A General Yield Function within the Framework of Linear Transformations of Stress Tensors for the Description of Plastic-strain-induced Anisotropy

2011 ◽  
Author(s):  
Shun-lai Zang ◽  
Myoung-gyu Lee
Keyword(s):  
Plastic Strain ◽  
Yield Function ◽  
Induced Anisotropy ◽  
Linear Transformations ◽  
Stress Tensors

Constitutive Modeling of Multiaxial Deformation and Induced Anisotropy in Superplastic Materials

2000 ◽  
Author(s):  
Marwan K. Khraisheh
Keyword(s):  
Constitutive Modeling ◽  
Continuum Theory ◽  
Yield Function ◽  
Yield Potential ◽  
Induced Anisotropy ◽  
Dynamic Yield ◽  
Fixed End ◽  
Unit Vectors

Abstract The multiaxial deformation of superplastic materials is modeled within a continuum theory of viscoplasticity using a generalized anisotropic dynamic yield function. The anisotropic dynamic yield function is capable of describing the evolution of the initial anisotropic state of the yield potential through the evolution of unit vectors defining the direction of anisotropy. The evolution of the direction of anisotropy is represented by a constitutive spin such that initially it is identical to the Eulerian spin and as deformation continues, it tends towards an orthotropic spin. Experiments on the model Pb-Sn alloy were conducted and used to calibrate and verify the constructed model. It is shown that the model in conjunction with the anisotropic dynamic yield function is capable of predicting the actual trend of the induced axial stresses recorded in fixed-end torsion experiments.

A Hardening Rule Between Stress Resultants and Generalized Plastic Strains for Thin Plates of Power-Law Hardening Materials

1993 ◽  
Vol 60 (2) ◽  
pp. 548-554 ◽  
Author(s):  
C. H. Chou ◽  
J. Pan ◽  
S. C. Tang
Keyword(s):  
Plastic Strain ◽  
Power Law ◽  
Potential Surface ◽  
Equivalent Stress ◽  
Yield Function ◽  
Constitutive Law ◽  
Thin Plates ◽  
Plastic Strain Rate ◽  
Hardening Rule ◽  
Stress Resultant

For power-law hardening materials, a stress resultant constitutive law of incremental plasticity nature for thin plates is constructed. The yield function in the stress resultant space is approximated in quadratic form and an equivalent stress resultant is defined. One of two parameters in the yield function is analytically determined based on the concept of complementary potential surface. The other is determined by the least square method to fit the complementary potential surface of Chou et al., (1991). In analogy to the work of Hill (1979), the equivalent work-conjugate generalized plastic strain rate is derived. Finally, the hardening rule between the equivalent stress resultant and generalized plastic strain is obtained based on the results of Chou et al. (1991) for power-law materials under proportional straining conditions.

Anisotropic yield functions with plastic-strain-induced anisotropy

1996 ◽  
Vol 12 (3) ◽  
pp. 417-438 ◽  
Author(s):  
Y.S. Suh ◽  
F.I. Saunders ◽  
R.H. Wagoner
Keyword(s):  
Plastic Strain ◽  
Induced Anisotropy ◽  
Yield Functions

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

2019 ◽  
Vol 794 ◽  
pp. 260-266
Author(s):  
Seung Yong Yang ◽  
Wei Tong
Keyword(s):  
Finite Element ◽  
Plastic Strain ◽  
Strain Ratio ◽  
Yield Function ◽  
Sixth Order ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Anisotropic Plasticity ◽  
Plastic Strain Ratio ◽  
Hole Expansion

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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