HPLP310 Biblio_35 Fissures radial intern in a thick cylinder under pressure and thermal loading

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defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 1/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : HPLP310 Biblio_35 Fissures rdil intern in thick cylinder under pressure nd therml loding Summry: This test is resulting from the vlidtion independent of version 3 in breking process. It is bout two-dimensionl test in sttics in which one models to it not linerity of contct due to refermeture prtil of the crck. The behvior of the structure is thermoelstic liner isotropic. The cse test understnds two modelings D plne for which one studies the influence of the mechnicl lod fctor. In the first modeling contct with mteril infinimement rigid is used to represent refermeture (symmetricl) crck while in the second boundry condition of type unilterl connection is put in work. rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : /15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : 1 Problem of reference 1.1 Geometry y r A B C D E r1 x Cross-section of thick tube presenting one internl rdil crck Report of the rys Depth of the crck b=r /r 1 =r 1 =1mm, r =mm / r r 1 =0,05 1. Properties of mteril The mteril is thermoelstic liner isotropic stndrd. Young modulus Poisson's rtio Liner diltion coefficient Yield stress E=1000 MP =0,3 T =1E-6 0 =1 MP (being used to define the initil stress field creted by the process of utofrettge on the ssumption of former behvior of elstoplstic type of Von Mises) 1.3 Boundry conditions nd lodings Boundry conditions (for hlf-prt in the re y 0 ) Blocking UY =0 on the segment AB nd on the ligment DE (symmetry). Liner reltion UX AUX E =0 (to block the horizontl djustment) rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 3/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : Lodings Loding n 1: Loding n : rdil trction rr r = 0 on the externl fce; this mechnicl loding produces the sme one tht n internl pressure cting simultneously on the internl ry r 1 nd on the lips of the crck, without tking into ccount of nonthe linerity of contct. therml loding re equivlent to n utofrettge defined s follows: 4 0 1 T1 T ln 3 E r T 1 T1 T r T T1 ln r1 r r 1 ln r 1 T T r r In these formuls, indicte the mximum ry of the zone hving undergone utofrettge, T 1 the temperture with the ry r 1 nd T the temperture with the ry r= in the thick tube not fissured. In the ppliction concerned here, one tkes =r, which corresponds to the utofrettge of the totlity of the section of the thick tube, nd one does not tke into ccount it not linerity of contct. One is expected K negtive for positive tempertures (put in compression of the tube not fissured). Loding n 3: liner combintion loding n + * loding n 1, ( T!) indicting the mechnicl lod fctor; one tkes here into ccount it not linerity of contct, which supposes n incrementl ppliction of the mechnicl lod. rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 4/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : Reference solution.1 Method of clculting used for the reference solution Clcultion by finite elements with code ABAQUS. Nonthe linerity of contct is modelled using onewy GAP elements. The fctor of intensity of the constrints is clculted strting from the integrl J.. Results of reference Adimensionl fctor of intensity of the constrints ccording to the mechnicl fctor of loding, in the cse of loding n 3 Nottion: FL K IL / 0 liner fctor of intensity dimensionl (obtined by liner combintion of the effects of utofrettge nd mechnicl loding, in stopped feture) FN K IN / 0 nonliner fctor of intensity dimensionl (obtined by tking ccount of nonthe linerity of contct, in full feture). K I EJ 1 rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 5/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : Empiricl formul of the fctor of intensity of the constrints under externl rdil tension r r C1 C 0, lnb lnb KI 0 P 0, 01 0, 8 et 15, b 3, 0 1 1 b C C 1 1 0, 5, 397, 705 0, 884 0, 5 0, 44 1, 447 0, 809 Empiricl formul of the fctor of intensity of the constrints in utofrettge in full section K C C b 1 ln I 0 1 18, 4 b C C 1 0, 01 0, 8 et 15, b 3, 0 30, 1 57, 714 9, 954, 444 0, 5 1 0, 75 51, 5 111, 07 63, 44 0, 05 0, 15 1, 5 0, 05 1 0, 5 0, 15 1, 5 3, 631.3 Bibliogrphicl references 1) H.M. SHU, J. SMALL nd G. BEZINE: Rdil stress intensity fctors for ces in thick wlled cylinders. I. Symmetricl ces II. Combintion of utofrettge nd internl presses. Engng.Frct.Mechs., 49, n 4, 611-69, 1994. rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 6/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : 3 Modeling A 3.1 Chrcteristics of modeling The model consists of qudrngles with 8 nodes nd tringles with 6 nodes. It comprises 4877 nodes nd 1598 elements. 3. Chrcteristics of the grid Use of the procedure FISSD_V1. The topologicl prmeters concerning refinement round the bottom of crck re: nc=4 (mny crowns) ns=8 (mny sectors) nbcour =1 (mny crowns of dérffinement) Y X rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 7/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : Zoom of the fissured zone Zoom of the zone fissured with block of contct rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 8/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : 3.3 Sizes tested nd results Identifiction Reference Type of reference Tolernce, loding n 1, crown 0, neglected contct 1.148 SOURCE_EXTERNE.0%, loding n 1, crown 1, neglected contct 1.148 SOURCE_EXTERNE.0%, loding n 1, crown, neglected contct 1.148 SOURCE_EXTERNE.0%, loding n 1, crown 3, neglected contct 1.148 SOURCE_EXTERNE.0% Identifiction Reference Type of reference Tolernce, loding n, crown 0, neglected contct 0.4137 SOURCE_EXTERNE 7.0%, loding n, crown 1, neglected contct 0.4137 SOURCE_EXTERNE 7.0%, loding n, crown, neglected contct 0.4137 SOURCE_EXTERNE 7.0%, loding n, crown 3, neglected contct 0.4137 SOURCE_EXTERNE 7.0% Identifiction Reference Type of reference Tolernc e, loding n 3, contct, =0,33, crown 0 1,075E-3 SOURCE_EXTERNE 6.0%, loding n 3, contct, =0,335, crown 0 3,0187E-3 SOURCE_EXTERNE.5%, loding n 3, contct, =0,34, crown 0 5,4336E-3 SOURCE_EXTERNE 1.0%, loding n 3, contct, =0,345, crown 0 8,5865E-3 SOURCE_EXTERNE 4.0%, loding n 3, contct, =0,35, crown 0 1,075E- SOURCE_EXTERNE 4.0%, loding n 3, contct, =0,36, crown 0,1757E- SOURCE_EXTERNE 1.0% rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 9/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision :, loding n 3, contct, =0,40, crown 0 6,6478E- SOURCE_EXTERNE 1.0% Identifiction Reference Type of reference Tolernce KI, loding n 3, contct, = 0.33, crown 1 1,075E-3 SOURCE_EXTERNE.0% KI, loding n 3, contct, = 0.335, crown 1 3,0187E-3 SOURCE_EXTERNE.0% KI, loding n 3, contct, = 0.34, crown 1 5,4336E-3 SOURCE_EXTERNE 1.0% KI, loding n 3, contct, = 0.345, crown 1 8,5865E-3 SOURCE_EXTERNE 4.0% KI, loding n 3, contct, = 0.35, crown 1 1,075E- SOURCE_EXTERNE 4.0% KI, loding n 3, contct, = 0.36, crown 1,1757E- SOURCE_EXTERNE 1.0% KI, loding n 3, contct, = 0.40, crown 1 6,6478E- SOURCE_EXTERNE 1.0% Identifiction Reference Type of reference Tolernce KI, loding n 3, contct, = 0.33, crown 1,075E-3 SOURCE_EXTERNE 4.5% KI, loding n 3, contct, = 0.335, crown 3,0187E-3 SOURCE_EXTERNE.0% KI, loding n 3, contct, = 0.34, crown 5,4336E-3 SOURCE_EXTERNE 1.0% KI, loding n 3, contct, = 0.345, crown 8,5865E-3 SOURCE_EXTERNE 4.0% KI, loding n 3, contct, = 0.35, crown 1,075E- SOURCE_EXTERNE 4.0% KI, loding n 3, contct, = 0.36, crown,1757e- SOURCE_EXTERNE 1.0% KI, loding n 3, contct, = 0.40, crown 6,6478E- SOURCE_EXTERNE 1.0% Identifiction Reference Type of reference Tolernce, loding n 3, contct, =0,335, crown 3 3,0187E-3 SOURCE_EXTERNE 3.0%, loding n 3, contct, =0,34, crown 3 5,4336E-3 SOURCE_EXTERNE 1.0%, loding n 3, contct, =0,345, crown 3 8,5865E-3 SOURCE_EXTERNE 4.0%, loding n 3, contct, =0,35, crown 3 1,075E-3 SOURCE_EXTERNE 4.0%, loding n 3, contct, =0,36, crown 3,1757E- SOURCE_EXTERNE 1.0%, loding n 3, contct, =0,40, crown 3 6,6478E- SOURCE_EXTERNE 1.0% rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 10/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : 3.4 Remrks The tbles below give the rte of refund of energy G for two vlues of the coefficient who correspond to nonthe seprtion of the lip of the crck. (There is seprtion of the lip for > 0,3 ). Identifiction Reference G ASTER G, loding n 3, contct, =0,30, crown 0 0 8.7941 10 16 G, loding n 3, contct, =0,30, crown 1 0 4.4308 10 15 G, loding n 3, contct, =0,30, crown 0 3.331 10 15 G, loding n 3, contct, =0,30, crown 3 0 4.4794 10 13 Identifiction Reference G ASTER G, loding n 3, contct, =0,3, crown 0 0 1,17E-14 G, loding n 3, contct, =0,3, crown 1 0 3,6E-16 G, loding n 3, contct, =0,3, crown 0 1,0E-15 G, loding n 3, contct, =0,3, crown 3 0 4,3E-13 rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 11/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : 4 Modeling B 4.1 Chrcteristics of modeling The model consists of qudrngles with 8 nodes nd tringles with 6 nodes. It comprises 4877 nodes nd 1598 elements. 4. Chrcteristics of the grid Use of the procedure FISSD_V1. The topologicl prmeters concerning refinement round the bottom of crck re: nc=4 (mny crowns) ns=8 (mny sectors) nbcour =1 (mny crowns of dérffinement) Y X rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 1/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : Zoom of the fissured zone 4.3 Sizes tested nd results Identifiction Reference Type of reference Tolernce, loding n 1, crown 0, neglected contct 1.148 SOURCE_EXTERNE.0%, loding n 1, crown 1, neglected contct 1.148 SOURCE_EXTERNE.0%, loding n 1, crown, neglected contct 1.148 SOURCE_EXTERNE.0%, loding n 1, crown 3, neglected contct 1.148 SOURCE_EXTERNE.0% Identifiction Reference Type of reference Tolernce, loding n, crown 0, neglected contct 0.4137 SOURCE_EXTERNE 7.0%, loding n, crown 1, neglected contct 0.4137 SOURCE_EXTERNE 7.0% rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 13/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision :, loding n, crown, neglected contct 0.4137 SOURCE_EXTERNE 7.0%, loding n, crown 3, neglected contct 0.4137 SOURCE_EXTERNE 7.0% Identifiction Reference Type of reference Tolernc e, loding n 3, contct, =0,33, crown 0 1,075E-3 SOURCE_EXTERNE 4.5%, loding n 3, contct, =0,335, crown 0 3,0187E-3 SOURCE_EXTERNE 3.0%, loding n 3, contct, =0,34, crown 0 5,4336E-3 SOURCE_EXTERNE 1.0%, loding n 3, contct, =0,345, crown 0 8,5865E-3 SOURCE_EXTERNE 4.0%, loding n 3, contct, =0,35, crown 0 1,075E- SOURCE_EXTERNE 4.0%, loding n 3, contct, =0,36, crown 0,1757E- SOURCE_EXTERNE 1.0%, loding n 3, contct, =0,40, crown 0 6,6478E- SOURCE_EXTERNE 1.0% Identifiction Reference Type of reference Tolernce KI, loding n 3, contct, = 0.33, crown 1 1,075E-3 SOURCE_EXTERNE 4.5% KI, loding n 3, contct, = 0.335, crown 1 3,0187E-3 SOURCE_EXTERNE 3.0% KI, loding n 3, contct, = 0.34, crown 1 5,4336E-3 SOURCE_EXTERNE 1.0% KI, loding n 3, contct, = 0.345, crown 1 8,5865E-3 SOURCE_EXTERNE 4.0% KI, loding n 3, contct, = 0.35, crown 1 1,075E- SOURCE_EXTERNE 4.0% KI, loding n 3, contct, = 0.36, crown 1,1757E- SOURCE_EXTERNE 1.0% KI, loding n 3, contct, = 0.40, crown 1 6,6478E- SOURCE_EXTERNE 1.0% Identifiction Reference Type of reference Tolernce KI, loding n 3, contct, = 0.33, crown 1,075E-3 SOURCE_EXTERNE 4.5% KI, loding n 3, contct, = 0.335, crown 3,0187E-3 SOURCE_EXTERNE 3.0% KI, loding n 3, contct, = 0.34, crown 5,4336E-3 SOURCE_EXTERNE 1.0% KI, loding n 3, contct, = 0.345, crown 8,5865E-3 SOURCE_EXTERNE 4.0% KI, loding n 3, contct, = 0.35, crown 1,075E- SOURCE_EXTERNE 4.0% KI, loding n 3, contct, = 0.36, crown,1757e- SOURCE_EXTERNE 1.0% KI, loding n 3, contct, = 0.40, crown 6,6478E- SOURCE_EXTERNE 1.0% Identifiction Reference Type of reference Tolernce, loding n 3, contct, =0,335, crown 3 3,0187E-3 SOURCE_EXTERNE 3.0%, loding n 3, contct, =0,34, crown 3 5,4336E-3 SOURCE_EXTERNE 1.0%, loding n 3, contct, =0,345, crown 3 8,5865E-3 SOURCE_EXTERNE 4.0%, loding n 3, contct, =0,35, crown 3 1,075E-3 SOURCE_EXTERNE 4.0%, loding n 3, contct, =0,36, crown 3,1757E- SOURCE_EXTERNE 1.0%, loding n 3, contct, =0,40, crown 3 6,6478E- SOURCE_EXTERNE 1.0% 4.4 Remrks The tbles below give the rte of refund of energy G for two vlues of the coefficient who correspond to nonthe seprtion of the lip of the crck. (There is seprtion of the lip for 0,3 ). rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 14/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : Identifiction Reference G ASTER G, loding n 3, contct, =0,30, crown 0 0 8.7941 10 16 G, loding n 3, contct, =0,30, crown 1 0 4.4308 10 15 G, loding n 3, contct, =0,30, crown 0 3.331 10 15 G, loding n 3, contct, =0,30, crown 3 0 4.4794 10 13 Identifiction Reference G ASTER G, loding n 3, contct, =0,3, crown 0 0 1,17E-14 G, loding n 3, contct, =0,3, crown 1 0 3,6E-16 G, loding n 3, contct, =0,3, crown 0 1,0E-15 G, loding n 3, contct, =0,3, crown 3 0 4,3E-13 rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

defult Titre : HPLP310 - Biblio_35 Fissure rdile interne dns u[...] Dte : 0/09/011 Pge : 15/15 Responsble : TRAN Vn Xun Clé : V7.0.310 Révision : 5 Summry of the results The clcultion of G is correct in ll the cses, including for completely closed crck. Modelings with block of contct nd unilterl connection give similr results. rning : The trnsltion process used on this website is "Mchine Trnsltion". It my be imprecise nd inccurte in whole or in prt nd is provided s convenience.

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