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following the requirement of the company that installed the pipeline, addressed to the
National Institute of Standards and Technology (then the National Bureau of Standards –
NBS) for help. Detailed analysis of fracture mechanics parameters, based on the concept
of crack tip opening displacement, covered assessment of the crack growth driving force
on one hand, and resistance of the material (weld metal) to crack growth [13-16] on the
other hand. The results of that research were officially accepted, so that the scope of
repair was dramatically reduced, due to which unnecessary costs were avoided as well as
risks of occurrence of new defects caused by repair welding. Thanks to that research it
was concluded that the analysis of fracture mechanics is an acceptable base for admissible
exception from the existing standards under certain circumstances, if such analysis
provides convincing and conservative (safe) assessment of structural integrity. It should
also be emphasized that this level of application of fracture mechanics was reached not
only through this detailed investigation, but also through preceding intensive develop-
ment of fracture mechanics as a scientific discipline.
It is thus obvious that the fundamental change that fracture mechanics has brought into
engineering practice is the recognition of the fact that existence of cracks and similar
defects cannot be avoided, and that their effects on structural integrity should be analysed.
The basic role of fracture mechanics is to mathematically connect three variables (stress,
defect dimensions, and fracture toughness), as shown in Fig. 1, which enables evaluation
of the third, based on two known variables. For example, if the stress is known, based on
loading and structural geometry, and the fracture toughness of the material of the struc-
ture based on tests, then one can define critical defect size. In practice, it also frequently
happens that methods of non-destructive tests (NDT) reveal a crack or a similar defect in
a structure, for which critical stress is subsequently defined, based on known fracture
toughness of the material, or either the minimal fracture toughness of the material is
subsequently defined based on the stress state of a structure. This concept can be applied
already in the phase of structural design, if one assumes existence of cracks, dimensions
of which correspond to the sensitivity of the NDT equipment.
The methodology of application of fracture mechanics depends on available data of
material properties, effects of surrounding media and external loading of a structure. In
case of static loading, one should recognize the material behaviour described as linear
elastic (‘relatively small-scale yielding’) from the behaviour of the material whose plastic
properties should not be neglected. In the first case, linear elastic fracture mechanics
(LEFM) is applied, while in the second case, depending on the form of plastic yielding,
various methods of elastic plastic fracture mechanics (EPFM) are applied. In case of
dynamic loading, one should also recognise linear elastic from elastic plastic behaviour of
the material, where the fatigue is of particular significance as a typical mechanism of
crack growth under cyclic external loading. Finally, ambient effects could be crucial, due
to elevated temperatures or corrosion.
1. APPLICATION OF LINEAR ELASTIC FRACTURE MECHANICS
The application of LEFM is based on the stress intensity factor, KI, which on one hand
represents loading and structural geometry, including crack dimensions, and on the other,
its critical value, KIc, represents the material property. Based on this interpretation of
LEFM parameters and Griffith’s energy criterion, one can establish simple dependencies
for the assessment of structural integrity.
KI ≤ KIc – structural integrity is not threatening, (1a)
KI > KIc – structural integrity is threatening due to possibility of brittle fracture (1b)