A kink in the fatigue crack growth curve

IntJ Fatigue 6 No 4 (1984) pp 217-220

A

in the fatigue crack growth

culwe V. M. R a d h a k r i s h n a n The effect of grain size on the near threshold stress intensity factor in a low-carbon steel has been studied. In Stage I crack propagation depends on the microstructure of the material; in Stage II the growth rate curves for different grain sizes appear to merge together. There is a kink or a dip in the crack propagation rate where Stages I and II meet, representing a retardation in crack growth. Analysis of published data shows that such a kink often occurs. It is proposed that this temporary retardation in crack growth is due to the resistance offered by the grain boundary to the plastic zone when it tries to cross the first grain and move on to the adjacent grains. Key words: fatigue; fatigue crack growth rates; Stage I/Stage II transition; temporary retardation, grain size; low-carbon steel

Stage I (near-threshold) fatigue crack growth is the nucleation of a crack at the tip of a pre-existing crack and its subsequent growth; the growth rate will be in the range • . 10 - 8 - 1 0 - 6 mm/cycle. In th~s crack propagauon range, %it has been postulated ~ that the plastic zone size is smaller than the grain size of the material, and the crack path is along the shear plane, z This stage is strongly dependent on the microstructure and metallurgical properties of the material. As the crack length increases, the zone size becomes larger and eventually becomes bigger than the grain size; therefore the surrounding grains are also brought into the plastic zone. The crack plane becomes normal to the tensile axis and general yielding in more than one grain starts controlling crack growth. Stage II crack growth normally starts from this point, with the growth rate approximately equal t o 1 0 -6 ram/cycle. On the assumption that the plastic zone size is equal to the grain size at the transition point when the crack growth changes from Stage I to Stage II, Yoder e t al 3 have shown that the stress intensity factor range, AKT, corresponding to the transition point can be given as: AKT = 5-5OysV/~-

The material used in the present investigation was a lowcarbon steel of composition (weight %): C 0.09, Mn 0.2, Si 0.12, P and S <0.03. The material was heat-treated at 900°C, 950°C and 1000°C for 4 h to give a grain size variation from 1 5 - 5 0 gin. The specimen was a single edge notched type with a starter notch to initiate a fatigue crack. After the fatigue crack had grown to at least three times the initial notch depth, the load decrement method was used to study the crack propagation rate. To avoid residual stress effects due to load reductions, the crack was allowed to grow to a length corresponding to two or three times the plane stress maximum plastic zone size of the previous loading for each load decrement. When the threshold value corresponding to a crack growth rate of around 10-Tmm/cycle was arrived at, the load was maintained constant and the crack growth rate was measured at regular intervals. The machine used was a Vibrophore with a frequency of 135 Hz. The load accuracy was 20 N and the crack growth was measured by a travelling microscope (x 30) with an accuracy of 0.01 ram.

(1)

where Oys is the yield stress and d the grain size of the material. They have shown that the above relation is in good agreement with many of the data reported in the literature. However, the experimental results of Higo et al 4 on copper and its alloys have shown that the threshold stress intensity factor range (AKth) decreases as the grain size is increased. They prefer to characterize the threshold based on the range of crack opening displacement (COD) given in the form: A(COD) = 0.5(AK2/2Oys E)

Experimental details

(2)

where E is the Young's modulus. The present study was undertaken to analyse the transition of the crack growth curve from Stage I to Stage II and the influence of grain size on AK.

Results and discussion The variation of crack growth rate (da/dN) with AK for the low-carbon steel is shown in Fig. 1, on a log-log plot. Stage I can be described by a smooth curve with a steep slope in all three cases. It can be seen that A K increases with increasing grain size. Up to around 2 x 1 0 - 6 m m / cycle da/dN increases with increasing AK. Thereafter there is a slight dip in the crack growth rate. However, this lasts only until AK has increased by 1 - 2 MPax/m. The crack growth rate then picks up again. After the onset of Stage II, the variation of da/dN with A K is more or less linear, ie the Paris law is valid. This kink or dip in the crack growth curve, which occurs around 1 to 2 x l 0 - 6 m m / cycle at the transition point between Stage I and Stage II, has been observed for all three heat treatments.

0142-1123/84/040217--04 $3.00 © 1984 Butterworth & Co (Publishers) Ltd Int J Fatigue October 1984

217

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In their analysis of a three component method for a wide range of fatigue crack growth (FCG) rate data, Saxena and Hudak 6 investigated the FCG of 2219 T 851 aluminium alloy. Their data are reproduced in Fig. 4; the full and d o t t e d lines are due to the present author. It can be seen that Stage I and Stage II can be described by two lines with a dip in the crack growth curve at their intersection point. When the stress ratio, R, =0.1, the dip occurs at around 6 × 10 -6 mm/cycle and for R = 0.3, it is around 3.5 × 10 -6 mm/cycle. When R is increased both A K T and the crack growth rate level at which the kink occurs decrease. A similar kink in the crack growth curve can be easily identified in the data of Romaniv et al 7 on mild steel, of Suresh e t al s on bainitic SA 542-3 steel, of Minakawa and McEvily 9 on AISI 1018 steel and P/M MA 67T6 alloy, of Beevers l° on mill annealed Ti-6A1-4V tested in air and of Cooke e t a111 on a medium-carbon alloy steel. The existence of such a kink can also be noted in the analysis discussed by HobsonJ 2 Some other data were also studied, but there were not sufficient data points at the transition level to indicate a dip. The values of the grain size, yield stress, A K T and the plastic zone size at transition are given in Table 1 for the low-carbon steel used in the present study. At the transition point, where the crack propagation changes from shear mode to tensile mode, the plastic zone size is just equal to the grain size. As the stress intensity factor increases the

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This kink point was observed because the crack growth rate was measured frequently. Other researchers' data was analysed to see if such a phenomenon could also be detected in their results. The first set was the data of Gray e t al s on a 0.8% C steel. The material was treated to give fine and coarse prior-austenite grain size. The crack length was measured by a travelling microscope (× 30) and the precision of crack length measurement was 0.01 ram. The data were replotted and are shown in Fig. 2. (The full and dotted lines have been marked in by the present author.) Stage I and Stage II can be described b y straight lines, with the transition point around 10 -6 mm/ cycle. The threshold values for these microstructures are 7 M P a x / m and 10 MPax/m. The values of A K T as calculated by the formula suggested by Yoder e t al (Equation (1)) are 6.7 and 9.5 M P a ~ / m respectively, which shows that the plastic zone size is equal to the pearlite colony size at the transition point. A closer look at the data reveals a kink in the crack growth curve at the transition point, as shown by the dotted line. The data on pure copper of Higo e t al 3 were also analysed. In this case the fatigue crack growth was measured b y the potential drop method. Figure number three in their report was retraced for different grain sizes and replotted as shown in Fig. 3. Here again one can see a kink in the d a / d N vs A K curve at around 10 -s mm/cycle. The scatter for the specimen with 1 3 0 0 / a n grain size is quite large, possibly because the data points of two or three specimens tested for reproducibility are plotted on the same figure. However, it can still be seen that there is a tendency for d a / d N to retard for a short period at around 10 -s mm/cyclc.

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Table 1. Threshold data for the low-carbon steel studied Heat treatment temperature (°C)

Grain size (/am)

ors (MPa)

AKth (MPa ~/m)

AK T , theoretical (MPa ~/m)

AK T , actual (MPa~/m)

Plastic zone size* (/~m)

900 950 1000

18 28 44

320 280 230

6.2 7.1 8.4

7.4 8.0 8.4

8 9 10

16.87 27.89 51.04

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218

I nt J Fatigue October 1984

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AK for pure copper: (a) d = 15/Jm, ay== 65 MPa; (b) d = 8 0 F m , ay= =.54 MPa; (c) d = 140#m, Ors = 50 MPa; ( d ) d = 1300/~m;

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plastic zone also tries to grow, and spread over to the adjoining grains. In this process the plastic zone encounters a resistance from the grain boundary which retards the easy growth of the zone. This retardation results in the dip or kink in the crack growth rate. However, as the stress concentration builds up at the leading dislocations which are held up by the grain boundary, sources in the adjacent grains will be activated and the plastic zone will again start spreading into the neighbouring grains. A typical nucleation of a crack in the adjacent grain, just at the transition point, is shown in Fig. 5. The retardation effect may also be due to the tendency of the crack to bifurcate when entering another grain. Experimental results obtained using both the travelling microscope (which measures only the surface crack growth rate) and the potential drop method (which gives the average growth rate across the specimen thickness)

I n t J Fatigue O c t o b e r 1984

Fig, 5 Crack nucleation in an adjacent grain due to stress concentration at the grain boundary of a sample heat-treated at 9500C. The experiment was stopped just at the kink point

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growth. An analysis of published data in the literature also indicates the occurrence of such a kink at the transition point. The kink occurs at a crack propagation rate of 1 to 2 × 10 -6 mm/cycle for lowcarbon steel at R = 0.1 the crack propagation rate and the stress intensity factor range at the transition point depend on the stress ratio - they both decrease with increasing stress ratio.

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Acknowledgement

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The author expresses his thanks to Dr P. Rama Rao, Director, DMRL, for his constant encouragement and kind permission to publish this paper.

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References

i(~ 4

1.

Yoder, G. R., Cooley, L. A. and Crooker, T. W. "Quantitative analysis of microstructural effects on fatigue crack growth in Widmanstatten Ti-6AI-4V and Ti-8AI-1Mo-IV' Engng Fracture Mech 11 (1976) pp 805--816

2.

Liu, H. W. and Liu, D. 'Near threshold fatigue crack growth behaviou r' Scripta Met 16 (1982) pp 595--600

3.

Yoder, G. R., Cooley, L. A. and Crooker, T. W. "A critical analysis of grain size and yield strength dependence of near threshold fatigue crack growth in steels' NRL Memorandum Report 4576 (Naval Research Lab, Washington DC, USA, 1981 )

4.

Higo, Y., Pickard, A. C. and Knott, J. F. 'Effects of grain size and stacking fault energy on fatigue crack propagation thresholds in Cu-AI alloys' MetSci 15 (1981) pp 233--240

5.

Gray, G. T., Thompson, A. W., Williams, J. C. and Stone, O. H. 'Influence of microstructure on fatigue crack growth behaviour in fully pearlitic steels' Proc 2nd Int Conf on Fatigue and Fatigue Threshold 1 ( 1981 ) pp 345--361

6.

Saxena, A. and Hudak, S. J. 'Evaluation of the three component model for representing wide range fatigue crack growth rate data' Scientific paper 76-1D 3-MSLRA-PI (Westinghouse R and D Centre, Pittsburgh, PA, USA, 1979)

7.

Romaniv, O. N., Siminkovich, V. N. and Tkach, A. N. 'Near threshold short fatigue crack growth' Proc 2nd Int Conf on Fatigue and Fatigue Threshold 2 (1981) pp 799--807

8.

Suresh, S., Parks, D. M. and Ritchie, R. O. 'Crack tip oxide formation and its influence on fatigue threshold' ibid 1 pp 391--408

9.

Minakawa, K. and McEvily, A. J. 'On threshold fatigue crack in steels and AI alloys" ibid 1 pp 373--390

Conclusions

10.

Beevers, C. J. 'Some aspects of the influence of microstructu re and environment on ~K thresholds" ibid 1 pp 257--275

From the experimental investigations carried out to study the crack growth near the threshold region in a low-carbon steel, it has been observed that:

11.

Cooke, R. J., Irving, P. E., Booth, G. S. and Beevers, C. J. "The slow fatigue crack growth and threshold behaviour of a medium carbon alloy steel in air and vacuum' Engng Fracture Mech 7 (1975) pp 69--77

1)

12.

Hobson, P. D. 'The formation of a crack growth equation for short cracks' Fatigue o f Engng Mater and Structures 5 No 4 (1982) pp 323--327

Fig. 6 Relationship between da/dN at kink and (AKT/E)a

indicate the kink at the transition point and so this retardation may not be confined to surface grains only. The crack growth curves for different grain sizes appear to merge together, as seen in Fig. 1, indicating that structure or yield strength has little influence on crack growth in Stage II. The FCG rate in Stage II can be described by the normalized stress intensity factor range, AK/E, and, taking the transition point as one lying on the Stage I1 curve, the FCG rate at the kink can be given as: d~_a oc dNIT

(3)

where n is a constant. The relation between da/dN at transition and the normalized stress intensity factor range is shown in Fig. 6 for different materials. Taking n as equal to 2 appears to agree well the values from experiment. AK T depends on R, probably in the form: AK T = AKTo(1 -- R) 3'

(4)

where AKTo refers to the value when R is zero. The exponent 3' is a constant. As R increases, the value of AK T and consequently da/dNiT will decrease.

2) 3)

220

the threshold stress intensity factor, AKth, increases with increasing grain size and Stage I crack propagation is structure-sensitive the crack growth rates in Stage II appear to merge together for the different grain sizes investigated at the transition point where Stage I and Stage II meet, there is a dip or a kink in the crack growth rate, indicating a temporary retardation in the crack

Author The author is with the Department of Metallurgy at the Indian Institute of Technology, Madras-600 036, India.

Int J Fatigue October 1984