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.

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.

Ratcheting Simulation of Z2CN18.10 Austenitic Stainless Steel under Pre-Strain Conditions

2016 ◽  
Vol 853 ◽  
pp. 112-116
Author(s):  
Yong Wang ◽  
You Gang Peng ◽  
Xu Chen
Keyword(s):  
Stainless Steel ◽  
Austenitic Stainless Steel ◽  
Kinematic Hardening ◽  
Isotropic Hardening ◽  
Good Prediction ◽  
Strain Accumulation ◽  
Modified Model ◽  
Hardening Model ◽  
Ratcheting Strain ◽  
Independent Model

Uniaxial ratcheting behaviors of Z2CN18.10 austenitic stainless steel under both tensile pre-strain (TP) and compressive pre-strain (CP) were experimentally studied at room temperature. The experimental results show that: TP restrains ratcheting strain accumulation of subsequent cycling with positive mean stress; lower level of CP is found to accelerate ratcheting strain accumulation while higher level of CP retards the accumulation. Based on the Ohno-Wang II kinematic hardening rule, rate-independent model, viscoplastic model, isotropic hardening model and a modified model were constructed to describe the ratcheting behaviors under various pre-strain conditions. All the four models gave fairly good prediction on ratcheting strains for various TP. The isotropic hardening model and modified model predicted acceptable ratcheting strain though still showed slight tendency of over prediction.

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.

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