The elastic stress distribution near the root of an elliptically cylindrical notch subjected to mode III loadings

2004 ◽  
Vol 42 (17-18) ◽  
pp. 1831-1839 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Elastic Stress ◽  
Mode Iii

The Mode I Elastic Stress Distribution Near the Root of a Deep Notch With a Parabolic Root Profile

2007 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Elastic Stress ◽  
Notch Root ◽  
Peak Stress ◽  
Fracture Initiation ◽  
Radius Of Curvature ◽  
Mode I ◽  
Mode Iii ◽  
Root Radius ◽  
Notch Root Radius

The basis of a fracture mechanics type methodology for fracture initiation at a blunt notch is the elastic stress distribution immediately ahead of a notch root. Earlier work, presented at the 2006 ASME PVP Conference [7], for the Mode III deformation of a deep notch with a parabolic root profile, has shown that the shear stress σ(x) at a distance x ahead of the root is uniquely defined by the peak stress σp, x and ρ (the notch root radius of curvature), when x and ρ are both small compared with the notch depth, irrespective of the loading characteristics and the notch shape away from the root. This paper is concerned with the corresponding Mode I deformation situation, with the objective of providing support for the viability of a similar conclusion for Mode I deformation.

The Mode III Elastic Stress Distribution Near the Root of a Deep Sharp Notch With a Parabolic Root Profile

2006 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Elastic Stress ◽  
Notch Root ◽  
Peak Stress ◽  
Fracture Initiation ◽  
Radius Of Curvature ◽  
Mode Iii ◽  
Root Radius ◽  
Notch Root Radius ◽  
Starting Point

In developing a fracture initiation methodology for blunt notches, the basic starting point is the elastic stress distribution immediately ahead of a notch root. Earlier work for Mode III deformation of a two-dimensional blunt notch has shown that the shear stress immediately ahead of the notch root (i.e. at a distance small compared with the notch root radius of curvature) is dependent on the peak stress and notch root radius, but is independent of the notch shape and the loading characteristics. However there are many situations, i.e. with sharp notches, where we are interested in the stress at a distance that is not necessarily small compared with the notch root radius. Thus this paper shows that with a notch that has a parabolic root profile, when this distance and the notch root radius are both small compared with the notch depth, then the stress at this distance is again dependent on the peak stress and notch root radius, but is independent of the notch shape away from the root and the loading characteristics.

The Mode III Elastic Stress Distribution in the Immediate Vicinity of an Inclusion

2005 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Elastic Stress ◽  
Notch Root ◽  
Research Programme ◽  
Local Stress ◽  
Peak Stress ◽  
Radius Of Curvature ◽  
Mode Iii ◽  
Root Radius ◽  
Notch Root Radius

As part of a wide ranging research programme aimed at developing a fracture mechanics methodology for blunt notches, earlier work for a general two-dimensional blunt notch Mode III model has shown that the stress at a distance × ≪ ρ (notch root radius of curvature) ahead of the notch root only depends on x, ρ and the peak stress σp, irrespective of the notch shape and the loading characteristics. This uniqueness has been confirmed for various notch profiles and loading scenarios. In this paper we show that the uniqueness of the local stress distribution is peculiar to a notch and does not apply to an inclusion.

Elastic Stress Singularities: Implications for the Attachment of Tendon to Bone

2011 ◽  
Author(s):  
Yanxin Liu ◽  
Victor Birman ◽  
Chanqing Chen ◽  
Stavros Thomopoulos ◽  
Guy M. Genin
Keyword(s):  
Stress Distribution ◽  
Abrupt Change ◽  
Elastic Stress ◽  
Insertion Site ◽  
Stress Singularities ◽  
Local Stresses ◽  
Material Mismatch ◽  
Moduli Of Elasticity

The material mismatch at the attachment of tendon to bone is amongst the most severe for any tensile connection in nature. This is related to the large difference between the stiffness of tendon and bone, whose moduli of elasticity vary by two orders of magnitude. Predictably, such an abrupt change in the stiffness realized over a very narrow insertion site results in high local stresses. One of the implications of the stress distribution is a potential for stress singularities at the junction of the insertion to the bone.

Calculation of contact stresses at contacts between conical bodies

1972 ◽  
Vol 7 (2) ◽  
pp. 141-145
Author(s):  
H McCallion ◽  
C B Hallam
Keyword(s):  
Stress Distribution ◽  
Finite Difference ◽  
Elastic Stress ◽  
Finite Difference Methods ◽  
The Body ◽  
Iterative Technique ◽  
Frictionless Contact ◽  
Influence Coefficients ◽  
Difference Methods ◽  
Selection Of

A method for calculating the elastic-stress distribution in two axi-symmetrical conical bodies caused by frictionless contact between them is described. Finite-difference methods were used to solve the governing differential equations. Equilibrium and compatibility over the contacting surfaces was achieved by using the finite-difference solutions to derive a matrix of influence coefficients. By means of an iterative technique, using this matrix, the portion of each surface in the contact zone and the stresses on it were found. With equilibrium and compatibility achieved, the stresses throughout the body of each component were calculated. A selection of results for one case is given.

Stress Distribution in and Around Spheroidal Inclusions and Voids at Finite Concentration

1986 ◽  
Vol 53 (3) ◽  
pp. 511-518 ◽  
Author(s):  
G. P. Tandon ◽  
G. J. Weng
Keyword(s):  
Stress Distribution ◽  
Energy Distribution ◽  
Uniaxial Tension ◽  
Elastic Stress ◽  
Three Dimensional ◽  
Tensile Loading ◽  
Form Solution ◽  
Finite Concentration ◽  
The Matrix ◽  
Close Form

A simple, albeit approximate, close-form solution is developed to study the elastic stress and energy distribution in and around spheroidal inclusions and voids at finite concentration. This theory combines Eshelby’s solution of an ellipsoidal inclusion and Mori- Tanaka’s concept of average stress in the matrix. The inclusions are taken to be homogeneously dispersed and undirectionally aligned. The analytical results are obtained for the general three-dimensional loading, and further simplified for uniaxial tension applied parallel to the axis of inclusions. The ensuing stress and energy fields under tensile loading are illustrated for both hard inclusions and voids, ranging from prolate to oblate shapes, at several concentrations.

Elastic Stresses in Layered Snow Packs

1972 ◽  
Vol 11 (63) ◽  
pp. 407-414 ◽  
Author(s):  
F. W. Smith
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Computer Program ◽  
Elastic Stress ◽  
Two Dimensional ◽  
Strength Data ◽  
Elastic Stresses ◽  
Stress Levels ◽  
Dimensional Finite Element

Abstract A two-dimensional finite element computer program has been used to compute the elastic stress distribution in realistic multi-layered snow packs. Computations have been done on three-layered and five-layered snow packs intended to simulate conditions on the Lift Gully at Berthoud Pass, Colorado. Calculations have been performed to determine the effect of a layer of new snow and the effect of a weak sub-layer. Stress levels were obtained which are reasonable compared with available snow strength data.

Stress Distribution Around Edge Slits in a Plate Loaded in Tension —the Effect of Finite Width of Plate

1962 ◽  
Vol 66 (617) ◽  
pp. 320-322 ◽  
Author(s):  
J. R. Dixon
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Flat Plate ◽  
Elastic Stress ◽  
Width Ratio ◽  
Finite Width ◽  
Two Dimensional ◽  
Finite Plate ◽  
Edge Slit ◽  
Plate Width

SummaryTwo-dimensional photoelastic tests have been carried out on uni-axially loaded flat-plate specimens with two collinear edge slits, to investigate the effect of finite plate width on the elastic stress distribution. It was found that the effect of slitlength/ plate-width ratio on the elastic stress concentration at the end of the edge slit of length l was virtually the same as that for a central slit of length 2l in a plate of the same width, and could be adequately expressed by existing theories.

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