Elasto-Plastic Analysis Using Natural Strain: Shape of Yield Surface Generated after Pre-Deformation of Large Simple Shear

2014 ◽  
Vol 875-877 ◽  
pp. 518-523
Author(s):  
Yasuyuki Kato ◽  
Akihiro Kazama
Keyword(s):  
Simple Shear ◽  
Yield Surface ◽  
Effective Strain ◽  
Pure Copper ◽  
Strain Curve ◽  
Combined Loading ◽  
Proportional Loading ◽  
Natural Strain ◽  
Test Pieces ◽  
Loading Tests

The Natural Strain suggested in this paper satisfies the additive law of strain on an identical line element in a body. Therefore, it can be defined from anywhere on the basis of the deformed intermediate state. So, this is an effective strain notation to describe the phenomenon that depends on the deformation history such as the plastic deformation. In this paper, the shape of the yield surface generated after applying the pre-deformation of large simple shear is estimated on the basis of the Natural Strain theory. Using the test pieces made of pure copper, which is already subjected to the pre-deformation of large simple shear, the proportional loading tests for combined loading of tension and torsion are carried out beyond the elastic region. The yield stress for each direction in the stress space is determined by investigating the tangent modulus of deviatoric stress- deviatoric strain curve, and the shape of yield surface is elucidated by comparing with the shape by conventional proof stress.

NATURALLY STRAINED YIELD SURFACE SHAPE ESTIMATED UNDER PRE-DEFORMATION OF TENSION AND TORSION

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Yasuyuki Kato
Keyword(s):  
Yield Stress ◽  
Yield Surface ◽  
Pure Copper ◽  
Strain Curve ◽  
Surface Shape ◽  
Proof Stress ◽  
Proportional Loading ◽  
Test Pieces ◽  
Loading Tests ◽  
Yield Surfaces

The purpose of this study is to investigate the shape of yield surfaces formed under large pre-deformations, based on the Natural Strain theory, and to make clear the mechanism of the development of anisotropy of yield surfaces under large deformations. In particular the shape of yield surfaces obtained after applying the pre-deformation of tension and shear with proportional loading states is examined. Using pure-copper test pieces already pre-deformed, proportional loading tests were carried out again changing the ratio of tension and torsion to determine yield stress in each direction of the stress space. The yield stress was estimated by examining the slope of tangent for the principal deviatoric stress-deviatoric strain curve in proportional loading tests. It was revealed that the shape of the yield surface becomes convex at the side of pre-deformation and becomes flat in the opposite direction of the pre-deformation. Moreover, the shape of the estimated yield surface was compared with the shape of conventional proof stress. Consequently, it became clear that the shapes of both yield surfaces almost coincide at the side of pre-deformation, but on the opposite side, the yield surface by proof stress becomes smaller compared with the estimated yield surface.

YIELD SURFACE SHAPE ESTIMATED BY USING NATURAL STRAIN UNDER PRE-DEFORMATION OF TENSION AFTER SIMPLE SHEAR

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Yasuyuki Kato
Keyword(s):  
Simple Shear ◽  
Yield Surface ◽  
Effective Strain ◽  
Surface Shape ◽  
Strain Component ◽  
Deformation History ◽  
Proportional Loading ◽  
Strain Behavior ◽  
Natural Strain ◽  
Deformation State

Since the rigid body rotation can be clearly removed from the shearing strain component, and the additive law of strain can be satisfied, the Natural Strain is effective strain representation for expressing the stress-strain behavior under large elasto-plastic deformation. Based on the Natural Strain theory, the purpose of this study is to clarify the mechanism of development of anisotropy in the yield surface that occurs with the progression of deformation by examining the shape of yield surface obtained under large deformation. In our previous studies, using test pieces that the large pre-deformation of uniaxial tension, simple shear and the proportional loading of them are applied, proportional loading tests are carried out again by changing the ratio of tension and shear. In the present paper, another type of the pre-deformation that the deformation path is different but the final deformation state is the same as the predeformation of proportional loading of tension and shear, is chosen as the subject of this study. In particular, the deformation history of tension after simple shear is examined in this study. Then, the relationship between the development of anisotropy in yield surface and the deformation history is revealed in this paper.

SHAPE OF YIELD SURFACE ESTIMATED BY USING NATURAL STRAIN UNDER PRE-DEFORMATION OF SHEAR AFTER UNIAXIAL TENSION

2016 ◽  
Vol 3 (2) ◽  
Author(s):  
Yasuyuki Kato
Keyword(s):  
Yield Stress ◽  
Large Deformation ◽  
Uniaxial Tension ◽  
Yield Surface ◽  
Strain Curve ◽  
Deformation History ◽  
Proportional Loading ◽  
Natural Strain ◽  
Test Pieces ◽  
History Of

In the present paper, the anisotropy of yield surface generated under large deformation is investigated on the basis of the Natural Strain theory, which can be treated systematically from the infinitesimal deformation to the large deformation. After applying the pre-deformation of uniaxial tension, simple shear and combined load of them to the test pieces, proportional loading tests are carried out again with changing the ratio of tension and torsion. Then, the shape of yield surface is investigated by estimating the yield stress in an arbitrary direction in the stress space. As the method for determining the yield stress, the slope of the tangent at yielding in the deviatoric stress-deviatoric strain curve is used. In order to reveal the influence of deformation history on the development of anisotropy in yield surface, the pre-deformation that the deformation history is different from previous study, namely, the pre-deformation of shear after uniaxial tension, is examined in this study. Then, the relation between the development of anisotropy in the yield surface and the deformation history of pre-deformation is revealed by comparing with the results of previous study.

YIELD STRESS BASED ON NATURAL STRAIN THEORY UNDER CYCLIC SHEAR LOAD AFTER LARGE SIMPLE SHEAR

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Yasuyuki Kato
Keyword(s):  
Yield Stress ◽  
Simple Shear ◽  
Strain Curve ◽  
Forward Direction ◽  
Reverse Direction ◽  
Elastoplastic Behavior ◽  
Cyclic Shear ◽  
Natural Strain ◽  
Test Pieces ◽  
Tension And Compression

This paper describes the variation of yield stress under cyclic loads after applying large pre-deformation. In this research, the Natural Strain is used as a strain representation for describing an elastoplastic behavior under large deformation. Using test pieces which is already given a pre-deformation of large simple shear, the yield stress under cyclic shear loads in the forward direction and the reverse direction is examined. As for the method for estimating yield stress in each cycle, the slope of a tangent in the principal deviatoric stress and the principal deviatoric strain curve is adopted. The experiments are conducted with the different sizes of pre-deformation and strain amplitude in order to reveal the effect of pre-deformation on the yield phenomenon. Then, these experimental results are compared with the results of yield stress in the previous study, which is obtained under cyclic load for tension and compression after applying the large uniaxial tension.

On Proportional Combined Loading Tests of an Aluminum Alloy and Its Analytical Formulation

1976 ◽  
Vol 98 (3) ◽  
pp. 282-288 ◽  
Author(s):  
Y. Ohashi ◽  
K. Kawashima ◽  
N. Mori
Keyword(s):  
Aluminum Alloy ◽  
Plastic Strain ◽  
Equivalent Stress ◽  
Strain Curve ◽  
Experimental Results ◽  
Combined Loading ◽  
Stress Deviator ◽  
Third Invariant ◽  
Simple Tension ◽  
Loading Tests

Proportional combined loading tests using axial load and torque were conducted on thin-walled tubular specimens of annealed isotropic aluminum alloy 5056. The experimental results showed that the third invariant of stress deviator affects considerably the plastic deformation of the material; that is, an equivalent stress-equivalent strain curve for simple tension or compression appears higher than that for pure torsion and the plastic strain vector is generally noncoaxial with the deviatoric stress vector. These results were formulated in the form of a nonlinear tensor relation between stress deviator and plastic strain on the basis of the general relation between coaxial tensors. The tensor equation derived was found to represent well the experimental results.

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