An Investigation of Yield Potentials In Superplastic Deformation

1999 ◽  
Vol 122 (1) ◽  
pp. 93-97 ◽  
Author(s):  
Marwan K. Khraisheh
Keyword(s):  
Effective Strain ◽  
Yield Function ◽  
Yield Potential ◽  
Anisotropic Yield Function ◽  
Superplastic Alloy ◽  
Degree Of Anisotropy ◽  
Anisotropic Function ◽  
Experimental Yield ◽  
Dynamic Yield ◽  
Von Mises

Recent results (Khraisheh et al., 1995 and 1997) have indicated that superplastic materials exhibit a strong degree of anisotropy and that the plastic flow cannot be described by the isotropic von Mises flow rules. In this study, the yield potential for the model Pb-Sn superplastic alloy is constructed experimentally for different effective strain rates using combined tension/torsion tests. A generalized anisotropic “dynamic” yield function is also proposed to represent the experimentally constructed yield potentials. The anisotropic function is not only capable of describing the initial anisotropic state of the yield potential, it can also describe its evolution through the evolution of unit vectors defining the direction of anisotropy. The anisotropic yield function includes a set of material constants which determine the degree of deviation of the yield potential from the isotropic von Mises yield surface. It is shown that the anisotropic yield function successfully represents the experimental yield potentials, especially in the superplastic region. [S0094-4289(00)01401-8]

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.

Influence of Anisotropic Yield Functions on Parameters of Yoshida-Uemori Model

2013 ◽  
Vol 554-557 ◽  
pp. 2440-2452 ◽  
Author(s):  
Hirotaka Kano ◽  
Jiro Hiramoto ◽  
Toru Inazumi ◽  
Takeshi Uemori ◽  
Fusahito Yoshida
Keyword(s):  
Effective Strain ◽  
Yield Function ◽  
Strain Response ◽  
Material Parameters ◽  
International Conference ◽  
Polynomial Type ◽  
Calculated Stress ◽  
Yield Functions ◽  
Order Polynomial ◽  
Von Mises

Yoshida-Uemori model (Y-U model) can be used with any types of yield functions. The calculated stress strain response will be, however, different depending on the chosen yield function if the yield function and the effective strain definition are inappropriate. Thus several modifications to Y-U model were proposed in the 10th International Conference on Technology of Plasticity. It was ascertained that in the modified Y-U model, the same set of material parameters can be used with von Mises, Hill’s 1948, and Hill’s 1990 yield function. In this study, Yld2000-2d and Yoshida’s 6th-order polynomial type 3D yield function were examined and it was clarified that the same set of Y-U parameters can be used with these yield functions.

Yield and Flow Behavior of Initially Anisotropic Aluminum Tube Under Multiaxial Stresses

1993 ◽  
Vol 115 (1) ◽  
pp. 77-82 ◽  
Author(s):  
Takenobu Takeda
Keyword(s):  
Stress Field ◽  
Internal Pressure ◽  
Principal Stress ◽  
Yield Surface ◽  
Flow Behavior ◽  
Yield Function ◽  
Strain Behavior ◽  
Anisotropic Yield Function ◽  
Initial Anisotropy ◽  
Von Mises

By means of combining Drucker’s yield function with Hill’s quadratic yield function, an anisotropic yield function of the sixth degree is proposed. It is able to include the effects of the third deviatoric stress invariant and initial anisotropy. Experiments are carried out on fully annealed 1050 aluminum tubes under multiaxial stress states. By applying proportional loadings of axial load, internal pressure and torsion to the specimens, the change in yield stress with a rotation of the principal stress axes and the difference between the directions of the principal stress and principal strain increment are examined. The yield surface in the tension-internal pressure stress field reveals orthotropic anisotropy. The yield surface in the tension-torsion stress field lies outside von Mises’ yield surface. Such behavioral characteristics can be expressed precisely by the proposed yield function. In addition, it is experimentally verified that the normality rule is obeyed in strain behavior.

Elasto-Plastic Analysis of Reissner-Mindlin Plates

1990 ◽  
Vol 43 (5S) ◽  
pp. S40-S50 ◽  
Author(s):  
Panayiotis Papadopoulos ◽  
Robert L. Taylor
Keyword(s):  
Yield Function ◽  
Rate Equations ◽  
Test Problems ◽  
Field Equations ◽  
Element Analysis ◽  
Linear Hardening ◽  
Nonlinear Version ◽  
Plastic Analysis ◽  
Von Mises ◽  
Predictor Corrector

A finite element analysis of elasto-plastic Reissner-Mindlin plates is presented. The discrete field equations are derived from a nonlinear version of the Hu-Washizu variational principle. Associative plasticity, including linear hardening, is employed by means of a generalized von Mises-type yield function. A predictor/corrector scheme is used to integrate the plastic constitutive rate equations. Numerical simulations are conducted for a series of test problems to illustrate performance of the formulation.

Effect of Material Frame Rotation on the Hardening of an Anisotropic Material in Simple Shear Tests

2018 ◽  
Vol 85 (12) ◽  
Author(s):  
Kelin Chen ◽  
Stelios Kyriakides ◽  
Martin Scales
Keyword(s):  
Simple Shear ◽  
Plastic Anisotropy ◽  
Yield Function ◽  
Strain Response ◽  
Shear Tests ◽  
Stress Strain ◽  
Anisotropic Yield Function ◽  
Torsion Experiment ◽  
Thin Walled Tube ◽  
Material Frame

The shear stress–strain response of an aluminum alloy is measured to a shear strain of the order of one using a pure torsion experiment on a thin-walled tube. The material exhibits plastic anisotropy that is established through a separate set of biaxial experiments on the same tube stock. The results are used to calibrate Hill's quadratic anisotropic yield function. It is shown that because in simple shear the material axes rotate during deformation, this anisotropy progressively reduces the material tangent modulus. A parametric study demonstrates that the stress–strain response extracted from a simple shear test can be influenced significantly by the anisotropy parameters. It is thus concluded that the material axes rotation inherent to simple shear tests must be included in the analysis of such experiments when the material exhibits anisotropy.

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