Minimum polynomial extrapolation: Difference between revisions

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The '''strain energy release rate''' (or simply energy release rate) is the [[energy]] [[dissipation|dissipated]] during [[fracture]] per unit of newly created fracture surface area. This quantity is central to [[fracture mechanics]] because the energy that must be supplied to a [[Fracture|crack]] tip for it to grow must be balanced by the amount of energy dissipated due to the formation of new surfaces and other dissipative processes such as [[plasticity (physics)|plasticity]].
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For the purposes of calculation, the energy release rate is defined as
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:<math>
  G := -\cfrac{\partial (U-V)}{\partial A}
</math>
where <math>U</math> is the potential energy available for crack growth, <math>V</math> is the work associated with any external forces acting, and <math>A</math> is the crack area (crack length for two-dimensional problems). The units of <math>G</math> are J/m<sup>2</sup>.


The energy release rate [[material failure theory|failure criterion]] states that a crack will grow when the available energy release rate <math>G</math> is greater than or equal to a critical value <math>G_c</math>
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:<math>
  G \ge G_c
</math>
The quantity <math>G_c</math> is the '''fracture energy''' and is considered to be a material property which is independent of the applied loads and the geometry of the body.


== Relation to fracture toughness ==
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For two-dimensional problems ([[plane stress]], [[plane strain]], [[antiplane shear]]) involving cracks that move in a straight path, the [[mode I]] [[stress intensity factor]] (<math>K_I</math>) is related to the energy release rate (<math>G</math>) by
:<math>
  G = \cfrac{K_I^2}{E'}
</math>
where <math>E</math> is the [[Young's modulus]] and <math>E' = E</math> for [[plane stress]] and <math>E' = E/(1-\nu^2)</math> for [[plane strain]].


Therefore the energy release rate failure criterion may also be expressed as
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:<math>
  K_I \ge K_{Ic}
</math>
where <math>K_{Ic}</math> is the mode I [[fracture toughness]].


== See also ==
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{{Continuum mechanics|cTopic=[[Solid mechanics]]}}
*[[Fracture]]
*[[Fracture mechanics]]
*[[Fracture toughness]]
*[[J integral]]
*[[Stress intensity factor]]
*[[Tearing energy]]
*[[Configurational force]]
*[[Crack driving force]]
 
==References==
<references>
</references>
 
*Rivlin, R. S., & Thomas, A. G. (1953). Rupture of rubber. I. Characteristic energy for tearing. Journal of Polymer Science, 10(3), 291-318.
*[http://dx.doi.org/10.1016/B978-0-12-394584-6.00010-8 Chapter 10 – Strength of Elastomers], A.N. Gent, W.V. Mars, In: James E. Mark, Burak Erman and Mike Roland, Editor(s), The Science and Technology of Rubber (Fourth Edition), Academic Press, Boston, 2013, Pages 473-516, ISBN 9780123945846, 10.1016/B978-0-12-394584-6.00010-8
 
[[Category:Mechanical failure]]
[[Category:Fracture mechanics]]
[[Category:Solid mechanics]]
[[Category:Mechanics]]
[[Category:Rubber properties]]

Latest revision as of 11:55, 4 September 2014

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