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{{Language_sel|LANG=ger|ARTIKEL=Energiefreisetzungsrate}}
{{PSM_Infobox}}
Energy release rate or energy delivery rate
__FORCETOC__

==Variety of terms==

The fracture mechanics term ‘energy release rate’ is defined in a ‘very vague’ manner in German and Anglo-Saxon literature on [[Fracture Mechanics|fracture mechanics]], prompting [[Blumenauer, Horst|Blumenauer]] [1] and Schwalbe [2] to attempt to propose a uniform terminology at a very early stage. The energy term ''G'', which represents the energy provided by the elastic stress field of the test [[Specimen|specimen]] for [[Crack Propagation|crack propagation]], is called

* energy delivery rate
* energy release rate
* specific fracture energy
* crack propagation energy or
* crack propagation force

and is expressed with the symbol ''G'' in memory of [[Griffith, Alan Arnold|Griffith]].

==Physical definition==

The energy release rate has the physical dimension N mm-1 and can be determined experimentally by compliance measurements (see also: [[J-Compliance Method|J-Compliance method]]).

The energy release rate ''G'' can be regarded as the energy released per unit of [[Fracture Surface|fracture surface]] and consumed by the crack propagation process; alternatively, ''G'' is often interpreted as the force that drives the [[Crack|crack]] through the [[Material & Werkstoff|material]] per unit of crack front length.

{|
|-
|width="20px"|
|width="500px" | <math>G_I\,=\,\frac{\partial U_e}{\partial \left(2a \right)}\,=\, \frac{\sigma_ \infty^2\, \pi\, a}{E}\, \cdot \, \left( 1 \, - \, \nu ^2 \right)</math>
|}

with
{|
|-
|<math>\partial a</math>
|width="15px" |=
|infinitesimal crack length increase
|-
|''E''
|=
|[[Elastic Modulus|elastic modulus]]
|-
|<math>\nu^2</math>
|=
|[[Poisson's Ratio]]
|-
|''U''e
|=
|elastic shape change energy
|-
|''σ''∞
|=
|applied stress (formed with full cross-section)
|}

Not all terms are compatible with this definition, as it refers to an amount of energy supplied by the elastic stress field. In the sense of this definition, only terms such as '''energy release rate''' and '''energy delivery rate''' can be considered meaningful. The term ‘crack propagation force’ introduced in the literature is not physically correct, as ''G'' does not represent a force, but rather a force per length or energy per unit of [[Fracture Surface|fracture surface]] created.

==Energy fracture criterion==

Von [[Blumenauer, Horst|Blumenauer]] [1] introduces the specific crack propagation energy as a critical value ''G''c.

The fracture energy is a material property that is in equilibrium with ''G'' and is designated ''R'' for better differentiation.

For ideal brittle fracture behaviour,

{|
|-
|width="20px"|
|width="500px" | <math>R\,=\,G_c\,=\,2\, \gamma_0</math>
|}

with
{|
|-
|<math>\gamma_0</math>
|width="15px" |=
|specific [[Surface Energy|surface energy]],
|}

as no energy is required for [[Deformation#Plastic deformation|plastic deformation]]. In the case of [[Ductility Plastics|ductile]] [[Material & Werkstoff|material]] behaviour, ''R'' is determined by the processes in the [[Plastic Zone|plastic zone]] (see: [[Effective Crack Length|effective crack length]]) or the [[Fracture Process Zone|fracture process zone]].

The energy criterion for [[Crack Propagation|crack propagation]] is therefore ''G'' ≥ ''R'', which means that the energy expended to increase the crack must be greater than the crack resistance force. This fracture criterion has led to the so-called crack resistance or R-curve concept (see: [[Crack Resistance (R) Curve|crack resistance (R) curve]]).

==See also==

* [[Adhesive Energy Release Rate|Adhesive energy release rate]]
* [[Fracture Formation|Fracture formation]]
* [[Fracture Process Zone|Fracture process zone]]
* [[J-Integral Concept|J-Integral concept]]
* [[Hybrid Methods, Examples|Hybrid methods, examples]]

==References==

{|
|-valign="top"
|[1]
|[[Blumenauer, Horst|Blumenauer, H.]], Pusch, G.: Technische Bruchmechanik. Verlag für Grundstoffindustrie, Leipzig (1982) 1st Edition, p. 60 (see [[AMK-Library]] under E 29-1)
|-valign="top"
|[2]
|Schwalbe, K.-H.: Bruchmechanik metallischer Werkstoffe. Carl Hanser, Munich Vienna (1980) (ISBN 3-446-12983-9; see [[AMK-Library]] under E 15)
|}

[[Category:Fracture Mechanics]]

Energy Release Rate - Revision history