Energy Release Rate

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Energy release rate or energy delivery rate

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, prompting 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 for 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.

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).

The energy release rate G can be regarded as the energy released per unit of fracture surface and consumed by the crack propagation process; alternatively, G is often interpreted as the force that drives the crack through the material per unit of crack front length.

$G_{I}\,=\,{\frac {\partial U_{e}}{\partial \left(2a\right)}}\,=\,{\frac {\sigma _{\infty }^{2}\,\pi \,a}{E}}\,\cdot \,\left(1\,-\,\nu ^{2}\right)$

with

$\partial a$	=	infinitesimal crack length increase
E	=	elastic modulus
$\nu ^{2}$	=	Poisson's Ratio
Ue	=	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 created.

Energy fracture criterion

Von 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,

$R\,=\,G_{c}\,=\,2\,\gamma _{0}$

with

$\gamma _{0}$

=

specific surface energy,

as no energy is required for plastic deformation. In the case of ductile material behaviour, R is determined by the processes in the plastic zone (see: effective crack length) or the fracture process zone.

The energy criterion for 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).

See also

• Adhesive energy release rate
• Fracture formation
• Fracture process zone
• J-Integral concept
• Hybrid methods, examples

References

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