A Consistent Criterion for Diffuse Necking in Sheet Metals Using Hill’s 1979 Yield Surface

1998 ◽  
Vol 120 (2) ◽  
pp. 177-182 ◽  
Author(s):  
S. K. Esche ◽  
R. Shivpuri
Keyword(s):  
Plastic Deformation ◽  
Yield Surface ◽  
Shape Factor ◽  
Biaxial Tension ◽  
Yield Function ◽  
Surface Shape ◽  
Principal Strain ◽  
Sheet Metals ◽  
Diffuse Necking ◽  
Anisotropic Yield Function

A review of some existing criteria for diffuse necking in sheet metals is given and their limitations are discussed. The introduction into production of new sheet materials whose plastic deformation is impossible to be modeled using Hill’s 1948 anisotropic yield function necessitates improvements of these existing criteria to accurately describe their necking behavior. In this paper, a generalization of the existing diffuse necking criteria for materials describable by Case IV of Hill’s 1979 anisotropic yield function is presented. The proposed criterion is consistent with the previous criteria. It predicts a significant effect of Hill’s 1979 yield surface shape factor on the critical principal strain in the range of negative minor strains while in the range of biaxial tension this influence is small.

A Gurson Yield Function for Anisotropic Porous Sheet Metals and its Applications to Failure Prediction of Aluminum Sheets

2003 ◽  
Vol 19 (1) ◽  
pp. 161-168 ◽  
Author(s):  
D.-A. Wang ◽  
W. Y. Chien ◽  
K. C. Liao ◽  
J. Pan ◽  
S. C. Tang
Keyword(s):  
Finite Element ◽  
Cell Model ◽  
Three Dimensional ◽  
Yield Function ◽  
Sheet Metals ◽  
Element Analysis ◽  
Aluminum Sheets ◽  
Anisotropic Yield Function ◽  
The Matrix ◽  
Three Dimensional Finite Element

ABSTRACTAn approximate anisotropic yield function is presented for anisotropic sheet metals containing spherical voids. Hill's quadratic anisotropic yield function is used to describe the anisotropy of the matrix. The proposed yield function is validated using a three-dimensional finite element analysis of a unit cell model under different straining paths. The results of the finite element computations are shown in good agreement with those based on the yield function with three fitting parameters. For demonstration of applicability, the anisotropic Gurson yield function is adopted in a combined necking and shear localization analysis to model the failure of AA6111 aluminum sheets under biaxial stretching conditions.

scholarly journals An extended super/subloading surface model for soft rock considering structure degradation

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0258813
Author(s):  
Kai Cui ◽  
Bin Hu ◽  
Aneng Cui ◽  
Jing Li ◽  
Erjian Wei ◽  
...  
Keyword(s):  
Yield Surface ◽  
Soft Rock ◽  
Yield Function ◽  
Surface Shape ◽  
Surface Model ◽  
Test Results ◽  
Structure Degradation ◽  
Proposed Model ◽  
Comparison Results ◽  
Cam Clay

The strain-softening and dilatancy behavior of soft rock is affected by the loading history and the development of structure. This study regards soft rock as a structured and overconsolidated soil and develops a new elastoplastic model based on the classical super yield surface Cam-clay model. The proposed model is capable of capturing the effect of yield surface shape on the mechanical behavior of soft rock by introducing a new yield function. The proposed model is validated against the triaxial test results on different types of soft rocks under drained condition. The comparison results indicate that the proposed model is suitable for describing the constitutive behavior of soft rock.

DEFORMATION OF CLOSED-CELL FOAMS INCORPORATING THE EFFECT OF INNER GAS PRESSURE

2010 ◽  
Vol 02 (03) ◽  
pp. 489-513 ◽  
Author(s):  
ZHI MIN XU ◽  
WEI XU ZHANG ◽  
T. J. WANG
Keyword(s):  
Plastic Deformation ◽  
Yield Surface ◽  
Yield Function ◽  
Gas Pressure ◽  
Uniaxial Tensile ◽  
Face Centered Cubic ◽  
Body Centered Cubic ◽  
Closed Cell ◽  
Hydrostatic Stresses ◽  
Face Centered

The objective of this work is to numerically investigate the elastic–plastic deformation of closed-cell foams incorporating the effect of inner gas pressure. Both body-centered cubic (BCC) and face-centered cubic (FCC) arrangements of pores are considered in analysis. It is seen that the inner gas pressure has a significant effect on the plastic deformation of closed-cell foams, which is different for the foams with different microstructures and is discussed in detail. The inner gas pressure results in the asymmetry of uniaxial tensile-compressive stress–strain curves and the nominal Poisson's ratio. It is shown that the inner gas pressure makes the yield surface move to the negative direction of the hydrostatic axis in the plane of equivalent and hydrostatic stresses, and the moving distance is equal to the magnitude of inner gas pressure in the foams. Moreover, a new yield function incorporating the effect of inner gas pressure is developed for closed-cell foams. The material constants in the yield function depend on the microstructures of the foams.

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.

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