Review Article

Celebrating the 100th Anniversary of Inglis Result: From a Single Notch to Random Surface Stress Concentration Solutions

[+] Author and Article Information
Hector E. Medina

Department of Mechanical
and Nuclear Engineering,
Virginia Commonwealth University,
Richmond, VA 23284-3028
e-mail: hedmedina@yahoo.com

Ramana Pidaparti

Department of Mechanical
and Nuclear Engineering,
Virginia Commonwealth University,
Richmond, VA 23284-3028

Brian Hinderliter

Department of Mechanical
and Industrial Engineering,
University of Minnesota-Duluth,
1305 Ordean Court,
Duluth, MN 55812

Or, at least he should be called one of the fathers of the SCF, to give credit to Neuber's account of the facts.

1Corresponding author.

2Neuber explicitly states [1] that Kolosov had developed a similar work and reported it four years earlier [2] in a paper written in Russian.

Manuscript received December 17, 2013; final manuscript received July 17, 2014; published online September 10, 2014. Assoc. Editor: Bart Prorok.

Appl. Mech. Rev 67(1), 010802 (Sep 10, 2014) (9 pages) Paper No: AMR-13-1102; doi: 10.1115/1.4028069 History: Received December 17, 2013; Revised July 17, 2014

We celebrate the first quantitative evidence for the stress concentration effect of flaws analyzed by Inglis. Stress concentration factor (SCF) studies have evolved ever since Inglis' 1913 result related to the problem of the elliptical hole in a plate, which also approximately applies to the half-elliptical notch case. We summarize a hundred years of development of the SCF with the exclusive focus on analytical solutions, with a very specific route: the series of works reviewed and presented herein include a parade of solutions beginning with (and those that followed) Inglis famous result, continue with periodic discrete discontinuities, sinusoidal periodic surfaces, and end with more complex continuous configurations such as random surfaces. Furthermore, we show that the form of Inglis' result is powerful enough to serve as first-order approximation for some cases of multiple discontinuities and even continuous rough topologies. Thus, we proposed the Modified Inglis formula (MIF), to estimate the SCF for a variety of configurations, in honor to Inglis' historical result. The impetus of this review stems from the fact that for many engineering problems involving multiphysical solid–fluid interactions, there is a broad interest to couple stress concentration relationships with thermodynamics, fluid dynamics, or even diffusion equations in order to expand understanding on stress-driven interactions at the solid–fluid interface. Additionally, a handy first-order estimate of the SCF can serve in the initial stage of designs of structures and parts containing discontinuities.

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Grahic Jump Location
Fig. 1

(a) Elliptical hole in a infinite elastic thin plate. (b) Semi-elliptical notch in a semi-infinite elastic thin plate. In both cases, remote load is applied perpendicular to major axis and at location very far from the discontinuity.

Grahic Jump Location
Fig. 3

(a) 3D specimen with hole through. (b) 3D notched specimen.

Grahic Jump Location
Fig. 4

(a) Single-notch stress lines. (b) Periodic-discrete-notch configuration. Stress is relaxed due to neighboring notches.

Grahic Jump Location
Fig. 5

A sinusoidal surface. The maximum SCF is found at the troughs of the waves [61].

Grahic Jump Location
Fig. 6

Random rough surface with a prescribed finite autocorrelation length and whose heights are normally distributed. An analytical solution for the root-mean-square SCF of the 2D version was derived and reported in Ref. [65].

Grahic Jump Location
Fig. 7

An example case to illustrate the random surfaces resulting from corrosion, the stress distributions, and the SCF (K in the figures) for: (a) and (b) an early stage corroded surface, and (c) and (d) the same surface at a later stage of corrosion. (a) and (c) are atomic force scans and (b) and (d) are finite element models.




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