A comparison of Mode I and Mode III results for the elastic stress distribution in the immediate vicinity of a blunt notch

2004 ◽  
Vol 42 (5-6) ◽  
pp. 473-481 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Elastic Stress ◽  
Mode I ◽  
Mode Iii ◽  
Blunt Notch

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.

The Behaviour of a Process Zone at the Root of a Deep Sharp Flaw for Mode I Loading

2003 ◽  
Author(s):  
E. Smith
Keyword(s):  
Stress Distribution ◽  
Process Zone ◽  
Fracture Initiation ◽  
Radius Of Curvature ◽  
Mode I ◽  
Zone Size ◽  
Mode Iii ◽  
Root Radius ◽  
Mode I Loading ◽  
Linear Behaviour

The process zone representation of non-linear behaviour at the root of a flaw or crack is frequently used to quantify fracture initiation scenarios. In a paper presented at the 2002 PVP Conference, the author showed that with regard to a process zone at the root of a deep sharp flaw for Mode III loading conditions, its behaviour can be described, to a good degree of accuracy, by inputting the stress distribution ahead of the actual flaw root into an analysis of a process zone at the root of a semi-infinite crack in an infinite solid. The present paper describes an analysis of the analogous Mode I loading situation, with the results being compared with those obtained by a procedure which blends the small and large s/ρ behaviours where s is the process zone size and ρ is the flaw root radius of curvature.

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.

Fracture Behaviour of Modified Spruce Wood: A Study Using Linear and Non Linear Fracture Mechanics

Holzforschung ◽  
2002 ◽  
Vol 56 (2) ◽  
pp. 191-198 ◽  
Author(s):  
Alexander Reiterer ◽  
Gerhard Sinn
Keyword(s):  
Fracture Energy ◽  
Heat Treatments ◽  
Critical Stress Intensity Factor ◽  
Mode I ◽  
Mode Iii ◽  
Fracture Properties ◽  
Specific Fracture Energy ◽  
Wedge Splitting Test ◽  
Splitting Test ◽  
Specific Fracture

Summary The fracture properties of unmodified and modified (heat treatments under various conditions and acetylation) sprucewood are investigated using the wedge splitting test. Fracture parameters measured include critical stress intensity factor and specific fracture energy under Mode I loading and specific fracture energy under Mode III loading. The Mode I fracture properties are reduced by all kinds of modification. However, acetylation leads to a reduction of only 20%whereas heat treatments reduce the properties to a much greater extent, approximately 50%to 80%. The Mode III fracture properties are influenced less. SEM pictures of the fracture surfaces support the described findings.

Sign in / Sign up

Export Citation Format

Share Document