Fatigue of Weldments

Transcription

1 Faigue of Weldmens June nd 6 h, 014, Aalo Universiy, Espoo, Finland Prof. Grzegorz Glinka Universiy of Waerloo, Canada 010 Grzegorz Glinka. All righs reserved. 1

2 Faigue Analysis of Weldmens y he Local Sress-Srain Mehod (-N) 010 Grzegorz Glinka. All righs reserved.

3 Informaion Pah for Srengh and Faigue Life Analysis Maerial Properies Componen Geomery Loading Hisory Sress-Srain Analysis Damage Analysis Faigue Life 010 Grzegorz Glinka. All righs reserved. 3

4 Informaion pah for faigue life esimaion ased on he -N mehod F LOADING GEOMETRY, K f MATERIAL PSO 0 E Sress-Srain Analysis Damage Analysis MATERIAL N f Faigue Life

5 Seps in faigue life predicion procedure ased on he -Napproach a) Srucure peak hs n peak hs n ) Componen c) Secion wih he welded join d) 010 Grzegorz Glinka. All righs reserved. 5

6 Seps in faigue life predicion procedure ased on he -N approach ,7' e) 5,5',' 1,1' 3 log (/) f /E e /E f peak 0 Neuer : f) 1 1' peak E ' f E ' N f f N f c 0 ' f ' f Faigue damage: D ; D ; D ; D ; N N N N Toal damage: D D D D D ' f ' f,,, N f?,? ' f ; 1 ' n ' E ' f K p e = 0 N log(n f ) 010 Grzegorz Glinka. All righs reserved. 6 N e Faigue life: N lck =1/D

7 The sepwise -Nprocedure for esimaing faigue life (can e summarised as follows - see he Figure elow). Analysis of exernal forces acing on he srucure and he componen in quesion (a), Analysis of inernal loads in chosen cross secion of a componen (), Selecion of criical locaions (sress concenraion poins) in he srucure (c), Calculaion of he elasic local sress, peak, a he criical poin (usually he noch ip, d) Assemling of he local sress hisory in form of he form of peak and valley sequence (f), Deerminaion of he elasic-plasic response a he criical locaion (h), Idenificaion (exracion) of cycles represened y closed sress-srain hyseresis loops (h, i), Calculaion of faigue damage (k), Faigue damage summaion (Miner- Palmgren hypohesis, l), Deerminaion of faigue life (m) in erms of numer of sress hisory repeiions, N lck, (No. of locks) or he numer of cycles o faigue crack iniiaion, N. The deails concerning many oher aspecs of ha mehodology are discussed elow. 010 Grzegorz Glinka. All righs reserved. 7

8 Maerial properies used in he srain-life (-N) faigue analysis of weldmens 010 Grzegorz Glinka. All righs reserved. 8

9 Smooh Laoraory Specimens Used for he Deerminaion of he Curve under Monoonic and Cyclic Loading Sress and srain sae in specimens used for deerminaion of maerial properies yy y y yy x x z y x yy 33 yy xx zz yy 6-8mm ij yy ij 0 0 xx 0 yy zz yy 010 Grzegorz Glinka. All righs reserved. 9

10 The Srain-life and he Cyclic Sress-Srain Curve Oained from Smooh Cylindrical Specimens Tesed Under Srain Conrol (Uni-axial Sress Sae) f Srain - Life Curve Sress -Srain Curve log (/) f /E c e /E E 0 log (N f ) N e 1 ' ' c n f N ' N E f f f E K ' Grzegorz Glinka. All righs reserved. 10

11 The effec of he weld and he ase maerial properies on he srainsress and srain-life properies of welded Aluminum 5183 maerial Sress, (ksi) Srain ampliude, Srain, (ksi) No. reversals o failure, N f The sress-srain and srain-life daa ses for he weld meal and he paren maerial lie in he same scaer and! Therefore he paren maerial faigue properies are used for he analysis of faigue life of weldmens. (source: J.D Burk and F.V. Lawrence, ref. 40) 010 Grzegorz Glinka. All righs reserved. 11

12 a) Faigue cracks in weldmens iniiae mos ofen a he weld oe or he weld roo, i.e. in he Hea Affeced Zone (HAZ). ) Faigue maerial properies of he Hea Affeced Zone (HAZ) and he Weld Meal (WM) have higher mean values of faigue srengh parameers, han he Base Meal properies, u hey are also characerized y wider scaer. The scaer of Base Meal properies ofen lies wihin he scaer of he HAZ and WM scaer ands. c) Therefore he Base Meal cyclic and faigue properies are mos ofen used for faigue analyses wihin he Local Srain (-N) mehod. 010 Grzegorz Glinka. All righs reserved. 1

13 Sress parameers used in he srain-life (-N) faigue analysis of weldmens 010 Grzegorz Glinka. All righs reserved. 13

14 Weldmens, like mos engineering componens, conain sress concenraion regions locaed around weld oes and weld roos. The high local sresses in hose locaions conrol he faigue process of welded componens. Therefore he sress peak a he weld roo or oe mus e deermined or accouned for wihin he procedure aimed a he evaluaion of faigue lives of weldmens. 010 Grzegorz Glinka. All righs reserved. 14

15 Sress concenraion & sress disriuions in weldmens 1 peak r E hs D P M peak A B F C Various sress disriuions in a T-u weldmen wih ransverse fille welds; n C Normal sress disriuion in he weld hroa plane (A), Through he hickness normal sress disriuion in he weld oe plane (B), Through he hickness normal sress disriuion away from he weld (C), Normal sress disriuion along he surface of he plae (D), Normal sress disriuion along he surface of he weld (E), Linearized normal sress disriuion in he weld oe plane (F). 008 Grzegorz Glinka. All righs reserved. 15

16 The IIW reference 1-mm oe and roo radius concep F M = 1 mm peak M 1 P peak The roo and oe regions in welded joins are modelled as a noch wih he ip radius of = 1 mm! 008 Grzegorz Glinka. All righs reserved. 16

17 Recommended FE mesh models for he sress analysis around weld oes and roos having he effecive = 1mm ip radii Recommended elemen size in he ip region s < /4! s s Typical FE mesh for he noch sress analysis around he weld oe region (elemens wih quadraic shape funcion) Typical FE mesh for he noch sress analysis around he weld roo region (elemens wih quadraic shape funcion) 008 Grzegorz Glinka. All righs reserved. 17

18 The recommended IIW faigue S-N curve associaed wih he effecive =1 mm weld oe and roo radius FAT 5 18

19 The Universal GY sress analysis mehod appropriae for any conemporary faigue analysis mehod of weldmens -Nominal sress, S-N -Local elasic-plasic srain and sress, -N -Fracure mechanics, da/dn-k 008 Grzegorz Glinka. All righs reserved. 19

20 The sress sae a he weld oe Muliaxial sae of sress a weld oe One shear and wo normal sresses Due o sress concenraion, xx is he larges componen Predominanly responsile for faigue damage xz zz xx zx xx zz 008 Grzegorz Glinka. All righs reserved. 0

21 p pea r h p k hs D E n h B A P M C Various sress disriuions in a T-u weldmen wih ransverse fille welds; A) remoe (nominal) hrough hickness sress, B) he acual hrough-hickness sress disriuion in he weld oe cross secion, C) linearized hrough-hickness sress disriuion in he weld oe cross secion, D) he acual sress disriuion in he plae surface, E) exrapolaed (linearly) sress disriuion in he plae surface 008 Grzegorz Glinka. All righs reserved. 1

22 Sress magniudes and disriuions oained from various FE models: Wha sress is he righ one for faigue analyses? Fine 3-D FE mesh Experimenal Shell elemens Coarse 3-D FE mesh 008 Grzegorz Glinka. All righs reserved.

23 Wrong Finie Elemen Modeling and wrong resuling sress daa! peak!! nom peak nom FEM peak Srain gauge nom Wha sress for faigue life esimaions? 008 Grzegorz Glinka. All righs reserved. 3

24 The meaning of he nominal (reference) sress and he sress concenraion facor n n V C H K, n peak n p n H A M I r n peak n V C H 008 Grzegorz Glinka. All righs reserved. 4

25 Non-uniqueness of he sress concenraion facor K,n ased on he nominal (ho spo) sress as he reference 1) K ) 1, n K, n!! y 1 1 peak K, n 1 n y peak K, n n = n a1 = n peak x peak x 1 n 1 peak 1, m hs 1, hs n The sress concenraion K,n depends on he memrane o ending sress raio, hsm / hs!! 008 Grzegorz Glinka. All righs reserved. 5 peak, m hs, hs 1 n 1, m, n hs hs 1, m 1, hs hs

26 Inconsisency concerning he definiion of he sress concenraion facor K r n 1 peak ) 1 n m n n T m n n 1 n n 1 n n n m 1 n hs n n n K K K m n n peak m n peak n peak n peak m n n n The sress concenraion m facors, K, and are n K n K no consan and no he same! They depend on he geomery and on he sress raio: m n/ n! a) A ody wih an angular noch sujeced o muliple loading modes and resuling hrough-he-hickness sress disriuion, ) decomposiion of he nominal (linear) sress disriuion in he noch cross secion ino he memrane and ending conriuion 008 Grzegorz Glinka. All righs reserved. 6

27 Universal sress concenraion facor K m.hs and K.hs y a) Pure axial load hs m m peak x F K m, hs m peak m hs K m, hs Kh, s Sress concenraion facors K m,hs and K,hs DO NOT DEPEND on he sress raio m hs/ hs and hey are consan for given geomery!! ) y hs peak x M ) Pure ending load K, hs peak hs 008 Grzegorz Glinka. All righs reserved. 7

28 a) y Universal cominaion of sress concenraion facors independen of he loading mode a peak ) a hs m hs hs x T c) m hs hs a a a m hs m hs hs hs hs d) peak K K, m, hs m hs The sress concenraion facors K, hs hs m K, hs hs and depend only on he geomery and hey m hs / hs can e used for any sress raio!! a) T-u weldmen and resuling hrough-he-hickness sress disriuion, ) decomposiion of he nominal (linear) sress disriuion in he weld oe plae cross secion, c) he ho spo sress as a sum of he ho spo memrane and ending sress, d) he acual peak sress as a sum of he sress concenraion on he ho spo memrane and ending sress 008 Grzegorz Glinka. All righs reserved. 8

29 The ho spo and he weld oe peak sresses The advanage of using expression K peak m m, hs hs K, hs hs lies in he fac ha he memrane sress hsm and he ending sress hs can e deermined y simple decomposiion of he linearized hrough-hickness sress field, (x=0,y), which can e direcly oained from he coarse mesh 3-D or shell Finie Elemen (GY) analysis. Thus he equaion aove provides he link eween he FE sress analysis daa, hsm and hs, and he peak sress, peak, a he weld oe, necessary for he faigue analysis 008 Grzegorz Glinka. All righs reserved. 9

30 Coarse 3D FE mesh model of a welded T-join a = hs! a A Nodal forces F x,i A The linearized sress field ( a, ) is deermined from he disriuion of nodal forces F x,i! (mehod of D. Pingsha, Baelle Columus) 008 Grzegorz Glinka. All righs reserved. 30

31 1 y m n n n (y 1 ) (y i ) n 0 peak n ydy 6 y 0 yy 6 i 1 1 x n ydy y y y i i y n y i y n y i Deerminaion of nominal sresses from discree FE daa y he linearizaion mehod 0 0 n i y 1dy y dy y y P 1 ; n y1 ydy 6 y ydy 6 yyiy cm 1 n 3 I 1 1 m n (y n ) 010 Grzegorz Glinka. All righs reserved. 31 i ;

32 A shell finie elemen and he memrane, m hs, and ending, hs, shell sresses The FE formulaion for shell elemens gives op and oom sresses, op, and oom The sress disriuion hrough he hickness is considered o e linear The memrane and ending sresses are oained from m hs a hs a a op Shell elemen a midplane oom 008 Grzegorz Glinka. All righs reserved. 3

33 a) The use of he FE-shell sress analysis daa: a) welded join; ) shell FE model hs 1 n r m hs hs 1 1 ) Non-unique K (depends on m hs/ hs)! K m peak hs hs hs K 1 Unique K facors depend on geomery only! m m peak K, hs hs K, hs hs 008 Grzegorz Glinka. All righs reserved. 33

34 Single fille weld wihou peneraion; he shell FE model a) c) Middle plane of he aachmen p middle plane of he main plae h h p physical common plane for he aachmen and he main plae y ) 0 y x GY model d) h z 0 x z (h+/) h/ (h/+/) (h/+ p /) (h+ p /) h/ h/ h/ h/ h/ 008 Grzegorz Glinka. All righs reserved. 34 Noe! The recangles wih lue edges are weld simulaing shell elemens wih hickness equal o he hickness of he hinner plae.

35 Single fille weld in doule-overlap ype configuraion; FE model douler middle plane h physical common plane for he douler and he main plae p main plae middle plane ( p / + /) h/ / / / / h 008 Grzegorz Glinka. All righs reserved. 35

36 The memrane, m hs, and ending, hs, ho spo sresses and he weld oe peak sress peak The advanage of using expression K peak m m, hs hs K, hs hs lies in he fac ha he memrane sress hsm and he ending sress hs can e deermined y simple decomposiion of he linearized hrough-hickness sress field, (x=0,y), which can e direcly oained from he coarse mesh 3-D or shell Finie Elemen (GY) analysis. Thus he equaion aove provides he link eween he FE sress analysis daa, hsm and hs, and he peak sress, peak, a he weld oe, necessary for he faigue analysis 008 Grzegorz Glinka. All righs reserved. 36

37 Sress concenraion facor for a u weldmen under axial loading l = h p g = h r P P K en W 1 exp 0.9 h 1 h 1 W W r 1 exp h where: W h0.6h p 0.65 Range of applicaion - reasonaly designed weldmens, (K.Iida and T. Uemura, ref. 14) 008 Grzegorz Glinka. All righs reserved. 37

38 Sress concenraion facor for a u weldmen under ending load l = h p g = h r M M K en W 1 exp 0.9 h r h h p r anh anh 1 W 1 h r exp 0.45 r h where: W h0.6hp Range of applicaion - reasonaly well designed weldmens, (K.Iida and T. Uemura, ref. 14) 008 Grzegorz Glinka. All righs reserved. 38

39 Sress concenraion facor for a T-u weldmen under ension load; (non-load carrying fille weld) Validaed for : 0.0 r/ 0.16 and 30 o 60 o, source [14] 1 = p h p r h x P P K W 1 exp 0.9 h 1 h 1 W W r 1 exp h y 0.65 p p where: W h 0.3 h 008 Grzegorz Glinka. All righs reserved. 39

40 Sress concenraion facor for a T-u weldmen under ending load; (non-load carrying fille weld) Validaed for : 0.0 r/ 0.16 and 30 o 60 o, source [14] 1 = p h p r h x M M K y W 1 exp 0.9 h r h p r anh anh ; 1 W h r exp 0.45 r h where: 008 Grzegorz Glinka. All righs reserved p p W h h

41 T-u weldmen sujeced o pure ension; Monahan s equaion for he dominan sress componen over he enire criical cross secion Where: y 1 3 K n y y 1 r r G K G G E m m m m r y 1 for 0.3 r EmTm 0.94e y for EmT 1E T e m r q 0.18 r 1.05 q0.1 T 0.6 y r 0.3. m m Derived for: 008 Grzegorz Glinka. All righs reserved. 41 m 1 r 1 and and 0 y

42 T-u weldmen sujeced o pure ending; Monahan s equaion for he dominan sress componen over he enire criical cross secion y Where: y K n y y r r G K G G E T r y 1 for 0.4 r ET 0.93e y for ET 1E T e r r 0.9 y r 0.4. Derived for: 1 r 1 and and 0 y Grzegorz Glinka. All righs reserved. 4

43 Theoreical hrough-hickness sress disriuion (Monahan s equaions for mixed mode loading, i.e. simulaneous axial and ending) x 0, y 1 3 m K y 1 1 y 1 1 r r G m hs m x 0, y y K s y y r r G h y m m m K hs K hs y y Gm G r r y y y 008 Grzegorz Glinka. All righs reserved. 43

44 Tuular Welded Join under Torsion and Bending Couresy of John Deere Co. 008 Grzegorz Glinka. All righs reserved. 44

45 Solid and FE model Couresy of John Deere Co. 008 Grzegorz Glinka. All righs reserved. 45

46 Shell Elemen Model Deails nodes elemens (linear quads) dof Follows GY- modeling pracice Maerial: AH Seel (ASTM A500 Cold Formed Seel for Srucural Tuing) Couresy of John Deere Co. 008 Grzegorz Glinka. All righs reserved. 46

47 Through-he-Thickness Sress Disriuion for Uni Load (Loc. 1) 0 Sress in he ue wall (psi) D-FE GY () and Monahan eq Couresy of John Deere Co. Disance from hr weld oe(in) 008 Grzegorz Glinka. All righs reserved. 47

48 Modeling of he residual sress effec KS r N N E - Neuer s rule E KS r E E E 0 d - ESED mehod e e KS r E KS E r r KS E r KS E KS E e KS E E e KS r E 010 Grzegorz Glinka. All righs reserved. 48 KS r E

49 Case Nominal sress S A r < 0! max B B C Time B r = 0! Sress peak y S x Residual Sress Effec on he Sress-Srain Response a he Noch Tip r Case 1 r > 0! A S B r > 0! B max m A 0 m A 0 m m r < 0! C r = 0! C C min min C r A 010 Grzegorz Glinka. All righs reserved. 49

50 Two plaes A and B are conneced y a doule sided u weld. Anoher plae C is welded o plaes A y fille welds as shown in he Figure elow. The plae is sujeced o cyclic loading wih a consan sress range of S = 80MPa. I is assumed ha he faricaion mees he sandard requiremens which allow he maximum misalignmens of he u weld o e e = 3 mm. - Where are faigue cracks mos likely o e expeced? - Wha is he expeced faigue life of he join? Maerial: welded seel ys = 3 MPa, us = 414MPa, E = MPa K = 1097 MPa, n = 0.49 f = 1014MPa, = f = 0.71, c = Example: = u weld, weld oe radius, r = 0.8 mm, = 0mm = fille weld 010 Grzegorz Glinka. All righs reserved. 50

51 S e A B - ending momen a he u weld: M = 10 (S )( e) - ending momen a fille welds: M = 5 (S )( e) 010 Grzegorz Glinka. All righs reserved. 51

52 C S A B S e S R M S M S e RLM 0 M S e S 0e S e R L L R 010 Grzegorz Glinka. All righs reserved. 5

53 C S A B Secion - II Secion - I 5 M 3 S R II M I M W 6 6 S e MI R S e 5 S e MII R75 M 75 S 0e 5S e 5 MI 10S e 3e SI S SI S S S 1 3 W 0 6 MII 5S e 3e SII S SII S S S 1 3 W Grzegorz Glinka. All righs reserved. 53 M S R

54 C S A B Welded join S e Saic represenaion 3e SI S S S 3 SI S 1 S SII S 1 e 3e 010 Grzegorz Glinka. All righs reserved. 54

55 Sress Concenraion Facor for Bu and T-Bu Weldmens under Axial and Bending Load: geomerical parameers and noaion l = h p g = h r Bu weldmen M P P M 1 = p h p T-Bu weldmen r h x M P P M 010 Grzegorz Glinka. All righs reserved. 55 y

56 Bu Weld Sress Concenraion Facors (K.Iida and T. Uemura, ref. 11) = 0mm, g = h = 3.5mm, = 18 o, l = h p = 3mm, r = 0.8 mm Pure Tension (K.Iida and T. Uemura, ref. 11) K 0.65 W 1exp h h ; W W 1 exp r h K. 14 W h0.6h p K W 1 exp 0.9 h r h r anh anh 1 W r 1 3 1exp0.45 r h W h0.6hp Pure Bending K Grzegorz Glinka. All righs reserved. 56

57 Tensile nominal sress S S Nominal ending sress 3e 33 S S S 0.45S 0 Resulan ho spo sress S S S S 0.45S 1.45S hs Ho spo sress hisory S 0, S 116, S 0, S 116,... hs,0 hs,1 hs, hs,3 Ho spo sress concenraion facor K S K S K S K, hs hs, hs K 0.45S K S S0.45 K K ; S K K S K K S 1.45S hs 0.45K K s reversal 0 = 0, 0 = 0, = MPa; 1 = ; 1 = = = MPa; 1 = = = nd reversal 1 = , 1 = = MPa; = ; = 1 - = = MPa; = 1 - = = Grzegorz Glinka. All righs reserved. 57

58 m MPa ' f m ' E N f f N f c N f N f N f cycles (end of u weld) 010 Grzegorz Glinka. All righs reserved. 58

59 Fille Weld Sress Concenraion Facors (K.Iida and T. Uemura, ref. 11) = 0mm, g = h = 3.5mm, = 18 o, l = h p = 3mm, r = 0.8 mm Pure Tension K 0.65 W 1exp h h ; W W 1 exp r h Pure Bending K p p W h h K W 1 exp 0.9 h r h r anh anh p 1 W h r 1 r3 1exp0.45 h W h h p p K. 010 Grzegorz Glinka. All righs reserved. 59

60 Tensile nominal sress S S Nominal ending sress 3e 33 S S S 0.5S 0 Resulan ho spo sress S S S S 0.5S 1.5S hs Ho spo sress hisory S 0, S 98, S 0, S 98,... hs,0 hs,1 hs, hs,3 Ho spo sress concenraion facor K S K S K S K, hs hs, hs K 0.5S K S S0.5 K K ; S K K S K K S 1.5S hs 0.5K K s reversal 0 = 0, 0 = 0, = MPa; 1 = ; 1 = = = MPa; 1 = = = nd reversal 1 = , 1 = = MPa; = ; = 1 - = = MPa; = 1 - = = Grzegorz Glinka. All righs reserved. 60

61 m MPa ' f m ' E N f f N f c N f N f N f cycles (end of fille weld) 010 Grzegorz Glinka. All righs reserved. 61

62 Fracure Mechanics Approach o Faigue Analysis of Weldmens (da/dn-k) 010 Grzegorz Glinka. All righs reserved. 6

63 Informaion pah for faigue life esimaion ased on he da/dn-k mehod F LOADING GEOMETRY, K PSO 0 MATERIAL E Sress-Srain Analysis MATERIAL Damage Analysis da dn n K h K Faigue Life 008 Grzegorz Glinka. All righs reserved. 63

64 Seps in he Faigue Life Predicion Procedure Based on he da/dn-k Approach a) Srucure e) Sress, S S 3 S 4 ) Componen S 1 Q H F S S 5 c) Secion wih welded join Weld R V P d) 008 Grzegorz Glinka. All righs reserved. 64

65 Seps in Faigue Life Predicion Procedure Based on he da/dn-k Approach (con d) i) f) (x, y) Sress inensiy facor, K (indirec mehod) Weigh funcion, m(x,y) K A K Y a n,, x y m x y dxdy a f Crack deph, a a i Faigue Life Sress inensiy facor, K (direc mehod) Numer of cycles, N g) a K x I yfe FE n or du K E EG da K Y a h) Inegraion of Paris equaion f 0 i1 m a C K N i i i N a a a N N i i 008 Grzegorz Glinka. All righs reserved. 65

66 Maerial properies used in faigue analyses of weldmens y he Fracure Mechanics Mehod (da/dn-k) 010 Grzegorz Glinka. All righs reserved. 66

67 Residual Sress Disriuions in Welded Joins; Bu Weldmens Specimens Residual sress disriuions Welds 007 Grzegorz Glinka. All righs reserved. Page 67

68 Residual Sress Effec on he Faigue Crack Growh Rae (Specimens P and L and U) 007 Grzegorz Glinka. All righs reserved. Page 68

69 Faigue cracks in weldmens may grow hrough he HAZ u mos ofen hey iniiae in he HAZ u grow away from he weld and hrough he ase meal. Therefore he Base Meal faigue crack growh properies are used for faigue crack growh analysis of weldmens. da C K dn m Where: C and m - Base Meal properies 010 Grzegorz Glinka. All righs reserved. 69

70 Calculaion of Sress Inensiy Facors (K) for Cracks in Weldmens 010 Grzegorz Glinka. All righs reserved. 70

71 There are wo mehods availale for oaining sress inensiy facors for cracks in weldmens: a) The Handook ready made sress inensiy facors K for cracks in weldmens like he handook of SIFs y Y. Murakami e. al, (edior), Sress Inensiy Facors Handook, Pergamon Press, Oxford, 1987 (unforunaely he numer of soluions for cracks in weldemns is very limied); The ready made K soluions are usually oained for fixed geomery (such as specific geomerical dimensions of he weld) and hey can e used for esmaing he K facor resulin from residual sresses. ) The Weigh Funcion (WF) mehod; The WFs make i possile o solve a wide variey of K prolems for cracks in weldmens y using a very limied numer of general weigh funcions. The same WF can e used for he esimaion of K facors associaed wih he presence of residual sresses. 010 Grzegorz Glinka. All righs reserved. 71

72 Handook SIF K=S(a)Y; Y form he handook 008 Grzegorz Glinka. All righs reserved. 7

73 The Effecive and he Residual Sress Inensiy Facors in a Bu Weldmen S K S a Y and K ( x) m( x, a) dx S r a 0 r Weld r (x) S 007 Grzegorz Glinka. All righs reserved. Page 73

74 Tuular Welded Join under Torsion and Bending Couresy of John Deere Co. 008 Grzegorz Glinka. All righs reserved. 74

75 Shell Elemen Model Deails nodes elemens (linear quads) dof Follows GY- modeling pracice Maerial: AH Seel (ASTM A500 Cold Formed Seel for Srucural Tuing) Couresy of John Deere Co. 008 Grzegorz Glinka. All righs reserved. 75

76 FE Shell Linear Sress Field for Uni Load- Loc GYl () 8 Sress in he ue wall (psi) hs m hs Disance from he weld oe (in)

77 Theoreical hrough-hickness sress disriuion (Monahan s equaions for mixed mode loading, i.e. simulaneous axial and ending) x 0, y 1 3 m K y 1 1 y 1 1 r r G m hs m x 0, y y K s y y r r G h y m m m K hs K hs y y Gm G r r y y y 008 Grzegorz Glinka. All righs reserved. 77

78 Through-he-Thickness Sress Disriuion for Uni Load (Loc. 1) 0 Sress across he ue wall (psi) D-Fine mesh FE model Shell FE coarse mesh model Disance from he weld oe (in) Fig.15

79 Residual Sress Disriuion Through hickness residual sress disriuion (ksi) Through hickness disance from he weld oe (in) Fig. 17

80 Simulaed Faigue Crack Growh and Faigue Crack Evoluion in a Weldmen Based on he Non-Linear Through-he-Thickness Sress Disriuion a [in] 0.3 a/c 1.0 Crack deph 0. a -N 0.1 a/c - N Grzegorz Glinka. All righs reserved. 80 Cycles N f 0

81 Experimenal and Simulaed Faigue Crack Growh Curves (c-n) Welded Join wih Load = 4000 l (a i /c i =0.86) r = 45 ksi r = 0 ksi Crack Lengh c (in) Pred. Loc.1 Wih Res Pred. Loc.1 No Res Exp. Spec. #11 Exp. Spec. #1 Exp. Spec. #14 Exp. Spec. #15 Exp. Spec. #16 Exp. Spec. #17 Exp. Spec. # Faigue life N (cycles)

82 Geomery of he real final faigue crack

83 This is proaly all.. wha I waned o say Thank You! 007 Grzegorz Glinka. All righs reserved. Page 83