Fatigue crack propagation in threshold regime under residual stresses

International Journal of Fatigue 32 (2010) 1050–1056

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Fatigue crack propagation in threshold regime under residual stresses Jozef Predan a,*, Reinhard Pippan b, Nenad Gubeljak a a

University of Maribor, Faculty of Mechanical Engineering, Smetanova 17, SI-2000 Maribor, Slovenia Christian Doppler Laboratory for the Local Analysis of Deformation and Fracture, Erich Schmid Institute of Materials Science, Austrian Academy of Science, Jahnstrasse 12, A-8700 Leoben, Austria b

a r t i c l e

i n f o

Article history: Received 20 February 2009 Received in revised form 17 November 2009 Accepted 10 December 2009 Available online 4 January 2010 Keywords: Welded joints Effective stress ratio Fatigue threshold regime Residual stresses

a b s t r a c t The effect of residual stress on the fatigue crack propagation was analysed for a loading regime close to threshold stress intensity factor range. Fatigue crack propagation experiments were performed on singleedge-notched bending specimens machined from a welded plate. The residual stresses induced a variation in the crack propagation rate along the crack front. By varying the stress ratio and the stress intensity factor range, different shapes of crack front can be realized. From the shape of the crack front and the variation of the crack front, the resulting residual stresses and local stress intensity can be determined by means of finite element modelling. By using some simplifications, it is possible to estimate the limit values of the stress intensity factor induced by the residual stresses at selected regions. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Weld joints can contain various types of flaws such as slag inclusions, gas pores or stick spots. From such flaws during the service, a crack can initiate, grow slowly and finally lead to catastrophic failure. Fatigue behaviour of a welded structure is complicated by many factors intrinsic to the nature of welded joints [1]. The residual stresses as consequence of thermal multi-pass welding cycles can be a dominant effect on fatigue crack propagation. There have been many studies on the effect of residual stresses on fatigue crack propagation behaviour [2–8]. The majority of the studies have analysed the effect of transversal or longitudinal distribution of residual stresses in welded plate, and their effect on fatigue crack propagation. Just a few studies are dealing with through thickness residual stress distributions along the fatigue crack front [9,10]. The numerous measurements show that residual stresses through thickness vary from tension to compression [10–12]. The information about residual stress distribution through the thickness is very important, because the local stress intensity factor along the crack front can cause fast fatigue crack propagation and a final catastrophic failure. Failure can occur when the applied superimposed value (external applied stress intensity factor Kapp and stress intensity factor induced by residual stresses KRS) in one region of the crack front achieves the fracture toughness of the material, especially in brittle materials. This can be exhibited also as a local ‘‘pop-in” effect in ductile materials with local brittle

zones [13]. It is well known that the mean stress has a significant effect on fatigue crack propagation. Therefore, residual stresses, which change the local stress ratio, have a large effect on the fatigue life time of components. In order to estimate the variation of stress intensity factor along the fatigue crack front, it is necessary to consider actual fatigue crack fronts during fatigue crack propagation. Determination of residual stress on fatigue crack growth is difficult, because the applied stress intensity factor Kapp can be significantly different from local effective crack driving force value which is affected by residual stresses KRS. Problems arise if the fatigue crack front is uneven, because in this case, the local stress intensity factor range can additionally vary through the thickness. In order to visualize the effect of residual stress on fatigue crack growth in the threshold region, the specimens cut out of the welded plate are subjected to low maximum stress intensity factor (which is kept constant) and two significantly different fatigue loading range Rapp = 0.05 and Rapp = 0.90 where Rapp = Kmin/Kmax is the loading ratio. It will be shown that such experiments are useful to determine stress intensity induced by residual stresses. In order to take into account irregular shape of the fatigue crack front, a finite element method was applied for stress intensity factor determination.

2. Experimental procedure 2.1. Material and specimen

* Corresponding author. Tel.: +386 2 220 76 62; fax: +386 2 220 79 93. E-mail address: [email protected] (J. Predan). 0142-1123/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2009.12.006

In this study, a high-strength, low-alloy HSLA steel (ASTM grade HT 50), in a quenched and tempered condition, was used as the

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Nomenclature a B BM da/dN Fmax Fmin H KRS

crack length thickness of specimen base metal fatigue crack growth rate maximum fatigue load minimum fatigue load width of weld gap value of stress intensity factor caused by residual stresses mismatch factor (ratio of the yield stress of the weld metal to the yield stress of the base metal)

M

base metal (BM). Fig. 1 shows the arrangement for the welding of the plates. A Flux Cord Arc Welding (FCAW) procedure was applied for the welding in order to produce welded joints in over-matched configuration. The chemical compositions and mechanical properties of the base metal and the weld metal are given in Tables 1 and 2. The strength mismatch factor M, i.e., the ratio of the yield stress of the weld metal to the yield stress of the base metal, is 1.19. In Table 2, Rp0.2 is the engineering yield strength (offset at 0.2% of plastic strain), and Rm is the engineering ultimate tensile strength-UTS. Welding with filler wire for over-match configuration was made with preheating at temperature of 55 °C. Welding was performed using MAG procedure (82% Ar and 18% CO2). The heat input was in the range of 16–20 kJ/cm, and the suit cooling time between 800 and 500 °C was Dt8/5 = 9 12 s. The interpass temperature was 150 °C.

Kapp Kmax Kmin Rapp W Rp0,2 Rm DKapp Kcl

applied stress intensity factor maximum stress intensity factor minimum stress intensity factor applied stress loading ratio width of specimen yield stress of material ultimate maximum stress of material range of applied stress intensity factor crack closure stress intensity factor

In order to estimate effect of residual stresses on fatigue crack growth, the specimens are cut out from the welded plate. Standard specimens with a through thickness notch were cut out of the welded plate as shown in Fig. 2. The notch was machined in the center line of welded joint. The thickness B and width W are the same, B = W = 25 mm. The machined notch was 4 mm in depth. 2.2. Preparation of specimen In order to eliminate the effect of the notchs radius on the initial fatigue crack growth, a very sharp notch radius between 0.01 and 0.015 mm was prepared by a razor blade polishing technique. In pre-preparation stage, the specimen was subjected to four-bend compression loading, as is shown in Fig. 3. It is supposed that in the early shape under cycling compression loading of the notch, the residual stresses have less effect on initial fatigue crack growth [14]. The generated pre-crack was very small (below 0.1 mm), and it is similar in length along through thickness. 2.3. Fatigue crack propagation experiment The single-edge-notched specimen was subjected to three point bending. The sequence of fatigue loading is listed in Table 3. Note that the mean crack lengths (see Table 3) are calculated at the end of the fatigue test, during post-examination fractographic analysis of the fracture surface, see Fig. 4. Fatigue was performed under constant load (i.e., constant load ratio Rapp, as well) from the beginning until the end of each sequence of loading. Both crack stress intensity factors Kmax and DKapp increase. The increase of the maximum applied stress intensity factor was up to 6%, what can be as-

Fig. 1. Welding arrangement (2H = 6, all units in mm).

Table 1 Chemical composition of base metal and weld metal in weight percentages. Material

C

Si

Mn

P

S

Cr

Mo

Ni

Over-match Base metal

0.040 0.123

0.16 0.33

0.95 0.56

0.011 0.003

0.021 0.002

0.49 0.57

0.42 0.34

2.06 0.13

Table 2 Mechanical properties of base metal and as-welded weld metal. Material

E (GPa)

Rp0.2 (MPa)

Rm (MPa)

M Rp0.2,WM/ Rp0.2,BM

Charpy Cv (J/80mm2)

Over-match Base metal

184 203

648 545

744 648

1.19 –

>40 J at >60 J at

60 °C 60 °C

Fig. 2. Position of specimen, notch orientation and consider residual stresses acting in the welding plate are sketched.

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Fig. 3. Four point bending for cyclic compression load for pre-cracking (white pins) and tree point tension loading for fatigue crack propagation test (grey pins).

Table 3 Fatigue loading regimes and stress intensity factor corresponding to main crack length. Number of sequence 1 2 3 4 5 6 7 8 9 10 11 12 13

Kmax (MP m½)

DKapp (MP m½)

R

Stage

26.53 27.67

0.0417

40

27.68 28.88

Start End

24.319 24.319

43.61 44.49

0.8974

1000

Start End

26.60 26.60

1.330 1.330

0 8

43.67 45.44

41.49 43.17

0.0500

Start End

25.93 25.93

23.268 23.268

1000

44.29 45.09

4.54 4.62

0.8974

0.41

Start End

8.54 9.19

22.99 22.99

1.150 1.150

8

39.99 41.12

37.99 39.07

0.0500

0.65

Start End

9.19 9.31

20.56 20.56

18.447 18.447

1000

36.76 36.96

3.77 3.79

0.8974

0.12

Start End

9.31 10.00

20.91 20.91

1.045 1.046

10

37.59 38.72

35.71 36.78

0.0500

0.69

Start End

10.00 10.12

18.76 18.76

16.834 16.835

2000

34.74 34.93

3.56 3.58

0.8974

0.12

Start End

10.12 11.39

19.03 19.03

0.952 0.951

20

35.43 37.45

33.66 35.58

0.0500

1.27

Start End

11.39 11.71

16.06 16.06

14.413 14.412

3000

31.60 32.06

3.24 3.29

0.8974

0.33

Start End

11.71 13.12

16.31 16.31

0.816 0.816

20

32.57 34.74

30.94 33.00

0.0500

1.41

Start End

13.12 13.80

13.93 13.93

12.500 12.500

2000

29.66 30.64

3.04 3.14

0.8974

0.68

Start End

13.80 15.86

14.25 14.25

0.712 0.713

20

31.34 34.87

29.78 33.13

0.0500

2.06

Start End

aavr mm

Da (mm)

Fmax (kN)

Fmin (kN)

5.92 6.80

0.88

17.95 17.95

0.748 0.748

6.80 7.24

0.44

27.10 27.10

7.24 8.13

0.89

8.13 8.54

sumed as uniform stress intensity factor within particular sequence. The applied range of stress intensity factor DKapp was at large Rapp near the threshold. At Rapp = 0.1, the applied DKapp was in the Paris regime [15], however, due to the local variation of the R ratio in certain regions along the crack front, the local DK is in the near threshold fatigue regime. A sketch of the crack front, the variation of the stress intensity factor along the crack front for the different load conditions is shown in Figs. 5 and 6. In spite of the fact that the residual stress is redistributed during crack propagation [2], it is reasonable to consider that for one single sequence of loading, the residual stress along the crack front is nearly constant. Let us consider the first fatigue loading sequence at Rapp = 0.05. The pre-crack initially has a straight crack front. Therefore, at the beginning, the stress intensity range is constant along the crack front. The residual stresses do not change the stress intensity range DKapp, however, the local stress ratio is affected. In other words, the

N (cycles) (103)

4.47 4.564

minimum and the maximum stress intensity factor is shifted to lower values in the compression regions and higher values in the tension regions. The crack growth rate is significantly influenced by the stress ratio, especially at lower and negative R ratios. For R ratios larger than 0.5, the effect of stress ratio on the fatigue crack propagation rate is relatively small near the threshold regime. The large variation of the fatigue crack propagation rate affects directly the variation in the local stress ratio. In the region A, no crack extension is detected in the 1st and 3rd loading sequence which indicates that the local DK is below or near the threshold for the corresponding local R ratio. At negative R ratios, the Kmax value at the threshold is about the Kmax,th value at Rapp = 0.05 or somewhat smaller [16]. Therefore, the DKmax,th value in the loading sequence 1 and 3 should be about 7 MPa m0.5 or smaller. The compressive stress intensity factor induced by residual stresses is larger than 37 MPa m0.5 (Kmax Kmax,th = 44 7 = 37 MPa m0.5 in the 3 local regime). In the region B, the largest (tensile) residual stresses are

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Fig. 4. Obtained fatigue crack propagation fronts by loading with different stress ratios Rapp.

Fig. 5. Schematic over-view of fatigue crack growth behaviour under residual stresses for loading regime R = 0.05: (a) shape of crack front at the loading sequence 1; (b) distribution along the crack front of the local stress intensity induced by the residual stresses KRS; (c) distribution of local DK and DKeff along the crack front at the beginning of load sequence 1; (d) distribution along the crack front Kmax, Kmin and Kcl at the beginning of load sequence 1; (e) distribution of local DK and DKeff along the crack front at end of load sequence 1; (f) distribution along the crack front Kmax, Kmin and Kcl at the end of load sequence 1; (g) the variation of the crack growth rate and the DK values for position A and B in loading sequence 1 presented in a da/dN vs. DK plot.

present. Due to these large differences in local crack growth rate, an irregular crack front developed and the local DK begins to vary along the crack front. In the compression region A, DK increases and in the tension region B, DK decreases until the steady state case is reached where the growth rate in both regions is equal.

In the present experiment, we were not interested in the steady state, a loading sequence with very large Rapp ratio was introduced to straighten again the crack front. With the knowledge of da/dN vs. DK as a function of R and the local crack growth rate, the variation of the local stress ratio and the local stress intensity factor along the crack front can be deter-

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Fig. 6. Schematic over-view of fatigue crack growth behaviour under residual stresses for loading regime R = 0.90: (h) shape of crack front at the loading sequence 2; (i) distribution of local DK and DKeff along the crack front at the beginning of load sequence 2; (j) distribution along the crack front Kmax, Kmin and Kcl at the beginning of load sequence 2; (k) distribution of local DK and DKeff along the crack front at the end of load sequence 2; (l) distribution along the crack front Kmax, Kmin and Kcl at the end of load sequence 2; (m) the variation of the crack growth rate and the DK values for position A and B in loading sequence 2 presented in a da/dN vs. DK plot.

mined from such experiments. However, one should note that the local DK is only equal to the applied nominal DKapp if the crack front is straight. 2.4. Determination of stress intensity factor distribution The irregular shape of the fatigue crack front requires a special attention. ABAQUS 6.8 (academic version) [17] was used to determine the stress intensity factor distribution along the uneven fatigue crack front. Since the fatigue crack front shape is nonsymmetric, the full-half of the specimen with the fatigue crack along the whole thickness is used in this FEM analysis. Only two fatigue crack front lines are considered, which corresponds to the loading in the third and forth sequence of Rapp = 0.05 and Rapp = 0.9, respectively. Fig. 7 shows the used 3D numerical model with the fatigue crack front shape at the beginning of the third sequence of loading. Each 3D model of the specimen is subjected to the maximum fatigue load at the beginning and at the end of the loading sequence in order to simulate experimental loading conditions (see Table 3). The obtained stress intensity factor distribution as a consequence of external applied load Fmax = 26.6 kN is shown in Figs. 8 and 9, the loading sequence 3 (Rapp = 0.05) and loading sequence 4 (R = 0.9), respectively. Due to the irregular shape of the crack front, a variation of Kmax, Kmin and DK occurs for both the initial and the final shape of the crack front. It should be noted that the residual stresses here are not taken into account. For this considered case, Kmax, Kmin and DK are directly related to each other via the applied Rapp ratio. In region A and B, the maximum and the minimum of the local DK occur, respectively. Initially, in the loading sequence in re-

Fig. 7. 3D numerical model with irregular fatigue crack front shape at the beginning of third segment of loading (a), detail view at the edge of specimenright (b).

J. Predan et al. / International Journal of Fatigue 32 (2010) 1050–1056

Fig. 8. Distribution of stress intensity factors through the thickness of specimen caused only by the irregular fatigue crack front shape at the start and at the end of fatigue loading in sequence No. 3.

Fig. 9. Distribution of stress intensity factors through the thickness of the specimen caused only by irregular fatigue crack front shape at the start and at the end of loading sequence No. 4.

gion A, the DK is 35% larger than in B or 16% larger than the nominal applied DKapp. This difference increases during the loading sequence to 62%, In the loading sequence 4, the opposite behaviour is observed, the difference in the local DK between A and B decreases. Since the applied Rapp ratio in the loading sequence 4 is vary large, Kmax is larger than the local K value caused by the residual compressive stresses in region A. Along the crack front, a relatively large local R value occurs, therefore, the propagation rate is mainly controlled

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by DK and hence a smoothing during this loading sequence takes place. On summarizing, this simulation shows that for an accurate determination of the stress intensity factors induced by the residual stresses, the local variation of the DK values can be significant and has to be taken into account for an accurate analysis. From the presented experiments and simulations it becomes evident that there exist different possibilities to estimate the effect of residual stresses. One possibility is to determine the local crack propagation rate and to take always into account the shape of the fatigue crack, i.e., to take into account the local variation of DK. From the local DK and the local da/dN, the local R or local Kmax and as a consequence a KRS can be estimated. Another possibility is to perform the fatigue experiment in such a way that the crack front remains nearly straight. This requires a large number of loading cycles at high Rapp (Kmax > KRS + 2 or 5  DKeffth) with a DK only somewhat larger than DKeffth. This permits a straighten of the crack from. The number of loading cycles at low Rapp ratios with larger DK necessary to determine the local variation of R due to the residual stresses should be small in order to avoid the development of larger irregularities of the crack front. In such case, the local variation of da/dN at a given DKapp can be simply used to estimate KRS. One advantage of this technique is that the possible changes of the residual stress distributions due to the irregularity of the crack front can be avoided. The best accuracy of these type of techniques to determine the residual stresses are in the cases when the local R ratios are negative or the local Kmax near Kmax,th. The variation of the growth rate by a small change of KRS is very large, this is evident from Fig. 10. The effect is clearly visible in the presented experiments. In region A in the first loading sequence Kmax is only somewhat larger than Kmax,th. Therefore, KRS in A should be about 30 MPa m0.5 or large if we do not take into account the irregularity of the crack front. If we take it into account, the KRS should be around 40 MPa m0.5. In region B, the determination of KRS is not as accurate, because R is already positive, and the variation in the growth rate by a variation of R in this regime is not very pronounced. The growth rate in region corresponds to da/dN values at Rapp = 0.5 or somewhat larger. Therefore, KRS in B should be about 30 MPa m0.5. The rough estimation is in quite a good agreement with the measured residual stresses on the surface [12]. 3. Conclusions In the paper, the effect of residual stresses on fatigue crack propagation was systematically analysed in a welded sample. The loading regime was close to the threshold stress intensity factor range. During fatigue loading with high DKapp and low Rapp, the residual stresses cause an increase of the crack shape irregularities, and an opposite fatigue loading with small DKapp amplitude (at same Kmax) and high Rapp causes a smooth crack shape front. From

Fig. 10. Crack propagation rate as a function at Kmax and R for constant DK. Only the da/dN values at R = 0.1 and 0.5 are real measured values from the base material. The other part is an estimation based on the da/dN vs. DK values at Rapp = 0.1 and 0.5.

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the difference in the crack propagation rate at lower Rapp, the local stress intensity induced by the residual stresses can be estimated. The FE analysis indicates the variation of the local stress intensity factors. This variation is essential for the understanding of the resulting shape of the crack front, and it should be taken into account for an accurate determination of the local stress intensity factor caused by the residual stresses. Additionally, the residual stress intensity factor has been estimated as difference between SIF range of base metal and weld metal by considering the crack closure effect. References [1] Madox SJ. Information of tensile residual stress on the fatigue behaviour of welded joint in steel. In: Kala K, editor. Residual stress effect in fatigue. ASTM STP 776; 1982. p. 63-96. [2] Lee YB, Chung C-S, Park Y-K, Kim H-K. Effects of redistributing residual stress on the fatigue behaviour of SS330 weldment. Int J Fatigue 1998;20(8):565–73. [3] Shi Y, Chen BY, Zhang JX. Effect of welding residual stresses on fatigue crack growth behaviour in butt welds of a pipeline steel. Eng Fract Mech 1990;36(6):893–902. [4] Ninh NT, Wahab MA. The effect of residual stresses and weld geometry on the improvement of fatigue life. J Mater Process Manuf 1995;48:581–8. [5] Dong P. Residual stresses in aluminium–lithium welds and effects on structural fabricability and integrity. In: Cerjak H, editor. Mathematical modelling of weld phenomena, vol. 5. p. 507–28. [6] Parker AP. Stress intensity factors, crack profiles and fatigue crack growth rates in residual stresses files. In: Residual stress effects in fatigue, ASTM STP 776; 1982. p. 224–34.

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