plastic strain and stress. If elastic strain is included, the relationship for uniaxial deformation is given
as:
ε
εσ
σασ
o o σon
= +
where σ 0 is the reference stress (the yield stress of the material), and ε 0 = σ 0 /E, α is a dimensionless
constant, and n is the hardening component. They showed that, at a distance very close to the crack
tip and well within the plastic zone, the crack-tip stress and strain ahead of crack tip can be expressed
as:
σij= θ
1and
ε θ
=
+For elastic material, n = 1 and the above equation predicts the / r singularity which is consistent
with linear elastic fracture mechanics.
11.1.2.2. Energy-Release Rate
The energy-release rate, limited to linear elastic fracture mechanics, is based on the energy criterion for
fracture proposed by Griffith and further development by Irwin. In this approach, the crack growth occurs
when the energy available for crack growth is sufficient to overcome the resistance of the material.[ 1 ]
The energy-release rat e G is defined in elastic materials as the rat e of change of potential energy released
from a structure when a crack opens. For example, the following illustration shows a crack of length
2a in a large elastic body with modulus E subject to a tensile stress (σ):
The energy-release rat e is given by:
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