Central "through" crack with a concentrated load

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Discussion Overview

The discussion revolves around the practical implications and scenarios involving a central through crack subjected to a concentrated load. Participants explore theoretical and real-world applications, particularly in the context of fracture mechanics and material behavior under stress.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Kajal questions the existence of practical scenarios involving a concentrated load opening a crack and seeks clarification on what constitutes a "concentrated load."
  • Another participant mentions that elliptical cracks have established analytical solutions and are used to calculate stress concentration factors, referencing a textbook on the Theory of Elasticity.
  • A participant asserts that the problem is commonly found in textbooks on Fracture Mechanics and asks for practical examples, noting a mention of cracks in rivet holes.
  • One participant expresses skepticism about the relevance of concentrated loads in riveted joints, arguing that rivets and the materials involved are typically ductile, which complicates the application of stress concentration factors.
  • Tom provides a counterpoint by citing known issues with stress cracks in airplanes, particularly around rivet holes, and shares links to articles discussing these problems.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the practical relevance of concentrated loads in cracks, with some asserting its applicability in specific contexts like aviation, while others challenge the assumptions regarding riveted joints and ductility.

Contextual Notes

Participants express uncertainty regarding the practical implications of concentrated loads in cracks, particularly in relation to ductility assumptions in riveted connections and the applicability of theoretical models to real-world scenarios.

kajalschopra
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Hi, Please consider the problem below of a central through crack with a concentrated load as shown below.

Can someone please help where does one come across such a problem in a practical world?

How will I have a concentrated load opening the crack? In the physical world, what is that "concentrated load"?

Regards
Kajal
conc_load.gif
 

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I have never heard of an elliptical crack with a concentrated load. The usual case of an elliptical crack is as shown below:
upload_2018-9-7_17-37-11.png


The figure is from Advanced Strength of Materials, by J.P. Den Hartog. Elliptical cracks have a simple analytical solution that is valid for any ratio of b/a. They are used to calculate theoretical stress concentration factors for holes ranging from round all the way to sharp cracks. The general topic is Theory of Elasticity.
 

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The problem is in every textbook of Fracture Mechanics. Can someone please help - in what practical scenarios does one come across such a problem, it is mentioned ina text that the scenario occurs in cracks in rivet holes, however, I cannot understand how.
 
I cannot think of a practical scenario involving a concentrated load in a crack. It certainly does not apply to riveted joints because rivets are ductile, as is the material being riveted. Standard analysis methods for riveted connections assume ductility, so are not based on calculated stress concentration factors.
 

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