-
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
l t
l l
f
' } {
'
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
643
UserRettangolo
-
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.
644
t
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
\
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
\
'
NON-METALLIC AND PM MATERIALS
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