Stress concentration formulae useful for any shape of notch in a round test specimen under tension and under bending

The notch sensitivity of a material is a measure of how sensitive a material is to notches or geometric discontinuities. Notch sensitivity is influenced by many parameters such as notch geometry. Three types of notch geometries, V-shape, U-shape and -shape notches of various sizes are considered in this investigation. Two steel alloys of high and low strength (designated by HS-steel and LS-steel) are used in this work. Stress concentration is obtained by numerical simulation and the literature and fatigue reduction factor is determined by experiment using rotating bending fatigue device, Moore. The results show that the notch geometry has profound effect on fatigue life of materials. For HSsteel this reduction is roughly about 50%. For LS-steel alloy, however, the reduction depends on fatigue life and varies from 20% for low cycle fatigue tests up to 75% for high cycles fatigue tests. The maximum and minimum fatigue life reduction occurs for the V-shape and U-shape notches, respectively. The Equations proposed by Hardrath and Peterson underestimate the fatigue reduction parameters, q and K f and it seems that they are not adequate for prediction of notch sensitivity and they must be used with care.

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“…Simulation [12] Simulation [12] 60 o 5.76 6. Table 7: Notch sensitivity factor for u-shape notched specimens made of LS-steel R(mm) q (Eq.…”

Section: Stress Concentrationmentioning

confidence: 99%

The effects of notch geometry on fatigue life using notch sensitivity factor

Majzoobi

Daemi

2010

Trans Indian Inst Met

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“…The dimensionless notch radius ρ d has been assumed to be equal to 0.1, 0.2 and 0.7. Table 1 shows the SCF values determined through the above finite‐element analysis and the SCF values obtained from the formulae proposed by Noda and Takase, 22 for tension F and bending M X . A good agreement between the different results can be observed for both loading conditions.…”

Section: Stress‐concentration Factor Due To a Circular‐arc Notchmentioning

confidence: 99%

Sickle‐shaped surface crack in a notched round bar under cyclic tension and bending

Carpinteri

2009

Fatigue Fract Eng Mat Struct

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A B S T R A C T A sickle-shaped surface crack, also called crescent-moon (or crescent) crack, is assumed to exist at the root of a circular-arc circumferential notch in a round bar under tension and bending. For different notch sizes (i.e. different values of the stress concentration factor), the stress intensity factor along the crack front is computed through a three-dimensional finite-element analysis. The effect of the stress concentration factor on the stress intensity factor values is examined for several crack configurations. Finally, the surface crack growth under cyclic loading is analysed through a numerical procedure that employs the stress intensity factor values obtained. Some results of the present study are compared with those by other authors. a = crack depth for point A on the flaw front a el , b el = semi-axes of the ellipse c = notch depth D = bar diameter in the reduced cross-section S-S D 0 = bar diameter in an unnotched cross section F = tension loading K I,F , K * I,F = stress-intensity factor (SIF) and dimensionless SIF, respectively, for tension K I,MX , K * I,MX = stress-intensity factor (SIF) and dimensionless SIF, respectively, for bending M X K t,F , K t,MX = stress-concentration factor (SCF) for tension (F) and bending (M X ), respectively M X = bending loading about the X axis SCF = stress-concentration factor SIF = stress-intensity factor α = a el /b el = aspect ratio of the elliptical-arc crack front δ = c/D 0 = relative notch depth σ F = nominal tensile stress (referred to the reduced cross section) σ MX = nominal maximum bending stress (referred to the reduced cross section) ρ, ρ d = ρ/D 0 = notch radius and dimensionless notch radius ξ = a/D = relative crack depth for point A on the flaw front ζ , ζ * = ζ /h = coordinate and normalized coordinate, respectively, of the generic point P along the crack front Correspondence: A. Carpinteri.

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“…Additionally, some attempts have been carried out to consolidate stress concentration formulas and factors, mostly via empirical methods (Pearson, 1997;Neuber, 1958;Noda and Takase, 1999). Although the foregoing referenced work is commendable, it is mostly focused on stress-concentration factors and not on the stress distribution along the surfaces of the geometries analyzed.…”

Section: Introductionmentioning

confidence: 99%

A stress-concentration-formula generating equation for arbitrary shallow surfaces

Medina

2015

International Journal of Solids and Structures

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a b s t r a c tAnalytical understanding of how stress concentrates is invaluable. An equation that generates stress concentration formulas is derived and shown to apply very well to a number of shallow irregularities on surfaces, for the plane stress conditions and to a first-order approximation. Under shallow conditions, for any first-order Hölder-continuous surface function f ðxÞ, the derived equation is:where H is the Hilbert transform and f 0 ðxÞ is the spatial derivative of f with respect to the independent variable.It is shown that using this generating equation, well-known traditional results can be easily derived. Also, a number of other stress concentration formulas for various cases are generated. Furthermore, a second-order approximation is introduced, which shows the dependence of k t on not only the slope but also on the concavity of the surface. The approach used herein can be extended to finding closed-form solutions to other integral equations possessing similar kernels for applications such as the variation of the stress intensity factor due to an arbitrary crack front profile (work in progress).

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Stress concentration formulae useful for any shape of notch in a round test specimen under tension and under bending

Cited by 38 publications

References 12 publications

The effects of notch geometry on fatigue life using notch sensitivity factor

The effects of notch geometry on fatigue life using notch sensitivity factor

Sickle‐shaped surface crack in a notched round bar under cyclic tension and bending

A stress-concentration-formula generating equation for arbitrary shallow surfaces

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