1. THE MODELING OF THE LIMIT STATE OF DUCTILE THICK-WALLED PIPES WITH AXIAL SURFACE DEFECTS
Orynyak I.V., Ageyev S.M.
G.S. Pisarenko Institute for Problems of Strength, Kiev, Ukraine

2. Plan Existing models for pipes with defects.
The problems of modeling of the thick-walled pipes.
The proposed analytical model for thick-walled pipes.
The theoretical analysis of the results.
The comparison with experimental data.
Discussion.
Application to a repair technology.

3. Existing models for pipes with defects
C – crack half-length
ℓ – crack half-width
a – crack depth
- dimensionless ligament thickness
- dimensionless crack length
dimensionless limit pressure or
strength reduction coefficient
- «local» formula of the Battelle Memorial Institute
- «global» formula of the Battelle Memorial Institute
- «global» formula Staat
- «local» formula Staat
- formula DNV

4. The problems of modeling of the thick-walled pipes
1. The choice of limit characteristic. 2. The choice of criterion of ductile failure. 3. The irregularity of defect’s form. 4. Interaction of closely situated defects. 5. The taking into account the wall thickness. 6. External/internal defects.

5. The choice of limit characteristic

6. The choice of criterion of ductile failure (for unflawed thick-walled pipes).№ mm
Specimen orientation
MPa 1
88,9
4,0
longitudinal
336
486
42,7-47,0
45,8
52,9 2
8,8
324
457
94,2-100,6
100,8
116,4 3
22,2
288
438
307,1
303,1
350,0 4
101,6
10,0
284
408
97,5
89,9
103,3 5
transverse
390
100,2
115,7 6
139,7
12,5
266
400
73,5-76,0
78,9
91,1 7
338
432
85,2
98,4 8
512
642
57,9-61,8
60,5
69,93 9
506
634
135,4-170,7
139,9
161,5 10
473
614
416,9-421,8
424,9
490,6 11
689
740
162,2
187,3 12
717
759
166,4
192,1 13
648
702
152,0
138,4
159,8 14
668
719
141,8
163,7

7. The proposed analytical model for thick-walled pipes
The proposed analytical model for thick-walled pipes. Analytical model of the Institute for problems of strength (for thin-walled pipes)
the equation of forces equilibrium
in the radial direction
- the circumferential force;
х – axial coordinate;
- transverse force
- limit condition
- external
- internal
dimensionless limit pressure for the thin-walled
pipe with axial surface defect

8. External/internal defects
the limit bending moment

9. The taking into account the wall thickness
local equation of equilibrium
for thin-walled pipe
the solution of differential equation
The pipe with external defect
The pipe with internal defect

10. The theoretical analyze of the results
The dimensionless limit pressure versus dimensionless crack length for the model of thick-walled pipes with external/internal defects.
The comparison of analytical
models for thin-walled pipe:
and for the thick-walled pipe:

11. The comparison with experimental data (Staat’s data)№ 1
3,105
0,8
0,865
0,85
0,851
0,014
-0,001
0,826
-0,025 2
1,769
0,5
0,681
0,639
0,744
-0,063
-0,105
0,704
0,598
-0,04
-0,146 3
3,656
0,566
0,549
0,583
-0,017
-0,034
0,605
0,533
0,022
-0,05 4
9,63
0,52
0,518
0,502
0,018
0,016
0,541
0,497
0,039
-0,005 5
4,009
0,35
0,408
0,393
0,417
-0,009
-0,024
0,473
0,377
0,096
internal № 1
3,642
0,48
0,564
0,546
0,633
-0,069
-0,087
0,585
0,476
-0,048
-0,157 2
6,549
0,525
0,518
0,506
0,019
0,012
0,551
0,451
0,045
-0,055 3
15,018
0,49
0,52
0,519
0,491
0,029
0,028
0,536
0,445
-0,046 4
1,044
0,284
0,693
0,622
0,705
-0,012
-0,083
0,689
0,424
-0,016
-0,281 5
2,456
0,433
0,396
0,477
-0,044
-0,081
0,495
0,309
0,018
-0,168 6
3,783
0,31
0,389
0,371
-0,035
-0,053
0,45
0,306
0,026
-0,118 7
6,69
0,327
0,321
0,35
-0,023
-0,029
0,378
0,263 8
6,775
0,3
0,338
0,332
0,311
0,027
0,021
0,387
0,274
0,076
-0,037 9
15,159
0,302
0,009
0,008
0,339
0,251
0,037
-0,051 10
15,244
0,24
0,262
0,281
-0,018
-0,019
0,294
0,209
0,013
-0,072 11
1,411
0,091
0,415
0,337
0,584
-0,169
-0,247
0,527
0,133
-0,057
-0,451 12
0,034
0,362
0,249
0,574
-0,212
-0,295
0,502
0,051
-0,523
external

12. 1. The comparison our models with experimental data for the pipe with internal defect.
- “external” formula
- “internal” formula
2. The comparison our models with Staat’s “local” formula.
internal
external
3. The comparison our models with Staat’s “global” formula.
internal
external

13. Discussion external (Staat) Influence of the form of the defects № 11
1,186
0,091
0,492 (0,415)
0,404 (0,337)
0,584 12
1,172
0,034
0,448 (0,362)
0,355 (0,279)
0,574

14. Application - pipe’s geometry - defect’s geometry
the pipe with sleeve
the pipe with defect
- pipe’s geometry
- defect’s geometry 1.
- the pipe without defect 2.
- the pipe with defect
3. Numerical analyze and simplify analytical model
- the added thick pipe’s wall as a result of used sleeve (equal 8 MPa) 4.
- the pipe with sleeve 5.
- experiment