Shape of Yield Surface under Large Simple Shear Estimated by Using Natural Strain Theory

2017 ◽  
Vol 2017 (0) ◽  
pp. G0300104
Author(s):  
Yasuyuki KATO ◽  
Tohur AKIBA
Keyword(s):  
Simple Shear ◽  
Yield Surface ◽  
Strain Theory ◽  
Natural Strain

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.

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

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Yasuyuki Kato ◽  
Hiroki Uchida
Keyword(s):  
Yield Stress ◽  
Uniaxial Tension ◽  
Simple Shear ◽  
Strain Theory ◽  
Experimental Result ◽  
Cyclic Loads ◽  
Yield Behavior ◽  
Compression Load ◽  
Natural Strain ◽  
Tension And Compression

Many researches on the yield behavior under cyclic loads have been conducted for many years. However, almost these studies have been done within the range of relatively small size deformation. Hence, the detailed studies for yield phenomenon under cyclic loads after applying a large pre-deformation have not been sufficiently elucidated. Therefore, in the series of our studies, using test pieces of high purity tough pitch copper, the yield behavior generated under cyclic loads after applying the predeformation of large uniaxial tension or large simple shear have been investigated. However, as for the case that the type of pre-deformation differs from the type of deformation in the cyclic load, detailed studies have not been conducted yet. Hence, in the present study, the yield behavior generated under cyclic loads for tension and compression after applying a large pre-deformation of simple shear is examined based on Natural Strain theory. Furthermore, experimental results in the present study are compared with results of previous studies concerning cyclic loads for tension and compression after applying the large uniaxial tension. Consequently, it is revealed that the decreasing tendency of yield stress at the compression side appears more strongly as compared with the experimental result by previous study that the pre-deformity is a uniaxial tension.

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.

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