Contact Stress Analysis of Normally Loaded Rough Spheres

1962 ◽  
Vol 29 (3) ◽  
pp. 515-522 ◽  
Author(s):  
L. E. Goodman
Keyword(s):  
Shear Stress ◽  
Normal Stress ◽  
Contact Stress ◽  
Contact Region ◽  
Stress Component ◽  
Theory Of Elasticity ◽  
Relative Slip ◽  
Normal Stress Component ◽  
Incremental Formulation ◽  
Stress Functions

The Hertz analysis of contact stresses is extended to include the effects of friction on the interface between two elastic spheres compressed along the line connecting their centers. The problem is shown to be one of a class which requires incremental formulation. Stress functions of interest in connection with the analysis of the shear-loaded half-space in the linear theory of elasticity are developed. The distribution of shear stress needed to prevent relative slip of surficial points after they enter the contact region is found to be finite everywhere in the region. The ratio of this shear stress to the coexisting normal stress component is shown to exhibit a singularity at the edge of the contact region. This implies that when elastically dissimilar spheres are pressed together microscopic slip must occur in a narrow annulus at the boundary of the contact region.

Evaluation of the Accuracy of Out-of-Plane Normal Stress Detection Using Novel Piezoresistive CMOS Sensors

2009 ◽  
Author(s):  
Benjamin Lemke ◽  
Rajashree Baskaran ◽  
Oliver Paul
Keyword(s):  
Normal Stress ◽  
Stress Component ◽  
Stress Detection ◽  
Free Surfaces ◽  
Plane Normal ◽  
Uncertainty Sources ◽  
Stress Components ◽  
Normal Stress Component ◽  
Out Of Plane ◽  
The Individual

This paper discusses the measurement opportunities arising from a novel piezoresistance sensor featuring vertical currents. Temperature-compensated measurements of a sum of the three normal stress components including the vertical normal stress, are presented. In specific applications with sensors located at free surfaces where the vertical normal stress component vanishes, a combination of this temperature-compensated measurement and a pseudo-Hall measurement yields the individual in-plane normal stresses. Furthermore, the temperature-uncompensated extraction of the vertical normal stress component is discussed with respect to the new measurement possibilities provided by the presented sensor. A sensitivity analysis illustrates the influence of individual uncertainty sources to the overall uncertainty of the measurement. Based on these results possible improvements in stress detection are suggested.

A general method for obtaining shear stress and normal stress functions from parallel disk rheometry data

2004 ◽  
Vol 44 (3) ◽  
pp. 270-277 ◽  
Author(s):  
Y Leong Yeow ◽  
Dolly Chandra ◽  
Albert A Sardjono ◽  
Hartono Wijaya ◽  
Yee-Kwong Leong ◽  
...  
Keyword(s):  
Shear Stress ◽  
Normal Stress ◽  
Parallel Disk ◽  
Stress Functions ◽  
General Method

Representation of Three-Dimensional Stress Distributions by Mohr Circles

1955 ◽  
Vol 22 (2) ◽  
pp. 273-275
Author(s):  
G. A. Zizicas
Keyword(s):  
Normal Stress ◽  
Stress Component ◽  
Three Dimensional ◽  
Stress Distributions ◽  
Shearing Stress ◽  
Principal Stresses ◽  
Normal Stress Component

Abstract O. Mohr has developed a diagram representing the normal stress component snn = σn and the total shearing stress component τn on an element of surface of any prescribed orientation with respect to the directions of the principal stresses. His procedure, however, does not give the orientation of the shearing stress τn within the element or, which is equivalent, the components of this shearing stress in a plane co-ordinate system within the element under consideration. An extension of the Mohr method that overcomes this limitation is presented in this note.

scholarly journals Fatigue Strength Evaluation of Welded Structure on Aluminum Alloy Car Body Based on Multi-Axial Stress

2021 ◽  
Author(s):  
Yiming Shangguan ◽  
Wenjing Wang ◽  
Chao Yang ◽  
Anrui He
Keyword(s):  
Shear Stress ◽  
Aluminum Alloy ◽  
Fatigue Strength ◽  
Normal Stress ◽  
Welded Joint ◽  
Axial Stress ◽  
Stress Component ◽  
Local Coordinate System ◽  
Strength Evaluation ◽  
Welded Structure

Abstract With the continuous development of the subway, the demand for its safety and stability is getting higher and higher. It is of great significance to accurately evaluate the fatigue life of the carbody to ensure the subway's safe operation. In this paper, the finite element model of a subway head carbody was established, and the fatigue strength of the welded structure on the carbody was evaluated based on Multi-axial stress. The local coordinate system was defined according to the geometrical characteristics of the welds. Local stresses perpendicular and parallel to the weld seam were obtained to calculate the stress ratio, stress range, and allowable stress value corresponding to the stress component. According to the joint fatigue resistance, the components of the degree of utilization and comprehensive degree of utilization are calculated to evaluate the structural fatigue strength under the survival rate of 97.5% and load cycles of 10 7 . The evaluation of the fatigue strength of the pivotal weld joints shows that the fatigue strength of the aluminum alloy carbody meets the design requirements, the weld of the carbody has a strong ability to resist fatigue damage. The fatigue strength of the weld is mainly affected by the normal stress component, while the shear stress has little effect on the fatigue strength of the structure. In addition, compared with the filleted weld joint and the butt-welded joint, the normal stress parallels to and perpendicular to the weld direction and shear stress have the greatest effect on the lap-welded joint. Meanwhile, the comprehensive degree of utilization of the lap-welded joint is the largest at 0.49. The introduction of multi-axial stress for the fatigue strength evaluation is beneficial when considering the material utilization degree in multiple structural directions. This research results provide a reference for fatigue strength evaluation of subway carbody's welded structure.

Non-Linear Two-Equation Model Taking Into Account the Wall-Limiting Behaviour and Redistribution of Stress Components

2003 ◽  
Author(s):  
Hirofumi Hattori ◽  
Yasutaka Nagano
Keyword(s):  
Normal Stress ◽  
Nonlinear Models ◽  
Stress Component ◽  
Equation Model ◽  
Normal Direction ◽  
Turbulence Energy ◽  
Proposed Model ◽  
Stress Components ◽  
Normal Stress Component ◽  
Limiting Behaviour

Nonlinear k–ε models have been extensively used in technological applications. It is clear from the assessment of the existing nonlinear k–ε models using DNS databases that the nonlinear models can not satisfy and reproduce exactly the wall-limiting behaviour and the anisotropy of Reynolds normal stress components. Especially, the Reynolds normal stress component, u22, in the wall-normal direction, which is proportional to x24 near the wall is not satisfied. Since the wall limiting behaviour of Reynolds normal stress components in the nonlinear model is determined by the turbulence energy k, which is proportional to x22 in the model, the Reynolds stress components, u12, u22 and u32 are proportional to x22. In this study, we have proposed a new nonlinear k–ε model which satisfies exactly the wall limiting behaviour of Reynolds normal stress components in the inertial and the noninertial frames. The proposed model can also predict well the anisotropy of the Reynolds normal stress components near the wall.

Bounds on the Maximum Contact Stress of an Indented Elastic Layer

1971 ◽  
Vol 38 (3) ◽  
pp. 608-614 ◽  
Author(s):  
Y. C. Pao ◽  
Ting-Shu Wu ◽  
Y. P. Chiu
Keyword(s):  
Half Space ◽  
Contact Stress ◽  
Elastic Layer ◽  
Theory Of Elasticity ◽  
Contact Conditions ◽  
Practical Applications ◽  
Method Of Solution ◽  
Elastic Layers ◽  
Maximum Contact ◽  
Contact Stress Distribution

This paper is concerned with the plane-strain problem of an elastic layer supported on a half-space foundation and indented by a cylinder. A study is presented of the effect of the contact condition at the layer-foundation interface on the contact stresses of the indented layer. For the general problem of elastic indenter or elastic foundation, the integral equations governing the contact stress distribution of the indented layer derived on the basis of two-dimensional theory of elasticity are given and a numerical method of solution is formulated. The limiting contact conditions at the layer-foundation interface are then investigated by considering two extreme cases, one with the indented layer in frictionless contact with the half space and the other with the indented layer rigidly adhered to the half space. Graphs of the bounds on the maximum normal stress occurring in indented elastic layers for the cases of rigid cylindrical indenter and rigid half-space foundation are obtained for possible practical applications. Some results of the elastic indenter problem are also presented and discussed.

Effect of Shear Surface Boundaries on Stress for Shearing Flow of Dry Metal Powders—An Experimental Study

1987 ◽  
Vol 109 (2) ◽  
pp. 232-237 ◽  
Author(s):  
K. Craig ◽  
R. H. Buckholz ◽  
G. Domoto
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Normal Stress ◽  
Particle Diameter ◽  
Surface Boundary ◽  
Metal Powders ◽  
Shear Surface ◽  
Shear Cell ◽  
Shearing Flow ◽  
Solids Content

This paper studies the rapid simple shearing flow of dry cohesionless metal powders contained between parallel rotating plates. In this study, an annular shear cell test apparatus was used; the dry metal powders are rapidly sheared by rotating one of the shear surfaces while the other shear surface remains fixed. Such a flow geometry is of interest to tribologists working in the area of dry or powder lubrication. The shear stress and normal stress on the stationary surface are measured as a function of the following parameters: shear surface boundary material and roughness, the shear-cell gap thickness, the shear-rate and the fractional solids content. Both the fractional solids content and the gap thickness are kept at prescribed values during stress measurements. In this experiment the metal powder tested is different from the shear transmission surface material; the effect on the measured normal and shear stress data are reported. The results show the dependence of the normal stress and the shear stress on the shear-rate, particle density and particle diameter. Likewise, a significant stress dependence on both the fractional solids content and the shear-cell gap thickness was observed.

Stress in Bonded Adherends for Single Lap Joints

1996 ◽  
Vol 12 (03) ◽  
pp. 167-171
Author(s):  
G. Bezine ◽  
A. Roy ◽  
A. Vinet
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Numerical Model ◽  
Stress Distribution ◽  
Normal Stress ◽  
Lap Joints ◽  
Axial Loads ◽  
Normal Stress Distribution ◽  
Single Lap Joints ◽  
Element Technique

A finite-element technique is used to predict the shear stress and normal stress distribution in adherends for polycarbonate/polycarbonate single lap joints subjected to axial loads. Numerical and photoelastic results are compared so that a validation of the numerical model is obtained. The influences on stresses of the overlap length and the shape of the adherends are studied.

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