A Comparison of the Capability of Four Hardening Rules to Predict a Material’s Plastic Behavior

1976 ◽  
Vol 98 (1) ◽  
pp. 66-74 ◽  
Author(s):  
B. Hunsaker ◽  
D. K. Vaughan ◽  
J. A. Stricklin
Keyword(s):  
Biaxial Loading ◽  
Kinematic Hardening ◽  
Finite Difference Methods ◽  
Strain Analysis ◽  
Small Strain ◽  
Isotropic Hardening ◽  
Plastic Behavior ◽  
Metal Structures ◽  
Hardening Rules ◽  
Uniaxial And Biaxial Loading

Isotropic hardening, Prager-Ziegler kinematic hardening, the Mroz model, and the mechanical sublayer model are investigated to determine which of these hardening rules are better suited for use in nonlinear small strain analysis of metal structures by the finite element or finite difference methods. The material response predicted by each hardening rule is compared with experiments from the literature for uniaxial and biaxial loading of metals. Computer storage requirements for each model are then presented along with the results of the elastic-plastic analysis of an impulsively loaded plate. Recommendations are then made of appropriate hardening rules based on material characteristics and loading conditions.

Predictions of microtorsional experiments by micropolar plasticity

2005 ◽  
Vol 461 (2053) ◽  
pp. 189-205 ◽  
Author(s):  
Paschalis Grammenoudis ◽  
Charalampos Tsakmakis
Keyword(s):  
Size Effects ◽  
Bauschinger Effect ◽  
Kinematic Hardening ◽  
Circular Cylinders ◽  
Isotropic Hardening ◽  
Gradient Plasticity ◽  
Material Response ◽  
Micropolar Plasticity ◽  
Classical Plasticity ◽  
Hardening Rules

Kinematic hardening rules are employed in classical plasticity to capture the so–called Bauschinger effect. They are important when describing the material response during reloading. In the framework of thermodynamically consistent gradient plasticity theories, kinematic hardening effects were first incorporated into a micropolar plasticity model by Grammenoudis and Tsakmakis. The aim of the present paper is to investigate this model by predicting size effects in torsional loading of circular cylinders. It is shown that kinematic hardening rules compared with isotropic hardening rules, as adopted in the paper, provide more possibilities for modelling size effects in the material response, even if only monotonous loading conditions are considered.

Three-dimensional plasticity with kinematic and isotropic hardening

2020 ◽  
pp. 421-428
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Plastic Strain ◽  
Kinematic Hardening ◽  
Three Dimensional ◽  
Small Strain ◽  
Back Stress ◽  
Isotropic Hardening ◽  
Evolution Law ◽  
Hardening Model ◽  
Rate Dependent ◽  
Viscoplastic Models

This chapter provides an introduction to combined isotropic-kinematic hardening plasticity models in the three-dimensional small strain setting. The additive decomposition of the strain is introduced along with the concepts of plastic strain, equivalent tensile plastic strain, and back stress for three-dimensional problems. Plastic flow is discussed and defined, and a complete model of plasticity is formulated with Kuhn-Tucker loading/unloading conditions. The kinematic hardening model is based upon the Armstrong-Fredrick evolution law. Both rate-independent and rate-dependent (viscoplastic) models are discussed.

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.

scholarly journals On the Plastic and Viscoplastic Constitutive Equations—Part I: Rules Developed With Internal Variable Concept

1983 ◽  
Vol 105 (2) ◽  
pp. 153-158 ◽  
Author(s):  
J. L. Chaboche ◽  
G. Rousselier
Keyword(s):  
Plastic Strain ◽  
Kinematic Hardening ◽  
Strain Tensor ◽  
Internal Variable ◽  
Cyclic Behavior ◽  
Internal Variables ◽  
Plastic Behavior ◽  
Hardening Rules ◽  
Plastic Strain Tensor ◽  
Natural Description

The description of monotonic and cyclic behavior of material is possible by generalizing the internal stress concept by means of a set of internal variables. In this paper the classical isotropic and kinematic hardening rules are briefly discussed, using present plastic strain tensor and cumulated plastic strain as hardening variables. Some additional internal variables are then proposed, giving rise to many possibilities. What is called the “nonlinear kinematic hardening” leads to a natural description of the nonlinear plastic behavior under cyclic loading, but is connected to other concepts such as the Mroz’s model, limited to only two surfaces, and similarities with other approaches are pointed out in the context of a generalization of this rule to viscoplasticity.

scholarly journals On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems

2021 ◽  
Author(s):  
Cyprian Suchocki
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Constitutive Models ◽  
Small Strain ◽  
Cyclic Plasticity ◽  
Isotropic Hardening ◽  
Mapping Algorithm ◽  
Hardening Rule ◽  
Return Mapping ◽  
Cyclic Plasticity Model

AbstractIn this work the finite element (FE) implementation of the small strain cyclic plasticity is discussed. The family of elastoplastic constitutive models is considered which uses the mixed, kinematic-isotropic hardening rule. It is assumed that the kinematic hardening is governed by the Armstrong–Frederick law. The radial return mapping algorithm is utilized to discretize the general form of the constitutive equation. A relation for the consistent elastoplastic tangent operator is derived. To the best of the author’s knowledge, this formula has not been presented in the literature yet. The obtained set of equations can be used to implement the cyclic plasticity models into numerous commercial or non-commercial FE packages. A user subroutine UMAT (User’s MATerial) has been developed in order to implement the cyclic plasticity model by Yoshida into the open-source FE program CalculiX. The coding is included in the Appendix. It can be easily modified to implement any isotropic hardening rule for which the yield stress is a function of the effective plastic strain. The number of the utilized backstress variables can be easily increased as well. Several validation tests which have been performed in order to verify the code’s performance are discussed.

Necessity of Kinematic Strain Hardening in Simulating Impact Events

2017 ◽  
Author(s):  
Sharang Kirloskar ◽  
Gurmeet Singh ◽  
Avinash Kumar
Keyword(s):  
Strain Hardening ◽  
Impact Loading ◽  
High Speed ◽  
Kinematic Hardening ◽  
Material Behavior ◽  
Isotropic Hardening ◽  
Measurement Systems ◽  
Tension And Compression ◽  
Hardening Rules ◽  
Impact Events

Impact events are very high speed and short duration events. Experimental analysis of such events tends to be extremely expensive and challenging to study because of the apparatus and measurement systems required to capture the event. Due to this, impact events are studied extensively through simulations. The ability to simulate these events is a dictating factor for developing better and more efficient designs. Traditionally, loads occurring due to impact events are assumed to monotonically increase and hence pure isotropic strain hardening is sufficient to model the material behavior. However, this assumption doesn’t hold true for all impact events. When the loads caused by an impact do not monotonically increase but instead oscillate causing tension and compression cycles, pure isotropic hardening could lead to unrealistic results. In this work, different strain hardening rules are studied and analyzed for a plate under impact loading. The process to obtain a parameter which sets a realistic combination of isotropic and kinematic strain hardening rules is demonstrated and discussed. Limitations of the existing practice of using isotropic hardening in impact loading cases are studied. An alternative approach to accommodate the kinematic hardening rule into material models using LS-DYNA, a finite element solver, is discussed.

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