View source for Geometry Function

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<span style="font-size:1.2em;font-weight:bold;">Geometry function</span>
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==The geometry function f (a/W)==

The finite geometry of each [[Plastic Component|component]] and test [[Specimen|specimen]], as well as the crack geometry, are taken into account in [[Fracture Mechanical Testing|fracture mechanics material testing]] by introducing a geometry function ''f'' (''a''/''W''), whereby the [[Fracture Mechanics|stress intensity factor]] ''K'' introduced by Irwin can be written in the form

{|
|-
|width="20px"|
|width="500px" | <math>K=\sigma_N \cdot \left(\pi a \right)^\frac{1}{2} \cdot f \left( a/W \right)</math>
|}

The functions ''f'' (''a''/''W'') have been calculated for a large number of [[Specimen for Fracture Mechanics Tests|fracture mechanics test specimens]]. The figure shows the dimensions of test specimens used primarily for [[Plastics|plastics]]. For an infinitely extended test specimen and the

limiting case of a [[Crack|crack]] with a [[Notch Sensitivity|notch radius]] ~ 0 is ''f'' (''a''/''W'') = 1.

At the beginning of unstable [[Crack Propagation|crack propagation]], the stress intensity factor reaches a critical value ''K''<sub>Ic</sub>, which is referred to as [[Fracture Mechanics|fracture]] or [[Crack Toughness|crack toughness]] and has the dimension MPa mm<sup>1/2</sup>. The three most commonly used test specimens are the [[SENB-Specimen|SENB-specimen]], the [[SENT-Specimen|SENT-specimen]], and the [[CT-Specimen|CT-specimen]].

==Selected test specimen shapes==

The geometry functions ''f'' (''a''/''W'') have been calculated for a number of [[Specimen for Fracture Mechanics Tests|fracture mechanics test specimens]]. '''Table 1''' shows the dimensions of test specimen shapes that are preferred for [[Plastics|plastics]] in testing practice.

'''Table 1''': Summary of frequently used test specimen shapes with their dimensions, the corresponding equations for calculating [[Fracture Toughness|fracture toughness]], and the geometric functions.

[[File:Geometry Function Tble_1-1.jpg|600px]]

[[File:Geometry Function Tble_1-2.jpg|600px]]

==See also==

* [[Fracture Safety Criterion|Fracture safety criterion]]
* [[CT-Specimen|CT-specimen]]
* [[Geometry Criterion|Geometry criterion]]
* [[Plastic Component|Plastic component]]
* [[SENB-Specimen|SENB-specimen]]
* [[SENT-Specimen|SENT-specimen]]

==References==

* [[Grellmann,_Wolfgang|Grellmann, W.]], [[Seidler,_Sabine|Seidler, S.]] (Eds.): Polymer Testing. Carl Hanser, Munich (2022); 3rd Edition, pp. 233/234 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-807-5; see [[AMK-Library]] under A 22)
* Anderson, T. L.: Fracture Mechanics. Fundamentals and Applications. 3rd Edition, CRC Press Boca, Raton (2005) (ISBN 978-0849342608; see [[AMK-Library]] under E 8-2); DOI: https://doi.org/10.1201/9781315370293
* Irwin, G. R.: Analysis of Stress and Strains Near the End of a Crack Traversing a Plate. J. Appl. Mech. 24 (1957) 361; https://doi.org/10.1115/1.4011547
* Tada, H., Paris, P. C., Irwin, G. R.: The Stress Analysis of Cracks Handbook. 3rd Edition, ASME Press, New York (2000) (ISBN 978-1-8605-8304-9); https://doi.org/10.1115/1.801535

[[Category:Fracture Mechanics]]