JPE - Sept09 - cover2-4.pmd - Pipes & Pipelines International ...

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axis, due to the existence of the flaw, compared with
the unflawed condition.
• Global collapse: corresponds to failure, by yielding
mechanisms, of the whole section containing the
flaw. This is deemed to occur when the global
deformation, displacement and/or rotation, of the
section become unbounded. Global collapse occurs
at a higher load than that corresponding to local
collapse.
Most codified limit-load or reference-stress solutions for
part-thickness (surface or embedded) flaws are based on the
local-collapse approach. Although some standards, such as
R6 [2] also provide solutions based on the global-collapse
approach, further checks, such as against finite-element
analyses, may be required to verify that such solutions
provide safe assessments.
An alternative method for determining limit loads, which
requires J data from finite-element analyses, consists of
defining the limit load such that it is consistent with the J
data and the reference stress J-estimation scheme represented
by Equn 2. The main benefit of this approach is that it does
not require the analyst to specify in advance whether a localor
global-collapse model is more suitable. The limit load is
found by solving Equns 2 and 3 using J results from an
elastic-plastic finite-element analysis of the flawed
component. A simple version of this approach is
recommended in Section B.6.4.3(e) of API 579 [3] and in
a slightly different form in Section B.1.89 of API-579-1/
ASME-FFS-1 [4] as follows:
L
r
t
Fig.3. Idealized elliptical embedded flaw in a flat plate, used in BS 7910 (BSI, 2005).
P
=
P
ref
where P ref is determined from the following relationship:
(9)
The Journal of Pipeline Engineering
J 0.002E 1 ⎛ 0.002E⎞
⎟
= 1+ +
⎜
⎜1
⎟
Je σy 2
⎜ + ⎟
⎜⎝ σ ⎟ y ⎠
P= Pref
−1
(10)
where J is the total value of J determined from an elasticplastic
analysis of the flawed component; J e is the elastic J
determined from an elastic analysis by, for example, using
Equns 4 or 5; P is a characteristic applied load (or stress)
such as axial force, bending moment, or a combination
thereof; and P ref is the reference load (or stress) defined as
the load at which the ratio J/J e reaches the value defined by
Equn 10.
If P ref is used to construct a BS 7910 Level 3C FAD (with L r
defined according to Equn 9), it will intersect the
corresponding BS 7910 Level 2B/3B material-specific FAD,
and give the same K r value, at L r = 1.0. Thus, the limit load
P ref is defined in a manner which is consistent with the Level
2B/3B material-specific FAD, at least at L r = 1.0. In this
case, the limit load may depend on the strain-hardening
characteristics of the material.
Sample issue
Codified reference-stress
solutions for embedded flaws
General
Whereas there are several well-established reference-stress
solutions for circumferential surface flaws in pipe girth
welds, there are no such solutions for circumferential
embedded flaws. Consequently, most analysts use referencestress
solutions originally derived for flat plates to assess
circumferential embedded flaws in pipe girth welds. The
most widely used of these solutions are the reference-stress
equations given in BS 7910 [1] and R6 [2]. These are given
in terms of the membrane stress, P m , and through-wall