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

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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Calculation of Stress Relaxation Properties for 1CrMoV Bolt Material

Design and Analysis Methods and Fitness for Service Evaluations for Pressure Vessels and Components ◽

10.1115/pvp2003-1939 ◽

2003 ◽

Author(s):

Fred V. Ellis ◽

Sebastian Tordonato

Keyword(s):

Stress Relaxation ◽

Power Law ◽

Uniaxial Stress ◽

Flow Rule ◽

Creep Equation ◽

Relaxation Properties ◽

Stress Levels ◽

Long Time ◽

Power Law Creep ◽

Good Agreement

Analytical life prediction methods have been developed for high temperature turbine and valve bolts. For 1CrMoV steel bolt material, long time creep-rupture and stress relaxation tests were performed at 450°C, 500°C, and 550°C by the National Research Institute for Metals of Japan. Based on analysis of their data, the isothermal creep behavior can be described using a power law: ε=Kσn(t)m+1 where ε is the creep strain, t is the time, σ is the stress, K, n, and m are material constants. The time power is a primarily a function of temperature, but also depends slightly on stress. To obtain the value for the time power typical of low stress, the creep equation constants were found in two steps. The time power was found using the lower stress data and a heat-centered type regression approach with the stress levels taking the place of the heats in the analysis. The heat constants were then calculated at all stress levels and regression performed to obtain the stress dependence. For comparison with the measured uniaxial stress relaxation properties, the relaxed stress as a function of time was calculated using the power law creep equation and a strain hardening flow rule. The calculated stress versus time curves were in good agreement with the measured at initial strain levels of 0.10%, 0.15%, and 0.20% for all temperatures except 500°C. At 500°C, good agreement was found using the creep properties typical of a stronger (within heat variation) material.

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

10.32920/ryerson.14656803.v1 ◽

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

Journal of Pressure Vessel Technology ◽

10.1115/1.4028970 ◽

2015 ◽

Vol 137 (3) ◽

Cited By ~ 10

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.

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Finite Element Analysis of V-Bending of Polypropylene Using Hydrostatic-Pressure Dependent Plastic Constitutive Equation

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.340-341.1103 ◽

2007 ◽

Vol 340-341 ◽

pp. 1103-1108 ◽

Cited By ~ 1

Author(s):

Kunio Hayakawa ◽

Yukio Sanomura ◽

Mamoru Mizuno ◽

Yukio Kasuga ◽

Tamotsu Nakamura

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Hydrostatic Pressure ◽

Constitutive Equations ◽

Kinematic Hardening ◽

Uniaxial Stress ◽

Isotropic Hardening ◽

Element Analysis ◽

Hardening Rule ◽

Stress Strain Relation

Finite element analysis of V-bending process of polypropylene was performed using hydrostatic-dependent elastic-plastic constitutive equations proposed by the present authors. Kinematic and isotropic hardening rule was employed for the plastic constitutive equations. The kinematic hardening rule was more suitable for the expression of the stress reversal in uniaxial stress - strain relation than the isotropic hardening. For the result of the finite element analysis of V-bending, the kinematic hardening rule was able to predict the experimental behavior of springback more properly than the isotropic hardening. Moreover, the effects of hydrostatic pressure-dependence were revealed by examining the calculated distribution of bending plastic strain, bending stress and the width of the bent specimen.

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