The Effect of the Rotation of the Stress Axes on the Yield Criterion of Prestrained Materials

1966 ◽  
Vol 88 (1) ◽  
pp. 61-70 ◽  
Author(s):  
Tao-Ching Hsu
Keyword(s):  
Yield Stress ◽  
Stress Ratio ◽  
Biaxial Tension ◽  
Yield Criterion ◽  
Yield Locus ◽  
Characteristic Index ◽  
Axial Tension ◽  
Combined Stresses ◽  
Stress Direction ◽  
Tubular Specimens

The yield locus of a prestrained material can be based on different systems of combined stress, such as biaxial tension and combined tension and shear. No matter what the combined stresses may be, however, the deviatoric yield stress is a function of only two variables, the characteristic index, which represents the stress ratio, and the stress direction, or the inclination of the principal stress axes. It is shown that, when tubular specimens are tested under combined torsion and axial tension, the results show the mixed effects of the characteristic index and the stress direction on the yield stress. In such tests, the two effects can, however, be separated if the strain vectors as well as the yield stresses are known. The theory is applied to several groups of experimental results on the yield locus of prestrained materials, including Taylor and Quinney’s results.

Anisotropic Loading Functions for Combined Stresses in the Plastic Range

1955 ◽  
Vol 22 (1) ◽  
pp. 77-85
Author(s):  
L. W. Hu ◽  
Joseph Marin
Keyword(s):  
Plastic Flow ◽  
Biaxial Tension ◽  
Strain History ◽  
Test Results ◽  
Axial Tension ◽  
State Of Stress ◽  
Loading Function ◽  
Combined Stresses ◽  
Shift Of Origin ◽  
Tubular Specimens

Abstract A loading function is a relation between combined stresses for which the beginning of plastic flow takes place. The loading function for a given material is different depending upon the initial plastic strains produced. That is, the initial stress or strain history influences the subsequent loading function. This paper gives the results of an experimental investigation to determine the validity of certain loading functions proposed for anisotropic materials. The study reported was conducted for an aluminum alloy 24S-T and the state of stress covered was biaxial tension. These stresses were produced in the usual way by subjecting thin-walled tubular specimens to axial tension and internal pressure. The test results showed that none of the existing loading functions is adequate for interpreting the plastic stress-strain relations obtained. Tests also were made to determine the change in the loading function with increase in plastic flow. It was found that the loading function did not remain symmetrical with respect to the original function, nor was the new loading function the same as the original except for a shift of origin. However, the test results support in a qualitative way the concept of the so-called “yield corner.”

A theory of the yield locus and flow rule of anisotropic materials

1966 ◽  
Vol 1 (3) ◽  
pp. 204-215 ◽  
Author(s):  
T. C. Hsu
Keyword(s):  
Experimental Data ◽  
Linear Relationship ◽  
Yield Stress ◽  
Plane Stress ◽  
Stress Ratio ◽  
Yield Criterion ◽  
Anisotropic Materials ◽  
Yield Locus ◽  
Flow Rule ◽  
Stress Components

A general yield criterion for anisotropic materials is derived from the linear relationship between strain and stress components. The particular forms of the yield criterion for plane stress and for certain types of symmetry are discussed and are compared with available experimental data. The separate effects of the stress ratio and the direction of the stress axes on the yield stress are also determined.

scholarly journals Lower Bound Yield Locus Calculations

1990 ◽  
Vol 12 (1-3) ◽  
pp. 89-101 ◽  
Author(s):  
William Hosford ◽  
Aitor Galdos
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Work Hardening ◽  
Stress Ratio ◽  
Yield Criterion ◽  
Yield Locus ◽  
Stress Strain ◽  
Strain Behavior ◽  
Yield Loci ◽  
The Hill

A lower-bound model for the deformation of work-hardening polycrystals is proposed. All grains are assumed to be loaded under the same stress and the stress–strain behavior is found by averaging the strains in all grains. The shapes of the yield loci have been calculated for textured metals which deform by {111} 〈110〉 slip (fcc) and by 〈111〉-pencil glide (bcc). As with the corresponding upper-bound models, the yield loci are best described by an anisotropic yield criterion with an exponent of 6 to 10 (instead of 2 as in the Hill theory). Also it is shown that a model of polycrystal deformation in which the grains are loaded to the same stress ratio (but not the same level of stresses) violates normality and is not a lower bound.

scholarly journals Investigation of the prediction capability of Yld89 yield criterion for highly anisotropic sheet materials

2021 ◽  
pp. 7-13
Author(s):  
Bora ŞENER
Keyword(s):  
Plastic Strain ◽  
Yield Stress ◽  
Yield Surface ◽  
Stress Ratio ◽  
Yield Criterion ◽  
High Strength ◽  
Elastic Region ◽  
Sheet Plane ◽  
Sheet Materials ◽  
Prediction Capability

In the present work, the prediction capability of Yld89 criterion from anisotropic yield func- tions was investigated in the view of the anisotropic behavior of the sheet metals. Investigation was conducted on two highly anisotropic sheet materials: an aluminum alloy (AA2090-T3) and an advanced high strength steel (TRIP 780). The in-plane variation of material anisotropy and normalized yield surface contours were considered in the evaluation of the prediction capability of the criterion. Firstly, the model coefficients were determined according to stress and strain based definitions. Then, the planar variations of the yield stress and plastic strain ratios and normalized yield surface contours of the materials were predicted according to both identification procedures. Finally, the computed results were compared with experiments to evaluate prediction capability of the model. It was observed from the comparisons that the pla- nar variations of the yield stress ratio could successfully predicted by stress based definition, while the variations of the plastic strain ratios in the sheet plane could accurately predicted by strain based definition. Besides, it was determined that elastic region predicted from strain based definition was larger than stress based definition for AA2090-T3, while the predicted elastic region from stress based definition was slightly larger in than that of strain based defi- nition for TRIP 780 material.

Biaxial Strength of HY 80 Steel

1985 ◽  
Vol 107 (2) ◽  
pp. 132-137 ◽  
Author(s):  
K. S. Chan ◽  
U. S. Lindholm ◽  
J. Wise
Keyword(s):  
Biaxial Tension ◽  
Strain Ratio ◽  
Thin Wall ◽  
Plastic Strain Ratio ◽  
Axial Tension ◽  
Diffuse Necking ◽  
Stress States ◽  
Von Mises ◽  
Tube Geometry ◽  
Good Agreement

The biaxial deformation behavior of HY 80 steel has been examined by testing thin wall tubes under combined axial tension and internal pressure. The effective stress-strain curves and the hardening response have been found to vary with the stress state. The plastic strain ratio at a given stress ratio deviates from the von Mises value except at the stress states near uniaxial tension, plane strain and equi-biaxial tension. Using Drucker theory, these deviations are eliminated and the resulting yield locus is in good agreement with both the Bishop-Hill theory and the experimental results. Influenced by the tube geometry, the instability strains at the onset of diffuse necking are decreased by an increase in hoop tension. The diffuse necking strains are reasonably predicted by the Swift and the Lankford-Saibel/Mellor criteria.

scholarly journals On the Ratchet Analysis of a Cracked Welded Pipe

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Tianbai Li ◽  
Haofeng Chen ◽  
Weihang Chen ◽  
James Ure
Keyword(s):  
Yield Stress ◽  
Maximum Temperature ◽  
Limit Loads ◽  
Axial Tension ◽  
Circumferential Crack ◽  
Temperature Load ◽  
Cyclic Temperature ◽  
Temperature Ranges ◽  
Welded Pipe ◽  
Linear Matching Method

This paper presents the ratchet limit analysis of a pipe with an axisymmetric circumferential crack in a mismatched weld by using the extended linear matching method (LMM). Two loading conditions are considered: (i) a cyclic temperature load and a constant internal pressure and (ii) a cyclic temperature load and a constant axial tension. Individual effects of (i) the geometry of the Weld Metal (WM), (ii) the size of the crack, (iii) the location of the crack, and (iv) the yield stress of WM on the ratchet limits, maximum temperature ranges to avoid ratchetting, and limit loads are investigated. Influence functions of the yield stress of WM on the maximum temperature ranges and limit loads are generated. The results confirm the applicability of the extended LMM to the cracked welded pipe.

scholarly journals Effect of Combined Stress on Yield and Fracture Behavior of Zircaloy-2

1961 ◽  
Vol 83 (4) ◽  
pp. 499-508 ◽  
Author(s):  
R. L. Mehan
Keyword(s):  
Plastic Flow ◽  
Biaxial Tension ◽  
Effective Strain ◽  
Tension Stress ◽  
Combined Stress ◽  
Flow Properties ◽  
Axial Tension ◽  
Fracture Ductility ◽  
Stress States ◽  
Single Stress

The yielding and fracture characteristics of Zircaloy-2 as a function of stress state were investigated at room temperature through the medium of thin-walled cylindrical specimens under internal pressure and axial tension. Stress states from uniaxial longitudinal tension to uniaxial tangential tension were examined. Two tests at elevated temperature were performed at a single stress ratio. It was found that the fracture ductility lessened with increasing biaxiality. A minimum in ductility was found at balanced biaxial tension where the fracture ductility, as expressed by the effective strain, was 29 per cent. The yielding and plastic flow properties were found to be highly anisotropic. Two methods were used to express the plastic flow data: a graphical approach and a theoretical analysis based on a theory proposed by R. Hill, either one of which is suitable to express the flow properties of Zircaloy-2 under various states of combined stress.

Effect of multiaxial stresses on the fracture strength of silicon carbide

1969 ◽  
Vol 4 (2) ◽  
pp. 81-87 ◽  
Author(s):  
E K Priddle
Keyword(s):  
Silicon Carbide ◽  
Fracture Strength ◽  
Room Temperature ◽  
Fracture Behaviour ◽  
Axial Tension ◽  
Straight Line ◽  
Failure Envelopes ◽  
Tension And Compression ◽  
Failure Theories ◽  
Tubular Specimens

This work describes the fracture behaviour of silicon-carbide tubular specimens under multi-axial stresses at room temperature. A method of obtaining combinations of stresses in the form of torsion, hoop, axial tension, and compression is described and failure envelopes for silicon carbide are included from the data obtained. Failure theories are reviewed and the results from the work show that the available theories are inadequate to describe both the tension-tension and tension-compression quadrants. For practical purposes a straight-line relation can be used joining axial and hoop tensile strengths and the axial compression strength.

Off-Axis Torsion Tests on Tubular Specimens of Steel

2001 ◽  
Vol 123 (3) ◽  
pp. 268-273 ◽  
Author(s):  
Takenobu Takeda ◽  
Zhongchun Chen
Keyword(s):  
Shear Stress ◽  
Yield Stress ◽  
Maximum Shear Stress ◽  
Torsion Test ◽  
Combined Loading ◽  
Anisotropic Hardening ◽  
Principal Stresses ◽  
Maximum Value ◽  
The Difference ◽  
Tubular Specimens

In order to analyze the anisotropic hardening behavior of metals, an off-axis torsion test by combined loading is developed. In this test, the maximum shear stress direction φ can be changed from 0 deg to 90 deg while the ratio of maximum and minimum principal stresses is kept at −1. With increasing angle φ, the yield stress of the torsional-prestrained steel decreases; the difference between the directions of the maximum shear stress and principal shear strain increment rises to a maximum value and then decreases. It is experimentally verified that anisotropy is more severe when a smaller offset strain is used in defining the yield stress.

Ratchet Limits for a Crack in a Welded Pipe Subjected to a Cyclic Temperature Load and a Constant Mechanical Load

2011 ◽  
Author(s):  
Tianbai Li ◽  
Haofeng Chen ◽  
Weihang Chen ◽  
James Ure
Keyword(s):  
Yield Stress ◽  
Mechanical Load ◽  
Maximum Temperature ◽  
Limit Loads ◽  
Axial Tension ◽  
Temperature Load ◽  
Cyclic Temperature ◽  
Temperature Ranges ◽  
Welded Pipe ◽  
Symmetric Crack

This paper presents the ratchet limit analysis of a pipe with a symmetric crack in a mismatched weld by using the extended Linear Matching Method (LMM). Two loading conditions are considered: i) a cyclic temperature load and a constant internal pressure; and ii) a cyclic temperature load and a constant axial tension. Individual effects of i) the geometry of the Weld Metal (WM), ii) the size of the crack, iii) the location of the crack and iv) the yield stress of WM on the ratchet limits, maximum temperature ranges to avoid ratchetting and limit loads are investigated. Influence functions of the yield stress of WM on the maximum temperature ranges and limit loads are generated. The results confirm the applicability of the extended LMM to the cracked welded pipe.

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