Plastic Stress-Strain Relations

1948 ◽  
Vol 159 (1) ◽  
pp. 95-114 ◽  
Author(s):  
W. M. Shepherd
Keyword(s):  
Shear Stress ◽  
Tensile Stress ◽  
Shear Strain ◽  
Maximum Shear Stress ◽  
The Other ◽  
Plastic Strains ◽  
Stress Strain ◽  
Thin Tube ◽  
Shear Strains ◽  
Comparable Magnitude

The author derives stress-strain relations which are applicable to problems in which the elastic and plastic strains are of comparable magnitude. Two alternative criteria are used, one based on the Mises-Hencky function and the other on the maximum shear stress. Shear stress-shear strain curves are deduced from tensile stress-strain curves and the result is in one case compared with experiment. The problem of a thin tube strained in tension beyond the onset of plasticity and then subjected to an increasing torque is considered, and the tensile and shear strains due to the torque are found. A result relating to the energy lost in plastic straining is obtained.

Study on Thermal Cycling of Sn0.7Cu Solder

2013 ◽  
Vol 791-793 ◽  
pp. 362-365
Author(s):  
Li Yang ◽  
Ju Li Li ◽  
Jing Guo Ge ◽  
Meng Li ◽  
Nan Ji
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
High Temperature ◽  
Thermal Cycling ◽  
Shear Strain ◽  
Maximum Shear Stress ◽  
Steady State Creep ◽  
Maximum Shear Strain ◽  
Cycle Number ◽  
State Cycle

Thermal cycling of a unit Sn0.7Cu solder was studied based on the steady-state creep constitutive equation and Matlab software. The results show that there is a steady-state cycle for the thermal cycling of unit Sn0.7Cu eutectic solder. In steady-state thermal cycling, the shear stress is increased with the increase of temperature. There is a stage of stress relaxation during high temperature. A liner relationship between maximum shear stress and maximum shear strain is observed during thermal cycling. The metastable cycle number is declined greatly with the increase of maximum shear strain.

Analysis of Performance Decay Behavior for Asphalt Pavement Based on Aging

2013 ◽  
Vol 723 ◽  
pp. 22-26 ◽  
Author(s):  
Pei Long Li ◽  
Zhan Ding ◽  
Zheng Qi Zhang
Keyword(s):  
Shear Stress ◽  
Service Life ◽  
Tensile Stress ◽  
Simulation Analysis ◽  
Asphalt Pavement ◽  
Maximum Shear Stress ◽  
Maximum Tensile Stress ◽  
Pavement Structure ◽  
Analysis Of Performance ◽  
Decay Behavior

Aging is a main factor affecting the durability of asphalt pavement. To study decay behavior of asphalt pavement with aging, aged asphalt was extracted from stratified pavement mixtures for different service-life. The changes of asphalt properties with service time and depth variations of the pavement were discussed. And numerical simulation analysis of pavement structure was conducted with pavement gradient modulus changes caused by aging. The results indicate that asphalt stiffness increases and low-temperature performance decays sharply with the extension of pavement service life, especially in the first several years. The vertical aging differences from top to bottom of pavement were significant, the aging extents decrease continuously from the surface, which cause the gradient changes of pavement modulus. The maximum tensile stress and maximum shear stress all increase with surface modulus increasing, so more serious aging can induce greater gradient modulus, shear stress and tensile stress are larger under the same loads, which have more serious damage to the pavement structure.

scholarly journals Uniaxial Tensile Stress-Strain Response on the 3D Angle Interlock Woven Fabric Composite

2019 ◽  
Vol 7 (4.14) ◽  
pp. 430
Author(s):  
F. M.Z. Nasrun ◽  
M. F. Yahya ◽  
M. R. Ahmad ◽  
S. A. Ghani
Keyword(s):  
Tensile Stress ◽  
The Other ◽  
Woven Fabric ◽  
Uniaxial Tensile ◽  
Strain Response ◽  
Woven Composite ◽  
Stress Strain ◽  
Fabric Composite ◽  
Uniaxial Tensile Stress ◽  
Set Up

An experimental study have been performed to investigate the uniaxial tensile stress-strain response on the 3D angle interlock (3DAI) woven fabric composite. The tensile analysis were examined based on different woven fabric set-up parameter of draw-in plan ; pointed (DRW 1), broken (DRW 2), broken mirror (DRW 3), and straight (DRW 4). Meanwhile, the woven fabric composite were produced based on 22 and 25 pick.cm-1 of weft densities. The outcomes produced shown that woven composite sample with 25 pick.cm-1 on DRW 4 projected the highest stress response, 113 MPa. Extensive review indicated that DRW 1 and 4 gave better tensile stress-strain response than the other counterpart. 

The Force Impact Analysis of Steel Bridge Deck Pavement Layer Modulus and Pavement Thickness to Pavement System

2011 ◽  
Vol 368-373 ◽  
pp. 289-292
Author(s):  
San Qiang Yang ◽  
Pei Wen Hao ◽  
Li Qun Tang ◽  
Tao Liu
Keyword(s):  
Shear Stress ◽  
Elastic Modulus ◽  
Tensile Stress ◽  
Bridge Deck ◽  
Maximum Shear Stress ◽  
Maximum Tensile Stress ◽  
Steel Bridge ◽  
Epoxy Asphalt ◽  
Pavement Thickness ◽  
Bridge Deck Pavement

This epoxy asphalt used by the U.S., Japan Epoxy Asphalt two steel bridge deck pavement materials at different thickness analysis of pavement deformation force. Pavement derived the maximum tensile stress, shear stress and elastic modulus, pavement thickness of mathematical models. The results showed that: Pavement maximum tensile stress, shear stress, pavement elastic modulus with available four times a polynomial equation fitted, pavement surface transverse maximum stress increases as the pavement thickness decreases, horizontal maximum shear stress between layers does not increase with the pavement thickness decreases, but the thickness of the pavement at 40-50mm have a peak, then gradually increases with the thickness decreases.

Uniaxial strain derivatives of the Fermi surface of copper

1983 ◽  
Vol 61 (2) ◽  
pp. 177-187 ◽  
Author(s):  
D. W. Ruesink ◽  
J. M. Perz
Keyword(s):  
Experimental Study ◽  
Tensile Stress ◽  
Fermi Surface ◽  
Shear Strain ◽  
Cross Sections ◽  
The Other ◽  
Quantum Oscillations ◽  
Self Consistent ◽  
Torque Values ◽  
Derivatives Of

From a comprehensive experimental study of quantum oscillations in magnetostriction and torque, values have been deduced for all nonvanishing tetragonal and angular shear strain derivatives for the five principal extremal cross sections of the Fermi surface of copper, viz., the neck and belly normal to [111], the dogsbone normal to [110], and the rosette and belly normal to [001]. It is found that the neck is most sensitive to angular shear strain, whereas the bellies are most affected by uniform dilation. For the other orbits the magnitudes of shear and dilation derivatives are comparable.The results are self-consistent and agree with the experimental tensile stress results of Shoenberg and Watts. Earlier magnetostriction results for the neck obtained by Aron and by Slavin can be brought into agreement with the present data by recalculating the former using the now accepted value for the neck effective mass. The present experimental derivatives are in qualitative agreement with the theoretical values calculated by Lee, except for the tetragonal shear derivative of the [001] belly, for which the theoretical value is about 50% higher than the experimental one. This discrepancy is not fully understood.

Effect of Interlayer on the Elastic-Plastic Deformation of Coating Systems

2019 ◽  
Vol 35 (3) ◽  
pp. 373-380 ◽  
Author(s):  
Y. X. Guo ◽  
Y. W. Zhao
Keyword(s):  
Shear Stress ◽  
Elastic Modulus ◽  
Yield Strength ◽  
Tensile Stress ◽  
Maximum Shear Stress ◽  
Indentation Load ◽  
Interlayer Thickness ◽  
The Finite Element Method ◽  
Thickness Increase ◽  
Elastic Plastic

ABSTRACTThe finite element method (FEM) was used to study the elastic-plastic contact in the coating systems with interlayer. The results reveal that with the increase of interlayer thickness, the maximum shear stress of coating/interlayer and interlayer/substrate interfaces decreases. Moreover, the sharply changed shear stress between the interfaces of coating/interlayer and interlayer/substrate decreases too. There is no further decrease when interlayer thickness increase to 0.04 mm and above. With the increasing of interlayer elastic modulus, the shear stress of coating/interlayer interface decreases while the shear stress of interlayer/substrate interface increases. Meanwhile, the higher elastic modulus leads to the intensive tensile stress concentration on the interface of coating/interlayer. Hence, the interlayer with appropriate elastic modulus not only reduces the shear stress of coating/interlayer and interlayer/substrate interfaces but also decreases the tensile stress of coating/interlayer interface. The mechanical properties of coating systems were investigated with different interlayer yield strength. The effective hardness and elastic modulus increase with the increase of interlayer yield strength, which is good to protect the substrate from the deformation. In addition, higher indentation load can lead to the decrease of effective hardness and elastic modulus.

scholarly journals NUMERICAL STUDY ON THE SENSITIVITY ANALYSIS FOR STRENGTH AND STIFFNESS OF REGULAR CELLULAR SOLIDS

2013 ◽  
pp. 294-299
Author(s):  
SILVA H. M ◽  
PEIXINHO N. R ◽  
SILVA F. S.
Keyword(s):  
Sensitivity Analysis ◽  
Shear Stress ◽  
Shear Strain ◽  
Numerical Study ◽  
Axial Stress ◽  
Maximum Shear Stress ◽  
Axial Displacement ◽  
Cellular Solids ◽  
Maximum Shear Strain ◽  
Geometric Variables

The aim of this study is to present a sensitivity analysis of geometric variables on the mechanical behavior of regular cellular solids. The cellular solids studied are named “spherical” and “elliptical”, if there is part of an empty sphere inside or if there is part of an empty revolved ellipse, respectively. Pure loads are applied separately, namely compression and shear, in order to study the influence of the variables on axial stress and axial displacement (compression) and shear stress and shear strain on shear. The sensitivity analysis is useful to establish limits for the studied variables in an optimization process and to know the influence of the variables on the results. In the case that a variable has little or no influence on the results; it must be evaluated if it is worth using it. In this work, the influence of two geometric variables, namely stacking and radius were studied for two types of regular cellular solids. The solids are composed by 7*7*7 base cells. The maximum axial stress and axial displacement were measured on compression for each model. On shear, the maximum shear stress and the maximum shear strain on the plane that is sensitive to the variation of the studied variable were taken. Three models were studied in each case. The influence of the studied geometric variables on the results are presented and discussed. It is found that all the variables have influence on the results, although in a different manner.

scholarly journals Parametric stress-strain analysis for upstream slope of the asphaltic concrete core rockfill dams in static state

2021 ◽  
Vol 34 (06) ◽  
pp. 1800-1818
Author(s):  
Shahram Shiravi ◽  
Arash Razmkhah
Keyword(s):  
Shear Stress ◽  
Static Analysis ◽  
Maximum Shear Stress ◽  
Strain Analysis ◽  
Asphaltic Concrete ◽  
Total Stress ◽  
Stress Strain ◽  
Concrete Core ◽  
Static State ◽  
Upstream Slope

In this study, the effects of various geometric parameters of a dam in 2D static analysis of stress-strain on the upstream slope of the asphaltic concrete core rockfill dams were investigated. For this purpose, first the geometric characteristics of a large number of world's dams were collected and assessed, then by geometric modeling of these dams, many numerical models were developed for static analysis using GeoStudio software in eight height classes, three cases of upstream and downstream slopes, three different shape and thickness of the asphaltic concrete core under different Impounding states including "Full Reservoir", "Half full Reservoir", "End of construction and "Rapid Drawdown on a rigid type of foundation. The results of this study demonstrated that in four different construction and impounding states and in three different cases of slopes, Increasing the height parameter, causes increasing the Maximum total stress, Maximum total strain, Shear strain and Maximum shear stress for all construction and impounding states. The Maximum total stress decreased for all operating situations as the upstream slope reduced. According to the obtained results from the static stress-strain analysis, increasing both vertical and inclined asphaltic concrete core thicknesses, leads to decreasing the Maximum shear stress in Full Reservoir state but it increases in other state of impoundment. Moreover, by comparing the displacements related to specified points on the upstream slopes, increasing the height parameter, leads to increasing both horizontal and vertical displacements, the volumetric strain, deviator strain and deviator stress for all impounding conditions. In the following, the additional results were provided along with diagrams for further analysis.

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.

Finite element investigation into the torsion test in the range of large strains and deformations

2001 ◽  
Vol 36 (4) ◽  
pp. 401-409
Author(s):  
X Peng ◽  
Y Qin ◽  
R Balendra
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Shear Strain ◽  
Twist Angle ◽  
Large Strains ◽  
End Effect ◽  
Stress Strain ◽  
Strain Relationship ◽  
Thin Walled ◽  
Tubular Specimens

Torsion tests with thin-walled tubular, solid cylindrical and Lindholm-type tubular specimens were simulated using the finite element code ABAQUS, in the range of large strains and deformations. The results showed that for thin-walled tubular and solid cylindrical specimens the radii of the specimens almost remained straight during torsion; for Lindholm-type tubular specimens the twist angle of the cross-section at the two ends of the gauge section did not stay constant, due to the change of the specimen geometry (i.e. the end effect). A correction which considers the end effect should therefore be introduced when the stress-strain relationship is characterized. Compared with the stress-strain relationship obtained previously from experiment, a distinct difference was noted when conventional formulae were used to convert the torque and twist angle into the shear stress and shear strain. Further, the influence of axial constraint conditions at the two ends of the specimen was examined; the results showed that axial strains and stresses had no significant influence on the definition of the shear stress-shear strain relation, and hence these can be neglected when the stress-strain relationship is characterized.

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