A theoretical study of the effect of weld geometry parameters on fatigue crack propagation life

~

Pergamon

Engineering Fracture Mechanics Vol. 51, No. I, pp. 1-18, 1995 Copyright © 1995 ElsevierScienceLtd 0013-7944(94)00241-X Printed in Great Britain. All rights reserved 0013-7944/95 $9.50+ 0.00

A T H E O R E T I C A L S T U D Y OF THE E F F E C T OF W E L D GEOMETRY PARAMETERS ON FATIGUE CRACK P R O P A G A T I O N LIFE T. NINH NGUYEN and M. A. WAHAB Department of Mechanical Engineering, The University of Adelaide, SA 5005, Australia Abstract--In the present work, the effect of important butt weld geometry parameters e.g. tip radius of undercut at weld toe, weld toe radius, flank angle, plate thickness and edge preparation angle, and the effect of initial crack geometry on the fatigue crack propagation life have been studied by using Linear Elastic Fracture Mechanics (LEFM), Finite Element Analysis (FEA) and superposition approaches. A simple mathematical model has been developed to predict the co-influence effect of the above-mentioned weld geometry parameters on the fatigue stress range vs life (S-N) curve. This model gives an explanation for the overall effect of weld geometry parameters as the main reason of scatter phenomenon in fatigue testing practice. The predicted scatter band of S-N curves subject to the variation of all the weld geometry parameters is in good agreement with S-N curves covered by design classes from D to W (BS 5400). The design class F which is commonly used for design of butt welded joints has fallen in the middle of the predicted scatter band of S-N curves. It suggests that for the sake of safe design practice class W should be used for fatigue design of butt welded joints instead of class F.

NOTATION r ~ t"

d !

tO

a

a/c (a/c)o b h ai of

Np C,m A,m A 0 ' Dlf)

CA, C~ K~o K~n

Ksc Ksc,A Ksc,B AKA AKB KL.A

K~.B Y

Yo Mk

M~ M~"

Q

tip radius of undercut at weld toe weld toe radius of butt welded joint depth of weld toe undercut plate thickness weld bead flank angle plate edge preparation angle parametric angle of the ellipse crack length (edge crack); also half-length of minor elliptical surface crack half-length of major elliptical surface crack; also half-length of central through-thickness crack crack aspect ratio initial crack aspect ratio half-width of cracked plate half-length of cracked plate crack initiation length final crack length fatigue crack propagation life material constants in Paris' equation constants in the model equation representing S N curve in the case of butt welded plate constants in the model equation representing S N curve in the case of un-welded plate (based plate) material constants in Paris' equation at points A and B of crack front, respectively stress intensity factor for edge crack in finite plate stress intensity factor for central through-thickness crack in finite plate stress intensity factor surface crack in finite plate stress intensity factor at point A for semi-elliptical surface crack in flat plate stress intensity factor at front surface point B for semi-elliptical surface crack in flat plate range of stress intensity factor at A range of stress intensity factor at B stress intensity factor of welded plate for edge crack stress intensity factor of welded plate for central through-thickness crack stress intensity factor at point A for semi-elliptical surface crack in welded plate stress intensity factor at front surface point B for semi-elliptical surface crack in welded plate geometry-configuration correction factor which depends upon the geometry of the crack and loading condition geometry-configuration correction factor due to cracked flat plate stress intensity magnification factor produced by weld profile geometry (M k = Y~ Y~) stress intensity magnification factor produced by weld profile geometry in through-thickness direction stress intensity magnification factor produced by weld profile geometry in through-plate width direction shape factor due to elliptical surface crack

2

T . N . N G U Y E N and M. A. WAHAB

S

S

tttttll y )}))))) ) ) ) ) )l)))ll _~2c =

2b

S

25

B~Zc-.4 ~

t

r

I

f

-

I S SURFACE CRACK IN BUTT WELDED JOINT (MODE I)

Fig. 1. Surface crack model for transverse butt welded joint.

F kin, k A f,,(. . .) fA(" " ") s S(x) S(y) X

Y re(a, x) G(c,y) R

stress intensity boundary correction factor proportional constants transformation functions for m transformation functions for .4 remotely applied nominal stress; also fatigue strength of butt welded joint stress distribution along potential crack line in x-direction stress distribution along potential crack line in y-direction through-thickness distance from weld toe through plate width distance from centre of plate thickness direction Bueckner's weight function for edge crack in a finite strip Kanazawa's weight function for through-thickness central crack in a finite plate cyclic stress ratio R (R = Kmin/Kmax).

INTRODUCTION FATIGUE behaviour of welded structures is complicated by many factors intrinsic to the nature of welded joints. Normally crack-like defects e.g. slag inclusions, gas pores, lack of penetration at weld root or undercut at weld toes may be introduced in welded joints. Fatigue behaviour of welded joints and welded structures is also greatly affected by the geometry of welded joints[I-7]. However, in design practice, the effect of weld geometry parameters is simply ignored or considered to be non-significant to fatigue behaviour of welded joints. This conservative attitude is no longer acceptable due to recent research progress concerning the effect of weld geometry on the fatigue of welded joints [2-7]. A recent proposal for revision of fatigue clauses in BS PD 6493 [2] has emphasised the importance of the "size effect" of weld geometry e.g. plate thickness and attachment length on the fatigue strength of welded joints. However, no further research has been attempted to study other important weld geometry parameters (e.g. weld toe undercut) or the co-influence effect of all the weld geometry parameters e.g. tip radius of undercut at weld toe, weld toe radius, flank angle, plate thickness and edge preparation angle, and the effect of initial crack geometry. The existence of crack-like flaws in the welded steel joints as a result of weld defects is unavoidable. Under cyclic loading, fatigue cracks are initiated from these defects and will propagate through the plastic thickness during the fatigue life. A study by Mattos and Lawrence [7] has revealed the important effect of weld geometry on fatigue crack initiation life. The effect of individual weld geometry parameters on fatigue of welded joints has been studied by many other researchers [8-14]. However, so far no complete theoretical analysis of the effect of weld geometry parameters on fatigue crack propagation has been carried out. Therefore, this study aims to develop a model to predict the effect of all the important butt weld geometry parameters on fatigue crack propagation life, as well as their overall effect on S-N curve. In this study, a semi-elliptical surface crack model was constructed to evaluate the contribution of the weld geometry to the stress intensity factor based on Linear Elastic Fracture Mechanics (LEFM), superposition and finite elements approaches. Then the co-influence effect of the above-mentioned weld geometry parameters on the fatigue behaviour of welded joints can also be evaluated by using dimensional analysis technique.

A theoretical study o f the effect of weld geometry parameters on fatigue crack propagation life

3

ANSYS 5.0 31 OCT 27 1993 12:21:38 PLOT NO. l ELEMENTS TYPE NUM U PRIES ZV =1 DIST = 55 XF = 50 YF = 6.928 CENTROID HIDDEN

ANSYS 5.0 31 OCT 27 1993 11:48:14

PLOT NO. 1 ELEMENTS TYPE NUM PRES ZV =1 * DIST = 15,243 * XF

= 6.486

~,* YF = 9 . 7 8 8 t CENTROID HIDDEN

Fig. 2. A 2-D finite element mesh used for the calculation of stress distribution along potential crack line in butt welded joints.

THEORETICAL I t is k n o w n mode

(mode

from Fracture

I) c a n b e e x p r e s s e d

Mechanics

APPROACH

that the stress intensity factor (K) for crack opening

in the following form:

r = r. s.

(1)

4

T . N . N G U Y E N and M. A. W A H A B

For the cracks which propagate in the region of stress concentrations produced by the geometry of welded joints, i.e. cracks at weld toes, a further correction factor (Mk) is introduced and known as geometry magnification factor [2, 3]. Then eq. (1) can be rewritten as follows: K = ]I0' Mk" S ' x / ( n • a).

(2)

Solutions for the stress intensity factor due to various crack geometries are available from literature in Fracture Mechanics and can be used for the fatigue assessment of welded structures. In this study a semi-elliptical surface crack with various initial crack shape aspect ratios (a/c)o (from 0.1 to 1.0) [Fig. 1] is assumed to be located at weld toe as a result of weld defect of the order of 0.1 mm (ai=0.1 mm). This conservative assumption was also supported by other researchers [1, 3, 12]. Then the total fatigue life of the welded plate can be considered as the number of cycles needed for this initiated semi-elliptical surface crack propagating through the thickness of welded plate. An empirical solution for the stress intensity factor due to a semi-elliptical surface crack in the centre of a finite plate in mode I loading is given by Newman and Raju [15] as follows:

Ksc = S"

( ~ x / ~ " F(a/t, a/c, c/b, ~b0).

(3)

However, by using this solution the effect of weld geometry of the welded joint can not be included. In order to overcome this obstacle, the weight function method was applied to calculate the stress intensity factor and it is necessary to assume the "similarity effect" between the stress intensity values of a notched and unnotched body due to various crack shapes. It means that the ratios of stress intensity values between a notched and unnotched body are the same for surface 25

20

•

~ r=O.3mm r =0.5 mm

";

15

-~--

r = 0.8 m m r = 1,2mm

,~-10

r = 2.0turn r = 2.5ram

5 !

I

0.2

0.4

'

I

I

0.6

0.8

a/t

(a) Effect of (r) on K~.A 0.9 0.8

--=--

r =0.5 mm

0.7

E

r = 0.3 m m

0.6

--°~r=O.Smm

0.5

----o---- r= 1.0ram

0.4

--,--

r = 1.2 m m r = 1.6ram

0.3 -----

0.2

r = 2.0 m m r = 2.5 m m

0.1

0 0

0.2

0.4

0.6

Relative crack length

0.8

1

(a / t)

(b) Effect of (r) on aspect ratio (a/c).

A theoretical study of the effect of weld geometry parameters on fatigue crack propagation life

5

1

0.9

.~=

0.8

¢

/

0.7

f

T

•

7 ;Iiiii f ililil

0.6

f

r =0.3mm

----c----

r = 0.5 mm

- - - - -

r = 0.8 mm r = 1.0mm

t

.~ 0 . 4

-

-

~

r = 1.2 m m r = 1.6mm

,-3 0.3 --*--

r = 2.0 m m

0.2 r = 2.5mm

0.1 0

I

I

I

I

I

I

I

1

2

3

4

5

6

7

Number of cycles,

8

N x 10 o

(c) Effect of (r) on crack propagation life. 1000

- - - - a - - r =0.3 mm r=0.5mm --'--

r = 0.8 mm

B, 100 r=l.2mm r =2.0mm r = 2.5ram

10 10 s

10 '

10"

Number of cycles N

(d) Effect of (r) on the S N curve. Fig. 3. The effect of the weld toe radius on the fatigue behaviour of butt welded joints.

crack, edge crack or central through-thickness crack. This assumption is already supported by other researchers [16, 17]. When a welded joint is considered as a notched body then the following equations can be written: K wsc,A/Ksc,A:KeWd/Ked= M A

(4)

K~,,/K~c., - Kc~,/K¢~, = M~.

(5)

- -

w

Using eqs (4) and (5) the stress intensity factors due to the semi-elliptical surface crack at the weld toe for point A and surface crack front point B (Fig. 1) can be calculated if the stress intensity solutions for edge crack and central through-thickness crack of welded plate and flat plate are known. Using Bueckner's weight functions for edge crack in a finite plate [18] and Kanazawa's weight function for central through-thickness crack [19], stress intensity factors can be calculated as follows: Kcd =

f"

S ( x ) " re(a, x)" dx

(6)

jo

K~n = 2

S(y)" G(c, y)" dy.

(7)

0

When S ( x ) and S(y) are the local stress distributions along potential crack direction x and y, respectively, then each of them should be a resulting stress due to local stress subjected to weld geometry and external loading in the proper direction.

6

T.N. NGUYEN and M. A. WAHAB

Eqs (4)-(7) enable us to study the effect of various weld geometry parameters on the stress intensity factor, as well as fatigue behaviour of welded joints, quite simply and satisfactorily once stress distribution along potential crack line in weldment is evaluated. By using 2D-Finite Elements [20] the local stress distributions subjected to weld geometry can be calculated (Fig. 2) and fitted into the polynomial form and used for the calculation of the stress intensity factor. With the above assumptions the stress intensity magnification factors, M A and M~, due to the co-influence effect of weld geometry parameters can be obtained, and also AKA and AKB can be obtained. The crack-growth rates were calculated by assuming that Paris' equation [21] is obeyed independently at points A and B at the crack front, and it can be rewritten as:

da/dNp =

CA" (AKA)"

(8)

dc/dNp =

Ca" (AK,)",

(9)

where Ca = 0.9" CA as suggested by Newman and Raju [15]. By integrating eqs (8) and (9) simultaneously the fatigue life and fatigue strength of a butt welded joint subjected to variations of various butt weld geometry parameters can be evaluated. A computer program was written to facilitate the numerical procedures discussed above and Simpson's rule was used for the calculation of the integrals. The material constant of Paris' equations was assumed as m = 3, CA = 3 × 10 -t3 mm/cycle as recommended by Maddox [3] for a wide range of structural steels. The failure criterion was chosen for the instant when the depth of the semi-elliptical surface crack in through-thickness direction reached the plate thickness (af = t). 16 14 12

--m--

0=0¢ 0=5 °

,,g ~ 8

--*-- - - ~

8= IO ° 8= 20 ©

6

0=400

4

9=60 a

2

0

S

I 0.2

= 80 MPa I 0.4

I 0.6

I 0.8

a/t

(a) Effect of (O) on K~:.A. 1.2 •

1

0=5*

o o

g

' 0=~

0.8

- - ' - - 0=I0' ----0----

0.6

0=15.! I

~.

0.4

0=20* e=3¢

~ - -

0.2

0=40 ~

------o-----0=50'

0

I 0.2

I 0.4

I 0.6

I 0.8

Relstlve crack length (s / t)

(b) Effect of (O) on aspect ratio (a/c).

--×--

0=60 •

A theoretical study of the effect of weld geometry parameters on fatigue crack propagation life

o.,

i

0.8

!

•

O=0*

0=5"

i

0.7

--'--

~

0.6

---o-- o=]~'

--

11.5

.L

-~0.4

~

7

e = 10"

0=20) 8=30 °

11.3

----'--

0.2

I"

0.1 0

S=80MPa I 2

I 4

O=~

-----o---O=5O ~

I I I ! 6 8 10 12 Number of cycles, N x 10 6

! 14

(c) E f f e c t o f ( O ) o n c r a c k p r o p a g a t i o n

--x--

0=60 •

16

life.

1000 •

0=0'

.------0-----0=5* --*--

:IE

0 = 10°

____¢1_ 0=20*

100

u

0=30"

e to

" - " ~ - - - - O= 40" ""~--

0=50'

-----0---0=60'

10 10

10' 10' Number o! cycles N (d) E f f e c t o f ( O ) o n S N c u r v e .

Fig. 4. The effect of flank angle on the fatigue behaviour of butt welded joints. In order to quantify the co-influence effect of all the weld geometry parameters on fatigue behaviour of a butt weld joint, a mathematical model for the S - N curve subjected to the variation of weld geometry parameters is proposed on the basis of the fatigue design rule BS 5400 [2] as follows: S".N

(10)

=A,

where m / m o = f m ( r ' / r , r/t, (9, dp, t / b ) A /Ao = f A ( r ' / r , r /t, 69, c~, t /b )

m0=3

and

Ao=f(t/b).

By using dimensional analysis technique and transformations [5, 6, 22] the expressions for m and A can be rewritten as follows: m / m o = k,, . f , , ( r ' / r ) . f , , ( r / t ) "f m ( ~ ) "Jr,,((/) ) "f , , ( t /b )

(! 1)

A /Ao = kA "f A ( r ' / r ) "f A ( r / t ) "f A ( O )

(12)

"fA(c~ ) "f A ( t / b )

A /Ao = kA "f A ( r ' / r ) "f A ( r / t ) ' f A ( O ) "fA(c~ ) "f A ( t /b ).

(13)

Once eqs (11) and (12) are determined, the co-influence effect of all the relevant butt weld geometry parameters can be evaluated.

8

T.N.

NGUYEN

and M. A. W A H A B

R E S U L T S AND DISCUSSION

Effect of weld toe radius Figure 3(a) shows the effect of the weld toe radius on the stress intensity factor KWA calculated the constant stress range S = 80 MPa (other weld geometry parameters are kept constant: 0, 6) = 30 °, q5 = 600 and t = 12 mm). It shows that the value of K sc,A w is decreased as the weld radius (r) increases. The significant difference between the values of K sc,A ~ is observed due to increase of the weld toe radius (r) from 0.3 to 2.0 mm. However, only little difference between values of K sc,A w is observed due to the increase of (r) from 2.0 to 2.5 mm. Figure 3(b) shows the effect of the weld toe radius on the crack aspect ratio (a/c). It shows that a semi-elliptical surface crack, with a certain initial crack shape [(a/c)o = const] propagating a butt welded joint with a higher value of weld toe radius, tends to develop at the crack shape with a higher value of (a/c) during crack propagation life. At the early stage of crack growth (a/t < 0.1) the surface crack tends to reach the shape with a higher value of (a/c), i.e. close to the shape of a semi-circular crack. However, the value of ratio (a/c) decreases as the crack propagates further. Figure 3(c) shows the effect of the weld toe radius on the fatigue crack propagation life. It is obvious that the fatigue crack propagation life is increased as the value of (r) increases. It means that the fatigue life of the butt welded joint can be improved by increasing the value of the weld toe radius (e.g. by grinding or other post-weld finishing techniques). This conclusion is consistent with the results claimed by several other researchers [1, 3, 8, 9]. This figure also shows that the improvement of the fatigue crack propagation life due to an increase of (r) from 0.3 to 2.5 mm is of the order of 4.5 × 1 0 6 cycles for a constant nominal applied stress range (S = 80 MPa). for r' toe the the

60 5O /" 4O

,/

~30

/

---'--

t = 9 mm

- ~ : ~ - - - t = 12 rnm

..-/

--'--

t = 16 mm t=2Omm

20

---'---

~

10 0

g.;.~ ......

I

I

I

I

0.2

0.4

0.6

0.8

t = 25 mm t = 32 mm

a/t

(a) Effect of (t) on K *sc.A"

1.6 1 ~ •

~1"4

t=9mm

t o t= 12mm

o

~0.8

• t= 16ram

io

o

o t = 20mm • t = 25ram

QD~

~o6~ "°OOo,: "'~. ~. . . . . 0.4 +

OJ 0

," .........

I 0.2

~

e

t =32ram

~

°.~oooooooooo°°~°~.*.

I 0.4

I 0.6

I 0.8

Relative c r a c k length (a / t)

(b) Effect o f (t) on aspect ratio

(a/c).

1

A theoretical study of the effect of weld geometry parameters on fatigue crack propagation life .,P-,,,Q

1 •

0.9 o

*

o

•

0.7

o

•

0.5

•

o

•

0.4 • /~

0.2

A~

•

"

0

:

. . . .

:

1

0

<> "

. . . .

¢DI •

.:

0

*

• t = 25 m m

• •

t~ t = ~ g m m

•

DI

. . . .

o t= 20mm

•

•

O []

*

t= 16mm

•

o

*

o

•

0.1 . . . .

o

•

o

•

"

•

o

*

o

o l= 12mm

• • •

~

•

¢

•

0.3

•

<>

• A

• •

t=9mm

•

o O o

•

¢ ¢

•

•

D

<> / •

•

o

o

0.6

.e.

•

D

e.'2:

0.8 v

9

S : 80 M P a

:

. . . .

:

2 3 4 Number of cycles, N x 10 s

. . . .

5

(c) Effect of (t) on crack propagation life. 1000

•

t=9mm

----D---

t = 12 m m

--*--

t = 16 m m

---'¢-~

t = 20 m m

----*--

t = 25 m m

-~----

t = 32 m m

100

10

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

10 e Number of cycles N

10 r

10 s

(d)

Effect

of

(t)

on

the

S

N

curve.

Fig. 5. The effect of plate thickness on the fatigue behaviour of butt welded joints.

Figure 3(d) shows the effect of weld toe radius on the S - N curve. It shows that the S - N curve tends to move from left to right as the value of the weld toe radius increases. As a result, the fatigue strength and fatigue life of butt welded joints can be improved correspondingly. This figure also shows that the fatigue strength of a butt joint at 2 × 106 cycles is increased by 34% as the weld toe radius increases from 0.3 to 2.5 ram.

Effect of flank angle Figure 4(a) shows the effect of the flank angle on the stress intensity factor K~.A calculated for the constant stress range S = 80 MPa (other weld geometry parameters are kept constant: r = I mm, r ' = 0, q~ = 60 ° and t = 12 mm). It shows that the value of Kw,Ais decreased as the value of flank angle decreases. The significant difference between the values of K*s c , A is observed due to the decreasing values of flank angle from 20 ° to 0 °. There is a non-significant difference between the values of K w s c , A corresponding to the values of flank angle from 20 ° to 60 °. Figure 4(b) shows the effect of the flank angle on the crack aspect ratio (a/c). It shows that a semi-elliptical surface crack with certain initial crack shape [(a/c)o = const] propagating in a butt welded joint with a lower value of flank angle tends to develop the crack shape with a higher value of (a/c) during crack propagation life. At the early stage of crack growth (a/t < 0.1) the surface crack tends to reach the shape with a higher value of (a/c), i.e. close to the shape of a semi-circular crack. For a base plate or flush-ground welded plate (with O = 0) the initial semi-elliptical crack becomes semi-circular after a few cycles. However, the value of ratio (a/c) decreases as the crack propagates further. It is also observed from this figure that there is no significant difference between

10

T.N. NGUYEN and M. A. WAHAB

crack shapes that developed during crack propagation life corresponding to various values of flank angles from 20 ° to 60 ° . Figure 4(c) shows the effect of flank angle on the fatigue crack propagation life. It is obvious that the fatigue crack propagation life is increased as the value of (O) decreases. It means that the fatigue life of the butt welded joint can be improved by decreasing the value of flank angle (e.g. by grinding or other post-weld finishing techniques). This conclusion is consistent with the results claimed by several other researchers [1, 3, 8, 9]. The improvement of fatigue crack propagation life due to the decrease of (6)) from 60 ° to 0 ° is of the order of 14 x 106 cycles for a constant nominal applied stress range (S = 80 MPa), while the improvement of the fatigue life due to the variation of (r) is of 4.5 × l06 [Fig. 3(c)]. It means that the degree of influence of the flank angle on the fatigue crack propagation life is more significant than that of the weld toe radius. Figure 4(d) shows the effect of the flank angle on the S-N curve. It shows that the S-N curve tends to move from left to right as the value of the flank angle decreases. As a result, the fatigue strength and fatigue life of butt welded joints can be improved with respect to a smaller flank angle, i.e. to smoother weld bead. The flush ground welded plate will have the highest fatigue strength and this is equal to the fatigue strength of the parent plate [3]. This figure also shows that the fatigue strength of butt welded joints at 2 x 106 cycles is increased by 21% as the flank angle decreases from 60 ° to 5° . However, the fatigue strength of the butt joint would be increased up to 54% as the flank angle decreases further to the level of the base plate (O = 0°).

Effect of plate thickness Figure 5(a) shows the effect of plate thickness on the stress intensity factor K*sc,A calculated for the constant stress range S = 80 MPa (other weld geometry parameters are kept constant: 16 14 -----a--

~b: 45'

12 -----0---- ~ = 50' <10 --*--

8

~ = 60'

~,=70'

6 - ' - - ' - " - - ~ = 80'

4 ----6--- ~=90 ~ 2

S = 80 MPa

0

0

I

I

I

I

0.2

0.4

0.6

0.8

1

a/t ( a ) E f f e c t o f (~b) o n K ~ , A.

0.8 ~

0.7

"~= 0.6 ._

~ o.s

~o

--m--

t~=45 o

----o---

t~=50 °

--°--

~=60 °

. 4

----o---- ~=70 •

0.3 ¢=SO ° .~

0.2 0.1

I

I

I

I

0.2

0.4

0.6

0.8

Relative crack length (a I t) ( b ) E f f e c t o f (q~) o n a s p e c t

ratio

(a/c).

A theoretical study of the effect of weld geometry parameters on fatigue crack propagation life

11

0.9

I -"-"~-- ¢=45* + ¢~=50* - - . - - ~,=60o

0.8 0.7 0.6

0.5, ,~

I/i/i

0.4

~--

251 ~.,"

0.3

m=80*

----~---, =9o*

0,2

0.1 ....

: .... 1

, .... 2

: .... 3

Number

: ....

: ....

4

5

of cycles,

N x 10

; .... 6

o

(c) Effect of (4)) on crack propagation life. 1000

~-=2

0=45. 0=50*

- - ' - - ¢=60' 100

---o-----0=70*

I

10

10 s

10 6

' ' ''"

~--

0=80*

~

0=90"

1() 7

Number of cycles N

(d) Effect of (4)) on S N curve. Fig. 6. The effect of the edge preparation angle on the fatigue behaviour of butt welded joints. r = 1 mm, r ' = 0, O = 30 ° and ~b = 60°). It shows that the value of KwA is increased as the value of plate thickness increases. This can explain the well-known effect of plate thickness [1] in reducing the fatigue life of a weld joint [Fig. 5(d)]. Figure 5(b) shows the effect of plate thickness on the crack aspect ratio (a/c). It shows that a semi-elliptical surface crack with certain initial crack shape [(a/c)o = const] propagating in a butt welded joint of thinner plate tends to develop the crack shape with a higher value of (a/c) during the crack propagation life. At the early stage of crack growth (a/t < 0.1) the surface crack tends to reach the shape with a higher value of (a/c), i.e. close to the shape of a semi-circular crack. However, the value of the ratio (a/c) decreases as the crack propagates further. Figure 5(c) shows the effect of plate thickness on the fatigue crack propagation life. It is obvious that the fatigue crack propagation life is decreased as the value of (t) increases. This conclusion is consistent with the experimental results obtained by several other researchers [I, 3, 12-19]. The improvement of the fatigue crack propagation life due to the decrease o f ( t ) from 32 to 9 m m is of the order of 3 x 106 cycles for a constant nominal applied stress range (S = 80 MPa), while the improvements of the fatigue life due to the variations of (r) and (O) are of the order of 4.5 × 106 and 14 x 106, respectively. It means that the degree of influence of plate thickness is less significant than that of both the weld toe radius and flank angle. Figure 5(d) shows that the fatigue life is significantly increased as the plate thickness decreases from 32 to 9 mm. However, the improvement of the fatigue life due to the decrease of plate thickness from 20 to 9 m m is non-significant. It means that for the lower range of plate thicknesses (less than 20 mm), the effect of plate thickness is ignorable. It is also clear from this figure that

12

T . N . N G U Y E N and M. A. W A H A B

the thicker plate tends to move the S-N curve from right to left. It means that the fatigue life and fatigue strength of welded plates are decreased with increasing value of plate thickness. Fatigue strength of butt joints at 2 × 106 cycles is decreased up to 21% as plate thickness increases from 9 to 32 mm.

Effect of edge preparation angle Figure 6(a) shows the effect of the plate edge preparation angle on the stress intensity factor Kw sc,A calculated for the constant stress range S = 80 MPa (other weld geometry parameters are kept constant: r = 1 mm, r' = 0, t = 12 mm and O = 30°). It shows that the value of KW.a is slightly increased as the value of the plate edge preparation angle increases from 45 ° to 90 ° . This effect of angle (05) becomes more significant at the later stage of crack propagation (a/t > 0.4). Figure 6(b) shows the effect of the edge preparation angle on the crack aspect ratio (a/c). It shows that a semi-elliptical surface crack with certain initial crack shape [(a/c)o = const] propagating in a butt welded joint with lower value of angle (05) tends to develop the crack shape with a higher value of (a/c) during crack propagation life. At the early stage of crack growth (a/t < 0.1) the surface crack tends to reach the shape with a higher value of (a/c), i.e. close to the shape of a semi-circular crack. However, the value of the ratio (a/c) decreases as the crack propagates further. Figure 6(c) shows the effect of the edge preparation angle on the fatigue crack propagation life. It is obvious that the fatigue crack propagation life is increased as the value of (05) decreases from 90 ° to 45 ° . The improvement of the fatigue crack propagation life due to the decrease of angle (05) from 45 ° to 90 ° is of the order of 1 x 10 6 cycles for the constant nominal applied stress range (S = 80 MPa), while the improvements of the fatigue due to variation of (r), ( 0 ) and (t) are of 35

=--

r ' = 0.05 m m r'= 0.10mm

. 2o

--*--

r ' = 0.15 m m r ' = 0.25 m m

15

r ' = 0.35 m m

10 r ' -. 0.50 rnm

5 I

I

0.2

0.4

' I

I

0.6

Relative crack length (a) Effect

0.8 (a / t)

of (r')

on

K~,A.

0.8 0.7 .~ .o

0.6

--m--

r ' = 0.05 m m

--'--

r ' = 0.15 m m

I

~.0.4

.~0.3 ..~ 0.2

--,--

~ 0.1 0 0.2

0.4

0.6

Relative crack length

0.8 ( a / t)

(b) Effect of (r') on aspect ratio (ale).

r ' = 0.10 rnm

r ' = 0.25 m m r ' = 0.35 m m r'= 0.50ram

A theoretical study of the effect of weld geometry parameters on fatigue crack propagation life

13

1

0.9

0.8 v~0.7

--'--

0.5 o ,~

>~

I

/ I /'7I

~0.6

0.4

?/

0.3

--°--

!g J /Y d

--'--

0.2

0.1 ! ! ! 0.5 1 1.5 Number of cycles, N x 10 e

r'=

0.05 mm

r' = 0.10 rnm r" = 0.15 mm r'=

0.25mm

r ' = 0.35 mm r ' = 0.50 mm

(c) Effect of (r') on crack propagation life. 1000

•

v

-----

100

r'=

0.05 mm

r'=

0.10mm

r' = 0.15 mm r'=

~ - -

v)

0.25 mm

r' = 0.35 mm r' = 0.50 rnm

10104

10 s

10 e

1{) 7

Number of cycles, N

(d) Effect of (r') on S N curve. Fig. 7. The effect of radius of curvature of undercut at weld toe on the fatigue of butt joints. the order o f 4.5 × 106, 14 x 106 and 2 × 106, respectively. It means that the degree of influence o f the edge preparation angle is less significant than that o f other weld geometry parameters, i.e. the weld toe radius, flank angle and plate thickness. Figure 6(d) shows the effect of the edge preparation angle on the S - N curve. It shows the S - N curve is slightly m o v e d from left to right as the value o f angle (~b) decreases. However, the small improvement o f the fatigue and fatigue life o f butt welded joints can be considered to be non-significant as S - N curves corresponding to various values o f angle (4)) almost overlap each other. This figure also shows that the fatigue strength o f butt joints at 2 × l06 cycles is increased by 7% as angle (~b) decreases from 90 ° to 45 °. This increment is ignorable due to the large scatter o f fatigue data often met in fatigue testing.

Effect of undercut at weld toe Figure 7(a) shows the effect o f the tip radius o f undercut at the weld toe (r') on the stress intensity factor K~,A calculated for the constant stress range S = 80 M P a (other weld geometry parameters are kept constant: r = 2 mm, 6) = 30', 4) = 60 c' and t = 12 mm). It shows that the value o f K sc.A W is slightly increased as the value o f (r') increases from 0.05 to 0.5 mm. This effect o f (r') on K,~.A can be used to explain the detrimental effect o f weld toe undercut on fatigue behaviour o f welded joints. However, when the crack propagates beyond the length of 0.3 times the plate thickness (0.3 × t) the value o f K w sc.A is decreased as the value o f (r') increases. It means that the effect o f weld toe undercut diminishes after that length, and the tip radius of undercut will act as the weld toe radius.

14

T . N . N G U Y E N and M. A. W A H A B

Figure 7(b) shows the effect of the tip radius of undercut at the weld toe (r') on the crack aspect ratio (a/c). It shows that a semi-elliptical surface crack with certain initial crack shape [(a/c)o = const] propagating in a butt welded joint with a higher value of tip radius of undercut (r') tends to develop the crack shape with a higher value of (a/c) during crack propagation life. At the early stage of crack growth (a/c < 0.1) the surface crack tends to reach the shape with a higher value of (a/c), i.e. close to the shape of a semi-circular crack. However, the value of the ratio (a/c) decreases as the crack propagates further. Figure 7(c) shows the effect of the tip radius of undercut at the weld toe (r') on the fatigue crack propagation life. It is obvious that the fatigue crack propagation life is increased as the value of (r') decreases. It means that the fatigue life of the butt welded joint can be improved by decreasing the value of (r') or by eliminating the undercut at the weld toe by grinding or other post-weld finishing techniques. The improvement of the fatigue crack propagation life due to the decrease of the tip radius of undercut from 0.5 to 0.05 mm is of the order of 1.7 x 10 6 cycles (S = 80 MPa), while that due to variation of (r), (O), (t) and (q~) is 4.5 x 10 6, 14 x l 0 6, 3 × l06 and I × 10 6 cycles, respectively. It means that the degree of influence of the tip radius of undercut on the fatigue behaviour of butt welded joints is less than that of (r), (O) and (t), but stronger than that of (tk). Figure 7(d) shows the effect of the tip radius of undercut at weld toe (r') on the S-N curve. It shows that the S-N curve tends to move from left to right as the value of (r') decreases. It means that the fatigue strength and fatigue life of butt welded joints can be improved by either partly or totally removing the weld toe undercut. This figure also shows that the fatigue strength of butt joints at 2 x 10 6 cycles is increased by 12% as the tip radius of undercut decreases from 0.5 to 0.05 mm. 20 18 •

a/c

:0.1

---o----

ale

: 0.2

--°--

a/c:0.3

16

14 ,<12

---'0---

~: 10 8

a / c : 0.5

• ..... a l e : 0 . 8

6

~

a/c=1.0

4 2 0 0

:

:

:

:

0.1

0.2

0.3

0.4

0.5

Relative crack length (a / t)

(a) Effect of ratio (a/c)o on K*sc, A"

1 0.9 -.~ 0.8 c:

v

o

• (alc), =0.1

0.7

o (a/c), =0.2

0.6

• (a/c), =0.3

c.:

~

0.5

o ( a / c ) , =O.S

~. 0.4

~

• ( a / c ) , :0.8

0.3 0.2

5, ~ e O n n n o n n n n n o n o n e o n o

( a / c ) , =1.0

ooooooo

0.1 I

I

l

0.2

0.4

0.6

0.8

Relative crack length (a / t)

(b) Effect of ratio (alc)o on aspect ratio (ale).

A theoretical study of the effect of weld geometry parameters on fatigue crack propagation life

j//U

0.8 0.7

0.6 o

~

0.5

0.4

~ 0.3 0.2

•

15

(a / c), :0.1 (a / c), =o.2

-----

(a/c),

=0.3

---o---

(a/c),

=o.5

(a / c), =0.8 ~

(a/C)o =1.o

0.1 0

I 6

I 8

I

I

10

12

I 14

I 16 N u m b e r of c y c l e s , N x 10 s

I 18

20

(c) Effect of (a/c)o on crack propagation life.

1000

o "s: v cJ~

100 o P

--m--

a / c =0.1

~

a/c=0.2

--'--

ale=0.3

-~o---

a / c = O.5

~ - -

a l e =0.8

- ~ - a - - - - a i c = 1.0

1010a

10 s

10 e

107

N u m b e r of c y c l e s , N

(d) Effect of (a/c) o on S - N curve. Fig, 8. The effect of initial aspect ratio (a/c)o on the fatigue behaviour of butt welded joints.

Effect of initial crack shape aspect ratio The effect of the initial crack shape aspect ratio (a/c)o on the fatigue behaviour of butt welded joints was investigated by keeping all the relevant butt weld geometry parameters constant and varying the value of (a/C)o. Figure 8(a) shows the effect of the initial crack shape aspect ratio (a/c)o on the stress intensity factor K~.A calculated for the constant stress range S = 80 MPa (other weld geometry parameters are kept constant: r ' = 0.15 mm, r = 2mm, 69 = 30 °, ~ = 6ff~ and t = 12 mm). It shows that the value of K w sc,A is decreased as the value of ratio (a/c)o increases from 0.1 to 1.0. However, this trend seems to be significant at the early stage of crack growth (a/t < 0.1) only. Figure 8(b) shows the effect of the initial crack aspect ratio (a/c)o on the crack shape during crack propagation life. It shows that the semi-elliptical surface cracks with various values of (a/C)o tend to develop the crack shape close to the shape developed by an initial semi-circular surface crack during crack propagation life. However, this effect of the initial crack shape ratio is significant only at the early stage of crack propagation (a/t < 0.1) and some of the fluctuations of the value of(a/c) are also observed. Then the value of(a/c) with respect to various values of (a/c)0 will follow the same curve as expected from the semi-circular surface crack when the crack propagates further. Figure 8(c) shows the effect of the initial crack shape aspect ratio (a/c)o on the fatigue crack propagation life. It is obvious that the fatigue crack propagation life is increased as the value of (a/c)o increases. It means that the initiated fatigue cracks with lower initial crack shape aspect ratio tend to be more detrimental to the fatigue life of butt welded joints compared to those with higher initial crack shape aspect ratios. This deduces that a semi-circular surface crack seems to be less harmful than the semi-elliptical or edge crack. EFM ~ l : l - B

16

T, N. N G U Y E N

a n d M. A. W A H A B

T a b l e 1. T r a n s f o r m a t i o n f u n c t i o n s f , , ( . . . ) , fA (' " ") a n d p r o p o r t i o n a l c o n s t a n t s k,, a n d k A o b t a i n e d f o r v a r i o u s d i m e n s i o n l e s s p r o d u c t s o f weld g e o m e t r y p a r a m e t e r s c o r r e s p o n d i n g to eqs (11) a n d (12) i n c l u d i n g the e q u a t i o n f o r A 0 No.

Transformation functions

1 2

f,~(r'/r) = 0.9715 + 0.1897 * (r'/r) - O. 1599 * (r'/r) * In(Y/r) - 0.2125 • (rx/(r'/r) f,,(r/t)=O.9487-O.O416*(r/t)+O.OOOll/(r/t)

3 4

fm ( O ) = 0.9203 -- 0.0001 * O + 0.0088 * I n ( O ) f,,(q~) = 0.9541 -- 0.4626/,~ f,,(t/b) = [1.0054 - 3.7887 * (t/b) + 3.7509 * (t/b)2]/[l - 3.7541 * (t/b) + + 3.7004 * (t/b) 2] ( f o r b = 50 m m )

5

k A or km k , , = 1.1837

(k,,= 1.1158 if r ' = 0)

1 2 3

fA(r'/r) = 0.0699 -- 0.1341 * (r'/r) -- 0.2304 *~r'/r) * In(Y/r) f A ( r / t ) = 0.2157 + 0 . 4 9 7 0 * (r/t) 3 - O.O196/x/(r/t ) f A ( O ) = 0.1894 - 0.0131 * In(0) + 2.9573 * e x p ( - O )

k A = 1823.363

4

fA (~b) = 0 . 3 1 6 5 . 0 1 8 , ~b - 0 . 0 3 5 4 * ( x / ~ f A ( t / b ) = O . 2 1 6 8 - O . 1 4 0 2 . x / ( t / b ) (for b = 5 0 m m )

(k A = 309.1123 if r'=0)

5

Coeff. r 2

A0 = [5.6078 + 4.3553 * (t/b) + 10.0300 * (t/b) 2] * 10 ~2 ( f o r b = 50 m m )

0.987 0.998 0.997 0.999 0.999 0.993 0.997 0.992 0.999 0.999 0.999

Figure 8(d) shows the effect of the initial crack shape aspect ratio (a/c)o on the S-N curve. It shows that the S-N curve tends to move from left to right as the value of (a/c)o increases from 0.1 to 1. This figure also shows that there is no significant difference between the effect of (a/c)o on the S-N curve for a large range of the initial crack shape aspect ratio from 0.2 to 1.0 mm. Therefore, it suggests that when using a semi-elliptical crack propagation model to evaluate fatigue behaviour of butt welded joints an initial crack with aspect ratio of 0.2 can be adopted.

A model to predict the co-influence effect of butt weld geometry parameters Table 1 shows the transformation functions fro(." "),fa (" " ) and proportional constants k,, and kA that were obtained for various dimensionless products of weld geometry parameters corresponding to eqs (11) and (12). The value of A0 can be obtained from Table 1 as a function of the normalised plate thickness. By substituting these transformation functions and suitable constants (kin and kA) into eqs (11) and (12), respectively, we can get the value of constants m and A for eq. (10). Then the S-N curve subjected to numerous variations of butt weld geometry parameters can be constructed correspondingly. Figure 9 shows a comparison between a scatter band of S-N curves due to variation of the butt weld geometry parameters and the available experimental data from ref. [23]. Several S-N curves representing design classes D, F and W (BS 5400) are also constructed for the comparison. It is obvious from this figure that the S-N curves predicted by the proposed model underestimate the experimental data. This may be due to the fact that a significant portion of fatigue crack initiation life has been ignored in this study. This figure also shows that the predicted scatter band of S-N curves subject to variation of the weld geometry parameters is in good agreement with S-N curves covered by design classes from 1000 •

R --*--

u~.

Class F (BS 5400) Class W (BS 5400)

o

S max, pred

100 •

10

S mln, pred

10 4

10 s

10 6

10 7

Exper. Data [NRIM]

10 s

Number of cycles, N

Fig. 9. A c o m p a r i s o n b e t w e e n a s c a t t e r b a n d o f S - N curves d u e to v a r i a t i o n s o f b u t t weld g e o m e t r y p a r a m e t e r s a n d the a v a i l a b l e e x p e r i m e n t a l d a t a f r o m ref. [23].

A theoretical study of the effect of weld geometry parameters on fatigue crack propagation life

17

D to W (BS 5400). The design class F which is commonly used for design of butt welded joints has fallen in the middle of the predicted scatter band of S - N curves. It is suggested that for the sake of a safe design concept, class W should be used for fatigue design of butt welded joints instead of class F.

CONCLUSIONS The analysis of the effect of weld geometry of butt welded joints on the fatigue crack propagation life gives the following important conclusions: (1) The fatigue life and fatigue strength of butt welded joints can be improved by modifying one of its weld geometry parameters as follows: • Increasing the radius of weld toes • Decreasing the value of flank angle. The significant improvement is obtained when the flank angle is decreased beyond the value of 20 ° . The best case is to flush-grind the weld bead to the level of the base plate • Decreasing plate thickness • Decreasing the edge preparation angle • Decreasing the tip radius of undercut at weld toes or eliminating the weld toe undercut completely. (2) The degree of influence of various weld geometry parameters on fatigue behaviour of butt joints is in the following order: flank angle, weld toe radius, plate thickness, tip radius of undercut and edge preparation angle. (3) The effect of butt weld geometry parameters on fatigue crack propagation life is due to the early stage of crack growth only. Beyond that crack length the weld geometry no longer has a significant effect on fatigue crack propagation life. (4) A theoretical explanation for the well-known side effect of plate thickness in decreasing the fatigue life and fatigue strength of welded joints is revealed. However, for the lower range of plate thicknesses (less than 20 mm) this effect is found to be non-significant. (5) The initial crack shape aspect ratios play important roles in fatigue crack propagation life. The initial semi-circular surface crack is less harmful than the semi-elliptical or edge one. However, there is no significant effect between the large range of initial crack shape aspect ratio from 0.2 to 1.0. It suggests that for the fatigue assessment of butt welded joints using LEFM, an initial crack aspect ratio of 0.2 can be adopted. (6) A mathematical model that developed in this study to predict the co-influence effect of butt weld geometry parameters satisfactorily gives a new insight into fatigue design. This analysis shows the basic understanding of the effect of weld geometry on the fatigue crack propagation life of butt welded joints in structural steel. It gives a good explanation for post-weld treatments (e.g. grinding of the weld toe) commonly used in practice to improve fatigue performance of welded structures. It also introduces the recommendation for more efficient use of post-weld treatments subject to particular cases.

REFERENCES [1] T. R. Gurney, Fatigue of Welded Structures. Cambridge University Press (1979). [2] S. J. Maddox, Revision of the fatigue clauses in BS PD 6493. Proc. Inter. Conf. on Weld Failures (Edited by J. D. Harrison), pp. 307-321 (1988). [3] S. J. Maddox, Fatigue Strength of Welded Structures. Abington (1991). [4] J. A. M. Ferreira and A. A. M. Branco, Influence of the radius of curvature at the weld toe in the fatigue strength of fillet welded joints. Int. J. Fatigue 11, 29 36 (1989). [5] T. N. Nguyen and M. A. Wahab, The effect of weld geometry parameters on stress intensity factor and fatigue life. Proc. 2nd Asian Pacific Conf. on Computational Mechanics (Edited by S. Valliappan, V. A. Pulmamo and F. Tin-loi). A. A. Balkema, Rotterdam, pp. 883 888 (1993). [6] T. N. Nguyen and M. A. Wahab, The combined effect of weld geometry parameters on fatigue strength and fatigue notch factor of butt welded joint. Proc. 4th Annual WTIA Welding Conf. and National AINDT CoJ!/i FABCON/FABFAIR, Toward a Competitive Edge (Edited by E. Siores), pp. 74-79 (1993). [7] Mattos and F. V. Lawrence, Estimation of the Fatigue Crack Initiation L!/b in Welds"using Low-cycle Concepts, Society of Automotive Engineers (1977).

18

T . N . NGUYEN and M. A. WAHAB

[8] F. V. Lawrence, Estimation of fatigue crack propagation life in butt welds. Welding J. 213 220 (1973). [9] F. V. Lawrence and W. H. Munse, Fatigue crack propagation in butt weld containing joint penetration defects. Welding J. 221-225 (1973). [10] T. R. Gurney and S. J. Maddox, Determination of fatigue design stresses for welded structures from an analysis of data. Metal Construction British Welding J. 418-422 (1972). [11] S. J. Maddox, Calculating the fatigue strength of welded joints using fracture mechanics. Metal Construction Welding J. 327-331 (1970). [12] A. Ohta, T. Mawari and N. Suzuki, Evaluation of effect of plate thickness on fatigue strength of butt welded joints by a test maintaining maximum stress at yield strength. Engng Fracture Mech. 37, 987 993 (1990). [13] S. Berge, On the effect of plate thickness in fatigue welds. Engng Fracture Mech. 21, 423-435 (1985). [14] R. Yee and D. J. Burns, Thickness effect and fatigue crack development in welded joints. Proc. 7th Inter. Conf. on Offshore Mechanics and Arctic Engineering. Houston, Texas, pp. 447-457 (1988). [15] J. C. Newman, Jr and 1. S. Raju, An empirical stress-intensity factor equation for the surface crack. Engng Fracture Mech. 15, 185 192 (1981). [16] X. Niu and G. Glinka, Stress intensity factors for semi-elliptical surface cracks in welded joints. Int. J. Fracture 40, 255-270 (1989). [17] J. Foth, R. Marissen, K. H. Trautmann and H. Nowack, Short crack phenomena in high strength aluminium alloy and some analytical tools for their prediction, in The Behaviour of Short Fatigue Cracks, EGF Pub. 1., Mechanical Engineering, London, pp. 353 368 (1986). [18] A. P. Parker, The Mechanics of Fracture and Fatigue, An Introduction. E. & F. N. Spon Ltd, London (1981). [19] D. V. Nelson, Effect of residual stress on fatigue crack propagation, in Residual Stress Effects in Fatigue, A S T M STP 776, 172-194 (1982). [20] Ansys User's Manual, Revision 5.0, Swanson Analysis Systems, Huston, PA, U.S.A. (1992). [21] P. C. Paris and F. Erdogan, A critical analysis of crack propagation laws. Trans. A S M E 85 Series D, 528 534 (1963). [22] H. L. Langhaar, Dimensional Analysis and Theory of Model. John Wiley & Sons, London (1967). [23] NRIM Fatigue Data Sheet, Technical Document No. 2, Fatigue Properties for Welded Joints of High Strength Steels .for Welded Structure. National Research Institute for Metal, Tokyo, Japan (1983). (Received 21 February 1994)