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Steel Designers' Manual - 6th Edition (2003)
7.3 Elastic–plastic fracture mechanics
The need to consider fracture resistance of materials outside the limits of validity
of plane strain linear elastic fracture mechanics (LEFM) is important for most engineering
designs. To obtain valid KIc results for relatively tough materials it would
be necessary to use a test piece of dimensions so large that they would not be representative
of the sections actually in use.
Historically, the approaches to fracture mechanics when significant plasticity has
occurred have been to consider either the crack tip opening displacement or the
J-integral. The current British Standard on fracture mechanics toughness tests, BS
7448: Part 1: 1991, describes how a single approach to linear elastic and general yielding
fracture mechanics tests can be adopted. 4
Significant yielding at a crack tip leads to the physical separation of the surfaces
of a crack, and the magnitude of this separation is termed the crack tip opening displacement
(CTOD), and has been given the symbol d.The CTOD approach enables
critical toughness test measurements to be made in terms of dc, and then applied to
determine allowable defect sizes for structural components.
The J-integral is a mathematical expression that may be used to characterize the
local stress and strain fields around a crack front. Like the CTOD, the J-integral
simplifies to be consistent with the stress intensity factor approach when the conditions
for linear elastic fracture mechanics prevail. When non-linear conditions
dominate either CTOD or J are useful parameters for characterizing the crack tip
fields.
The relationships between KI, d and JI under linear elastic conditions are
J G K
2
I
I = I = 1 -v
E
2 KI
d =
s E
2 ( )
in plane strain
Elastic–plastic fracture mechanics 255
(7.4)
(7.5)
where GI is the strain energy release rate, which was the original, energy based
approach to studying fracture.
In all cases, either linear elastic or general yielding, there is a parameter that
describes the loading state of a cracked body. This might be KI, d or JI as appropriate
to the conditions. The limiting case for a particular material is the critical value
at which failure occurs. Under elastic conditions this is the sudden fracture event,
and the material property is KIc. Under elastic–plastic conditions, failure is not
usually rapid, and the critical condition, dc or JIc, is usually associated with the onset
of the ductile fracture process.
The assessment of flaws in fusion welded structures is covered by BS 7910: 1999, 9
Y
which allows the use of material fracture toughness values in the form of KIc, dc or
JIc. In the absence of genuine fracture mechanics derived toughness data, estimates
of KIc may be made from empirical correlations with Charpy V-notch impact energies.
Caution should be exercised when doing so as the degree of fit of the correlations
tends to be poor.