Ratcheting Prediction of 1070 and 16MnR Steel Alloys Under Uniaxial Asymmetric Stress Cycles By Means of Ohno–Wang and Ahmadzadeh–Varvani Kinematic Hardening Rules

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
G. R. Ahmadzadeh ◽  
S. M. Hamidinejad ◽  
A. Varvani-Farahani
Keyword(s):  
Kinematic Hardening ◽  
Uniaxial Stress ◽  
Cyclic Stress ◽  
Processing Unit ◽  
Central Processing ◽  
Hardening Rule ◽  
Ratcheting Strain ◽  
Stress Cycles ◽  
Time Required ◽  
Hardening Rules

The present study predicts ratcheting response of 1070 and 16MnR steel samples using nonlinear kinematic hardening rules of Ohno–Wang (O–W) and Ahmadzadeh–Varvani (A–V) under uniaxial stress cycles. The ratcheting values predicted based on the O–W model were noticeably influenced by the magnitude of exponents and the number of backstress components. Taking into account both material and cyclic stress level dependent coefficients, the A–V hardening rule offered a simple framework to predict ratcheting strain over loading cycles. A comparative study of these hardening rules to assess ratcheting of 1070 and 16MnR steel samples undergoing uniaxial loading conditions resulted in a close agreement of the A–V and O–W models. The choice of hardening rules in the assessment of materials ratcheting was further discussed based on the complexity of the hardening rule, number of constants/coefficients required to characterize ratcheting response, and central processing unit (CPU) time required to run the models.

scholarly journals Modifications on A-F Hardening Rule to Assess Ratcheting Response of Materials and Its Interaction with Fatigue Damage under Uniaxial Stress Cycles

2021 ◽  
Author(s):  
Gholamreza Ahmadzadehrishehri
Keyword(s):  
Strain Rate ◽  
Fatigue Damage ◽  
Uniaxial Stress ◽  
Cyclic Stress ◽  
Uniaxial Loading ◽  
Rate Coefficients ◽  
Loading Conditions ◽  
Hardening Rule ◽  
Ratcheting Strain ◽  
Stress Cycles

Ratcheting deformation is accumulated progressively over three distinct stages in materials undergoing asymmetrical cyclic stresses. The present thesis evaluates the triphasic ratcheting response of materials from two stand points: (i) Mechanistic approach at which stages of ratcheting progress over stress cycles was related to mechanistic parameters such as stress level, lifespan, mechanical properties and the softening/hardening response of materials. Mechanistic approach formulated in this thesis was employed to assess ratcheting strain over triphasic stages in various steel and copper alloys under uniaxial stress cycles. Good agreements were achieved between the predicted ratcheting strain values based on the proposed formulation and those of experimentally reported. (ii) Kinematic hardening rule approach at which the hardening rule was characterized by the yield surface translation mechanism and the corresponding plastic modulus calculated based on the consistency condition. Various cyclic plasticity models were employed to assess ratcheting response of materials under different loading conditions. The Armstrong-Frederick (A-F) hardening rule was taken as the backbone of ratcheting analysis developed in this thesis mainly due to less complexity and number of coefficients in the hardening rule as compared with other earlier developed hardening rules in the literature. To predict triphasic ratcheting strain over stress cycles, the A-F hardening rule has been further developed by means of new strain rate coefficients γ2 and δ. These coefficients improved the hardening rule capability to calibrate and control the rate of ratcheting over its progressive stages. The modified hardening formulation holds the coefficients of the hardening rule to control stress-strain hysteresis loops generated over stress cycles during ratcheting process plus the ratcheting rates over stages I, II, and III. These coefficients were calibrated and defined based on the applied stress levels. The constructed calibration curves were employed to determine strain rate coefficients required to assess ratcheting response of materials under uniaxial loading conditions at various cyclic stress levels. The predicted ratcheting strain values based on the modified hardening rule were found in good agreements with the experimentally obtained ratcheting data over stages I and II under uniaxial loading conditions. The capability of the modified hardening rule to assess ratcheting deformation of materials under multi-step uniaxial loading spectra was also assessed. Subsequent load steps were considerably affected by previous load steps in multi-step loading conditions. Ratcheting strains for low-high stress steps were successfully predicted by the modified hardening rule. High-low loading sequences however resulted in an overestimated reversed ratcheting strain in the later load steps. The modified hardening rule proposed in this thesis was then employed to predict the ratcheting strain and its concurrent interaction with fatigue damage over stress cycles in steel alloys. The interaction of ratcheting and fatigue damage was defined based on mechanistic parameters involving the effects of mean stress, stress amplitude, and cyclic softening/hardening response of materials. The extent of ratcheting effect on the overall damage of steel samples was defined by means of the product of the average ratcheting strain rate over the stress cycles and the applied maximum cyclic stress, while fatigue damage was analysed based on earlier developed energy-based models of Xia-Ellyin and Smith-Watson-Topper. Overall damage induced by both ratcheting and fatigue was calibrated through a weighting factor at various ratios of mean stress/cyclic amplitude stress. The estimated lives based on the proposed algorithm at different mean stresses and stress amplitudes showed good agreements as compared with experiments.

scholarly journals Modifications on A-F Hardening Rule to Assess Ratcheting Response of Materials and Its Interaction with Fatigue Damage under Uniaxial Stress Cycles

2021 ◽  
Author(s):  
Gholamreza Ahmadzadehrishehri
Keyword(s):  
Strain Rate ◽  
Fatigue Damage ◽  
Uniaxial Stress ◽  
Cyclic Stress ◽  
Uniaxial Loading ◽  
Rate Coefficients ◽  
Loading Conditions ◽  
Hardening Rule ◽  
Ratcheting Strain ◽  
Stress Cycles

Ratcheting deformation is accumulated progressively over three distinct stages in materials undergoing asymmetrical cyclic stresses. The present thesis evaluates the triphasic ratcheting response of materials from two stand points: (i) Mechanistic approach at which stages of ratcheting progress over stress cycles was related to mechanistic parameters such as stress level, lifespan, mechanical properties and the softening/hardening response of materials. Mechanistic approach formulated in this thesis was employed to assess ratcheting strain over triphasic stages in various steel and copper alloys under uniaxial stress cycles. Good agreements were achieved between the predicted ratcheting strain values based on the proposed formulation and those of experimentally reported. (ii) Kinematic hardening rule approach at which the hardening rule was characterized by the yield surface translation mechanism and the corresponding plastic modulus calculated based on the consistency condition. Various cyclic plasticity models were employed to assess ratcheting response of materials under different loading conditions. The Armstrong-Frederick (A-F) hardening rule was taken as the backbone of ratcheting analysis developed in this thesis mainly due to less complexity and number of coefficients in the hardening rule as compared with other earlier developed hardening rules in the literature. To predict triphasic ratcheting strain over stress cycles, the A-F hardening rule has been further developed by means of new strain rate coefficients γ2 and δ. These coefficients improved the hardening rule capability to calibrate and control the rate of ratcheting over its progressive stages. The modified hardening formulation holds the coefficients of the hardening rule to control stress-strain hysteresis loops generated over stress cycles during ratcheting process plus the ratcheting rates over stages I, II, and III. These coefficients were calibrated and defined based on the applied stress levels. The constructed calibration curves were employed to determine strain rate coefficients required to assess ratcheting response of materials under uniaxial loading conditions at various cyclic stress levels. The predicted ratcheting strain values based on the modified hardening rule were found in good agreements with the experimentally obtained ratcheting data over stages I and II under uniaxial loading conditions. The capability of the modified hardening rule to assess ratcheting deformation of materials under multi-step uniaxial loading spectra was also assessed. Subsequent load steps were considerably affected by previous load steps in multi-step loading conditions. Ratcheting strains for low-high stress steps were successfully predicted by the modified hardening rule. High-low loading sequences however resulted in an overestimated reversed ratcheting strain in the later load steps. The modified hardening rule proposed in this thesis was then employed to predict the ratcheting strain and its concurrent interaction with fatigue damage over stress cycles in steel alloys. The interaction of ratcheting and fatigue damage was defined based on mechanistic parameters involving the effects of mean stress, stress amplitude, and cyclic softening/hardening response of materials. The extent of ratcheting effect on the overall damage of steel samples was defined by means of the product of the average ratcheting strain rate over the stress cycles and the applied maximum cyclic stress, while fatigue damage was analysed based on earlier developed energy-based models of Xia-Ellyin and Smith-Watson-Topper. Overall damage induced by both ratcheting and fatigue was calibrated through a weighting factor at various ratios of mean stress/cyclic amplitude stress. The estimated lives based on the proposed algorithm at different mean stresses and stress amplitudes showed good agreements as compared with experiments.

Ratcheting Prediction at the Notch Root of Steel Samples Over Asymmetric Loading Cycles

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
A. Shekarian ◽  
A. Varvani-Farahani
Keyword(s):  
Stress Relaxation ◽  
Notch Root ◽  
Kinematic Hardening ◽  
Strain Range ◽  
Medium Carbon Steel ◽  
Computational Time ◽  
Processing Unit ◽  
Central Processing ◽  
Hardening Rules ◽  
Neuber's Rule

Abstract The present study intends to evaluate local ratcheting and stress relaxation of medium carbon steel samples under various asymmetric load levels by means of two kinematic hardening rules of Chaboche (CH) and Ahmadzadeh-Varvani (A-V). The Neuber's rule was coupled with the hardening rules to predict ratcheting and stress relaxation at the vicinity of the notch root. Stress-strain hysteresis loops generated by the CH and A-V models were employed to simultaneously control ratcheting progress over stress cycles and stress relaxation at notch root while strain range kept constant in each cycle. The higher cyclic load levels applied at the notch root accelerated shakedown over smaller number of cycles and resulted in lower relaxation rate. The larger notch diameter of 9 mm on the other hand induced lower stress concentration and smaller plastic zone at the notch root promoting ratcheting progress with less materials constraint over loading cycles compared with notch diameter d = 3 mm. Predicted ratcheting results through the A-V and CH models as coupled with the Neuber's rule were found in good agreements with the experimental data. The choice of the A-V and CH hardening rules in assessing ratcheting of materials was attributed to the number of terms/coefficients and complexity of their frameworks and computational time/central processing unit (CPU) required to run a ratcheting program.

scholarly journals Development of a kinematic hardening rule to assess ratcheting response of materials under various multiaxial loading spectra

2021 ◽  
Author(s):  
SeyedMahdi Hamidinejad
Keyword(s):  
Experimental Data ◽  
Dynamic Recovery ◽  
Kinematic Hardening ◽  
Multiaxial Loading ◽  
Steel Alloys ◽  
Modified Model ◽  
Hardening Rule ◽  
Loading Paths ◽  
Ratcheting Strain ◽  
Stress Cycles

The present thesis develops an Armstrong-Frederick (A-F) type coupled kinematic hardening rule to assess ratcheting response of steel alloys under various multiaxial loading paths. The hardening rule is constructed on the basis of the recently proposed Ahmadzadeh-Varvani (AV) hardening rule to further evaluate the ratcheting response of materials under multiaxial loading spectra. The modified model offers a simple framework with limited number of terms and coefficients in the dynamic recovery portion of the model. The dynamic recovery further holds inner product of plastic strain increment p dand backstress unit vector a a with different directions under multiaxial stress cycles enables the model to track different directions. Term 1/ 2 n. a a taking positive values less than unity for multiaxial loading conditions is to control the accumulation rate of ratcheting strain and to prevent the modified model to experience plastic shakedown over stress cycles in stage II. Term(2 n. a a ) taking the values between 1 and 3 under multiaxial loading, magnifies the effect of coefficient γ2 to take into account the nonproportionality effect of various loading paths and further to shift down the predicted ratcheting strain over the stress cycles. The predicted ratcheting curves by the modified rule were compared with those predicted based on earlier developed hardening rules of Ohno-Wang (O-W), Jiang-Sehitoglu (J-S), McDowell, and Chen-Jiao-Kim (C-J-K) holding relatively complex framework and more number of coefficients. The O-W, the J-S, McDowell and C-J-K models mainly deviated from the experimental ratcheting strain of steel alloys for various multiaxial loading histories, while the predicted curves of the modified model closely agreed with experimental data of steel samples over ratcheting stages. The predicted ratcheting curves based on the modified model closely agreed with experimental data of steel samples under various multiaxial step-loading histories. The modified model was also found capable of predicting ratcheting in the opposite direction as the tensile axial mean stress dropped in magnitude. The O-W, J-S, McDowell and C-J-K models holding more backstress components and coefficients require longer Central Processing Unit (CPU) time. While time required for ratcheting assessment using the modified hardening rule was found to be twice shorter due to its simpler framework and limited number of coefficients.

scholarly journals Development of a kinematic hardening rule to assess ratcheting response of materials under various multiaxial loading spectra

2021 ◽  
Author(s):  
SeyedMahdi Hamidinejad
Keyword(s):  
Experimental Data ◽  
Dynamic Recovery ◽  
Kinematic Hardening ◽  
Multiaxial Loading ◽  
Steel Alloys ◽  
Modified Model ◽  
Hardening Rule ◽  
Loading Paths ◽  
Ratcheting Strain ◽  
Stress Cycles

The present thesis develops an Armstrong-Frederick (A-F) type coupled kinematic hardening rule to assess ratcheting response of steel alloys under various multiaxial loading paths. The hardening rule is constructed on the basis of the recently proposed Ahmadzadeh-Varvani (AV) hardening rule to further evaluate the ratcheting response of materials under multiaxial loading spectra. The modified model offers a simple framework with limited number of terms and coefficients in the dynamic recovery portion of the model. The dynamic recovery further holds inner product of plastic strain increment p dand backstress unit vector a a with different directions under multiaxial stress cycles enables the model to track different directions. Term 1/ 2 n. a a taking positive values less than unity for multiaxial loading conditions is to control the accumulation rate of ratcheting strain and to prevent the modified model to experience plastic shakedown over stress cycles in stage II. Term(2 n. a a ) taking the values between 1 and 3 under multiaxial loading, magnifies the effect of coefficient γ2 to take into account the nonproportionality effect of various loading paths and further to shift down the predicted ratcheting strain over the stress cycles. The predicted ratcheting curves by the modified rule were compared with those predicted based on earlier developed hardening rules of Ohno-Wang (O-W), Jiang-Sehitoglu (J-S), McDowell, and Chen-Jiao-Kim (C-J-K) holding relatively complex framework and more number of coefficients. The O-W, the J-S, McDowell and C-J-K models mainly deviated from the experimental ratcheting strain of steel alloys for various multiaxial loading histories, while the predicted curves of the modified model closely agreed with experimental data of steel samples over ratcheting stages. The predicted ratcheting curves based on the modified model closely agreed with experimental data of steel samples under various multiaxial step-loading histories. The modified model was also found capable of predicting ratcheting in the opposite direction as the tensile axial mean stress dropped in magnitude. The O-W, J-S, McDowell and C-J-K models holding more backstress components and coefficients require longer Central Processing Unit (CPU) time. While time required for ratcheting assessment using the modified hardening rule was found to be twice shorter due to its simpler framework and limited number of coefficients.

Cyclic Plasticity for Nonproportional Paths: Part 2—Comparison With Predictions of Three Incremental Plasticity Models

1978 ◽  
Vol 100 (1) ◽  
pp. 104-111 ◽  
Author(s):  
H. S. Lamba ◽  
O. M. Sidebottom
Keyword(s):  
Cyclic Loading ◽  
Material Property ◽  
Yield Surface ◽  
Strain Path ◽  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
Limit Surface ◽  
Hardening Rule ◽  
Hardening Models ◽  
Hardening Rules

Experiments that demonstrate the basic quantitative and qualitative aspects of the cyclic plasticity of metals are presented in Part 1. Three incremental plasticity kinematic hardening models of prominence are based on the Prager, Ziegler, and Mroz hardening rules, of which the former two have been more frequently used than the latter. For a specimen previously fully stabilized by out of phase cyclic loading the results of a subsequent cyclic nonproportional strain path experiment are compared to the predictions of the above models. A formulation employing a Tresca yield surface translating inside a Tresca limit surface according to the Mroz hardening rule gives excellent predictions and also demonstrates the erasure of memory material property.

Anisotropic Nonlinear Kinematic Hardening Rule Parameters From Reversed Proportional Axial-Torsional Cycling

1999 ◽  
Vol 122 (1) ◽  
pp. 18-28 ◽  
Author(s):  
J. C. Moosbrugger
Keyword(s):  
Kinematic Hardening ◽  
Transverse Isotropy ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Hardening Rule ◽  
Thin Walled ◽  
Hardening Rules ◽  
Type 304 ◽  
Type 304 Stainless Steel ◽  
Tubular Specimens

A procedure for determining parameters for anisotropic forms of nonlinear kinematic hardening rules for cyclic plasticity or viscoplasticity models is described. An earlier reported methodology for determining parameters for isotropic forms of uncoupled, superposed Armstrong-Frederick type kinematic hardening rules is extended. For this exercise, the anisotropy of the kinematic hardening rules is restricted to transverse isotropy or orthotropy. A limited number of parameters for such kinematic hardening rules can be determined using reversed proportional tension-torsion cycling of thin-walled tubular specimens. This is demonstrated using tests on type 304 stainless-steel specimens and results are compared to results based on the assumption of isotropic forms of the kinematic hardening rules. [S0094-4289(00)00301-7]

scholarly journals A Simple Inelastic Constitutive Model for Evaluation of Stable Cyclic Stress Response Under Nonproportional Straining

2002 ◽  
Author(s):  
Masao Sakane ◽  
Takamoto Itoh ◽  
Xu Chen
Keyword(s):  
Kinematic Hardening ◽  
Cyclic Stress ◽  
304 Stainless Steel ◽  
Surface Model ◽  
Cyclic Stress Response ◽  
Strain Relationship ◽  
Strain Paths ◽  
Hardening Rules ◽  
Type 304 ◽  
Type 304 Stainless Steel

This paper proposes a simple two-surface model for cyclic incremental plasticity based on combined Mroz and Ziegler kinematic hardening rules under nonproportional loading. The model has only seven material constants and a nonproportional factor which describes the degree of additional hardening. Cyclic loading experiments with fourteen strain paths were conducted using Type 304 stainless steel. The simulation has shown that the model was precise enough to calculate the stable cyclic stress-strain relationship under nonproportional loadings.

Transient elastohydrodynamic analysis of elliptical contacts. Part 2: Thermal and Newtonian lubricant solution

2005 ◽  
Vol 219 (3) ◽  
pp. 187-200 ◽  
Author(s):  
P Yang ◽  
J Cui ◽  
Z. M. Jin ◽  
D Dowson
Keyword(s):  
Surface Deformation ◽  
Computing Time ◽  
Elastohydrodynamic Lubrication ◽  
Thermal Conditions ◽  
Processing Unit ◽  
Transient Behaviour ◽  
Isothermal Conditions ◽  
Central Processing ◽  
Time Required ◽  
Transient Thermal

Transient thermal elastohydrodynamic lubrication (EHL) of general elliptical point contacts was investigated numerically in this study. Both entrainment directions along the major and the minor axes of the contact ellipse were considered, together with a transient load impulse. In this study, a Newtonian lubricant was assumed to highlight the thermal influence. The transient solution was achieved at every instant, starting from a steady state thermal EHL solution. At each instant, a multilevel solver was used for pressure and surface deformation, whereas a column-by-column relaxation technique was used for solving temperature. The unknown rigid central distance between the contact bodies was adjusted after each iteration between the transient fields of pressure and temperature, so that in each iteration, only one W cycle was required for pressure and only a few relaxation cycles were required for temperature. With these numerical techniques, the computing time required for a typical transient case was reduced to ∼ 12 h on a personal computer with a 3.0 GHz central processing unit. The transient thermal results were compared with those corresponding to isothermal conditions presented in Part 1 of this series of papers. It was found that, in general, the transient behaviour under thermal conditions was similar to that under isothermal conditions, however, the former was weaker than the latter when the slide-roll ratio was large enough.

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