Fatigue tests and life prediction of 16 Mn steel butt welds without crack-like defect

International Journal of Fracture 68: 275-285, 1994. 275 @ 1994 KluwerAcademic Publishers. Printed in the Netherlands.

Fatigue tests and life prediction of 16 Mn steel butt welds without crack-like defect

Z H E N G XIULIN, L() BAOTONG, CUI TIANXIE, LU XIAOYAN and LIN CHAO Department of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China

Received 20 December 1991; accepted in revised form 14 June 1994

Abstract. Fatigue test results of 16 Mn steel butt welds without crack-like defect under both constant and variable amplitude loads are reported and new procedures are used to predict fatigue crack initiation (FCI) life, fatigue crack propagation (FCP) life and total life of the butt welds. The results indicate that the FCI life and FCP life should be calculated separately and the total life is the sum of the FCI life and FCP life. For the butt welds investigated, stress cycles to initiate a crack of engineering size may occupy more than 70 percent of the total life of the butt welds and it is more suitable to express the total life as a power function of the equivalent stress amplitude A~reqv = [2(1 -- R)]-ll2KtAS. In predicting the FCI life, the expression of FCI life obtained from the test results of notched specimens is used but the effects of microstructure, surface condition, macro- and micro-geometrical discontinuities at weld toe should be taken into account. In predicting the FCP life, the formula developed by Zheng and Hirt is used and the stress ratio is taken as 0.6 to account for the residual stresses effect on the FCP rate. Because overload produced by the maximum load in a load spectrum has no effect on the FCI life of 16 Mn steel and weldment of the steel, according to the procedures outlined in the paper, one can use the FCI life expression mentioned and the linear damage accumulation role proposed by Miner to predict the FCI life of 16 Mn steel butt welds under variable amplitude loads. A good agreement is achieved between the predicted results and the test data.

1. Introduction

It has been recognized [1] that the fatigue life o f welded elements without crack-like defect comprises two phases: fatigue crack initiation (FCI) phase and fatigue crack propagation (FCP) phase. Frequently, the FCI life is predicted by the local strain approach [2]. It requires test data of cyclic stress-strain behaviour and the cyclic strain fatigue life of the materials at the FCI location, which are, sometimes, difficult and expensive to experimentally measure. Japanese researchers applied the empirical expressions FCI life obtained from the test data o f notched specimens to predict the FCI life of ship structural members [3]. However, a great deal of test data are required to determine the empirical constants in the expressions. The FCP life of welded elements is usually predicted by use of Paris' equation [4, 5] or modified Paris ' equation [5]. In the early stage of FCP in a welded element, the FCP rate may be as low as order of 10-9m/cycle [6]. In this region, the FCP rate, as well as the effect of stress ratio, can not be accurately predicted by Paris' equation [7].

In this paper, the test results of the fatigue life 16 Mn steel butt welds under both constant amplitude and variable amplitude loads are reported and new procedures are outlined and used to predict the FCI life and FCP life of the butt welds investigated.

2. Experimental procedures

Hot-rolled plates of 16 Mn steel were taken as test material. Its nominal thickness is 10 mm. The chemical composi t ion of the steel in weight percent is: 0.16 C, 1.42 Mn, 0.31 Si, 0.022P,

276 Zheng Xiulin et al.

, , O '-°1 , !

Fig. 1. Configuration of specimens and geometrical parameters of butt welds.

300

2O0

lO0

Fig. 2. Schematic illustration of load spectrum used in variable amplitude loading tests.

0.023 S, 0.10Cu and balance Fe. The tensile properties are: yield strength cry = 389MPa, ultimate tensile strength au = 550MPa and reduction in area ~b = 75.6%. The specimens are butt-welded by automatic merging-arc welding process and machined according to the configuration given in Fig. 1.

Fatigue tests were carried out on a ZD-100 type electrohydranlic servo test machine with load accuracy of 200 N. The loading frequency was 6 ~ 7 Hz. The maximum nominal stresses applied on the specimens were below the yield strength of material and the stress ratio adopted in the constant amplitude loading tests were in the range of 0.2 ~ 0.6. The loading spectrum applied in the variable amplitude loading tests comprised five blocks, as shown in Fig. 2. During the testing, a hand lens of 20 x magnification was used to monitor cracks. As soon as a crack was detected, the test was stopped to measure the crack length 2c0 and to record the number of cycles No. Then the test was continued. After final separation of the specimen, the fracture surface was observed and the crack depth a0 corresponding to the crack length 2c0 was determined. The total fatigue life N / w a s defined as the loading cycles when a crack penetrates the whole thickness of specimens and, following [8, 9, 10, 11], the FCI life Ni was defined as the loading cycles to initiate a crack of 0.25 mm depth.

3. F a t i g u e r e s u l t s

No crack-like defect was observed on the fracture surface of specimens tested. It is shown that the FCI life occupies a major part of the total life of 16 Mn steel butt welds if no crack-like defect exists. As a result, the fatigue life of the butt welds, in the range of this study, i.e. 2 × 104 ~ 2 x 106 cycles, can be expressed as a power function of the equivalent stress ampl i tude , Ao'eq v [8, 12]

jv s = Cp(/Xaeqv)kP, (1)

Fatigue tests and life prediction 277

250

200

<~ 15C

10C

. -

• 0 . 6

I t 2× 10 4 l0 s 10 j

~¢Ie$ to failure Nr

Fig. 3. Relationship between fatigue life and equivalent stress amplitude.

10 7

where

~ 2 1 ACreqv : ( 1 - R) KtAS' (2)

where Cp and kp are material constants [8], A S and R are, respectively, the nominal stress range and stress ratio, Kt is the stress concentration factor. Assuming that the Kt values of all specimens are identical (1) is rewritten as

Ns : vp(A¢oqv) : c~ 2(1 - R ) A S . (3)

Equation (3) represents a straight line with slope k. when N S and Acretqv are plotted on logarithmic scale. Regressing analysis of the fatigue test results gives the least-squares fit to the test data

N S = 1.66 × 1015(A0"teqv) -4"454. (4)

The least-squares fit line and the test data are illustrated in Fig. 3. The results in [9] indicate that the fatigue life of 16 Mn steel butt welds could also be expressed as a power function of nominal stress range A S with wider scatter and the fatigue life decreased with increasing stress ratio. Therefore, it seems that the fatigue life of the butt welds investigated is more suitably expressed as a power function of the equivalent stress amplitude, which implies the stress ratio effect on fatigue life.

4. Fatigue life prediction under constant amplitude loads

The fatigue life of a welded element, NS, is the sum of the FCI life Ni, and FCP life, Np

N s = g~ + Np. (5)


If no crack-like defect exists, initiation and early propagation of fatigue cracks occur normally at the weld toe but on the side of the base metal, where the microstructure and fatigue behaviour are different from those of the base metal [8, 10]. Therefore, the fatigue properties of material at the weld toe should be used in the life prediction, in order to obtain predicted results with higher accuracy. It is shown in [11] that the microstructure of 16 Mn steel at the weld toe can be simulated by a specific high-temperature normalization process. The fatigue properties of 16 Mn steel under the high-temperature normalization condition are believed to be close to those at the weld toe so that they can be used in fatigue life prediction of 16 Mn steel butt welds.

4.1. PREDICTION OF FCI LIFE

Theoretical analysis [13] and experimental results [8-11, 14-16] indicate that the FCI life of notched specimens can be expressed as the function of equivalent stress amplitude A~reqv,

¢ '~[A, , - 2 / ( l + n ) ( A , ~ - ~ 2 / ( 1 + n ) ] - 2 Ni = ,~t ,--~,eqv - ~, . .~veqv]th0 j , (6)

In (6) C is the FCI resistant coefficient, a material constant depending on the tensile properties, n is the strain hardening exponent and (Atreqv)th 0 is the FCI threshold; when Ao'eq v < ( A O ' e q v ) t h 0 the FCI life tends to infinite. For 16 Mn steel under the high-temperature normalization condition, the expression of FCI life is as follows [10]

. , ~ 1 4 e A 1.75 1 .75 ) -2 Ni = 4.23 x I v I,L-XO'eq v - - 281 . (7)

In order to determine FCI life of the butt welds accurately, the stress concentration induced by macro- and micro-geometrical discontinuities should be taken into account.

The value at the weld toe induced by the macro-geometrical discontinuity of the butt weld, denoted here as/(~nacro, Can be approximately calculated by following [17]

/(~nacro = 1 + f(O)(t~O - 1), (8)

where

f(O) = 11-.__exp_~.9 ~ 9~2)exp(-0"90x/~) [ 1 - 0.48 exp ( - 0 . 7 4 ~ ) ] (9a)

[1 cto = 2.82~1 - 2 (9b)

/3= [ 0 . 6 5 - 0 . 1 e x p ( 0 . 6 3 ~ ) ] (9c)

2h A 1 = 1 + - - (9d)

t

t A 2 = 1 + ~-~, (9e)

where 0, t, h, b and p are, respectively, the geometrical parameters of a butt weld to characterize the macro-geometrical discontinuity illustrated in Fig. 1. From the geometrical parameters


measured from the specimens tested, the values of K~ naer° calculated by (8) are in the range of 1.85 to 2.30, from which the mean value 2.08 is given.

Undercuts existing at the weld toe are referred to as the micro-geometrical discontinuity. The contribution of micro-geometrical discontinuity to the stress concentration of welded elements can only be estimated from experimental results as yet. According to the experimental results offered by Lieurade et al. [18], the additional stress concentration factor induced by the micro-geometrical discontinuity, denoted a s K~ nicr°, is about 1.4. The overall stress concentration factor of the butt welds, Kt, can be approximately estimated from product of stress concentration factors induced by the micro- and macro-geometrical discontinuities

Kt = K~cr°K~ nacr° : 1.4 x 2.08 = 2.9. (10)

Furthermore, the surface condition at the weld toe is another important factor which should be considered in the FCI life prediction. Equation (6) represents the least-squares fit to the test data of FCI life obtained from notched specimens with ground surface [10]. The surface at the weld toe, in the first order approximation, can be considered the same as that of a hot-rolled plate. For the welded elements of a steel with try, ~ 600 MPa (the ultimate tensile strength of 16 Mn steel under the high-temperature normalization condition is 589 MPa [10]), the fatigue strength of metal at the weld toe is about 78 percent of the ground specimens because of the difference in surface condition [19]. Substituting the surface modification factor 0.78 into (7), one finally obtains an expression of the FCI life of 16 Mn steel butt welds as follows

~,-,14~ A 1.75 2191.75)-2. (11) Ni = 1.78 × ltJ t~Creqv -

The FCI life curve of 16Mn steel butt welds shown in Fig. 4 can be drawn according to (11). The data of No, the number of cycles to initiate a crack of depth a0, are also represented in Fig. 4 for comparison. It is shown that the values of No, except one datum, are greater than those of the FCI life. This result is reasonable because the FCI life is defined as the number of loading cycles to initiate a crack of 0.25 mm depth [12] but the values of a0 measured in the present investigation are in the range of 0.3 to 2 mm. Obviously, No is the sum of the FCI life and the number of cycles required for a crack propagating from 0.25 mm to a0.

4 .2 . PREDICTION OF F C P LIFE

The fatigue crack propagates inward on the specimen as soon as the crack initiates at the weld toe surface, through the zones with various microstructures. In the early stage of FCP, the FCP rate may be very low because of low value of A K . For this reason, an expression which can formulate the FCP in the near-threshold region is a useful aid in the FCP life prediction [1,4, 6]. Zheng and Hirt [7] developed a FCP formula

da = B ( A K - AKth) 2, (12)

dN

where AKth is the FCP threshold and the coefficient B is a material constant relating to tensile properties and the FCP mechanism in the intermediate region, i.e., da/dN = 10 -8 to 10-6rn/cycle. Equation (12) has been proved to be applicable in the range of da/dN ~<-6rn/cycle, as indicated in [7, 10, 11,20]. It is recognized that the FCP rates in the near-threshold region are strongly dependent upon microstructures but those in the intermediate region are rather insensitive to microstructure [8, 10, 11,20], so that the data of FCP


O cycles to initiating a crack of depth aa

700 o ~

ooo O.

500 > , ~ o ooC~ °

<~ Predicted FIC life c/urve~~ ~Oo

3OO

I ! IO s 10 6

Cycles to init iat ion o f crack

Fig. 4. Comparison between the predicted line for FCI life and test data of No.

rate of 16 Mn steel near the weld toe surface or those of the steel under the high-temperature normalization condition should be used in the FCP life prediction, which are represented by the following expression [10]

da - 3.75 × 10-1°[AK - 7.4(1 - R)] 2. (13)

dN

Equation (13) describes the stress ratio effect on the FCP rate and threshold. The FCP life of the 16 Mn steel butt welds can be predicted by integrating (13)

fa aJ da Np = 3.75 × 10-1°[AK - 7.4(1 - R)] 2"

0

(14)

For a crack initiating from the weld toe, the stress intensity factor range, A K , is calculated as follows [5, 8, 21]

(15)

where Fg accounts for nonuniform stress distribution effect due to the stress concentration, Fs for the free surface, Fw for finite width effect and the F~ for crack shape. For a crack at the weld toe surface of butt welds, these factors can be estimated by the following expressions [5,8,21]

Fg = (--sa)log(l+°'°588°)/l°g(2°°) 0 ~< 0 ~< 45 ° (16)

1.122 + 0.097 a c

for comer crack

for semi-elliptical crack

(17)

(18)


lO: /

° 7"

ff

I0 I

101 I0 !

N, (calculated) cyc les

Fig. 5. Comparison between experimental and predicted remaining life of specimens.

2 [ ( ~ ) 1.65] Fe = 1 + 1 . 4 6 4 (19)

Because the butt welds investigated are applied under as - welding condition, residual stresses existing at the weld toe will influence the FCP. Smith [22] suggested that the stress ratio should be taken to be 0.6 in considering the residual stresses effect. Then, (13) can be rewritten as follows

f • s (FgFsF~F~/XS Np = 2.7 × 10 9 ~ - 3.0) -2 da. (19)

The integral limits, ai and aj, depend upon the problem considered. The test results in the present investigation indicate that the remaining life after a fatigue crack penetrating the whole thickness of the steel plate is no more than 5 percent of the total life of the specimens [8, 9]. In calculating the FCP life of the specimens, the lower integral limit ai, is taken to be 0.25 mm, the initial crack size, and the upper limit, af, to be the thickness of the steel plate, i.e., a/ =10mm. However, the lower integral limit ai, should be replaced by a0, the size of the crack first observed, when the remaining life, Nr, is computed.

The remaining life so calculated is compared with the test results in Fig. 5, where a reasonable agreement is shown. Because several cracks may initiate in one specimen, the life of a few specimens is shortened by colescence of the cracks. In this case, the remaining life predicted will be longer than that experimentally determined, as indicated in Fig. 5.

4.3. PREDICTION OF TOTAL LIFE

The total life of specimens can be predicted by simply adding the FCI life and the FCP life. The former is given by (11) and the latter is obtained by (20) where ai - 0.25mm and a/ = 10 mm. The results in Fig. 6 indicate that the total fatigue life thus predicted agrees well with the test data.


I0'

iO s

! 10 ~ 10 ~

Nr (celculatcd) cycles

Fig. 6. Comparison between experimental and predicted fatigue life of specimens.

Similarly, by taking ai = 0.25 mm and ay -- a0, from (20) the number of cycles required for a crack propagating from 0.25 mm depth to a0 can be calculated. Then, adding this value to the FCI life determined by (11), one will obtain the predicted value of No, corresponding to the number of cycles when a crack of depth a0 was detected at the weld toe. The predicted values of No are in good agreement with the test results, as indicated in Fig. 7.

The tests results and calculation again verify that the fatigue life is composed of the FCI life and FCP life, which should be predicted separately. Since the FCI life occupies more than 70 percent of the total life of 16Mn steel butt welds, it cannot be neglected in the life prediction. Otherwise, a great error will be produced.

Experimental results indicate that the residual stresses at the weld toe may reach to the yield strength of the material [22]. Superposition of local cyclic stress and the residual stresses during fatigue tests will produce great plastic deformation, so that the residual stresses will be relaxed. On the other hand, small plastic pre-strain has no influence on the FCI life of low carbon steel like 16 Mn [11 ] and statistical analysis of fatigue test data obtained from 16 Mn steel butt weld shows the residual stresses do not affect the fatigue life [23]. Therefore, in the present study, the effect of residual stresses is not considered in the FCI life prediction.

5. Prediction of FCI life under variable amplitude loads

It has been recognized [ 15, 24] that the effect of loading sequence, i.e., the interaction between cyclic loads at higher level and those at lower level, has to be considered in life prediction for FCI from a notch under variable amplitude loads. Tests results [11, 15, 14] show that the cyclic load interaction is mainly due to the overloading effect induced by the maximum load in a load spectrum and that the loading pattern after the overloading has no appreciable influence on FCI life. It has been shown that the overload has no effect on the value of FCI coefficient C and that the overloading effect on FCI life can be characterized by the so-called


overloading factor z, which is a material constant characterizing the overloading effect on the FCI threshold [11, 15, 16, 25]

~,(A,~ $2/( l+n) (21) (AO'eqv)th = (AO'eqv)th 0 + ~k,--~veqv/oL •

In (21) (AO'eqv)th 0 and (Ao'eqv)th are the FCI thresholds without overload and after overload, respectively, (Atreqv)OL is the equivalent stress amplitude during ovedoading, which is calculated with (2) by taking the stress ratio R = 0

(A t r eqv )OL = W/~I(tSmax, (22)

where Smax is maximum nominal stress in the load spectrum. Replacing the FCI threshold given by (21) with (AO'eqv)th 0 in (6), one obtains the FCI life expression considering the overloading effect. The linear damage accumulation rule proposed by Miner can be used to predict the FCI life of notched specimens when the FCI life expression considering the overloading effect is adopted [11, 15, 24, 25].

As mentioned above, the procedures for predicting the FCI life under variable amplitude loads are outlined as follows [15, 24]:

1. Calculating (Atreqv)OL from the maximum nominal stress in load spectrum, Smax, and the stress concentration factor Kt;

2. Substituting (Atreqv)OL in (6) to obtain the expression of the FCI life after overloading; 3. Substituting all the values of AS and R in the load spectrum and the values of Kt into

(2) to obtain the spectrum expressed by the equivalent stress amplitude; 4. Computering the accumulative fatigue damage according to Miner's rule, the equivalent

stress amplitude spectrum and the FCI life expression after overloading; 5. Obtaining the FCI life when the value of the accumulative damage is equal to 1.0.

The test results [11, 25] indicate that low carbon steels including 16 Mn and the weldments of the steels, the overloading factor z = 0, i.e. the overload has no influence on the FCI life, so (11) can be directly used to predict the FCI life of 16 Mn steel butt welds under variable amplitude loads. The FCI life data experimentally determined under the variable amplitude loads and the predicted results using the procedures described above are listed in Table 1. The results show that the average value of the critical damage for the FCI at the weld toe is 1.050, which is very close to the theoretical value 1.0.

Since the FCP life takes only a minor part of the total life of the butt welds tested, the fatigue tests were carded out under constant amplitude loads after a crack was detected. No attempt is made to study the FCP life prediction under variable amplitude loads.

6. Conclusions

(1) The fatigue life of 16 Mn steel butt welds under constant amplitude can be well expressed as a power function of equivalent stress amplitude, to take the effect of the stress ratio into account.

(2) The fatigue life of welded elements without crack-like defect is the sum of the FCI life and the FCP life. The FCI life and FCP life should be predicted separately. Since the FCI life may occupy more than 70 percent of the total life, it cannot be neglected in the life prediction.

(3) Because the microstructure and fatigue behaviour of the metal at the weld toe are remarkably different from those of the base metal, the fatigue properties of 16 Mn steel under


Table 1. Test date and predicted results of FCI life under variable amplitude loads

Z~eqv 467 579 529 198 559 (MPa)

nl n2 n3 n4 n5 ~-~ n._~.~ spc. ,,, N--/ " n, N-S

3

No, kilocycles kilocycles kilocycles kilocycles kilocycles

1 39.8 0.265 22.2 0.389 21.2 0.251 59,0 0.0 0.905 2 30.5 0.204 t6.0 0,281 43.0 0.509 39.6 0.0 I0.0 0.151 1.t45 3 30.7 0.205 17.6 0.309 24.5 0.290 41.0 0.0 9.4 0,t42 0.946 4 45.3 0.301 12.6 0.221 21.1 0.250 57.0 0.0 28.7 0.433 1.205

avg. 1,050

10 ~

10 ~

|

10 j 10 *

No (ealcutated) cycles

Fig. Z Comparison between experimental and predicted stress cycles to initiate a crack of depth ao.

the high-temperature normalization condition, which has a microstructure nearly the same as that at the weld toe, are used in the life prediction. This is one reason to achieve higher accuracy of life prediction.

(4) The contribution of both macro- and micro-geometrical discontinuities at the weld toe should be considered in determination of the stress concentration factor.

(5) In FCI life prediction, the surface condition modification should be made to take the effect of surface condition at the FCI location into account.

(6) The stress ratio can be fixed at 0.6 in the FCP life prediction to account for the residual stresses effect but this effect is not necessary for consideration in the FCI life prediction.

(7) Because no overloading effect exists in 16Mn steel, the FCI life prediction of 16Mn steel butt welds can be predicted by means of Miner's rule and the FCI life expression of the butt welds obtained from constant amplitude loading tests,


(8) By means of the procedures presented in this paper, high accuracy of life prediction can be obtained within the life range studied.

References

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Utah (1985) 37-46. 4. ECCS Recommendations for the Fatigue Design of Steel Structures, 1st edn., Switzerland (1985) 5. P. Albrecht and K. Yamada, Risk Analysis of Extending Bridge Service Life, Final Report Prepared for State

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I 17-127, also to appear in International Journal of Fatigue (1993). 25. C. Lin, G. Li and X. Zheng, in Proceedings of 4th ConferenceAPCS, Beijing, China (1991) 1317-1320.

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Fatigue tests and life prediction of 16 Mn steel butt welds without crack-like defect