Fatigue notch factor of gaps in welded joints reconsidered

Engineering Fracture Mechanics Vol. 57, No. 4, pp. 405-407, 1997

Pergamon PII: S0013-7944(97)00022-2

FATIGUE

© 1997 ElsevierScienceLtd. All rights reserved Printed in Great Britain 0013-7944/97 $17.00 + 0.00

NOTCH FACTOR OF GAPS JOINTS RECONSIDERED

IN WELDED

D. RADAJ Daimler-Benz AG, 70546, Stuttgart, Germany Abstract--The fatigue notch factor of short gaps or cracks in welded joints determined by the notch stress approach with fictitious notch rounding is modified on the basis of theoretical relations for notch stresses and stress intensity factors. The accuracy of the derived correction factors is proven by application to a cruciform welded joint with short internal gaps. © 1997 Elsevier Science Ltd Keywords--fatigue notch factor, welded joints, notch stress, short crack.

1, I N T R O D U C T I O N THE fatigue strength of welded joints in the high-cycle fatigue range may be assessed on the basis of the notch stress approach [1]. Within this method, the sharp notches at the toe and root of the weld are fictitiously rounded (notch radius pf = 1 mm for lower-strength steels) in order to take the microsupport effect of these notches into account. The strength reduction by the notch is overestimated in cases of relatively short gaps or cracks (gap length a ~ pf), Fig. 1. This is indicated by comparative evaluations based on the stress intensity factor approach [2].

2. E M P I R I C A L R E D U C T I O N FACTOR The empirically proposed short crack reduction factor ~ = 1/x/1 + a/pr (see ref. [2]) modifying the fatigue notch factor Kf determined for the fictiously rounded notch (Kf red = ffKf) is not generally applicable. It provides acceptable values for a/pr ~ 1.0 but not so for a/pf ~ 1.0 as will be shown later. It is converging to g--,0 instead of g---, 1.0 for a/pc-, oo. Therefore, the issue of the short crack reduction factor was reconsidered.

3. REDUCTION FACTOR BASED ON THEORY

The reduction factor x derived hereafter for transverse tensile loading is combined from the factors x~ and x2 which are based on different effects: Kf red = xKf

(1)

~=K1~2.

(2)

The factor x~ results from a better defined relation between stress intensity factor and maximum notch stress if proceeding from a mild notch. The limit value formulae for sharp notches (e.g. eq. (1) in ref. [2]) are based on large values of a/pf s o that Kr .~ 2 a x / ~ f instead of Kr = 1 + 2 ~ (see eq. (31) in ref. [2]). The reduction factor for mild notches therefore reads: 2 ~1 --

•

(3)

1 +2 ax/~f The factor g2 results from evaluating the increase of crack tip mean stress by the effect of the nearby opposed crack tip. The crack tip mean stress is higher for relatively short cracks than for long cracks by the factor x/1 + 2a/p*/2x/~p* with microsupport length p* = pf/2 (see eq. (28) in ref. [2]). This ratio is transferred to the fatigue notch factor assuming that the crack tip mean stress 405

406

D. RADAJ

a)

b)

d)

c)

Fig. 1. Welded joints with a short root gap fictitiously rounded for calculating the fatigue notch factor; V-groove butt joint (a), cruciform joint with single-bevel butt weld (b), double-V-groove butt joint (c), cruciform joint with double-bevel butt weld (d).

is controlling the fatigue strength: x2 -

x/l + 4a/pr ~

(4)

The combined reduction factor x results from eqs (2)-(4):

x/1 + 4a/pr x

=

.

(5)

1 + 2 ax//~r This factor is also directly derivable by equating the reduced notch stress concentration of the elliptical hole with the crack tip mean stress concentration of the short crack: x(1 + 2a x / ~ f ) = x/1 + 4a/pr.

(6)

Corresponding equations can be given for plane and antiplane shear loading based on eqs (29) and (32), and eqs (30) and (33) in ref. [2]. The fictitious notch radius pf has to be introduced depending on the loading case, pf = sp*, i.e. on the factor s which takes the multiaxiality of the stress state at the notch and the chosen strength hypothesis into account. The engineering approach for welded joints is simplified by using the uniform notch radius Pr = 2p* together with eq. (6). 4. DISCUSSION OF THE RESULTS The reduction factor x is plotted in Fig. 2 together with its components x~ and x2 dependent on the ratio a/pf. The old factor g is included for comparison. It can be seen from the figure that the condition x ~ 1.0 is valid both for a/pr~O and a/pr--* as demanded, whereas g is incorrectly decreasing, ~ 0 for a/pf---*oo. But the values of K and g for a/pf = 1.0 are close together, x = 0.745 vs ~ = 0.707. It must be kept in mind that these curves refer to the short crack in the tensile loaded infinite plate compared with fictitious elliptical holes with an apex radius of curvature Pf. This condition is transferred to welded joints as a local approximation, i.e. the gap or crack should be short in 1.5

=~

x --xlx2

~l.n

~

I

,

~0£

o

0.01

0.1 1 10 Crack length to notch radius ratio a/iDf

100

Fig. 2. Reduction of the fatigue notch factor dependent on the ratio of crack or gap length to fictitious notch radius.

Fatigue notch factor of gaps in welded joints reconsidered

407

relation to the plate thickness. Both internal and external gaps or cracks are acceptable, the first with length 2a, the second with length a as usual. 5. A P P L I C A T I O N T O W E L D E D J O I N T S The different reduction factors were applied to the cruciform welded joint with short internal gaps analyzed in ref. [2]. Substitution of the gap by a fictitious circular hole (a = Pr) resulted in Kf = 2.07 as shown by notch stress analysis and in Kf red = / ~ g f = 1.464. Evaluating the gap tip mean stress from the stress intensity factor resulted in Kr = 1.316 (eq. (37) in ref. [2] without short crack reduction) and K,. r~d = ~:2Kf= 1.474 (eq. (28) in ref. [2], no correction according to x~ because no fictitious rounding is involved). The correction according to eqs (1) and (5) results in Kf Fed= xKf = 1.542. The latter value is sufficiently close to the accurate value Kr r~ --- 1.474 given above. Despite the satisfactory accuracy of the reduced fatigue notch factors of the cruciform joint, it is not recommended to use the reduction generally. It can be seen from Fig. 2 that the reduction factor ~: converges rather slowly to 1.0 for increasing values of a/pf so that a reduction of the fatigue notch factor should be taken into consideration even with larger gap lengths. On the other hand, the reduction is dominated by x~ in the considered range of a/pf, i.e. by the effect of the mild notch. Similar effects are probable with the other fictitiously rounded notches of the welded joint. Therefore, in order to keep the fatigue notch factors directly comparable, it is recommended to use the reduction only in the case of gaps or cracks in welded joints which are short in relation to the plate thickness. 6. C O N C L U S I O N S The following conclusions are drawn in respect of the fatigue notch factor reduction: 1. The empirical reduction factor derived previously is sufficiently accurate only for a/pf .~ 1.0. 2. The reduction factor based on notch stress theory and fracture mechanics is valid for any values of a/pf as far as the infinite plate is considered. 3. It is recommended to use the reduction factor only in the case of gaps or cracks which are short in relation to the plate thickness when considering welded joints. REFERENCES 1. Radaj, D., Design and Analysis of Fatigue Resistant Welded Structures. Abington, Cambridge, 1990. 2. Radaj, D. and Zhang, S., On the relations between notch stress and crack stress intensity in plane shear and mixed mode loading. Engng Fracture Mech. 1993, 44, 691-704.

(Received 1 November 1996, in final form 30 January 1997, accepted 30 January 1997)

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