9.

10.

11

12.

13.

14.

15.

16.

c Mattheck p r-lorawietz, D.Munz, B.Wolf; "Ligarrent Yielding of a Plate wi.th Semi-~lliptical Surface cracks Under uniform Tension", accepted by Journal of Press. Vessels and Piping (1983).

c.Mattheck, P.M:>rawietz, D.Munz; "Li~~t Instability of Sani-ellip-tical Surface cracks in Plates and P~pes , SMIRI' (1983) Ocago, G/F4/6. c Mattheck p.M:>rawietz, D.Munz; "Stress Intensity Factor at the ~ur-f d ~ the ~st Point of a Sani -elliptical Surface crack 1n p~~:n un~ stress Gradients", Int.J.Fracture 23 (1983) 201-212. J. R. Rice; "Sare Remarks on Elastic Crack Tip Stress Fields", rnt.J.Sol. struct. ~ (1972) 751-758 T A Crus p M Besuner "Residual Life Prediction for Surface Cracks . e, t 1 ~tails" Journal of Aircraft 12 (1975) 369-375. ~n Ccmplex Struc ura , _ J .C.Newmm, r.s. Raju; "An Eir\'.irical stress Intensity Factor for the Surface crack", Eng.Fract. Mech ..}2 (1981) 185-192. K.Hasegawa, s.sakata, T.Shilllizu, . s.shi~; Tolerances for Stainless Steel P~pes w~th ASME 4th PVP COngress, Session 24.

"Prediction of Fracture Circunferential cracks",

J GOring "Versagensverllalten von Flachzugproben mit ein~ halbelli~tis~en ~ladlenriB aus einem Werkzeugstahl", Diplanarbe~t am. I~titut fr zuverlassigkeit urrl Schadenskurrle im MaschinenbaU, l.Jn~vers~tat Karlsruhe ('Jll}, (1983) (in Genw.n)

642

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1

FATIGUE ANALYSIS OF BUS STRUCTURES

C.M. BRANCO* and J.A. FERREIRA**

The paper presents the main results of a fatigue analysis of welded joints in rectangular tubes used in bus structures. S-N and crack propagation data was obtained loading the speci mens in plane bending in air at room temperature and at a load ing frequency of 1410 .cycles/min. Different steel grades wer~ tested and their fatigue strength was compared.

1 A defect tolerance analysis was performed based onstress intensity computation and fati gue crack growth data. Defect

or damage tolerance curves were obtained and compared with the experimental S-N curves. These curves can be used in the fati-gue design of the structure.

:iNTRODUCTION

Bus structures are often subjected to dynamic loads leading to fatigue fail ures. In public transport vehicles the dynamic loads are transmited from-the pavement to the structure causing fatigue in the welded joints of the tubes. The fatigue cracks usually initiate at the toes of fillet welds of T type connections made with rectangular thin walled tubes.

Welded rectangular thin walled 'sections with tube thicknesses ranging from 1.5 to 6 mm are extensively used as the main structural element in bus structures. These type of structures combine low weight with high val ues of the bending and torsion modulus. It is therefore possible to redu= ce the weight of the structure allowing an increasing load capacity in the vehicles and reducing the fuel consumption. However, fatigue failures should be avoided and therefore an appropriate fatigue desi!;n is required.

A considerable number of failures i.n bus structures have occured in the past in Portugal because fatigue loading was not taken into. account in the design of the structure. The need for fatigue studies was recognized and the authors have initiated three years ago a testing programme in order to assess the fatigue behaviour of welded rectangular hollow sections used ' in bus structures. Sorne results were published elsewhere (1-4) and report ed on the influence of tube thickness and weld surface finish. The crack-propagation phase was studied with fracture mechanics methods applying the similarity approach and two simple crack propagation models. Fractographic observations were carried out usi.ng both optical and scanning microscopes and

* University of Minho, Braga, Portugal ** University of Coimbra, Coimbra, Portugal

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as a result failure modes and crack initiation mechanisms were identified.

Research work in the field of fatigue of rectangular tubes has been e~ tensively done in Holland by Wardenier (5,6) and in the USA by Stephens (7) Wardenier tests are in different types of tubular connections such as K, T and Y joints loaded in tension and bending. The influence of the geometry of the joint and welding locationwas assessed. However the size of the tu-bes was considerably greater than those used in bus structures, and moreover no study of the influence of weld geometry was performed. In (7) stress i~ tensity solutions for surface cracks in square tubes subjected to torsion were obtained and in (8) similar results were obtained in rectangular tubes in bending. In these studies the similarity approach was applied for the K computation andthat was based on compact tension specimen data obtained in specimens takan from the tube walls in the locations where the crack was propagating in the tubes. In (2) the authors found a reasonable agreement between their solution and Stephens one but only for cracks growing in the lateral sides.

Recently in Japan a detailed stress analysis study was published quot-ing structural stress concentration factor results obtained in several ty-pes of rectangular tubular connections (9). The finite element method was used but the geometry of the weld was not considered in the investigation. It is worth while to mention that in none of those papers defect tolerance and weld geometry was considered and these are fundarnental pararneters in any fatigue analysis of welded structures.

More work is being publ.i:shed in the field of fatigue of welded joints in circular tubular structures used in off-shore applications. Sorne of the latest results may be found in (10). In these structures conclusive proof now exists that Fracture Mechanics can be used to assess fatigue life and therefore its applicability to rectangular tubes should be studied and deve loped further as reported herein.

In the present paper a fatigue analysis methodology for welded joints in rectangular and square tubes of mild steel used in bus structures is pre sented. Fatigue design data was obtained in specimens representing the more critical details in the structure. The influence on fatigue life of materi al, tube and weld geometry is assessed theoretically and experimentally in -sorne cases. A defect tolerance analysis was carried out using Fracture me-chanics and the results were compared with the appropriate experimental da-ta.

EXPERIMENTAL METHODS

The materials used were three mild steel grades St37-2,St44-2 and St 46 - 2 ac cording to DIN 17100 specification. The steels are law carbon steels, con-taining 0.157. carbon in the St 37-2 grade and 0.16 to 0.187. carbon in the St 44-2 and St . 46-2 grades respectively. The nominal dimensions of the tu-bes were 82x38x2 and 38x38x2 (height x width x thickness). These tubes are manufactured by cold bending of steel sheets with the same nominal thickness as the tube followed by resistance welding along the longitudinal direction. Hence the tubes have a welded longitudinal seam. The main mechanical proper ties obtained in tensile tests are presented in Table 1. Tensile tests were-also carried out in plate specimens taken from the tube wails, but the re-sults will not be reported here.

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TABLE 1 - Mechanical properties of rectangular tubes of mild steel (DIN 17100)

a 0 UTS ER ys Mate rial (MPa ) (MPa ) (7.)

St 37-2 Grade 398 440 9.3 (82x38x2 )

St 46-2 Grade 370 428 33 .8 (82x38x2)

St 46-2 Grade 396 449 26.7 (38x38x2)

St 44-2 Grade 381 458 ---(82x38x2)

1

St 44-2 Grade 402 468 ---(40x40x2)

The fatigue specimens were tubes provided with fillet welded gusset pla tes s imulating the critical detail in the structure where fatigue fail-ure initiated. Fig. 1 shows the nominal dimensions of the specimen. The gusse t plate shawn is 3 rom thick and it is welded at the built-in end of the specimen in arder to simulate the crack initiation point in service.Can tilever plane bending was chosen for the loading mode since that proved to be the appropria t e l oadinf, node Hilen checke

S-N data and the stress was monitored during the fatigue tests.

RESULTS AND DISCUSSION

Since crack propagated first in the upper part of the tube followed by pro-pagation in the lateral sides it was decided to carry out the s tress inten-sity factor computation separately for bath ;Jarts. ln the upperpa r t ,the K v~ lues were obtained numericaly applying the finite element method while for the lateral sides the similarity approach and an available K solution were applied.

Stress intensit art of the tubes

The stress intensity factor formulation for the upper part of the tubes (horizontal element) was computed based on the Albrecht method (11). This method is specially suited for welded joints and stress concentration geome tries and is simple and quick to apply. ln most practical cases the salut= ions derived for K are sufficiently accurate .

lt is known that in welded joints there is always a stress gradient in the weld toe section. Hence the stress intensity factor may be obtained using the equation

K' (1)

where . 0 is the complete second arder elliptic integral (0 ~ 1 for a con-tinuous crack), K' is .the stress intensity f actor for a similar geometry without the weld and assuming a constant stress distribution along the thick ness direction, and ~ is a magnifying factor taking due respect of the s:ress. non-uniformity in the weld region . ~ is equal to the stress concentration factor when the crack length is zero and can be computed knowing the distri bution of stress along the crack line and substituting these stress values-in the~ equation derived in (11).

For the specimen shawn in Figure 1 and in the upper part of the tube subjected to cantilever bending,an approximate stress distribution can be as sumed considering an uniform nominal tensile stress in the tube wall. This is approximately true due to the very small thickness of the tubewall~ The stress distribution along the tube thickness was obtained with finite e lement method ,Figure 2 shows th~ mesh used with eight node 2D isoparametric ele ments having two degrees of freedom in each node. ln this figure B is the-tube thickness, LG is the weld leg length and B1 is the gusset plate thick-ness. Since an uniform tensile stress was requ1red the loads were applied in tension in the nades 116 to 124, and the built-in condition at the ether end of the specimen was achieved by constraining the displacement in the no des along the Iine 1 to 13.

~values were obtained for values of ~ = 2,3 and 4 mm, B1= 3 and 6 mm and LG= 6,,12 and 20 mm. Table 2. presents the entire set of results for~ as a function of a/B and these can be fitted accurately by a power l aw equa! ion

1\ = p/(a/B)q (2)

where p and q are dependent on B,B1 and LG and the values are given .i n Tabl~2. The correlation coefficients for equation (2) are a lso quoted in the same ta ble thus confirming the validity of equation (2).

646

l 1 l t t

t

1

TABLE 2 - Values __ of-r--M.=-_i _n_ t _h_e _ _ u_p_p_e_r __ part of the tubes (M. = p/ (a/B) q) ~ -.--,--,) k k ~ 2 -- -r~---, ----:~r :f l LL l] t 1 l2 !fJ 20 20 4 0 4 0 .. .:~ ,' B

01 11 " .l.l. :.J :. . :.al 1 SJ J t ') l .fJ - 4 1.01 l.fl Jl 1 l. '..J -2 1 . 03'-1 ,f ~ --+-l . J37 t L. J! l ! 1 .0 :7 i l. ~., 1. 0:!~ 1 1 IJ __ \ 1 1 .ll '' ""'it;n .l'J;. ts >e i 0 1 ! -+---. " ' ' >S j .v;,~ , . Col .Coll i ')' e 1 ,,. ,

. Il)

~c .. , . ,, . ,,o\ ' "'' t1

7'

1'- 11 "~ ; .,_~c - 1 .9 : '' J .oo.; 1 .a, ; .'10lo: . 0 ... ,_0 .

;.:_ __ ~ , - .~.,o 99J 9'17 t h , ! .'1_~..":.__L:.:_l~"' lg~., . CJ -, ? i . G"" "'"'' ~e stress concentration factors K = (M.)( /B-:--0)-----h-- --- -(poirt6 A F ' 2) ' t l

sides increases with the number of cyc l es and the applied stress and it is higher in the St 46-2 tubes compared with the St ~4-2. Crack length values below 2 mm were not obtained s ince these occured 1n the upper part of the tu be where no experimental observation was possible.

Other objective of these tests was to eliminate the crack initiation phase. Therefore the tubes whose results are plot t ed in Figs . 4 and 5 wer e provided with 0.65 mm deep notches at the corner . The notch was severe enough to initiate the crack after a very small number of cycles and_t hat can be confirmed by the results shawn in Figs. 4 and S. However fatt gue crack growth measurements in plain s pecimens (not precracked) revealed a si gnificant crack initiation phase for law applie d stresses (3,4)

The S-N curves for the 0.65 mm deep precracked tubes (rectangular and square) in the St 46-2 and St 44-2 s teels are plotted in Fig . 6. Two cur -ves were obtained one for the 82x38x2 tubes and the o ther for the square c nes (38x38x2) . No influence of steel grade was found and only the height of the tube has influenced the S-N curve. Hence fati gue life is greater in the rectangular tubes due to the fact that the crack has to travel a bigge r dis tance in the rectangular tubes before final failure occurs at the mid height of the tube.

S-N data was obtained in the plain welded tubes. The range of fatigue lifes is from 5 x 104 cycles to 107 cyc les and in sorne t ests fatigue fail-ure did not occured. These results will be ana l ysed later in the paper and here only a discussion about the variation of the nominal stress during the t es t will be done. Hence Fig .7 shows t ypica l plots nominal stress aga inst number of cyc les in the strain gauge l ocation indicated i n Fig. 1 Nominal s tress (stress in the outerfibre subj ec ted to tension) r emained practically constant while no crack was initiated in the upper part of the tub~usually at the tube cor ner nea r the s train gauges) . Th is was foll owed by a sl i ght i~ crease in stress during crack propagatton in the upper part of the tube and finally the stress in the outer f ibre decreased sharply as the crack was propagating in the lateral side s. However the decrease in s tress only oc-cured when the crack was long, ve r y near the end o f the t es t. Hence it is accurate enough to consider a constant nominal stress in t he specimen throughout the fatigue life.

The S- N curves of the precracked tubes (F i g. 6) were ob tai~ed by line-a r regression of the experimental results.

Assuming that fatigue life is c rack pr opagation only, which is approxi matly true in this c ase , then the s lopes of the S-N curves plotted in Fig .

~ a re equal to the exponent rn of Paris law. The cons tant C may be obtain-ed by the following equation proposed by Gurney ( 13)

c = l. 315 x 10- 4 /895 .4m (4)

Hence the values of rn and C are

rn= 4.26 and c 3 . 494 x 10-17 for the rectangular tubes

rn= 4.68 and c 2 . 01 x 10-1 8 for the square tubes

These values of rn are in close agreemen t with t hose of da/dN, K curves ob-tained in fatigue crack propagation tests of centre cracked specimens i n tension (14) .These specimens were taken f r om the tube wa ll s and t he cr ack was propagating in the same direction as in the tubes (14). Hence it ap-pears that the method used herein for t he de t ermination of rn is accurate and

648

has the advan tage o f being fas t e r, mo re economi cal and e a s ier than the one ba sed on the de t e rmination o f the da/dN, K curve of the ma t e rial.

Ca l culation of s tress intensity factor in t he lateral sides of the tubes

Two me thods were used to obtain a K formulation for the lateral sides o f the t ubes . The fir s t one is the Murakami (15) so lution for a crack in the width d irection of a rectangular crosssetion bar subjected to cantilever or plane bending. In the present study the wldth of the specimen was taken as equiva lent to t he tube height since the tube is built-in. The equation for K is -

K = oflh ~ (0.7857a 2 + 0.6186a + 0 . 862 ) (5) where a = a/h , h is the height of the tube and a i s the nominal stress at the weld toe line as de fined before.

K values were also obtained applying the similarity approach and using the fati gue c rack propagation da ta r efe red in the previous section (Figs.4 and S).The equa tion to calcu l a te the geome tri ca l factor Y= f(a/ h) in the s tress in t ensity equa tion may be expres sed as (3)

Y = f (a/h) = --=-1-==~ a lfih c

da 1/m -;:rn) (6)

with the values of rn and C given above . From t he (a,N) da ta obtained in the tubes (see Figs . 4 and 5 for examp les) the da/dN equa tion was obtained in each specimen by numerical differentia tion wi th the best f it second arder polynomial. He nce f(a/h) can be computed in each s pecimen for a particular val ue of a (a/h) subs tituting in the above equation the da/dN va lue for that va l ue of a (a/h) taken from the da/dN equa tion in each specimen.

For the St 46 - 2 s t ee l Fig . 8 shows the plot f(a /h ) against a/h obtained in the rec t a ngula r tubes and Fig . 9 i s a s imilar plot for the square tubes. The da t a shawn was ob ta i ne d i n five rectangular specimens and four square spec imens. I t i s seen t ha t f(a/h) increases with the c r ack lenght fo r val -ues of a/h be t ween 0 .0 5 and 0 . 5 approximately. Crack propagation for values of a/ h below 0 .05 was not cons idered be cause it does not occur in the late-ral sides. For a/h values above 0.5 crack gr ow th rate is usually above 10-3 mm/cycle a nd the function f(a/ h) has little prac tical interest i n that regi-on . Also the failure in the t ubes was taken when the c r ack reached mid heigh t of the spec imen. A fourth arder polynominal produced the best fit fo r the da ta points i n Figs . 8 and 9 and the equations for f(a/h) are

Rec tangular tube s (82x38x2)

f(a) = 0 . 2162 + 2.23la- 12 . 214a 2 + 30.54la3 - 26.98Sa4 (7a)

Square tubes (38x38x2)

f(a) = 0.2632 + 1.848a - 6.172a 2 + 10. 17l a 3 - 6.418a4 (7b)

The r efore the s tre ss intensity fac t or may be computed in the tube s with the following equa tion s

(i) Rec tangular t ubes 82x38x 2 K = 0 . 7965 a-O . OgSS x K'

LG = 6 mm and s1 = 3 mm

for a=a/ B < 0.184

649

(Ba)

or

(ii)

K K' for 0.1S4 < a/B < 0.65 (Sb)

and

K =oit! lifO:(O .2162+2. 23la-12. 214a2 +30. 54la3 -26. 9S5a 4>

K =o~lif0:(0.7S57a2+0.61S6a+O.S62) Square tubes 3Sx3Sx2; LG=6 mm and B1# 3mm

K =0.7965a-o.ogss x K' for a/B < 0.1S4

a>B/h (Sc)

a>B/h (Sc)

(9a)

for 0.1S4 < a/B B/h

Fractographic analysis

Scanning and optical microscope photographs of fracture surfaces were ~aken in order to detect crack initiation points and modes of crack prop~gat1on. Two examples can be seen in Figs. 10 and 11. Fig. 10 shows the ent1re top left corner of a St 46-2 tube tested at a nominal stress of 232 MPa. The picture covers all the tube thickness, the weld toe and weld metal. The cracks have initiated beth at the weld toe and at the in~er su:face.of t~e tube. Propagation took place in the horizontal and ve:t7c~l ~1rect1ons 1n a similar pattern. This was the more often found crack.1n1~1at1on and.propa~~ tion mode and that fits, so far as the crack propagat1on 1n tqe vert1cal d1 rection is concerned, rather well with the theoretical model used in the pre sent work. In Fig. 10 an interna! flaw ~as observed (cleavage) probably due to HAZ cracking or material inhomogenity.

Fig. 11 with a higher magnification than Fig. 10 was taken in the lateral side of a rectangular tube of St 46-2 steel tested at a very low stres~ lev~ (154 MPa) Crack propagation is by mixed mode beth transgranular and 1nter-granular.

Two grains of the material are visible in the photograph and wi thin the grains striation formation is indicated despite the fact that these could o~ ly be seen with a higher magnification. This mixed mode was generally found for low stress levels only. For higher stress levels crack propagation was mainly intergranular.

Defect tolerance analysis and comparison with S-N data

Crack propagation S-N curves as a function of initial flaw size were derived 50 that a defect tolerance programme can be developed for this type of welded joints. The data can therefore be used in any defect tolerance analysis in bus structures since the results apply. to the more critical weld detail in the structure.

The equation equation

crack propagation S-N curves were the integration of the Paris law substituting the K values by equations (S) and (9). The resulting for the total number of cycles of crack propagation was

650

i ..

1

l v

l f l

N t

(10)

where N1 , N2 and N are the number of cycles of crack propagation for the three terms of t~e stress intensity equations respectively (a/B

0.65 mm initial flaw size curve. This is confirmed by the position of the experimental S-N curve i:n the 0. 65 mm precracked specimens, in the scat ter band of the St 46-2 S-N curves in plain as welded specimens, (Figs. 12 and 13) . Hence fatigue life is greatly dependent on the initial flaw sizes and good fatigue strength is obtained if the defect tolerance level is kept b~low 0.1 to 0.2 nm. If these limits are increased up to 0.65 mm as in the St 46-2 steel tubes fatigue strength is reduced by a factor o.f '2./3 and a f~ tigue limit may not be obtained (Fig.l2 and 13). However for the results in the St 44-2 steel tubes a fatigue limit may be defined with a value bet ween 160 to 170 MPa. For the St 46-2 tubes perhaps it is possible to defi ne a fatigue limit close to 120 MPa (Figs.l2 and 13).

CONCLUSIONS

1. Fracture Mechanics can be applied suc.,ssfully in the fatigue analysis of welded rectangular thin walled tub(s used in bus structures.

2. A stress intensity factor formulatn was derived to obtain the stress intensity values .for cracks ~ropagating in the top or bottom faces of the tube and in the lateral sides .

3.

4.

5.

6.

S-N data was obtained to establish appropriate design stresse,, and to compare the influence on fatigue life of steel grade and tube geometry

Fractographic analysis bas revealed that the fat .igue cracks are usual-ly initiated at the tube corner in the weld tue and then propagated in the horizontal and lateral side. The ~lin microstructural crack prop~ gation modes were identified and ccmpared.

Theoretical crack propagation S-N curves were de.c.i.ved tased on the stress intensity factor equations menti

lG fU .. 1.1

Figure 1 Tubular specimen with a fillet welded gusset plate used in the experimental programme .

.- .. -.,

.. ~-1 G ~~ . .~ -- : . : 1- 1: c.

--

~ .. . 1- 1- ~ ~- . . 1-

'" '" - -. '-

-

.

" 1 ~ ,.. 1- 1- 1-

l J

..... ____ . ____ _J

Figure 2 Fini te element mesh for stress computat ion i n the upper par t of the tube

654

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1 1

l 4

~ 1

l ~ - ---

1 1 '

--- ....... _ .. __ ~ -- .... -- ....

.... - ...

Th~lu:a~ss! B (mrot) j Varia t ion of Kt with B as a f unction of LG and a

1 or------r-----;------~--~-r----~~ : ..

t Figure \ 3

': li

~JO

"' ~ 25 ..

~ 20 u

1a

10

-a lt7tn 2 ;ST44.2 treaa rel i e:Yed

A- o 2911 / .. 2 ; sT4i .2 e-a297W/ .. 2;ST46 . 2 Lo2921/ .. 2; ST4i . 2

...

.

.

~~~------;t----~~~~--------~--~-~~------~~------_j 4 7 !10')

Figure 4 No. OF CY CLES, 1

Crack propagation curve in welded tubes 8Zx38xZ a 0.65 mm deep notch. Can t ilever bending. R=O

E or----.----.... -----,-----~

~ lS

"' ~ 20 u

15

10

St-

- Cl 2C 5 N / l ; S T 4 4 . 2 s t res r' elieved

- o 22 1N/a 2;S T46 . 2 L o 2 1 1N/ 2;ST46 . 2

with

0Lr _______ __ __ -u~~~~---~~-----------:~------------j 10 1 20 u 30(1o')

Figure 5 ho. OF CYCLES, R Crack propagation curve in welded tubes 8Zx38x2 with a 0 .65 mm deep notch . Can tilever bending. R=O

655

~500r-----~--~-r-r~rr~----~--~~~~-rrrr-----, ~450 10 -

.; 41Y. r:._:--::::s:.;_:-_:-_-c:::~ ~ 350 . ........ . ~ ........ :300 6 ...

E 25o ..

150 -12s38s2,ST46.2 o-82s38s2,ST44.2 ._lh3h2 ,S TU.2

atre relieYed A-38s31s2,ST46.2

0

- - - - ea curve(rectaacular tube) ----aeaa curve(square tube)

~ .. ::::,...

Mo . OF CYCLES , L

Figure 6 Experimental S-N curve in welded rectangular and square tubes wi th a 0.65 mm deep notch. Cantilever bending. R=O

-...

"' ~ oo 1 1 0

"'

"' Q) ...

u U)

.....

"' c: .....

6 0 z

-

0 0

~ , :"00

...

o .a.9/J-a . a l. A 4

0

0

... A

..

..

100l_ ______ _L ________ J_ _____ _ ~------~--- --~---~ o zo .o 10 ar ,.,. uoaClO')

No. OF CTCL~5 K

Figure 7 Typical variation of nominal stress with the number of cycles . Tubes 82x38x2 and 38x38x2

656

~

,,

' .

l ~

~ Ill "-'

~ : "' "'

" z 0

"' z

"' :r ;;

.a, ..

--~ ~ M .s .

"' '

... . .,.

J . .

. . . . ...

. . ...

. ...

3 .3

-2 . ~ .2

J ' ,, 0

1 2

-3 4 -~ 0 .1 .2 3 .4

CRACK LENCTH RATi , at h Figure 8 f(a/ h) agains t a/h for Fi gure 9 f(a/h) against a/h for

square tubes(38x38x2).St 46-2 steel

rectangular tubes (82x38x2~S t 46-2 steel

Figure 10 Fracture surface show ing c ra ck initiation-in the top left of a square tube (35x Magni fic ation)

657

Fi gure ll Mixed mode of crack pro-paga tion in the lateral s ide of a tube, in St 46 - 2 s teel( SOOx Magnifi c a.!:_ ion)

5

...

"' 0

..

...

..

..

..

...

...

~ "' ~

Figure

..

"' ,.

~ ..

..

..

..

..

..

..

...

~ z ;:. 0 z

1a4

---- -Theor e tic~l S-11 curvea(Murakai solutioa) ------Theoretical S - R curvea(Siilarity

--'!xperiental curvs O-ST46.2(ai0 . 6S)

No. OP CTCLES,

12 Theoretical and experimental S-N curves for the welded rectangu lar tubes (82x38x2) of St 44-2 and St 46-2 s teel. R:Q,Cantilever bending

0

-----Th : , retical S-M curvea (H,:r akai aolutioa)

---- -ThtJretical S-N curvea (s :~ ilarity approach) --Es ;' '! rieota~ curvea O- ST 4 2 (ai0.63l

,rf>

..

ta Mo. OP CYCLES, Nr

~ igure 13 Theoretical and experimental S-N curves for the welded square tubes (38x38x2)of St 44-2 and St 46-2 ste~ls . R:O. Cant ilever bending

658

1 f

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NON-METALLIC AND PM MATERIALS

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