Bending tests of fillet welded cruciform specimens in constant and variable amplitude loading.

Transcription

1 Lehigh University Lehigh Preserve Theses and Dissertatins Bending tests f fillet welded crucifrm specimens in cnstant and variable amplitude lading. Crnelia Elisabeth Demers Fllw this and additinal wrks at: Part f the Civil Engineering Cmmns Recmmended Citatin Demers, Crnelia Elisabeth, "Bending tests f fillet welded crucifrm specimens in cnstant and variable amplitude lading." (1980). Theses and Dissertatins. Paper 214. This Thesis is brught t yu fr free and pen access by Lehigh Preserve. It has been accepted fr inclusin in Theses and Dissertatins by an authrized administratr f Lehigh Preserve. Fr mre infrmatin, please cntact preserve@lehigh.edu.

2 BENDING TESTS F FILLET WELDED CRUCIFRM SPECIMENS IN CNSTANT AND VARIABLE AMPLITUDE LADING by Crnelia Elisabeth Demers A Thesis Presented t the Graduate Cmmittee f Lehigh University in Candidacy fr the Degree f Master f Science in Civil Engineering Lehigh University 1984

3 PrQuest Number: EP76590 All rights reserved INFRMATIN T ALL USERS The quality f this reprductin is dependent upn the quality f the cpy submitted. In the unlikely event that the authr did nt send a cmplete manuscript and there are missing pages, these will be nted. Als, if material had t be remved, a nte will indicate the deletin. uest PrQuest EP76590 Published by PrQuest LLC (2015). Cpyright f the Dissertatin is held by the Authr. All rights reserved. This wrk is prtected against unauthrized cpying under Title 17, United States Cde Micrfrm Editin PrQuest LLC. PrQuest LLC. 789 East Eisenhwer Parkway P.. Bx 146 Ann Arbr, Ml

4 CERTIFICATE F APPRVAL This thesis is accepted and apprved in partial fulfillment f the requirements fr the degree f Master f Science. ((date) Prfessar in Charge Chairman f Department ii

5 ACKNWLEDGMENTS I wuld like t express gratitude t Prf. Jhn W. Fisher fr his guidance in the executin and interpretatin f this research and fr his encuragement.. His enthusiasm during ur meetings and discussins. made my research a persnally and prfessinally rewarding experience. I wuld like t extend a special thank yu t the Chairman f the Department, Dr. David Van Hrn and Prf. Ben Yen. I have greatly appreciated their supprt. The discussins with my clleagues at Fritz Engineering Labratry were helpful and appreciated. Fr the assistance with the testing f the specimens, special typing, and preparatin f the drawings and phtgraphs, I thank the Fritz Labratry persnnel. Finally, I wuld like t express heartfelt gratitude t my parents - their lve, encuragement, and advice are invaluable and have made my career a success. iii

6 TABLE F CNTENTS ABSTRACT 1 1. INTRDUCTIN ' 1.1 Summary f Fatigue Tests n Nn-Lad Carrying Fillet We'lds 1.2 Research bjective 4 2. GENERAL ASSUMPTINS AND FINITE. ELEMENT MDELING Stress Cncentratin, K Stress Gradient Crrectin Factr, F 9 g. THER CRRECTIN FACTRS: F, F, F 11 e s w Page.1 Fatigue Crack Prpagatin: Stage Fatigue Crack Prpagatin:' Stage Fatigue Crack Prpagatin: Stage FATIGUE LIFE Stress-Intensity Range, AK Fatigue Life Estimate S -N Relatinships ' 18 r _ r 5. EXPERIMENTAL WRK DISCUSSIN SUMMARY AND CNCLUSINS 26 NMENCLATURE 29 TABLES 1 FIGURES > 9 REFERENCES 71 BIGRAPHICAL NTE 7 IV

7 LIST F TABLES Table Page 1 Calculatin f F 2 g 2 Calculatin f F(a) fr Specimen #12 Stress Rati and Threshld Stress Intensity Range 4 fr All Crucifrm Specimens 4 Fatigue Life Calculatins fr Specimen # Mean Stress, Stress Range, Stress Rati, and 6. Fatigue Life f Crucifrm Specimens Under Cnstant Amplitude Lading 6 Mean Stress, Maximum Stress, Minimum Stress, 7 Effective Stress^Range, Stress Rati, and Fatigue Life f Crucifrm Specimens Under Variable Amplitude Lading 7 Specimens Under Cnstant Amplitude Lading 8 with Similar S

8 LIST F FIGURES Figure Page 1 Summary f Cnstant Amplitude Fatigue Test Data A n Nn-Lad Carrying Fillet Welds 2 Summary f Variable Amplitude Fatigue Test Data Al n Nn-Lad Carrying Fillet Welds () Fatigue Crack Grwth Study Stress Spectrum A2 A Crucifrm Specimen fr Finite Element Analysis A 5 Carse Mesh AA 6 Fine Mesh A5 7 Ultra-Fine Mesh A6 8 Stress Cncentratin Factr amd Stress Gradient A7 Crrectin Factr Alng Crack Path 9 Stress Intensity Factr fr a Thrugh Crack A8 Under Bending 10 Frnt Free Surface Crrectin Factr and A9 Crack Shape Crrectin Factr 11 Specimen 11 Cnstant Amplitude Lading, R = Specimens 9 and 10 Cnstant Amplitude Lading, 51 R = Specimens A and 5 Variable Amplitude Lading, 52 R = 0.A7, 0.61 > 1A Specimen 12 Cnstant Amplitude Leading, R = Specimen 6 Variable Amplitude Lading, R = 0.A28 5A 16 Specimen 1A Cnstant Amplitude Lading, R = 0.AA Specimens 2, and 7 Variable Amplitude Lading, 56 R = 0.AA8, 0.A52, 0.AAA 18 Specimen 15 Cnstant Amplitude Lading, R = 0.A58 57 VI

9 Figure Page 19 Specimen 1 Cnstant Amplitude Lading, R = Specimen 8 Variable Amplitude Lading, R = Specimen 1 Variable Amplitude Lading, R =' Specimens 22 and 24 Cnstant Amplitude Lading, 61 R = Specimens 2, 25 and 27 Cnstant Amplitude Lading, 62 R = Speciments 16, 17 and 19 Cnstant Amplitude Lading, 6 R = Specimens 18, 20 and 21 Cnstant Amplitude Lading, 64 R = Specimen 26 Cnstant Amplitude Lading, R = Crucifrm Specimen in Test Setup Typical Crucifrm Specimen Crack Surface Frnt and Back. Weld Prfiles f the Tensin Weld 68 Angle Where the Fatigue Crack Initiated 0 Frnt and Back Weld Prfiles f the Tensin Weld 69 Angle Where the Fatigue Crack Initiated 1 Frnt and Back Weld Prfiles f the Tensin Weld 70 Angle Where the Fatigue Crack Initiated 2 Frnt and Back Weld Prfiles f the Tensin Weld 71 Angle Where the Fatigue Crack Initiated Frnt and Back Weld Prfiles f the Tensin Weld 72 Angle Where the Fatigue Crack Initiated VII

10 ABSTRACT The fatigue behavir f welded crucifrm specimens under bending with, cnstant and variable amplitude blck lading is examined. The crucifrms are cnstructed frm A514 steel. The welds are nn-lad carrying fillet welds and classify as a Categry C detail. A mathematical mdel is btained t predict fatigue life which is cmpared with test data fatigue life. The mdel estimates upper and lwer bund fatigue lives based n upper and lwer bund values f unknwn initial crack size and material cnstant. Included in the mdel are crrectin factrs, F, F_, F, and F_. Thrugh the c W g upper and lwer bund fatigue lives, S r -N curves are cnstructed prviding an estimated S -N regin int which the fatigue test data culd fall. Ninety-six percent f the test data either fell within the estimated regin r between the estimated regin and the Categry C detail S -N curve. The test data cmpare favrably with the previus cnstant and variable amplitude tests n nn-lad carrying fillet welds. Labratry tests were cnducted fr varying mean stresses f MPa (22.1 ksi) t MPa (64.80 ksi). A* increased mean stress simulates the presence f residual welding stresses.

11 The stress ranges varied frm 89.6 MPa (12.96 ksi) t 29.8 MPa (4.78 ksi). The effective stress ranges varied frm MPa (12.72 ksi) t MPa (21.60 ksi). Threshld stress ranges ccur at: MPa fr a mean stress f MPa; MPa, MPa, and MPa fr a mean stress f MPa; 89.6 MPa fr a mean stress f MPa. Fifty-six percent f all the fatigue cracked specimens failed at the weld te f the larger weld angle. Sixty-seven percent failed at a tensin weld te where the strain gage was attached. Thirty-nine percent failed at bth the te f the larger tensin weld angle and the te where the strain gage was attached.

12 1. INTRDUCTIN 1.1 Summary f Fatigue Testa n Nn-Lad Carrying Fillet Welds Tests n bending specimens under cnstant cycle lading have been reprted by Gergd) and Mueller(2). The summary f cns. :nt amplitude fatigue tests n nn-lad carrying fillet welds cmpeted f structural carbn steel (ST7 and A6) and high strength lw ally steel (St52) is shwn in Fig. 1 (). The test data vary in fatigue resistance frm the lwer bund Categry C detail t beynd the Categry B detail. The current bending tests n A514 steel crucifrm specimens are represented by pen circles in Fig. 1. Generally, these cnstant cycle tests prvide fatigue resistances cmparable with thse previusly reprted. The summary f variable amplitude fatigue test data n nn-lad carrying fillet welds is shwn in Fig. 2 (). The A588 steel crucifrm specimens were subjected t tensin tests as reprted by Albrecht(4). The randm variable stress range spectrum represented a skewed distributin and a rt-mean-cube stress range was used. These variable lad tests ' prvided fatigue resistances near the Categry B detail. The current bending tests cnducted n A514 steel are shwn as dts in Fig. 2. The variable amplitude randm blck lading sequence was the same as used by Zhng in Reference. A Rayleigh distributin represented the lad range spectra frequency f ccurrence as shwn in Fig. - Eight stress range levels

13 apprximated the distributin and the lad levels were randmized int 150 blcks. Within each f the 150 blcks, 960 cnstant amplitude cycles f lad were applied. The effective stress range, S, was defined by the rt-mean-cube stress range. These tests prvided fatigue resistances between the lwer bund Categry C detail and upper bund Categry B detail. 1.2 Research bjective This thesis fcuses n the cnstant and randm variable amplitude blck lading f welded crucifrm specimens subjected t bending tests. The crucifrms are cnstructed frm tw lateral attachments fillet welded t a lngitudinal bar, all f A514 steel as illustrated in Fig. 4. The welds are nn-lad carrying fillet welds. The residual welding tensin stresses are negligible due t the size f the crucifrm specimens. The attachments classify the weld regin as a Categry C detail. r The main bjective is t expand the knwledge n the fatigue behavir f cnstant and variable amplitude lading f crucifrm specimens under bending. The fatigue lives f bending specimens can be predicted with a mathematical mdel using: a finite element analysis t evaluate the stress cncentratin due t the welds and attachments; basically Green's functin t evaluate the stress gradient crrectin factr; the Maddx relatinship t evaluate the crack shape fr the crack shape crrectin factr; fracture / i,

14 mechanics principles t evaluate the stress intensity range which includes F, F s, F e, and F w ; and a rearrangement f the Paris Pwer Law t evaluate the fatigue life. The stresses used in the mathematical mdel were assumed the result f the applied lads withut residual welding stresses. Based n the abve, S -N curves were cnstructed thrugh the predicted fatigue lives. The S -N curves were cmpared with labratry fatigue tests. The tests were cnducted t determine the fatigue life behavir fr. varius stress ranges and varius mean stresses. An increased mean stress was used t simulate the presence f residual welding stresses. A ttal f 8 variable amplitude tests and 19 cnstant amplitude tests were cnducted.

15 2. GENERAL ASSUMPTINS AND FINITE ELEMENT MDELING The crucifrm used in this tudy is illustrated in Fig. 4. These crucifrm specimens were btained frm a previus study by Frank(5). The crucifrms were fabricated frm A514 steel plates. Tw 16mm x 50mm x 610mm plates were submerged arc welded with 12mm fillet welds t each side f a 610mm x 5mm plate. The individual crucifrm specimens were btained by saw cutting and milling the plates t a 0.5mm width. The welds are classified as nn-lad carrying welds. Residual welding stresses were assumed negligible due t the size f the crucifrm specimens. Fr mdeling purpses, the weld surface is cnsidered flat frming an angle f TT/4 with the main lngitudinal surface. The crucifrm material, including the weld, is assumed linear, istrpic, and hmgeneus. Yung's mdulus is taken as MPa (0000 ksi) and Pissn's rati as 0. The cmputer analysis is cnducted using SAP IV(6), a finite element cmputer prgram fr linear elastic systems. The results f the prgram give the stresses alng the crack path. These stresses are then used in the determinatin f the stress cncentratin factr, K fc. The weld te is a lcatin f stress singularity where the

16 elastic stress and stress cncentratin increase as the distance t the weld te decreases. SAP IV des nt cntain elements fr stress singularity; hwever, the prgram can be used prviding the finite element mesh at the weld te is n larger than the size f the initial flaw, a i. The minimum initial flaw size is mm (0.001 in.) and is taken as 0.047mm (0.0Q172 in.) fr the finite element analysis(7). The crucifrm is initially mdeled with a carse mesh as shwn in Fig. 5. The weld te regin is substructured int a fine and ultra-fine mesh as shwn in Figs. 6 and 7. The heavy lines in Figs. 6 and 7 shw the superimpsed previus mesh discretizatin. The carse mesh is cmpsed f the eight nde brick element. A vertical plane f symmetry exists at the crucifrm half length; therefre, nly ne-half the crucifrm length needs t be mdeled in the carse mesh. At the vertical plane f symmetry, hrizntal displacements are prevented. The lading is applied as a cncentrated lad. The fine mesh is cmpdsed f planar elements and mdels a small regin f the weld te frm the carse mesh. This regin is the shaded elements frm Fig. 5 and is taken at the crucifrm half width, D/2. Figure 6 shws the fine mesh discretizatin. The lading is input via displacements frm the carse mesh analysis. The ultra-fine mesh as shwn in Fig. 7, mdels a smaller regin f the weld te frm the fine mesh and is cmpsed f planar elements. Lading is input via displacements frm the fine mesh analysis. Fr bth the fine and ultra-fine

17 meshes, hrizntal and vertical displacements at new ndes alng the inside brders are linearly interplated frm the superimpsed previus mesh element ndes. The planar elements are taken t have a plane stress elasticity matrix; therefre, plane stress elements are used(7). The SAP IV analysis stresses used t evaluate the stress cncentratin are the principal tensile stresses. These principal tensile stresses are the average between principal stresses f adjacent finite elements alng the crack path. The d-irectin f the crack path is defined by a vertical plane thrugh the weld te. The assumptin f a cmpletely vertical crack path is in slight disagreement with the crack path f the crucifrm test specimens. The crack path grew perpendicular t the principal tensile stress. Appximately 2.50mm (0.098 in.) f the crack path deviated frm the assumed vertical. In this regin the principal tensile stress differed frm the tensile stress perpendicular t the vertical plane by ten percent and in directin by abut twenty degrees. 2.1 Stress -Cncentratin, K t The nminal stresses alng the crack path are calculated frm M -f (1)

18 The stress cncentratin alng the crack path results frm the finite element stress divided by the nminal stress at the crrespnding lcatin. The stress cncentratin curve is pltted with respect t the crack depth divided by the thickness f the lngitudinal bar. The curve is nn-dimensinalized. Figure 8 illustrates that less than eleven percent f the lngitudinal bar depth experiences a stress increase as a result f the lateral attachments and welds. As the crack depth increases, the K. curve decreases rapidly t a value apprximately The maximum stress cncentratin factr (SCF) at the weld te is fund by extraplating thrugh the stress cncentratin values alng the crack depth using a furth rder plynmial fit. The SCF btained frm the analysis is The bttm tw K fc values frm the fine and ultra-fine meshes are neglected due t bundary irregularities. 2.2 Stress Gradient Crrectin Factr, F Green's functin is used t evaluate F, the stress gradient crrectin factr. As suggested by Albrecht(8), the relatinship between stress intensity and stresses n a crack plane is: *? / 2 f i K = a Aa - d<l (2) 77 J \H ^ av a - I

19 Frm this F can be defined and evaluated as: 8 a K * ' fjz " 2 ' '//T^41 <) F can als be evaluated by a numerical slutin: F -1> K. 1. arc sin i±i_ J arc sin J - a a (4) where: K. =averaged K t between tw adjacent finite elements f equal distance frm the crack plane. I.,I =distance t the near and far side f finite element j as measured frm the crack rigin. m =number f finite elements alng the crack plane describing crack length 'a*. Table 1 summarizes the results f the F calculatins.^ Figure 8 shws F pltted with respect t the crack depth divided by the thickness f the lngitudinal bar. The F curve decays less rapidly than the K fc curve. As the crack depth increases the stress gradient crrectin decays t a value apprximately 1.0. Abut nine percent f the lngitudinal bar thickness will have a large stress gradient crrectin factr. 10

20 . ther Crrectin Factrs: F^, F Q, F All f the crrectin factrs, F, F e, F, and F s, are needed t determine the stress intensity factr, K. Values fr F-, F_, and F have been tabulated in Reference 9 fr varius crack shapes and stress distributins alng the crack path; hwever, these values assume a unifrm tensin lading(9). The crucifrm used in this study is a bending specimen. In additin t the linear stress distributin frm bending, eleven percent f the bar thickness experiences a stress increase due t the stress cncentratin frm the weld te. The stress distributin changes as the crack grws and als the crack shape. The crack shape prpagates frm an assumed initial semi-elliptical surface crack t a thrugh crack at failure. Therefre, F a and F will change accrding t crack length and can nt be cnsidered a cnstant value ver the fatigue life f the crucifrm. The stress intensity factr fr a thrugh crack under bending as given in Fig. 9 is(10): K = 0 /rra F(<*) (5) 11

21 . ther Crrectin Factrs: F e, F, F w All f the crrectin factrs, F, F, F, and F, are needed g e W 5 t determine the stress intensity factr, K. Values fr F g, F, and F have been tabulated in Reference 9 fr varius crack shapes and stress distributins alng the crack path; hwever, these values assume a unifrm tensin lading(9). The crucifrm used in this study is a bending specimen. In additin t the linear stress distributin frm bending, eleven percent f the bar thickness experiences a stress increase due t the stress cncentratin frm the weld te. The stress distributin changes as the crack grws and als the crack shape. The crack shape prpagates frm an assumed initial semi-elliptical surface crack t a thrugh crack at failure. Therefre, F g and F s will change accrding t crack length and can nt be cnsidered a cnstant value ver the fatigue life f the crucifrm. The stress intensity factr fr a thrugh crack under bending as given in Fig. 9 is(10): K = a /rta F(=) (5) 11

22 where: fc ~ (l - sin g) ^ = / tan T* (6) \ cs 2T The crrectin factr, F(<x), takes int accunt the frnt and back surface crrectin factrs, F g and F w, but nt the stress gradient crrectin, F. and crack shape, F, factrs. F(<x) is a functin f 6 e crack depth as F, F s, F w, and F g are. Initially, F( «) is calculated fr specific crack depths with F w under bending and F s taken as a cnstant value. F s is estimated as a cnstant crrespnding t a linear stress distributin ver a thrugh crack as seen in Fig. 10 and is remved frm F(<x) (9). F(«) accunts nw fr F and can be adjusted fr varying values f F, F, and F t w e s g btain the ttal crrectin factr, F(a), fr varying crack depths. The incremental crack grwth used is the same as fr the stress gradient crrectin factr calculatins and will be ' used fr subsequent calculatins. The fllwing estimated F Q and F values are frm Fig. 10. F and F will be divided int three stages fr the crucifrm life. These three stages are represented in Fig

23 .1 Fatigue Crack Prpagatin: Stage 1 Stage 1 crrespnds t an initial flaw prpagating as a semielliptical crack. F e is calculated frm the elliptical integral which is a functin f the elliptical crack's minr axis semidiameter, a, t majr axis semidiameter, c, rati a/c. As the, crack prpagates, the crack depth r minr axis semidiameter a increases and the crrespnding value f c is(12): c = a (in.) (7) Reference 11 prvides tabulated values f a/c, E k, and F and is reprduced in Fig. 10. F g crrespnding t an a/c value is btained by linear interplatin frm the values given in Fig. 10 (11). The initial flaw is in a regin f high stress cncentratin which can be represented between a cncentrated lad n the crack rigin and as the crack prpagates a linear stress distributin ver the crack frnt. F s is taken fr the half-circular crack as the average between the cncentrated lad and linear stress distributin as

24 .2 Fatigue Crack Prpagatin: Stage 2 Stage 2 crrespnds t the crack prpagating as a semielliptical crack. F Q is determined as described,, in Stage 1. The crack has prpagated ut f the high stress cncentratin regin f stage 1, but nt cmpletely ut f the ttal stress cncentratin regin. Additinal stress due t the stress cncentratin is superimpsed n the linear stress distributin due t bending. The crack frnt lading can be represented between a linear and unifrm stress distributin. F is taken fr the half-circular crack as the average between the linear and unifrm stress distributins as Fatigue Crack Prpagatin: Stage Stage is the final phase f crack grwth. The. semielliptical crack grws int a thrugh crack. F is determined as described in Stage 1. The crack has prpagated ut f the stress cncentratin regin. The crack frnt lading is a result f the bending stress. F s, fr the half-circular crack between the unifrm and linear stress distributins but clser t the linear distributin, is taken as An example f F(a) is tabulated in Table 2 fr specimen #12. Frm all the crrectin factrs cmprising F(a), F_ has the mst ) s certainty in its value. 14

25 4. FATIGUE LIFE The fatigue life f a specimen is the result f the crack initiatin and crack prpagatin phases. Part f the fatigue life is spent initiating a fatigue crack and the remainder prpagating the crack t its critical size. A mathematical mdel which results in a theretical crack prpagatin fatigue life can be used t predict test data fatigue life. The theretical crack prpagatin life is a functin f a material cnstant and stress intensity range integrated ver the crack length as(11): (8) Fr the integratin prcess, an initial crack size must be present. Therefre, the mdel des nt take int accunt the crack initiatin phase. The initial crack size can range frm mm (0.001 in.) t mm (0.0 in.). The integratin prcess t btain fatigue life can be c accmplished by taking incremental crack grwth, Aa, t btain incremental fatigue life, AN, by(11): Aa AN = C(AK) n (9) 15

26 The ttal fatigue life is the summatin f incremental life ver the ttal crack depth 6.27mm. 4.1 Stress Intensity Range, AK The stress intensity range, AK, is a functin f: the crrectin factrs, F(a); bending stress range, S r fr cnstant amplitude lading and S re fr.variable amplitude lading; and crack., length, a; in(11): AK = S /ira F(a) (10) The stress intensity range uses the average f each incremental crack length ver a range f crack lengths giving a ttal crack depth f 6.27mm (0.249 in.). These incremental lengths and final crack depth crrespnd t thse used in the finite element mdel t btain F. Fr all the crack increments, the stress intensity range must be greater thanthe threshld stress intensity range, AK fch. The threshld indicates a level belw which cracks d nt prpagate. The initial crack size crrespnds t either the minimum mm r the crack size fr which AK is equal t r greater than AK^. The AK th as determined by Barsm is(1): AK th = 7 ( R) (MPa) (11) 16

27 The variable R represents the stress rati defined as: R = f^ (12) rmax The stress rati fr the crucifrm specimens is based n the applied lads withut residual welding stresses. The residual welding stresses are cnsidered negligible due t the small crucifrm specimen size. The R and AK fch values fr each specimen is given in Table. 4.2 Fatigue Life Estimate The ttal fatigue life is the summatin f incremental fatigue life in equatin 9. Variable n, the negative slpe f the lg-lg S r -N curve, is knwn t be.0 fr all specimens(14). The incremental crack grwth used is the same as fr the stress gradient crrectin factr. The material cnstant, C, and initial crack size, a^, are nt knwn. These variables are dependent n the material and weld defects f each crucifrm specimen and are therefre uncntrlled variables. The variatin in material -1 cnstant has been limited t an upper bund 1.211x10 J cc- -10 c c ~) mnr* -VfPcycle (2x10 in.-\"ykips- > cycle) and lwer bund 2.179x10" 1 mm 5,5 /N cycle (.6x10" 1 in. 5,5 /kips cycle) value(15). The initial crack size is als limited t an upper bund mm (0.001 in.) and lwer bund mm (0.0 in.) value(7). Cmbining the upper bund C and a, values and the lwer bund C and a^ values, i> 17

28 an upper bund and lwer bund fatigue life fr a given stress range can be estimated. Fr each stress range tested, an upper bund fatigue life was btained using the Upper bund C and upper bund a^, r an a. such that AK is greater than AK... A secnd life was btained fr Cr2.179x10~ 1 and a.^0.5080mm (0.02 in.). A lwer bund fatigue life was btained using the lwer bund C and lwer bund a-. Table 4 illustrates the fatigue life calculatins fr specimen #12, 4. S-N Relatinships Fr a given stress range, the three theretical fatigue lives btained in the previus sectin are a result f varying the material cnstant, C, and initial crack size,-a.,. Upper and lwer bund fatigue lives fr a given stress range were estimated frm these assumed cnditins. Thrugh these upper t lwer bund fatigue life estimates, three S r -N curves each with a slpe f - can be cnstructed( 14). Crrespnding t the three initial crack sizes used t estimate the upper t lwer bund fatigue lives fr a given stress range, three threshld stress ranges, S th, can be determined. Th'e S rth is the hrizntal extensin f the S r -N curve f the same a^. The S t^ is, fr a given a^, the stress range belw which cracks d nt prpagate. The tw S r -N curves crrespnding t the upper and lwer limit a^ fr a given S, bund an estimated regin int which the test data fr that S r culd fall. The three S p -N curves fr each stress range tested have been cnstructed and 18

29 are shwn in Figs. 11 t 26. Figures 11 t 26 were individually cnstructed fr a given stress rati. Crucifrm specimens f variable amplitude lading with the same S re were pltted in the same figure. The mean stress varied slightly due t the i.n ividual respnse f the specimens t the lading. The stress rati varied slightly; hwever, the slight difference in stress rati was nt appreciable t cnstruct separate plts. The slping prtin f the three S -N curves is the same thrughut the stress ranges tested. The difference amng the stress ranges tested is the extensin f the slping prtin f the S -N curve t the apprpriate S ^. 26 (14). The Categry C detail S r -N curve is als shwn in Figs. 11 t 19

30 5. EXPERIMENTAL WRK The Amsler Vibrphre was used t lad the crucifrms. The test setup is shwn in Fig. 27. n each specimen, a mm ( inch) strain gage was attached as clse as pssible t a weld te in tensin in rder t cmpare the crucifrm lading with the applied vibrphre lad. A static test was als cnducted t cmpare the stress alng the crucifrm half length as measured by strain gages with the predicted stress fr a given lad. As a result f the static test the vibrphre stress readings were calibrated fr a reductin in stress. The stress ranges used in the cnstant cycle amplitude tests varied frm 89.6 MPa (12.96 ksi) t 29.8 MPa (*1.78 ksi). The mean stresses used were MPa (22.29 ksi), MPa (60.48 ksi), and MPa (64.80 ksi). The stress range, stress rati and fatigue life fr each crucifrm specimen tested under cnstant amplitude lad is given in table 5. The mean stress, maximum stress, minimum stress, effective stress range, stress rati, and fatigue life f the crucifrm specimens under variable amplitude lading is tabulated in Table 6. The effective stress ranges varied frm MPa (12.72 ksi) t MPa (21.60 ksi). The mean stresses varied frm MPa (22.1 ksi) t MPa (2.19 ksi). The stress range versus fatigue life f each crucifrm test is pltted in Figures 11 t 26 with the apprpriate upper and lwer bund S -M curves. 20

31 Failure f the crucifrms ccurred when the stress range culd nt be maintained. The fatigue crack at failure prpagated apprximately halfway thrugh the bar thickness as shwn in Fig. 28. Fr each fatigue crack, the weld prfile and the weld te where the fatigue crack initiated is shwn in Figures 29 t. 21

32 6. DISCUSSIN Figures 29 t shw the weld prfiles where the fatigue cracks initiated. N fatigue cracks initiated and prpagated fr runut specimens 1,, 1, 15, 19, 20, 2, 26, and 27. As expected, the fatigue cracks initiated at a weld te subjected t tensin lading; hwever, nt all f the fatigue cracks were lcated at the weld te f the larger weld angle. There is sme scatter present in the fatigue- crack lcatin. A fatigue crack initiated at the te f the larger weld angle fr specimens 4, 5, 7, 8, 10, 14, 17, 21, 22, and 24. As the weld angle increases, the stress cncentratin at the weld te increases(11). An initial flaw in the greater stress cncentratin regin wuld grw int a fatigue crack and prpagate. This is apparently true prvided the greatest initial flaw is in the greatest stress cncentratin regin. Hwever, the size and lcatin f the initial flaw is variat.. It is the variable cmbinatin f unknwn initial flaw size and stress cncentratin that prvides scatter in the fatigue crack lcatin. The scatter present is illustrated in specimens 2, 6, 9, 11, 12, 16, 18, and 25 where the fatigue cracks initiated at the te f the smaller weld angle. Therefre, fifty-six percent f all the fatigue cracked specimens failed at the weld te f the larger weld angle and frtyfur percent failed at the weld te f the smaller weld angle. ut f all the fatigue cracked specimens, sixty-seven percent failed at the weld te where the strain gage was attached. Specimens 2, 4, 6, 22

33 7, 14, 16, 17, 18, 21, 22, 24, and 25 represent the sixty-seven percent which failed at either the weld te f the larger r smaller weld angle where the strain gage was attached. Thirty-nine percent f all the fatigue cracked specimens failed at the weld te f bth the larger weld angle and where the strain gage was attached. Figures 11 t 26 cmpare the predicted stress range versus fatigue life curves with the data frm each crucifrm test. The S -N curves bunf an estimated regin int which the test data culd fall. This regin is partially based n uncntrlled variables a i and C, and estimated values f F, F Q, and F. Therefre, the G. regin bunded by the S -N curves is an estimated regin. The test data % except specimen 18, fall either within the estimated regin r between the estimated regin and the Categry C detail S -N curve. The test data that fall belw the estimated regin are a result f the difference in a^, K fc, and C values between the individual crucifrm specimen values and the theretically estimated values. The scatter amng crucifrm specimens tested at the same stress rati is a result f the variables a^ and C being different fr each crucifrm specimen. The theretical life calculatins and subsequently S r -N curves prvide a gd estimate f a S -N regin int which the test data culd fall. Tests with similar stress ranges but varying mean stresses fr 2

34 cnstant amplitude lading are tabulated in Table 7. Specimens in Table 7 are gruped accrding t similar stress range. Within each grup, the specimens are rdered accrding t increasing stress rati. Specimens 9 and 10 with a stress rati f 0.28 have apprximately similar fatigue lives as specimens 22 and 24 with a stress rati f The increased mean stress which represents increased residual welding tensin stresses des nt affect the fatigue life at higher stress ranges f apprximately MPa (27.6 ksi). The increased mean stress at abut MPa (20.16 ksi) stress range was ppsite t what was expected. Cmparing specimen 12 t specimens 2, 25, and 27 shws an increase in fatigue life fr an increase in the stress rati. Hwever, at the lwest stress range f MPa (16.56 ksi), (specimens 15 and 1 versus specimens 16T, 17> and 19) a decrease in fatigue life resulted frm an increase in stress rati. The threshld stress range fr varius mean stresses is shwn in Tables 5 and 6. Fr cnstant amplitude lading, a cnstant amplitude fatigue limit r threshld stress range ccurs at: S S mean r MPa (ksi) MPa (ksi) (22.29) (16.24) (60.48) (20.16) (60.48) (16.56) (60.48) (14.40) (64.80) 89.6 (12.96) 24

35 Fr variable amplitude lading, crack prpagatin des nt ccur when bth the maximum stress range and effective stress range are belw the cnstant amplitude fatigue limit. A cnstant amplitude fatigue limit ccurs fr: s rmax S re S mean MPa (ksi) MPa (ksi) MPa (ksi) (20.49) (12.72) (22.76) (27.45) (17.04) (22.59) 25

36 7. SUMMARY AND CNCLUSINS * Crucifrm specimens cmprised f nn-lad carrying fillet welds were tested in bending under cnstant and variable amplitude lading. The fllwing summary and cnclusins are based n the cnstant and variable amplitude test results and theretical analysis: 1. A finite element analysis was used t determine the stress cncentratin at the weld te. The SCF was fund as.6986 using a furth rder plynmial fit thrugh the K^ values. 2. Green's functin was used t evaluate the stress gradient crrectin factr. nly nine percent f the lngitudinal bar thickness has a large stress gradient crrectin factr, F, as a result f the lateral attachments and welds.. The Maddx relatinship was used t describe the crack shape fr semi-elliptical surface cracks. 4. The mathematical mdel utilizing the fracture mechanics principles t determine the stress intensity range, prvided a gd estimate f an upper and lwer bund fatigue life fr a given stress range. S -N curves cnstructed thrugh the upper and lwer bund fatigue lives prvided an estimated regin int which the test data culd fall. Ninety-six percent f all test data either fell within the estimated regin r 26

37 between the Categry C detail S r -N curve and the estimated isregin. 5. Fatigue crack grwth was assumed nt t ccur where AK was belw AK tl). 6. In each test, the fatigue crack initiated and prpagated frm a tensin weld te. 7. Fifty-six percent f all the fatigue cracked specimens failed at the weld te f the larger weld angle. Sixty-seven percent f all the crucifrm specimens that fatigue cracked failed at the weld te where the strain gage was attached. Thirty-nine percent failed at bth the te f the larger weld angle and the te f the strain gage lcatin. 8. The cnstant amplitude test data indicate the ccurrence f a cnstant amplitude fatigue limit at: s mean S r MPa (ksi) MPa (ksi) (22.29) (16.24) (60.48) (20.16) (60.48) (16.56) (60.48) (14.40) (64.80) 89.6 (12.96) 27

38 9. Fr variable amplitude lading, S rqax and S re are belw a cnstant amplitude fatigue limit fr: s max S re S mean MPa. (ksi) MPa (ksi) MPa (ksi) (20.49) (12.72) (22.76) (27.45) (17.04) (22.59) 10. The cnstant and variable amplitude tests prvide fatigue resistances cmparable t thse previusly reprted. 28

39 NMENCLATURE a crack length; minr axis semidiameter f elliptical crack Aa incremental crack grwth a average crack size per a a^ initial flaw r crack size c majr axis semidiameter f elliptical crack C material cnstant D lngitudinal bar width E k elliptical integral. F(a) ttal crrectin factr which includes the crrectin factrs F s, F, F e, F F e crack shape crrectin factr 0 F stress gradient crrectin factr F s frnt free surface crrectin factr F,, back surface crrectin factr w F( a ) bending stress crrectin factr which includes F s and F w AK stress intensity range AK^h threshld stress intensity range K stress intensity factr Kx. stress cncentratin factr 1 distance alng crack path 29

40 m number f finite elements alng crack plane describing crack length a n crack grwth expnent AN incremental fatigue life R stress rati S sectin mdulus S stress range S re effective stress range >rth threshld stress range SCF maximum stress cncentratin factr lcated at crack rigin T lngitudinal bar thickness W weld leg size a nminal stress 0

41 TABLES -1-

42 TABLE 1 CALCULATIN F F g j=l K arcsin I. + 1 _J - arcsin hi a (mm) S.. (mm) « (ram) K t F

43 TABLE 2 CALCULATIN F F(a) FR SPECIMEN #12 F(a) = "F(-) 1.21 (F ) (F ) (F ) g s e a (ram) F e F s F F(«) 1.21 F(a) , ' a. = mm l --

44 TABLE STRESS RATI AND THRESHLD STRESS INTENSITY RANGE *t FR ALL CRUCIFRM SPECIMENS Specimen» R MPa /m Ak TH (ksi /in.) (5.704) 9, (5.081) (4.491) (4.415) ,(4v6&) (4.052) (.982) (.966) (.944) (.922) ,75 (.890) (.846) (.58) (.21) 22, (2.95) 2, 25, (2.504) 16, 17, (2.260) 18, 20, (2.109) (2.006) -4-'

45 TABLE 4 FATIGUE LIFE CALCULATINS FR SPECIMEN #12 1 C = Aa C(AK) n n = C x 10" 1 ^ ' N cycle S = r MPa Aa (mm) a (mm) avg. F(a) S, (MPa) rb AK (MPa m) AN (X10 5 ) ' % ~\ r» 8.85 Upper bund a = 0.047mm C = x l -1 -y a. = mm C = x 10 l Lwer bund N cycle N = x 10 cycles N =.572 x 10 a ± = mm C x 10-1 N =.462 x 10-5-

46 TABLE 5 MEAN STRESS, STRESS RANGE, STRESS RATI, AND FATIGUE LIFE F CRUCIFRM SPECIMENS UNDER CNSTANT AMPLITUDE LADING Specimen S mean a MPa (ksi) (22.29) (22.29) (22.29) (22.29) (22.29) (22.29) (22.29) (60.48) (60.48) (60-48) (60.48) (60.48) (60.48) (60.48) (60.48) (60.48) (60.48) (64.80) (60.48) MPa (ksi) (27.45) (27.45) 29.8 (4.78) (20.49) (16.24) (17.28) (16.56) (16.56) (16.56) (14.40) (16.56) (14.40) (14.40) (27.6) (20.16) (27.6) (20.16) 89.6 (12.96) (20.16) R N(X10 6 ) R R R R R R R R = Runut -6-

47 TABLE 6 MEAN STRESS, MAXIMUM STRESS, MINIMUM STRESS, EFFECTIVE STRESS RANGE, STRESS RATI, AND FATIGUE LIFE F CRUCIFRM SPECIMENS UNDER VARIABLE AMPLITUDE LADING Specimen // MPa S mean (ksi) MPa S rmax (ksi) MPa S. rain (ksi) MPa S re (ksi) R N(X10 6 ) (22.76) (20.49) 7.1 (5.9) (12.72) R (22.) (27.45) (8.55) (17.04) (22.59)* (27.45) (8.77) (17.04) R I (22.28) 29.8 (4.78) (11.10) (21.60) (2,01) 29.8 (4.78) (11.17) (21.60) (2.19) 29.8 (*. 78) (8.8) (18.57) (22.1) (27.45) (8.78) (17.04) (22.25) 29.8 (4.78) (6.62) (1.92) *At x 10 6 cycles the S = MPa (21.29' ksi). r, mean fr the duratin f the test R = Runut

48 TABLE 7 SPECIMENS UNDER CNSTANT AMPLITUDE LADING WITH SIMILAR S Specimen # MPa (ksi) r MPa mean (ksi) N(X10 ) (27.45) (27.45) (27.6) (27.6) (22.29) (22.29) (60.48) (60.48) (20.49) (20.16) (20.16) (20.16) (22.29) (60.48) R (60.48) (60.48) R (16.56) (16.24) (16.56) (16.56) (16.56) (22.29) R (22.29) R (60.48) (60.48) (60.48) R R = Runut -8-

49 FIGURES -9-

50 Categry B t 200 I I 20 Ld < 10 cc - en C ir 5 l- t Jl -i *«*' -» Categry C Runut SI fll ~ D a. 10^ i i LI i i ij- I0 C 10' NUMBER F CYCLES I I 1 I '»- I0 C Fig. 1 Summary f Cnstant Amplitude Fatigue Test Data g n Nn-Lad Carrying Fillet Welds

51 -v- STRESS RANGE,KSI r J T c 1 l-t ^< i-h Z I f t rt CD BJ - rt n s r H - -^ I- 1 rt Q C a. Tl (II (- W rt rt rt p. T «C n> r a- H w r t rt MPa

52 I 50 0 <n ^ - 20 u z < QL 10 C ( UJ cc I- 5 Manual Welds Autmatic Welds ^ Autmatic Welds Runut -cuxn ~z Categry C i i i i i j i i L_L ^xl 10' 10 10' NUMBER F CYCLES Categry B ^ C A AA r J i. i i I0 C Fig. 2 Summary f Variable Amplitude Fatigue Test Data n Nn-Lad Carrying Fillet Welds

53 -TV r~ t> > 2 STRESS RANGE, KSI 01 Q f 00 Q. W C c CD Ml m 0 < x tt 1 1-! 0 (U -n M a* 0 0 -< 5 r 0 r v^,_, m rr C 00 c D- Tl C H- r- 1 Tl M B> (D rr rr H- 00 S C n> n> i-" a- H en re en rt» rt (U ) I I hi Q. CD (Q 5 \ I a <? ( / n ' I I I I MPa J L r 01

54 Variable Amplitude Lading Rayleigh Distributin Srd = 0.5 >rm Sr max ~ Sr min, W = - = Srd s s r min r m max Histgram N. f Stress Levels 8 N. f Blcks 150 N. f Cycles in a Blck 960 N. f Cycles in a Perid x 10 Fig. Fatigue Crack Grwth Study Stress Spectrum () -42-

55 Lateral Attachment I I Lngitudinal Bar -2 Vertical Plane Defining Crack Path L = 254 mm D = 0.5 T = 16 W=I2 L? ig. 4 Crucifrm Specimen fr Finite Element Analysis

56 0.50 T 0.96T 0.829T Shaded Elements = Regin f Fine Mesh 0.88T T 2.99I6T 0.295T i.p- I T 0.50T - 8 Nde Brick Elements Deep I Brick Element Width = T Fig. 5 Carse Mesh

57 T T T T 7@0.0862T T Shaded Elements = Regin f Ultra-Fine Mesh « T T T T T T T I T sym Fig. 6 Fine Mesh -45-

58 i i 1 2@0.0I9T 1 K T 5@0.0I287T 1 5@0.0I287T i, ~ : ~% 7 C T 4@0.0I92T I9T G 5>0.C )0257 T T sym Fig. 7 Ultra-Fine Mesh -46-

59 Weld Te (.6986,0.) Stage L/T Fig. 8 Stress Cncentratin Factr and Stress Gradient Crrectin Factr Alng Crack Path -47-

60 tub. ^Q k = cr/rra F(cc) («)-^tanff (I-sin J^) 4 cs 7TQ 2T Fig. 9 Stress Intensity Factr fr a Thrugh Crack Under Bending -48-

61 Crack Shape Stress Distributin pr fry M</t.025 h JLU.80 rr>^ Frnt Free Surface Crrectin Factr fr Varius Crack Shapes and Stress Distributins (5) a c E * K F e Crack Shape Thrugh Crack Circular Crack *E is the elliptical integral b. Crack Shape Crrectin Factr (7) Fig. 10 Frnt Free Surface Crrectin Factr and Crack Shape Crrectin Factr -49-

62 S r - N Curve 600 Qi mm (in) (0.001) (0.02) (0.0) D CL 400- I.2IIXI0" xl' x I LU CD < 200 h- gt I C LU CE \- c!^. / ^ C 100- Categry C b- I0~ j L_J ' i i' I J i i i iiil J i ii I f NUMBER F CYCLES, N Fig. 11 Specimen 11 Cnstant Amplitude Lading, R = 0.12 I0 C

63 en ' 1 -s- STRE.SS RANGE, MPa r '/ ' '/ ' /I - / * // H- UQ M M C/l a (D n H- z c M M z CD n m ) 0) rr t -n rt a -< r H- m c c CL n> z (- 1 t CL H- Q "» II l-l t U) % N D -,. z i *< a ^ tn 5* (D ^ * r b r X - i m J b g m - r r en Q N C CD / «< r - J w b r \ - r - en r X J - 1 J i C C r KSI J CD

64 s r - N Curve 600 1! 2 aj mm (in) (0.001) (0.02) (0.0) _ 400- n mm 5-5 I.2llxl xl x I0-1 N cycle UJ < 200 a: Ln in V C cc L\ ^ y C 100- Categry C b 10" J i i i i i I J I_I» ' ' 10 I0 f 10 NUMBER F CYCLES, N ^ Fig. 12 Specimens 9 and 10 Cnstant Amplitude Lading, R =

65 5 -TS- STRESS RANGE, MPa r 8 A 00 </> n> & <n U) z V c P z n U. m M J n -n en» < r - 1 T m M # rt z C U. (D M Pi a. H- 09 "?a n N W 00 a> -, C a CD >< r \ J / z d»< *-, m (n CD > "' r " " r X en _ -fc» i W r g en X «*-«* i w fv X J 1 00 IV) r r J J ^~* C I z < CD J L r KS.I J J I 1,1.1 en ) C

66 -I (.00258) S r -N Curve (0.02) xl' (0.0) x I !^ ^,/ 20 Categry C 10 i a ^A. J i i i 1111 I0 U I f 8 10 it NUMBER F CYCLES, N Fig. 1 Specimens 4 and 5 Variable Amplitude Lading, R = 0.47, 0.61

67 -zs- STRESS RANGE, MPa r l 5 I r } I - 1 \j 1 1/1 /I 0> - tn " (D H- (tl D U> 4> 01 Z a C Ui 2 CD < m B -U M I- 1 - cr -n M rt> a r - H- m rr c (X * ft> r 1 DJ a. H- a 0Q p ^1 z a> N ' 0D y - Vjff / / t ^ / * ff / Z ^ / * / ^ / < 5" (D *^^ 7 P r m 0) X l ^ 5 ~ - i b - J 8 " 00 " r 6 a =5 (X) J >< 00 q >< r i b r l\.a / r ~Q - (0 en r J X J \ ^ 1 CM b J C I z c < , 1 r l at > KSI

68 S r - N Curve (0.02) (0.0) L UJ xl0~ x I < 200 cr t UJ E I- C 'A. ^ C 100 Categry C J i i i iiil «t i i itil» i i i i i ' I0 C NUMBER F CYCLES, N Fig. 14 Specimen 12 Cnstant Amplitude Lading, R = 0.70

69 -es- STRESS RANGE, MPa rv> 5 1 T 1 T 1 \) 1 1 / 1 /I 0) 00 " m X) r H- r z c z CD m?] rf» -n rr -< r H- m rr C w a- r r 1 t D- p- q * p II L ~J z >.i -l / _Q / z / * // r ct U» 5' a> * *' - ^_ p r -t> - X J ->J. - - r " - r - Q r t \ i J X s 5 < b r *< J /. \ r CD P - C en r * X J >,, 1 1 III. I, 1 r KSI J m en 1 J CD I z <

70 S r -N Curve (0.02) 179 x I (0.0) x I I 0 C ^ T 7^ 20 Categry C 10 j i i iii il i i II iiil 10 10' I0 C NUMBER F CYCLES, N Fig. 15 Specimen 6 Variable Amplitude Lading, R = 0.428

71 <J1 5 u». -vs- STRESS RANGE, MPa r i r - ' ' / en i iy i /I - 1J T C/ -a (D H- (T> Z N 2 < CD m l-t J H- (1) cr i- 1 rt> -n t a -< H- r~ rt m c CD. I- 1 z W a. H- p T * pa II Pt- 00 a> N _. - / 5 / z / / w. ^z 00 X -J - i - 4^ 1 - r a C C w CJI j ^ 5" ^ ^ ^ i P " i b - - \ i S b I r r \ _. b mm~ i w ^0 X J I c < CD i i II, i, i f KSI 04 C

72 a. S r - N Curve a\ mm (in) (0.0016) (0.02) (0.0) 400- ^^^. UJ < 200 a: ^N. ' n mm 5-5 I.2IIXI xl" x I0-1 > N cycle en Ln C 1 LU r. i- c 100 ^\. *^. 'Sr 2 X ^ 20 / - ^^.^ Categry C L 1 1 L_ i i 11 i i i i i i i 1 i i i i i i i i 1 i ' I0 C NUMBER F CYCLES, N Fig. 16 Specimen 14 Cnstant Amplitude Lading, R = 0.441

73 -ss- STRESS RANGE, MPa 01 H- Q - M CT t (D H- S 9 Z,_ c 2 CD 0 c 0 J 01 <~» K "n rt 0 YCL Ampl H- m i? w a- - r 0 [U &. H "? II 0 p- *~ Z ^_ a> s C c < 00 KSI

74 S r -N Curve 600 a; mm (in) (0.004) (0.02) (0.0) xl xl x I CD < C l t LU \~ C 100- IX.,/,y - 20 Categry C b I0 _i i i L, ml I0 6 I0 7 I0 8 NUMBER F CYCLES, N Fig. 17 Specimens 2, and 7 Variable Amplitude Lading, R = 0.448, 0.452, 0.444

75 i r 1 1 r - 1 * -95- STRESS RANGE, MPa r 1' V 1 1/1 A CTC w -d <T> H- (D D (0 M J (1, a- z ^1 C 2 < CD M rn 1-1 J &> > H- c^ C ft) CL 0) «_ 0 t ^ N (X H- T " pa II 0 j>* 4>- 00 " 0. -p- Ln r «* 0 00 p-.c- C- ' - - V / a / 2 w / / * r ' a> 01 In ^ 5' * * r: c r t X r */[ / 1 b 0 J r * / " ^ - r p T U \ 5 CJl 0 00 C 0 r 0 >< _i_ v 0 J b r /. J r 0 - \ t en r " X J '_ 0 -L b " , 1, l r KSI J 4> ui <n J w a> C <

76 . ' 0.*ri>>* U-M1H..W- S r -N Curve NUMBER F CYCLES,N R = Cnstant Amplitude Lading, Fig. 18 Specimen

77 -zs- STRESS RANGE, MPa u,rr Tl H- Q I t/1 H- IS D Z c M 2 l_n CD m n rt n 9n -< IT -a r h- 1 m rt en c ^ ^ D- fd z >i r t a- H- D Q "» C "1 I z < a> II C~ Ln 00 C KSI

78 q mm (in) S r -N Curve (0.0016) (0.02) (0.0) llxl0' xl0~ x I0' ' lu ^ NUMBER F CYCLES, N FIR 19 Specimen 1 Cnstant Amplitude Lading, R = 0.466

79 5 en I 1 r > STRESS RANGE, MPa p a> 1 1 / i i/i A -) w -a (D M- P 2 C l-> 2 U> 00 m n 2 0 rf n (U * T) M C r- 05 a. H- - tw -< r- m t «z cn. // / CL / 1* w / bi 5" / ' a> * * C IN ' = -P> c ) - x - i - <T> m - r. a \ 7 N bi ^ 00 1 i b r <jt r - \ ~ je i INJ t. cn N) X 04 1 b J w C I z c < (0 1 1 i III. i 1 P KSI J cn cn a»

80 S r - N Curve aj mm (in) 0.111( ) (0.02) (0.0) 80 mm 5-5 N cycle I.2llxl0~ xl x I t «-n I C 20 Categry C N,.> ^ 10 J i i i i i i ' I0 C NUMBER F CYCLES, N Fig. 20 Specimen 8' Variable Amplitude Lading, R = 0.52 ft