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.

A Generalized Anisotropic Hardening Rule Based on the Mroz Multi-Yield-Surface Model

2008 ◽  
Author(s):  
K. S. Choi ◽  
J. Pan
Keyword(s):  
Cyclic Loading ◽  
Yield Surface ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Yield Function ◽  
Surface Model ◽  
Loading Conditions ◽  
Anisotropic Hardening ◽  
Hardening Rule ◽  
Strain Data

In this paper, a generalized anisotropic hardening rule based on the Mroz multi-yield-surface model is derived. The evolution equation for the active yield surface is obtained by considering the continuous expansion of the active yield surface during the unloading/reloading process. The incremental constitutive relation based on the associated flow rule is then derived for a general yield function. As a special case, detailed incremental constitutive relations are derived for the Mises yield function. The closed-form solutions for one-dimensional stress-plastic strain curves are also derived and plotted for the Mises materials under cyclic loading conditions. The stress-plastic strain curves show closed hysteresis loops under uniaxial cyclic loading conditions and the Masing hypothesis is applicable. A user material subroutine based on the Mises yield function, the anisotropic hardening rule and the constitutive relations was then written and implemented into ABAQUS. Computations were conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule and the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress-strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress-strain data for the nonlinear kinematic hardening rule.

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]

An Evaluation of Recent Developments in Hardening and Flow Rules for Rate-Independent, Nonproportional Cyclic Plasticity

1987 ◽  
Vol 54 (2) ◽  
pp. 323-334 ◽  
Author(s):  
D. L. McDowell
Keyword(s):  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
Modulus Function ◽  
Isotropic Hardening ◽  
Hardening Rule ◽  
Hardening Modulus ◽  
Recent Developments ◽  
Distance Vector ◽  
Plastic Hardening ◽  
Hardening Rules

The Mroz kinematic hardening rule has previously demonstrated superior capability to correlate cyclically stable nonproportional stress-strain response. In this paper, recently proposed kinematic hardening rules for single and multiple surface cyclic plasticity models are evaluated. Significant improvement over the Mroz rule, without loss of generality, is achieved with a deviatoric stress rate-dominated rule proposed by Tseng and Lee for two surface theory. Recent approaches for correlation of the modulus function and isotropic hardening are discussed. The norm of the Mroz distance vector is found to uniquely correlate the variation of plastic hardening modulus through a cycle; it is necessary to include a measure of instantaneous nonproportionality, however, to properly normalize the modulus function. A new evolution equation is offered to correlate the additional isotropic hardening observed during nonproportional loading, and several contemporary approaches are also considered.

scholarly journals Simulation of Cyclic Loading on Pipe Elbows Using Advanced Plane-Stress Elastoplasticity Models1

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Konstantinos Chatziioannou ◽  
Yuner Huang ◽  
Spyros A. Karamanos
Keyword(s):  
Cyclic Loading ◽  
Large Scale ◽  
Mechanical Response ◽  
Low Cycle Fatigue ◽  
Constitutive Relations ◽  
Cyclic Plasticity ◽  
Integration Scheme ◽  
Repeated Loading ◽  
Finite Element Software ◽  
Hardening Models

Abstract This work investigates the response of industrial steel pipe elbows subjected to severe cyclic loading (e.g., seismic or shutdown/startup conditions), associated with the development of significant inelastic strain amplitudes of alternate sign, which may lead to low-cycle fatigue. To model this response, three cyclic-plasticity hardening models are employed for the numerical analysis of large-scale experiments on elbows reported elsewhere. The constitutive relations of the material model follow the context of von Mises cyclic elasto-plasticity, and the hardening models are implemented in a user subroutine, developed by the authors, which employs a robust numerical integration scheme, and is inserted in a general-purpose finite element software. The three hardening models are evaluated in terms of their ability to predict the strain range at critical locations, and in particular, strain accumulation over the load cycles, a phenomenon called “ratcheting.” The overall good comparison between numerical and experimental results demonstrates that the proposed numerical methodology can be used for simulating accurately the mechanical response of pipe elbows under severe inelastic repeated loading. Finally, this paper highlights some limitations of conventional hardening rules in simulating multi-axial material ratcheting.

Elastic-Plastic Finite Element Simulation and Fatigue Life Prediction for Beam and Elbow Under Cyclic Loading

2007 ◽  
Author(s):  
Xian-Kui Zhu ◽  
Brian N. Leis
Keyword(s):  
Finite Element ◽  
Fatigue Life ◽  
Cyclic Loading ◽  
Plastic Strain ◽  
Kinematic Hardening ◽  
Kinematic Model ◽  
Cyclic Plastic ◽  
Hardening Models ◽  
Critical Location ◽  
Cyclic Plastic Strain

Work hardening and Bauschinger effects on plastic deformation and fatigue life for a beam and an elbow under cyclic loading are examined using finite element analysis (FEA). Three typical material plastic hardening models, i.e. isotropic, kinematic and combined isotropic/kinematic hardening models are adopted in the FEA calculations. Based on the FEA results of cyclic stress and strain at a critical location and using an energy-based fatigue damage parameter, the fatigue lives are predicted for the beam and elbow. The results show that (1) the three material hardening models determine similar stress at the critical location with small differences during the cyclic loading, (2) the isotropic model underestimates the cyclic plastic strain and overestimates the fatigue life, (3) the kinematic model overestimates the cyclic plastic strain and underestimates the fatigue life, and (4) the combined model predicts the intermediate cyclic plastic strain and reasonable fatigue life.

Prediction of Fatigue Crack Initiation Life Based on the Extended Cyclic Plasticity Model

2012 ◽  
Author(s):  
Seiichiro Tsutsumi
Keyword(s):  
Cyclic Loading ◽  
Kinematic Hardening ◽  
Fatigue Crack Initiation ◽  
Fatigue Cracking ◽  
Carbon Steels ◽  
Cyclic Plasticity ◽  
Plasticity Model ◽  
Hardening Law ◽  
Crack Initiation Life ◽  
Cyclic Plasticity Model

In order to simulate mechanical fatigue phenomena under macroscopically elastic condition, the plastic stretching within a yield surface has to be described, whilst the plastic strain is induced remarkably as the stress approaches the dominant yielding state. In this study, a phenomenological plasticity model, proposed for the description of the cyclic loading behavior observed for typical carbon steels during the high-cycle fatigue subjected to stresses lower than the yield stress, is applied for the prediction of fatigue initiation life. The model is formulated based on the unconventional plasticity model and is applied for materials obeying isotropic and kinematic hardening law. The mechanical responses under cyclic loading conditions are examined briefly. Finally, the initiation life of fatigue cracking is discussed based on the proposed model with the damage counting parameter.

scholarly journals Effects of Hardening Model and Variation of Elastic Modulus on Springback Prediction in Roll Forming

Metals ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 1005 ◽  
Author(s):  
Naofal ◽  
Naeini ◽  
Mazdak
Keyword(s):  
Elastic Modulus ◽  
Cyclic Loading ◽  
Kinematic Hardening ◽  
Roll Forming ◽  
Isotropic Hardening ◽  
Plastic Behavior ◽  
Forming Process ◽  
Hardening Models ◽  
Springback Prediction ◽  
Roll Forming Process

In this paper, the uniaxial loading–unloading–reloading (LUR) tensile test was conducted to determine the elastic modulus depending on the plastic pre-strain. To obtain the material parameters and parameter of Yoshida-Uemori’s kinematic hardening models, tension–compression experiments were carried out. The experimental results of the cyclic loading tests together with the numerically predicted response of the plastic behavior were utilized to determine the parameters using the Ls-opt optimization tool. The springback phenomenon is a critical issue in industrial sheet metal forming processes, which could affect the quality of the product. Therefore, it is necessary to represent a method to predict the springback. To achieve this aim, the calibrated plasticity models based on appropriate tests (cyclic loading) were implemented in commercial finite element (FE) code Ls-dyna to predict the springback in the roll forming process. Moreover, appropriate experimental tests were performed to validate the numerical results, which were obtained by the proposed model. The results showed that the hardening models and the variation of elastic modulus have significant impact on springback accuracy. The Yoshida-Uemori’s hardening represents more accurate prediction of the springback during the roll forming process when compared to isotropic hardening. Using the chord modulus to determine the reduction in elastic modulus gave more accurate results to predict springback when compared with the unloading and loading modulus to both hardening models.

On a Class of Kinematic Hardening Rules for Nonproportional Cyclic Plasticity

1989 ◽  
Vol 111 (1) ◽  
pp. 87-98 ◽  
Author(s):  
J. C. Moosbrugger ◽  
D. L. McDowell
Keyword(s):  
Kinematic Hardening ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Image Point ◽  
Isotropic Hardening ◽  
Proportional Loading ◽  
Modeling Material ◽  
Hardening Rules ◽  
Type 304 ◽  
Type 304 Stainless Steel

Two surface theories for rate-independent plasticity have previously been shown to offer superior correlative capability in modeling material response under non-proportional loading. In this study, a class of kinematic hardening rules characterized by a decomposition of the total kinematic hardening variable is discussed. The concept of generalized image point hardening in conjunction with mulitple loading surface interpretations is presented. The ability of this class of rules to correlate experimental data from stable nonproportional cycling of Type 304 stainless steel at room temperature is examined. In addition, the proper framework for inclusion of isotropic hardening for this class of models is discussed.

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