Environmental Engineering Reference
In-Depth Information
is called axial. Figure 8.2 and 8.3 show the arrangement of subsurface
cracks in a pressure vessel. The figures show a longitudinal crack 2 a 1 wide
ad 2 c 1 long [ s is the wall thickness of the vessel; D is the inner diameter of
the pressure vessel (pipeline)],
Since the pressure vessel or pipe wall are in the plane stress state with
principal stresses oriented along the axis or in the tangential direction,
then every possible set of critical size cracks can be schematised by axial
and transverse cracks and represented graphically in the coordinates ( a ; c ),
Figs 8.4 and 8.5. The ratio between the critical size a and c is such that
as a increases c decreases, and vice versa (these relationships are known
from fracture mechanics 113,etc ). In addition, the higher the load, the smaller
the critical crack size.
In order to ensure safety after conducting hydraulic tests, the pressure
and temperature during HT shall provide the conditions in which the critical
sizes of cracks in the HT mode are lower than during normal operating
conditions. Schematically, these conditions are shown in Fig. 8.6. In this
figure: 1 - a source-defect; 2 - crack of critical size for the pressure in HT
mode, 3 - a crack of critical size for loading pressure vessels and piping
in the operating mode.
8.2 Optimisation of the frequency of hydraulic tests 
During operation, the cracks can grow and increase in size. Figure 8.7 shows
the propagation of cracks over time. The initial sizes of the defect are denoted
by c 0 and a 0 . During operation, if the crack grows, the dimensions of a and
c change, when the critical size is reached, the crack becomes unstable and
total or partial destruction of the structure takes place. In Fig. 8.7 the period
of time from the moment of successful HT τ HT to the moment when the crack
size becomes equal to the critical size of the crack in the operating mode of
operation corresponds to the time of safe operation τ safe .
The growth of the entire set of cracks with a particular orientation can
be represented graphically (Fig. 8.8). If at the beginning of operation the
cracks are characterised by curve 1 (a family of critical size cracks to HT
pressure), then at certain points in time due to crack growth the curves
occupy the position of curves 2, 3 and 4. Curve 5 characterises the critical
crack size for the operating mode of operation. Curves 2 and 3 reflect the
safe operating conditions (the probability of bursting of a pressure vessel
is zero), and at the time of contact of curve 4 with curve 5 the probability
of rupture is different from zero.
The size of all the critical cracks depends on the load, such as
pressure. Figures 8.9 and 8.10 show the curves of the family of the critical
size subsurface transverse (tangential) and axial cracks at different pressures
p 1 , p 2 , p 3 , p 4 , and p 1 < p 2 < p 3 < p 4 . Curve 1 corresponds to pressure p 1 , curve
2 to p 2 , curve 3 to pressure p 3 , and curve 4 to pressure p 4 . The graphs show
that the critical crack size decreases with increasing pressure.
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