C d {\overset{true¯}{ε}}_{p} - γ_{1} ((), \overset{a}{true} - {⟨\overset{true¯}{n} . \frac{\overset{a}{true}}{(||, \overset{true¯}{a})}⟩}^{1 true/ 2} \overset{b}{true}) (⟨⟩, d {\overset{true¯}{ε}}_{p} . \frac{\overset{true¯}{a}}{|\overset{a}{true}|})

d \overset{b}{true} = ((), 2 - \overset{n}{true} . \frac{\overset{true¯}{a}}{|\overset{a}{true}|}) γ_{2} ((), \overset{a}{true} - \overset{b}{true}) (⟨⟩, d {\overset{true¯}{ε}}_{p} . \frac{\overset{true¯}{a}}{|\overset{a}{true}|})

where H p is the plastic modulus and is defined as

H_{p} = C - γ_{1} ((), \overset{a}{true} - {⟨\overset{true¯}{n} . \frac{\overset{a}{true}}{(||, \overset{true¯}{a})}⟩}^{1})

…”

Section: Formulation and Framework Of Hardening Rulesmentioning

confidence: 99%

“…Hassan and Kyriakides evaluated ratcheting response in mild steel samples tested at different step loading conditions. Ahmadzadeh and Varvani evaluated ratcheting response of a few steel alloys tested at various sequential step‐loading spectra through their recently developed hardening rule.…”

Section: Introductionmentioning

confidence: 99%

“…Over last half-century, coupled kinematic hardening rules were developed to formulate ratcheting of materials under various loading spectra. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] These hardening rules were proposed by Armstrong-Frederick (A-F), 6 Chaboche, 7 Bower, 8 Ohno-Wang (O-W), 9,10 Jiang-Sehitoglu (J-S), 11,12 McDowell, 13 Abdel-Karim-Ohno, 14,15 Chen et al [16][17][18] and Ahmadzadeh-Varvani (A-V). [19][20][21][22][23][24][25] Terms of linear strain hardening and dynamic recovery have collectively constructed the anatomy of the coupled nonlinear constitutive models of A-F type.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A comparative study in descriptions of coupled kinematic hardening rules and ratcheting assessment over asymmetric stress cycles

2016

The present study evaluates coupled kinematic hardening rules at which the calculation of plastic moduli is coupled with these models through the consistency condition of yield surfaces. The frameworks of the Ohno–Wang (O–W), McDowell, Jiang–Sehitoglu (J–S), Chen–Jiao–Kim (C–J–K) and Ahmadzadeh–Varvani (A–V) hardening rules and their incorporated dynamic recovery terms/coefficients were discussed for steel samples undergoing asymmetric stress cycles. Different hardening rules offered distinct procedures to determine terms/coefficients and to generalize hardening rule descriptions applicable for different materials and loading spectra. The progressive evolution of backstress over plastic deformation was attributed to the interaction of dislocations controlled by the dynamic recovery of the models. The predicted ratcheting curves through the C–J–K and A–V hardening rules closely agreed with ratcheting data of 1045 and 304 steel samples tested at different loading paths. The O–W, J–S and McDowell hardening rules showed some overprediction in ratcheting as compared with experimental data.

“…Several cyclic plasticity models have been developed to characterize ratcheting response of materials under various loading conditions. The coupled kinematic hardening rules consisted of the linear strain hardening, and dynamic recovery terms have been mainly constructed on the basis of Armstrong–Frederick (A–F) . The choice and capability of the coupled hardening rules have been highly dependent on how dynamic recovery term was modified.…”

Section: Introductionmentioning

confidence: 99%

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

Hamidinejad

Noban

2015

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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,