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

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.

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

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.

The choice of limit characteristic

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 11 689 740 183-175 162,2 187,3 12 717 759 166,4 192,1 13 648 702 152,0 138,4 159,8 14 668 719 141,8 163,7

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

External/internal defects the limit bending moment

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

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:

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

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

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

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