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.”

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.

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.

scholarly journals The theory of combined plastic and elastic deformation with particular reference to a thick tube under internal pressure

1947 ◽  
Vol 191 (1026) ◽  
pp. 278-303 ◽  
Keyword(s):  
Stress Distribution ◽  
Internal Pressure ◽  
Plastic Flow ◽  
Plastic Region ◽  
Strain Diagram ◽  
Combined Stresses ◽  
Usual Theory ◽  
Plastic Components ◽  
Longitudinal Extension ◽  
Elastic Strains

In certain problems of plastic flow, for example, a thick tube expanded by internal pressure, it is important to consider changes in the elastic strain of material which is flowing plastically in order to deduce the correct stress distribution and deformation. The usual plastic theory which neglects elastic strains in the plastic region may lead to considerable errors in certain cases. In this paper we review the theory of the deformation of a material under combined stresses which involves both elastic and plastic components of strain. The relationship between stress and strain is represented on a plane diagram, the reduced stress-strain diagram, which facilitates discrimination between the elastic and plastic components of strain and aids considerably the solution of certain problems. The diagram can also be used to express the relationships governing the dissipation of energy during plastic flow under combined stresses. The theory is applied to the deformation of a long thick tube under internal pressure with zero longitudinal extension. The solution is compared with that based on the usual theory which neglects elastic strains in the plastic region, revealing an error which reaches a maxi­mum of over 60% in the longitudinal stress distribution. The significance of the differences between the two solutions is discussed in detail.

An experimental study on the uniaxial and biaxial flexural tensile strength of concrete

1983 ◽  
Vol 10 (1) ◽  
pp. 104-115
Author(s):  
Zenon A. Zielinski ◽  
Ioanis Spiropoulos
Keyword(s):  
Tensile Strength ◽  
Biaxial Tension ◽  
Concrete Strength ◽  
Uniaxial Stress ◽  
Bottom Surface ◽  
Test Results ◽  
Flexural Tensile Strength ◽  
Modes Of Failure ◽  
Biaxial Tensile ◽  
Support Conditions

The flexural uniaxial and biaxial tensile strength of concrete was studied experimentally on one-way and two-way ribbed slab specimens. The specimens, consisting of a thin slab and deep ribs, constituted part of a waffle-like structure.Uniaxial tension was achieved by supporting the specimens at two points at the ends of one rib, and biaxial tension by supporting the specimens at four points at the ends of two cross ribs. In both support conditions, load was applied in the middle of the slab, thus introducing flexural tension in the ribs and compression in the slab.Measurements of tensile strain were carried out by means of uniaxial strain gauges attached to the bottom surface of the ribs. The modes of failure of concrete in uniaxial and biaxial tension were observed and are discussed in this paper. A revised biaxial failure envelope of concrete in tension is proposed.The test results indicate that the tensile strength of concrete is about 38% higher in the uniaxial stress state than in the biaxial. Keywords: concrete strength, uniaxial and biaxial tensile flexural strength, maximum strains, cracking, ribbed structure, waffle structure.

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.

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.

scholarly journals Experimental Study of the Relaxation Properties of Carbon Fiber Cloth

Materials ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 3603
Author(s):  
Qiang Wang ◽  
Hua-Lin Song ◽  
Chun-Ling Lu ◽  
Wan-Xu Zhu ◽  
Jia-Zhu Huang
Keyword(s):  
Carbon Fiber ◽  
Relaxation Rate ◽  
Calculation Model ◽  
Test Results ◽  
Relaxation Properties ◽  
Reinforced Plastics ◽  
Axial Tension ◽  
Carbon Fiber Cloth ◽  
Relaxation Loss ◽  
Rate Calculation

In this study, a new method was proposed to study the relaxation properties of carbon fiber reinforced plastics (CFRP) fabric under axial tension. Under the condition of constant temperature and humidity, six groups of 168 h stress relaxation tests were conducted. Considering the influence of the prestress level, the size of CFRP cloth, and the surface coating of CFRP cloth on the relaxation performance, the measures to reduce the relaxation loss were proposed. The relaxation rate calculation model was established based on the test results of the authors and other scholars and was validated through comparisons with the test results. The results indicate that the relaxation rate of CFRP cloth was between 1.92% and 6.1%. When the prestress level was smaller than 0.3 fu, the relaxation rate of CFRP cloth decreased with the increase of prestress level. When the prestress level was greater than 0.3 fu, the relaxation rate increased with the increase of the prestress level. Under the same conditions, the relaxation rate of the CFRP specimens coated with glue was smaller than the uncoated samples by 3.21–6.28%. The calculation model could well estimate the relaxation rate of CFRP cloth.

Creep Rupture Bending Test of 20 Percent Cold-Prestrained Ni-Fe-Cr Alloy Straight Tubes at 1100 F(593 C)

1981 ◽  
Vol 103 (4) ◽  
pp. 337-344 ◽  
Author(s):  
H. H. Woo ◽  
R. H. Ryder ◽  
K. H. Holko ◽  
R. F. Stetson
Keyword(s):  
Crack Initiation ◽  
Creep Rupture ◽  
Bending Test ◽  
Strain History ◽  
Test Results ◽  
Local Material ◽  
Initiation And Propagation ◽  
Nonuniform Stress Field ◽  
Point Bend ◽  
Four Point Bend Test

A four-point bend test was performed on 20 percent cold-prestrained Ni-Fe-Cr alloy tubes at 1100 F (593 C) to verify that creep rupture damage can be used to predict failure in a nonuniform stress field. Deflection control and acoustic emission techniques were used to detect crack initiation, strain gages were employed to record the strain history in the specimen, and a scanning electron microscrope was utilized to check crack initiation and propagation. Stress analyses were made using simplified and finite element methods. Comparison of test results and analyses concluded that creep rupture damage can be used to predict local material failure for structural components under multiaxial nonuniform loading conditions.

Deriving Plastic Constitutive Equations of the Material in Complex Stress State by Means of Simple Test Results

2011 ◽  
Vol 109 ◽  
pp. 100-104 ◽  
Author(s):  
Xiao Jiu Feng ◽  
Li Fu Liang
Keyword(s):  
Stress State ◽  
Constitutive Equations ◽  
Complex Stress ◽  
Complex Stress State ◽  
One Dimension ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Test Results ◽  
Loading Function ◽  
Simple Tension

By conducting simple tension and torsion tests to material, constitutive equations of one dimension are obtained. Plastic theories of continuum mechanics are used for analyzing deformation behavior of the material after yielding. Here, material is presumed to have isotropic hardening characteristic. By using Mises loading function and the associative flow rule, the derivations are made to extend the constitutive equations of one dimension in the simple tension and torsion tests to that of multi-dimension and obtain the plastic constitutive equations of the material in complex stress state , respectively.

A testing rig for cycling at high biaxial strains

1973 ◽  
Vol 8 (3) ◽  
pp. 168-175 ◽  
Author(s):  
J M H Andrews ◽  
E G Ellison
Keyword(s):  
High Strain ◽  
External Pressure ◽  
Multiaxial Fatigue ◽  
Axial Tension ◽  
Wide Range ◽  
Fatigue Data ◽  
Other Information ◽  
Tension And Compression ◽  
Tubular Specimens ◽  
Experimental Rig

There is a scarcity of multiaxial fatigue data available to designers especially in the high-strain régime. This is due in part of the complexity of the test equipment involved. A servo-hydraulic experimental rig has been developed for the application of biaxial high-strain reversed cycles to thin-walled tubular specimens, i.e. under axial tension and compression and internal and external pressure. It is capable of testing over a wide range of strain ratios and is reasonably versatile in that other information pertaining to buckling, Poisson's ratio, and criteria for yielding can be obtained.

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