The Stresses in Thick-Walled Cylinders of Mild Steel Overstrained by Internal Pressure

1934 ◽  
Vol 126 (1) ◽  
pp. 407-455 ◽  
Author(s):  
Gilbert Cook
Keyword(s):  
Shear Stress ◽  
Mild Steel ◽  
Internal Pressure ◽  
Wall Thickness ◽  
Maximum Shear Stress ◽  
Internal Surface ◽  
Principal Stresses ◽  
Constant Shear Stress ◽  
Axial Compressive Stress ◽  
Set Up

The paper describes a theoretical and experimental investigation of the stress distribution across the walls of thick cylinders of mild steel when the internal pressure is such that the elastic limit of the material is exceeded and a certain amount of overstrain occurs. The main conclusions are:— (1) That in the cylinders in which it was possible to produce overstrain over the whole wall thickness the observed pressure is in close agreement with that calculated on the assumption of constant shear stress equal to the shear stress observed during plastic yield in tension. (2) That in partially overstrained cylinders the maximum shear stress in the elastic region varies as overstrain proceeds. (3) That at the internal surface the effect of overstrain is to reduce the circumferential tensile stress, and to set up an axial compressive stress. With sufficient wall thickness all three principal stresses at the internal surface become compressive for pressures which still permit of the external portions remaining elastic.

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.

Internal Stresses in Elastohydrodynamic Lubrication of Rolling/Sliding Contacts

1989 ◽  
Vol 111 (1) ◽  
pp. 180-187 ◽  
Author(s):  
Farshid Sadeghi ◽  
Ping C. Sui
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Internal Stress ◽  
Maximum Shear Stress ◽  
Elastohydrodynamic Lubrication ◽  
Normal Pressure ◽  
Internal Stresses ◽  
Stress Distributions ◽  
Principal Stresses ◽  
Dimensionless Velocity

The internal stress distribution in elastohydrodynamic lubrication of rolling/sliding line contact was obtained. The technique involves the full EHD solution and the use of Lagrangian quadrature to obtain the internal stress distributions in the x, y, z-directions and the shear stress distribution as a function of the normal pressure and the friction force. The principal stresses and the maximum shear stress were calculated for dimensionless loads ranging from (2.0452 × 10−5) to (1.3 × 10−4) and dimensionless velocity of 10−10 to 10−11 for slip ratios ranging from 0 to pure sliding condition.

Influence of Internal Pressure on the Impact Behavior of Steel Pipelines

1996 ◽  
Vol 118 (4) ◽  
pp. 464-471 ◽  
Author(s):  
N. Jones ◽  
R. S. Birch
Keyword(s):  
Experimental Data ◽  
Mild Steel ◽  
Internal Pressure ◽  
Wall Thickness ◽  
Critical Values ◽  
Impact Behavior ◽  
Steel Pipes ◽  
Impact Tests ◽  
The Impact ◽  
Gas Pressures

This article presents some experimental data recorded from 54 impact tests on pressurized mild steel pipes. The pipes were fully clamped across a span which was ten times the outside pipe diameter of 60 mm. The pipes had a wall thickness of 1.70 mm and were impacted laterally by a rigid wedge indenter at the mid-span and one-quarter-span positions. The impact velocities ranged up to 13.6 m/s and caused large inelastic indentations for the lower values and at higher values a loss of integrity which could occur underneath the indenter and/or at an end support. The critical values for the two failure energies were obtained for a range of internal gas pressures.

Biezeno Pressure Vessel Heads

1956 ◽  
Vol 23 (4) ◽  
pp. 642-645
Author(s):  
R. A. Struble
Keyword(s):  
Shear Stress ◽  
Internal Pressure ◽  
Pressure Vessel ◽  
Maximum Shear Stress ◽  
Head Shape ◽  
Thin Walled ◽  
Constant Maximum

Abstract The equation of thin-walled pressure vessel heads with constant maximum shear stress throughout is derived. Such heads, used on cylindrical vessels with uniform internal pressure, were first conceived by Biezeno in 1922 who gave a semigraphical prescription for determining the head shape.

On the Analysis of Asymmetric Stress

1972 ◽  
Vol 39 (4) ◽  
pp. 1133-1136 ◽  
Author(s):  
V. K. Stokes
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Stress Tensor ◽  
Maximum Shear Stress ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Symmetric Part ◽  
Principal Stresses ◽  
Asymmetric Stress

An attempt has been made to analyze asymmetric stress. Bounds for the principal stresses have been established in terms of the principal stresses corresponding to the symmetric part of the stress tensor. Sufficient conditions for the existence of one or three principal stresses have been established. Bounds have also been established for the maximum shear stress. Detailed results have been given for the case of a quasi two-dimensional stress distribution.

The Initiation and Propagation of Fatigue Cracks in Mild Steel Pieces of Square Section

1954 ◽  
Vol 4 (1) ◽  
pp. 1-18 ◽  
Author(s):  
H. L. Cox ◽  
J. E. Field
Keyword(s):  
Shear Stress ◽  
Tensile Stress ◽  
Mild Steel ◽  
Fatigue Cracks ◽  
Maximum Shear Stress ◽  
Shear Stresses ◽  
High Shear ◽  
Stress Range ◽  
High Shear Stress ◽  
General Direction

SummaryAn investigation has been made to determine the positions and directions of initiation and the directions of propagation of fatigue cracks and to examine the correlation between these positions and directions and the planes on which maximum tensile and maximum shear stresses are generated.To afford as wide a range as possible of the ratio of maximum shear stress to maximum tensile stress, tests have been made under combinations of alternating bending and torsion; and in order to separate partially the regions of high shear stress from those of high direct stress, the tests have been made on pieces of square section with the plane of bending parallel to one diagonal of the section. Two series of tests have been made; one a preliminary series on pieces having no parallel portion and the other on pieces having a parallel portion about three times the length of the side of the square section. The positions and directions of initiation and the directions of propagation of fatigue cracks have been observed and compared with the positions and directions of the maximum tensile and shear stresses.Fatigue cracks may be initiated as a result of either high shear stress or high tensile stress and in the present series of tests on mild steel, cracking in tension has occurred in preference to cracking in shear when the ratio of the tensile stress range to the shear stress range has exceeded about 1.6; for values of this ratio less than 1.6, the cracks started in shear (and vice versa); propagation along the plane of maximum shear appears to be preferred up to a slightly greater value of the tensile/shear ratio (about 1.7 possibly). The general direction of a crack formed as a result of high tension usually follows the plane of maximum tension and that of a crack formed as a result of shear usually follows the plane of maximum shear. In detail both types of crack—in this mild steel—deviate quite widely from their general directions but this deviation bears no obvious relation to the microstructure of the material. Cracks propagating along one plane of maximum shear occasionally show a marked tendency to branch along the associated plane of maximum shear; but this tendency is not always observed and in other cases no tendency to branch has been noted.

Influence of Ductility on Creep Rupture Under Multiaxial Stresses

1962 ◽  
Vol 84 (2) ◽  
pp. 228-232 ◽  
Author(s):  
W. Sawert ◽  
H. R. Voorhees
Keyword(s):  
Shear Stress ◽  
Internal Pressure ◽  
Maximum Principal Stress ◽  
Creep Rupture ◽  
Principal Stresses ◽  
Relative Response ◽  
Combined Stresses ◽  
Thin Walled ◽  
Tubular Specimens ◽  
Stress Invariant

Creep-rupture times at 1200 and 1400 deg F were compared for notched versus unnotched bars and for thin-walled tubes in uniaxial tension versus combined tension and internal pressure to give a 1:1 ratio of longitudinal and transverse principal stresses. Relative response to multiaxial stresses of cast DCM alloy with low ductility was not essentially different from that of Rene´ 41 alloy with higher ductility. Creep rupture times of the tubular specimens under combined stresses correlated better in terms of the shear stress invariant than of maximum principal stress.

scholarly journals Calculation and strengthening of maximum stressed near support zones of high glue-wood beam constructions

2015 ◽  
Vol 5 (1) ◽  
pp. 187-197
Author(s):  
Лисятников ◽  
Mikhail Lisyatnikov ◽  
Грибанов ◽  
Aleksey Gribanov ◽  
Рощина ◽  
...  
Keyword(s):  
Shear Stress ◽  
Maximum Shear Stress ◽  
Engineering Calculation ◽  
Complex Stress ◽  
Minimal Effect ◽  
Principal Stresses ◽  
Method Of Calculation ◽  
Geometrical Characteristics ◽  
Wood Beams ◽  
Physical And Mathematical Models

We consider the engineering calculation of maximum stressed abutment sections of high glue-wood beam constructions, as well as strengthening these areas with glass nanoassembly. In supports of glued wood beams complex stress arises causing spalling along the fibers, crushing reproach fibers and stretching at an angle to the fibers. The article proposes a new way of strengthening these areas during the production of beams, the essence of which consists in the fact that the ends of the beam constructions are put in clip of glass in one or several layers glued to wood by epoxy resin composition including carbon nanotubes. In the calculations, wood is considered as transport materials described by rheological equations as viscosity elastic elastic body. Physical and mathematical models of fiberglass are selected. Strength of materials formulas calculated geometrical characteristics of the reduced section of strengthened near mounting area of high glued wood beams. Engineering method has shown that the existing method of calculation of wooden bent elements (on the maximum principal stresses in the middle of the span and the maximum shear stress on the support) is not applicable to high glue-wood beams. Tensile stresses at an angle to the fibers in the support areas reach peak values at a load of approximately twice lower than the load at which the maximum shear stress takes place. Engineering calculations found that supports of high beam constructions need to be strengthened. Minimal effect on enhancing by clip of glass nanoassembly by cleaving along the fibers ≥ 8 %, when crumpled across the fibers ≥ 7 %, in tension at an angle to the fibers ≥ 9 %. It was proposed to simplify the formula of geometrical characteristics of the reduced section in order to facilitate further calculations.

Influence of Phase Shift and Amplitude Ratio on the Principal Stresses and Directions in Multiaxial Fatigue Testing

2015 ◽  
Vol 1111 ◽  
pp. 103-109 ◽  
Author(s):  
Lorand Kun ◽  
Ion Dumitru ◽  
Daniel Achiriloaiei ◽  
Karla Noemy Kun
Keyword(s):  
Shear Stress ◽  
Phase Shift ◽  
Fatigue Testing ◽  
Amplitude Ratio ◽  
Maximum Shear Stress ◽  
Multiaxial Fatigue ◽  
Experimental Program ◽  
Shear Stresses ◽  
Principal Stresses ◽  
Normal And Shear Stresses

The maximum values of normal and shear stresses are the basic parameters which influence directly the initiation and propagation of multiaxial fatigue cracks.Based on the above, the first part of the paper presents an analysis of principal stresses (normal and shear) in case of symmetrical tension-compression loadings with superimposed phase-shifted symmetrical torsion cycles. The influence of stress amplitude ratio and phase shift on the maximum (normal and shear) stresses and on the directions of the planes along which these act is analyzed and graphically represented using stress hodographs.The second part of the paper highlights the possibility of using the maximum value of the normal or shear stress as base parameter for durability studies under multiaxial fatigue, based on existing experimental data. The mentioned data is correlated with the results of an original experimental program carried out by the authors on 41Cr4 steel and conclusions are formulated with regard to the role of maximum shear stress in life-time calculation.

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