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Elastic-plastic
fracture mechanics
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Crack tip opening displacement (CTOD)
Wells’ experiment:
crack faces had moved apart prior to fracture;
plastic deformation had blunted an initially sharp crack
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Crack tip opening displacement (CTOD)
CTOD by Irwin in small-scale yielding
displacement at the physical crack tip, assuming an effective
crack length of a+ ry
COD = 2uy
CTOD = 2uy (r = ry, = )
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Crack tip opening displacement (CTOD)
CTOD by Irwin in small-scale yielding
plastic zone
CTOD
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J integral
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J integral
assumes nonlinear elastic behavior may be valid for an elasticplastic material, provided no unloading occurs
J as an energy parameter
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still acceptable
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J integral
assumes nonlinear elastic behavior may be valid for an elasticplastic material, provided no unloading occurs
J as a stress intensity parameter
Stress-strain curve of a non-linear elastic material can be represented by
the Ramberg-Osgood equation
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J integral
assumes nonlinear elastic behavior may be valid for an elasticplastic material, provided no unloading occurs
J as a stress intensity parameter
HRR-solution (Hutchinson, Rice, and Rosengren)
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J integral
assumes nonlinear elastic behavior may be valid for an elasticplastic material, provided no unloading occurs
J as a stress intensity parameter
HRR-solution (Hutchinson, Rice, and Rosengren)
Relationship between J and CTOD

J   YSCTOD
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J integral
assumes nonlinear elastic behavior may be valid for an elasticplastic material, provided no unloading occurs
Definition of J
ASTM E813 Standard Practice
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Crack growth criterion
In NLFM the CTOD is a measure for the deformation at the crack tip, which
can be compared to a critical value in a crack growth criterion
CTOD = CTODC  Bf
f fracture strain
In NLFM, where the material behavior is described by the general
Ramberg-Osgood relation, the J-integral characterizes the stress at the crack
tip. It is thus obvious that it can be used in a crack growth criterion
J = Jc
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Crack growth criterion
Crack-growth resistance curves
For J resistance curves, the slope is usually quantified by a dimensionless tearing
modulus
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