11.3 Selected Stress Intensity Factor Cases

Size: px

Start display at page:

Download "11.3 Selected Stress Intensity Factor Cases"

Sheila Horton
5 years ago
Views:

1 Seleed Sress Inensiy or ses This seion will presen log o sress-inensiy or soluions or some ypil rk geomeries Mny o hese soluions re ound in ompuer progrms nd hndooks Tles hrough 5 summrie he soluions h re presened The soluions re egoried y he loion o he rk, eiher emedded, in ple (sure or edge), or hole, in Tles hrough Soluions or rks in ylinders nd sphere re summried in Tle, nd he ASTM sndrd speimens re lised in Tle 5 Tle 6 inludes lisings o he prmeers used in he drwings nd equions s well s heir deiniions ollowing hese les, he equions or he sress-inensiy or soluions re given The soluions re presened in he sme order s lised in he les The remoe loding soluions re presened in he orm: i σ () i where he oeiien i is expressed s union o geomery, nd i indies he loding ype Some o he ses onsidered n e used o develop more omplex soluions hrough he mehods o superposiion nd ompounding Tle Emedded rks esripion Illusrion Reerenes Emedded rk in Ple Newmn & Rju [98] ormn, e l [998]

2 Tle rks in Ple esripion Illusrion Reerenes Sure rk in Ple Newmn & Rju [98] ormn, e l [989] Through rk in he ener o Ple edderson [966] Pris & Sih [96] Roers & iler [97] ormn, e l [998]

3 orner rk he Edge o Ple Rju & Newmn [988] ormn, e l [998] Through rk he Edge o Ple Td, e l [97] ormn, e l [998]

Rju [98] ormn, e l [989] Rdil Through rk

[99] ormn, e l [998] Through rk rom Hole

4 Tle rks rom Holes esripion Illusrion Reerenes Rdil orner rk rom Hole Newmn & Rju [98] ormn, e l [989] Rdil Through rk rom Hole Shivkumr & Hsu [977] Z, e l [98] Isid [97] ormn, e l [989] orner rk rom Hole in Lug Newmn & Rju [98] ormn & Meu [99] ormn, e l [998] Through rk rom Hole in Lug Shivkumr & Hsu [977] Z, e l [98] ormn, e l [989]

5 Tle rks in ylinders nd Spheres esripion Illusrion Reerenes Sure rk in Solid ylinder ormn & Shivkumr [986] ormn, e l [998] Longiudinl Sure rk in ylinder Newmn & Rju [979] ormn, e l [989] Longiudinl Through rk in ylinder Newmn [976] ormn, e l [998] 5

6 Thumnil rk on Hollow ylinder Rju & Newmn [98] ormn, e l [989] irulr Through rk in ylinder ormn, e l [985] ormn, e l [998] Through rk in Sphere Erdogn & iler [969] ormn, e l [998] 6

7 Tle 5 ASTM Sndrd Speimens esripion Illusrion Reerenes Sndrd ener- rked Tension Speimen edderson [966] Sndrd omp Speimen ASTM E99 [] Sndrd Round omp Speimen ASTM E99 [] Sndrd Ar- Shped Speimen ASTM E99 [] 7

8 Sndrd Bend Speimen ASTM E99 [] 8

9 Tle 6 esripion o Prmeers Used or SI Soluions Prmeer B R σ σ nd σ σ esripion rk eph rk Lengh Thikness idh Hole dimeer; ylinder dimeer isne rom hole ener o edge o ple Thikness (ASTM sndrd soluions) ylinder rdius Remoe ension sress Bending sresses Bering sress 9

10 Tle 7 Sress Inensiy Soluions or Emedded rks Emedded rk in Ple σ os ) / ( ) / ( ) / ( g ) / ( M ) / ( M ) / ( M ) / ( M M M g M x w dn d or dn d or se w o o 9 See Tles or nd x equions

11 Tle 8 Sress Inensiy Soluions or rks in Ple H M g w x Sure rk in Ple Through rk in he ener o Ple orner rk he Edge o Ple Through rk he Edge o Ple Tension Bending Tension Bending Tension Bending σ σ σ σ σ σ σ w se o 9 o or d dn or d dn Tension σ se Bending σ See Tle or M, g,, nd x equions i i x, i, or i,, See Tles or, nd x equions nd Tle 9 or i n β se β β n β se β β β 75 7 β [ 9 99( sin β ) ] ( sin )

12 Tle 9 lulion o i or orner rk Soluion i,, oined rom inerpoling in,, les s ollows our d poins, I {(/) j, /, /} j,,,, re luled using ui spline inerpolion, where (/) j re lised ulr vlues o,, 5,,, 5, nd 5, nd, in generl, (/) j, < / nd (/) j, > / i (/) re hen luled rom he ove our d poins using pieewise Hermie polynomil inerpolion Tle o Vlues / / / / 5 / 8 / / / -ip -ip -ip -ip -ip -ip -ip -ip -ip -ip -ip -ip Tle o Vlues / / / / 5 / 8 / / / -ip -ip -ip -ip -ip -ip -ip -ip -ip -ip -ip -ip

13 Tle o Vlues / / / / 5 / 8 / / / -ip -ip -ip -ip -ip -ip -ip -ip -ip -ip -ip -ip

14 Rdil orner rk rom Hole Rdil Through rk rom Hole orner rk rom Hole in Lug Tle Sress Inensiy Soluions or rks rom Holes Tension Bending Bering Tension Bering Bering σ σ σ σ σ σ w w H w See Tles nd or ddiionl equions w w se λ w ( sin β ) β See Tles nd or ddiionl equions w See Tles nd or ddiionl equions

15 Through rk rom Hole in Lug Bering σ L w se se w L λ See Tles nd or ddiionl equions 5

16 Tle Addiionl Equions Used or luling SI Holes Thru rks Pr-hru rks λ B B d d g p d w x w g g g M µ os dn d or dn d or o o 8 6

17 Tle Addiionl Equions Used or luling SI or rks In Ple nd rks Holes Prmeer Equion M m m m H p sin H H H H H, µ, os, d, µ 85 µ v p g 5 β B > x sin os sin os, M m 9 7

18 m m 89 5 ( / ) ( 65 ( / )) ( ( / )) 5 ) ( ( / ) g 5 ( sin ) 5 ( / ) ( sin ) ( / ) g g [ ( os ) ] 9 ( os ) [ ] p 7 ( / ) ( / ) 6 5 ( / ) 9 ( / ) 7 6 ( / ) ( / ) 5 ( / ) 8

19 Sure rk in Solid ylinder Longiudinl Sure rk in ylinder Longiudinl Through rk in ylinder Tension Bending Tle rks in ylinders nd Spheres σ σ σ σ [ Y ] [ 9 99 Y ] β 7 9 se β Y sin β β k i i 97 M ( k ) ( k ) or or g 9 o o or or inernl exernl d dn d dn ( n β ) i β x 5 v rk rk See Tle or M, g,, nd x equions ( 5 9 λ λ ) λ 7 λ R 9

20 Thumnil rk on Hollow ylinder Tension σ Bending σ os sin B A os sin B A Y Y B A B A x x dn d or dn d or o o 9

21 irulr Through rk in ylinder Tension σ Bending σ I I [ ] R / or or v R k k o o h sin o o h g o h k g I k I > β β β β Through rk in Sphere σ R λ λ

22 Tle Sress Inensiy Soluions or ASTM Sndrd Speimens Sndrd enerrked Tension Speimen σ / se Sndrd omp Speimen σ ) ( / / Sndrd Round omp Speimen σ Sndrd Ar- Shped Speimen σ Y R R Y X Sndrd Bend Speimen σ

45 lpm. Part Number Spool Qty Max Flow Max Pressure Ports. 45 lpm. Relief Valve Standard Bar Range Power Beyong Plug included in every kit

45 lpm. Part Number Spool Qty Max Flow Max Pressure Ports. 45 lpm. Relief Valve Standard Bar Range Power Beyong Plug included in every kit Monoblock Valves M3 Monoblock art Number Spool Qty Max Flow Max ressure orts M3/S3/8L/G4-3-4 ylinder M3/2S3/8L/G4-3-4 ylinder 2 M3/3S3/8L/G4-3-4 ylinder 3 M3/4S3/8L/G4-3-4 ylinder 4 45 lpm 35 ar (25 ar