Finite Element Calculation of Anisotropy of Hole Expansion in a Thin Steel Sheet with Six Degrees Polynomial Yield Function

A sixth order yield function was used to analyze the anisotropic plasticity behavior of sheet metal forming. Based on a complete sixth order homogenous polynomial in plane stress, the yield function was implemented as user material subroutines in the FE code ABAQUS Explicit and Standard. The associated flow rule and isotropic hardening were assumed. Material parameter values in the yield function were decided by uniaxial yield stresses and plastic strain ratios along 7 different loading orientations and plane strain yield and equal biaxial stresses and plastic strain ratio. To show the superiority of the sixth order yield function, the hole expansion test by Kuwabara et al.[1] was considered. The results of finite element simulation using the sixth order yield function showed a better agreement with the test results than YLD2000-2D yield function with M=6.

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Use of Plane-Strain Tension and Shear Tests to Evaluate Yield Surfaces for AA1050 Aluminium Sheet

Materials Science Forum ◽

10.4028/www.scientific.net/msf.794-796.596 ◽

2014 ◽

Vol 794-796 ◽

pp. 596-601

Author(s):

Kai Zhang ◽

Bjørn Holmedal ◽

Odd Sture Hopperstad ◽

Stéphane Dumoulin

Keyword(s):

Experimental Data ◽

Plane Strain ◽

Yield Function ◽

Isotropic Hardening ◽

Flow Rule ◽

Shear Tests ◽

Anisotropic Plasticity ◽

Type Iii ◽

Plane Strain Tension ◽

Force Displacement

Plane-strain tension and shear tests were carried out for a fully annealed AA1050 sheet. The tests were simulated numerically with a commercial finite element method (FEM) code using an anisotropic plasticity model including the Yld2004-18p yield function, the associated flow rule and isotropic hardening. The advanced yield function was calibrated by three different methods: using uniaxial tension data combined with FC-Taylor model predictions of the equibiaxial yield stress and r-value, using 201 virtual yield points in stress space, and using a combination of experimental data and virtual yield points (i.e., a hybrid method). The virtual stress points at yielding were provided by the recently proposed Alamel model with the so-called Type III relaxation (Alamel Type III model). FEM simulations of the tests were then made with parameters of Yld2004-18p identified by these three methods. Predicted force-displacement curves were compared to the experimental data, and the accuracy of the parameter identification methods for Yld2004-18p was evaluated based on these comparisons.

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Stress update algorithm for non-associated flow metal plasticity

International Journal Sustainable Construction & Design ◽

10.21825/scad.v3i2.20562 ◽

2012 ◽

Vol 3 (2) ◽

pp. 106-110

Author(s):

Mohsen Safaei ◽

Wim De Waele

Keyword(s):

Plastic Strain ◽

Yield Stress ◽

Kinematic Hardening ◽

Quadratic Function ◽

Yield Function ◽

Plastic Strain Rate ◽

Isotropic Hardening ◽

Flow Rule ◽

Strain Rate Tensor ◽

Incremental Change

. In this paper we present the continuum plasticity model based on non-Associated Flow Rule (nonAFR) for Hill’s48 quadratic yield function. In case of non-AFR, Hill’s quadratic function used as plasticpotential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate.In addition, the yield function uses direction dependent yield stress data. Therefore more accuratepredictions are expected in terms of both yield stress and strain ratios at different orientations. Weimplemented a modified version of the non-associative flow rule originally developed by Stoughton [1] intothe commercial finite element code ABAQUS by means of a user material subroutine UMAT. The mainalgorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumesproportional loading cases and therefore only isotropic hardening effect is considered. In our model theincremental change of plastic strain rate tensor is not equal to the incremental change of the compliancefactor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finiteelement simulations with experimentally determined values for deep drawing steel DC06. A criticalcomparison is made between numerical results obtained from AFR and non-AFR based models.

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Constitutive Modelling of an Industrial Rolled Sheet for a DIN 1623 St14 (DC04) Steel

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.297.31 ◽

2019 ◽

Vol 297 ◽

pp. 31-50

Author(s):

Badreddine Regaiguia ◽

Oualid Chahaoui ◽

S. Boulahrouz ◽

N. Brinis ◽

Mohamed Lamine Fares

Keyword(s):

Biaxial Tension ◽

Strain Ratio ◽

Yield Function ◽

Constitutive Modelling ◽

Isotropic Hardening ◽

Plastic Behavior ◽

Tension Stress ◽

Rolled Sheet ◽

Plastic Strain Ratio ◽

St14 Steel

The comprehension of the anisotropy impacts on mechanical properties of the rolled steel sheets was investigated using a non-quadratic anisotropic yield function. In this study, experimental and modelling determination of behavior of an industrial rolled sheets for a DIN 1623 St14 steel were carried out. The yield stresses and Lankford r-values in uniaxial were experimentally determined but the balanced biaxial tension stress states and rb were assumed. The parameters of the associated yield equation, derived from the three orthotropic yield functions proposed by Hill48 and Yld2000-2d, were determined. Predictions and the evolution of normalized yield stress and normalized Lankford parameters (plastic strain ratio) obtained by the presented investigative are considered. In order to describe the path of equivalent plastic behavior, the isotropic hardening function is described using the following various empirical standard formulae based on: Hollomon, Ludwick, Swift and Voce model.

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Effect of specimen geometry, gage length, and width measurement locations on plastic strain ratio (R-value) in sheet metals

Metallurgical and Materials Transactions A ◽

10.1007/s11661-006-1043-5 ◽

2006 ◽

Vol 37 (12) ◽

pp. 3477-3487 ◽

Cited By ~ 8

Author(s):

A. Chamanfar ◽

R. Mahmudi

Keyword(s):

Plastic Strain ◽

Strain Ratio ◽

Gage Length ◽

Specimen Geometry ◽

Sheet Metals ◽

Plastic Strain Ratio ◽

Width Measurement ◽

R Value

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Effect of Cu Content on the Formability and Portevin-Le Chatelier Effect of Al-Mg Alloys

Materials Science Forum ◽

10.4028/www.scientific.net/msf.817.150 ◽

2015 ◽

Vol 817 ◽

pp. 150-157

Author(s):

Peng Cheng Ma ◽

Di Zhang ◽

Lin Zhong Zhuang ◽

Ji Shan Zhang

Keyword(s):

Plastic Strain ◽

Stress Drop ◽

Strain Ratio ◽

Mg Alloys ◽

Dynamic Strain ◽

Strain Hardening Exponent ◽

Drawing Ratio ◽

Plastic Strain Ratio ◽

Cu Content ◽

Al Mg Alloys

Al-Mg alloys developed for auto body sheets with different Cu contents were fabricated in the laboratory scale. The effects of Cu content on the microstructures, formability and Portevin–Le Chatelier(PLC) effect of the alloys were investigated by polarizied optical microscopy and room temperature tensile testing. It has been found that with increasing Cu content, there was little change of the strain hardening exponent, but the plastic strain ratio and limiting drawing ratio increased firstly and then decreased. A quantitative statistical analysis of the characteristics of the PLC effect was made, including the stress drop and the reloading time, which follow a common linear relationship with plastic strain, and the increase rate of stress drop and reloading time was bigger with more Cu content. A detailed discussion of the corresponding mechanism of Cu and Cu-containing precipitates on the dynamic strain aging(DSA) was made.

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