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.

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.

An Anisotropic Hardening Rule With Non-Associated Flow Rule for Pressure-Sensitive Materials

2009 ◽  
Author(s):  
K. S. Choi ◽  
J. Pan
Keyword(s):  
Cyclic Loading ◽  
Plastic Strain ◽  
Hysteresis Loops ◽  
Flow Rule ◽  
Loading Conditions ◽  
Anisotropic Hardening ◽  
Strength Differential ◽  
Hardening Rule ◽  
Pressure Sensitive ◽  
Associated Flow Rule

In this paper, cyclic plastic behaviors of pressure-sensitive materials based on an anisotropic hardening rule with two non-associated flow rules are examined. The Drucker-Prager pressure-sensitive yield function and the Mises plastic potential function are adopted to explore the cyclic plastic behaviors of pressure-sensitive materials or strength-differential materials. The constitutive relations are formulated for the initial loading and unloading/reloading processes based on the anisotropic hardening rule of Choi and Pan [1]. Non-associated flow rules are employed to derive closed-form stress-plastic strain relations under uniaxial cyclic loading conditions. The stress-plastic strain curves based on a conventional non-associated flow rule do not close, and show a significant ratcheting under uniaxial cyclic loading conditions. A new non-conventional non-associated flow rule is then formulated based on observed nearly closed hysteresis loops of pressure-sensitive materials. The stress-plastic strain curves based on the non-conventional non-associated flow rule show closed hysteresis loops under uniaxial cyclic loading conditions. The results indicate that the anisotropic hardening rule with the non-conventional non-associated flow rule describes well the strength-differential effect and the asymmetric closed hysteresis loops as observed in the uniaxial cyclic loading tests of pressure-sensitive materials.

scholarly journals Influences of Material Variations of Functionally Graded Pipe on the Bree Diagram

2020 ◽  
Vol 10 (8) ◽  
pp. 2936 ◽  
Author(s):  
Aref Mehditabar ◽  
Saeid Ansari Sadrabadi ◽  
Raffaele Sepe ◽  
Enrico Armentani ◽  
Jason Walker ◽  
...  
Keyword(s):  
Internal Pressure ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Bending Moment ◽  
Yield Function ◽  
Functionally Graded ◽  
Loading Conditions ◽  
Mapping Algorithm ◽  
First Case ◽  
Backward Euler

The present research is concerned with the elastic–plastic responses of functionally graded material (FGM) pipe, undergoing two types of loading conditions. For the first case, the FGM is subjected to sustained internal pressure combined with a cyclic bending moment whereas, in the second case, sustained internal pressure is applied simultaneously with a cyclic through-thickness temperature gradient. The properties of the studied FGM are considered to be variable through shell thickness according to a power-law function. Two different designs of the FGM pipe are adopted in the present research, where the inner surface in one case and the outer surface in the other are made from pure 1026 carbon steel. The constitutive relations are developed based on the Chaboche nonlinear kinematic hardening model, classical normality rule and von Mises yield function. The backward Euler alongside the return mapping algorithm (RMA) is employed to perform the numerical simulation. The results of the proposed integration procedure were implemented in ABAQUS using a UMAT user subroutine and validated by a comparison between experiments and finite element (FE) simulation. Various cyclic responses of the two prescribed models of FGM pipe for the two considered loading conditions are classified and brought together in one diagram known as Bree’s diagram.

scholarly journals Elaborated subloading surface model for accurate description of cyclic mobility in granular materials

2021 ◽  
Author(s):  
Koichi Hashiguchi ◽  
Tatsuya Mase ◽  
Yuki Yamakawa
Keyword(s):  
Cyclic Loading ◽  
Granular Materials ◽  
Accurate Description ◽  
Surface Model ◽  
Cyclic Mobility ◽  
Mixed Hardening ◽  
Hardening Rule ◽  
Elastic Domain ◽  
Translation Rule ◽  
Rotational Hardening

AbstractThe description of the cyclic mobility observed prior to the liquefaction in geomaterials requires the sophisticated constitutive formulation to describe the plastic deformation induced during the cyclic loading with the small stress amplitude inside the yield surface. This requirement is realized in the subloading surface model, in which the surface enclosing a purely elastic domain is not assumed, while a purely elastic domain is assumed in other elastoplasticity models. The subloading surface model has been applied widely to the monotonic/cyclic loading behaviors of metals, soils, rocks, concrete, etc., and the sufficient predictions have been attained to some extent. The subloading surface model will be elaborated so as to predict also the cyclic mobility accurately in this article. First, the rigorous translation rule of the similarity center of the normal yield and the subloading surfaces, i.e., elastic core, is formulated. Further, the mixed hardening rule in terms of volumetric and deviatoric plastic strain rates and the rotational hardening rule are formulated to describe the induced anisotropy of granular materials. In addition, the material functions for the elastic modulus, the yield function and the isotropic hardening/softening will be modified for the accurate description of the cyclic mobility. Then, the validity of the present formulation will be verified through comparisons with various test data of cyclic mobility.

Numerical Evaluation of Crashworthiness of Automotive Sheets

2007 ◽  
Vol 345-346 ◽  
pp. 1537-1540
Author(s):  
Han Sun Ryou ◽  
Myoung Gyu Lee ◽  
Chong Min Kim ◽  
Kwan Soo Chung
Keyword(s):  
Crystal Structures ◽  
Yield Surface ◽  
Numerical Evaluation ◽  
Kinematic Hardening ◽  
Sheet Thickness ◽  
Back Stress ◽  
Yield Function ◽  
Chaboche Model ◽  
Simulation Results ◽  
Function Shape

Crash simulations were performed for automotive sheets. To understand the influence of crystal structures in sheet materials on crashworthiness, the effect of the yield function shape was studied by adopting the recently developed non-quadratic anisotropic yield surface, Yld2004-18p. The effect of the back-stress was also investigated by comparing simulation results obtained for the isotropic, kinematic and combined isotropic-kinematic hardening laws based on the modified Chaboche model. In addition, the effects of anisotropy and sheet thickness on crashworthiness were evaluated.

A New Model to Describe Yield Surface Distortion Based on the Baltov and Sawczuk’s Model

2012 ◽  
Author(s):  
A. Nayebi ◽  
H. Rokhgireh
Keyword(s):  
Yield Surface ◽  
Kinematic Hardening ◽  
Experimental Results ◽  
Surface Model ◽  
New Model ◽  
Surface Distortion ◽  
Loading Direction ◽  
Reverse Loading ◽  
Reversed Loading ◽  
Yield Surface Distortion

In the present study Baltov and Sawczuk’s yield surface model is modified to represent compatible results with experimental observations. The proposed yield surface is determined during tension-torsion loading by considering kinematic hardening model and monotonic loading paths. The experimental results represent the nosed and flattened region in the loading and reverse loading direction respectively. The nosed region is dominant in tension than in torsion. The cross-effect is negligible in the small plastic strain amount. The Baltov and Sawczuk’s yield surface has nosed and flattened regions in both loading and reversed loading directions for negative and positive added material parameter respectively. Thus the elliptic Baltov and Sawczuk’s yield surface is modified by changing the sign of this parameter continuously from loading to reverse loading direction and the needed relations of the new model are obtained. The new model was able to predict properly the shape of yield surface. The experimental results compare well with the new model yield surface distortion predictions.

A Comparison of Two Self-Consistent Models to Predict the Cyclic Behavior of Polycrystals

2004 ◽  
Vol 126 (1) ◽  
pp. 62-69 ◽  
Author(s):  
A. Abdul-Latif
Keyword(s):  
Stainless Steel ◽  
Cyclic Loading ◽  
316L Stainless Steel ◽  
Kinematic Hardening ◽  
Cyclic Behavior ◽  
Loading Conditions ◽  
Local Responses ◽  
Self Consistent ◽  
Interaction Law ◽  
Local Levels

Being of particular interest in this work, the effect of the interaction law on the predicted non-linear overall and local behaviors of FCC polycrystals of two well-established self-consistent models is examined under uni, bi, and triaxial cyclic loading conditions. The principal difference between these models is related to their interaction laws. Comparisons between the predictions of the models are performed at the overall and local levels simultaneously. Some experimental cyclic results of two states of Waspaloy and 316L stainless steel are employed in calibrating the parameters of both models. The effects of loading complexity, aggregate type and the kinematic hardening on the polycrystal responses are investigated for each model. It is recognized that the connection between the aggregate constitution and the form of the loading paths play also an important role notably on the local responses of polycrystals.

On the Modeling of Nonproportional Cyclic Plasticity of Waspaloy

1994 ◽  
Vol 116 (1) ◽  
pp. 35-44 ◽  
Author(s):  
A. Abdul-Latif ◽  
M. Clavel ◽  
V. Ferney ◽  
K. Saanouni
Keyword(s):  
Cyclic Loading ◽  
Kinematic Hardening ◽  
Experimental Tests ◽  
Point Of View ◽  
Cyclic Plasticity ◽  
Loading Path ◽  
Isotropic Hardening ◽  
Loading Conditions ◽  
Effective Role ◽  
Deformation Modes

The isotropic hardening is known to play an effective role in the overhardening of materials under nonproportional cyclic loading. However, the behavior of the two states of Waspaloy (namely overaged and underaged states) under these loading conditions, shows that the kinematic hardening has also a considerable role in the overhardening. Experimental tests were carried out on these two states under various proportional and nonproportional cyclic loading conditions at room temperature. The effect of loading paths on micro-mechanisms of deformation was studied. From a microstructural point of view, it was shown that the deformation modes (quantitatively and qualitatively) depend on the loading path and the heat treatment. A constitutive model is proposed to describe the effect of overhardening, under the nonproportional loading conditions, on the kinematic hardening. The predicted responses are in good agreement with experimental results.

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