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

162
Table 3. s ref /s M1 estimates from J-based limit loads and flat-plate solutions.
Notes:
(1) K based on elastic stress, L uses elastic-plastic stress and is J-based at 0.5% strain.
r
(2) K based on elastic-plastic stress, L uses elastic-plastic stress and is J-based at 0.5% strain.
r
(3) Collapse of load bearing area around crack front.
(4) All plate solutions: width = p x mean pipe radius.
that modifying the R6 pin-loading model (Equn 13)
by adjusting the plate width can lead to solutions
that agree well with s ref /s M1 based on M J2B E 0.5% and
M J2B EP 0.5% .
It may be inferred from the above results that the
conventional definition of local collapse solutions for flat
plates, assuming that the load-bearing area extends one
plate thickness at either side of the flaw, leads to
overestimating the reference stress for embedded flaws in
pipes, which may result in overly conservative assessments.
On the other hand, limit loads based on global collapse of
the pipe cross section (M FEA ) or global collapse in a flat-plate
model, with plate width assumed equal to half the pipe
The Journal of Pipeline Engineering
Source Equn 4 Equn 5 BS 7910
R6 R6 R6 R6
Basis of
σ ef
/σ r M1
M J2B
E 0.
5%
FEA
@ 0.
5%
strain
M J2B
EP
0.
5%
FEA
@ 0.
5%
strain
Flat
plate,
local,
pinned
Flat
plate,
global,
pinned
Flat
plate,
global,
fixed
Flat
plate,
local,
pinned
Flat
plate,
local,
fixed
M odel
( 1)
( 2)
( 3)
, ( 4)
( 3)
, ( 4)
( 3)
, ( 4)
( 3)
, ( 4)
( 3)
, ( 4)
E1BH3L50L1_5M01. 077
1. 117
1. 176
1. 022
1. 013
1. 168
1.
091
E1BH3L50L3M01. 057
1. 099
1. 158
1. 020
1. 013
1. 150
1.
091
E1BH3L50L14M01. 052
1. 096
1. 158
1. 020
1. 013
1. 150
1.
091
E1BH3L50L6M01. 038
1. 082
1. 124
1. 016
1. 013
1. 117
1.
091
E1BH3L50L9M01. 031
1. 077
1. 103
1. 013
1. 013
1. 096
1.
091
E1BH6L50L3M01. 098
1. 138
1. 351
1. 037
1. 026
1. 308
1.
200
E1BH6L50L11M01. 097
1. 138
1. 351
1. 037
1. 026
1. 308
1.
200
E1BH9L50L3M01. 117
1. 157
1. 586
1. 049
1. 039
1. 459
1.
333
E1BH6L50L6M01. 075
1. 117
1. 260
1. 028
1. 026
1. 225
1.
200
E1BH6L50L1_5M01. 107
1. 146
1. 404
1. 041
1. 026
1. 357
1.
200
E1BH3L25L3M01. 042
1. 086
1. 106
1. 010
1. 006
1. 099
1.
061
E1BH3L100L3M01. 069
1. 110
1. 209
1. 041
1. 026
1. 202
1.
120
E1BH3L200L3M01. 077
1. 117
1. 249
1. 085
1. 053
1. 244
1.
143
E1BH3L250L3M01. 080
1. 120
1. 260
1. 109
1. 067
1. 255
1.
149
E1BH6L25L3M01. 066
1. 108
1. 227
1. 018
1. 013
1. 194
1.
130
E1BH6L100L3M01. 128
1. 167
1. 480
1. 076
1. 053
1. 437
1.
273
E1BH3L25L6M01. 024
1. 071
1. 084
1. 008
1. 006
1. 078
1.
061
Sample issue
mean circumference, underestimate the reference stress
compared with J-based solutions.
Based on the above, it may be concluded that the way
forward is to develop new pipe-specific J-based solutions,
which represent loading conditions between global collapse
and conventionally-defined local collapse. This implies
that the required J-based solutions correspond to a larger
load-bearing area (defined by the extent of the ligament on
either side of the flaw) than that associated with conventional
local-collapse solutions.
In further work, simple equations to estimate M J2B E 0.5%
have been developed using a semi-analytical approach