The effect of grain size on small fatigue crack growth in pure titanium

The effect of grain size on small fatigue crack growth in pure titanium K. Tokaji, T. Ogawa and K. Ohya* Department of Mechanical Engineering, Gifu University, 1-1 Yanagido, Gifu, Japan *Daido Steel Ltd, 2-30 Daido-cho, Minami-ku, Nagoya, Japan (Received 14 January 1994) The growth behaviour of small fatigue cracks has been studied in both fine- and coarse-grained versions of a pure titanium under axial loading at stress ratio, R, of -1. The growth behaviour and its statistical properties in a coarse-grained version of a different pure titanium have also been investigated under rotating bending (R = -1), and the results obtained were compared with those of a fine-grained version of this titanium in a previous report. Under both loading conditions, small cracks grew faster than large cracks. As the growth data were plotted in terms of the effective stress intensity factor range AKen (after allowing for crack closure), the growth rates could be well correlated with large-crack data in a large-crack regime. In a small-crack regime, however, small cracks still grew faster than large cracks. Small cracks in coarse-grained material showed higher growth rates than those in fine-grained material owing to a much smaller effect of microstructure such as grain boundaries and crack deflection. Stage I facets were observed in all the specimens tested, and their depths were less than the maximum grain size estimated by the statistics of the extreme values, but the distribution of stage I facet depths approximately corresponded to the maximum value distributions of grain size of the materials. The growth rates of small cracks followed log-normal distributions independent of grain size. The coefficients of variation, ~7, of growth rate in coarse-grained material were smaller than those in fine-grained material. The ~7 values were significantly large at a/d <~ 3 (a = crack depth, d = grain size), indicating that the relative size of microstructurally small cracks was not dependent on grain size. (Keywords: small fatigue cracks; crack growth; pure titanium; grain size; stage I crack; statistical property; microstructure)

Pure titanium has been widely used in the chemical industry because of its excellent corrosion resistance. Recently, with an increased interest in the structural applications of this material, several studies have been performed on the fatigue properties, and in particular on the crack propagation behaviour ~-5. The authors have investigated the propagation behaviour of large cracks in pure titanium, and have indicated that the propagation behaviour was considerably different from that of steels and was sensitive to the microstructure over the whole crack propagation regime tested 4. In a previous report 5, furthermore, the growth behaviour of small cracks and its statistical properties have also been examined, and the following experimental results were obtained. 1. Microstructurally small cracks (MSSC), whose growth rates were markedly affected by microstructure, did not always correspond to stage I cracks, and the growth after the transition from stage I to stage II was still influenced by the microstructure. 2. Stage I cracks were almost in the order of grain size. 3. The maximum variation in growth rate was attained when the crack size was comparable to the average grain size of the material. 0142-1123/94/080571-08 © 1994 Butterworth-Heinemann Ltd

It can easily be seen that all these findings are strongly related to the microstructure of the material. Therefore, for a better understanding of the growth behaviour of small cracks in pure titanium, it is necessary to study the above behaviour using material with a different microstructure. In the present paper, the growth behaviour of small fatigue cracks was studied in both fine- and coarsegrained versions of a pure titanium under axial loading, and the growth behaviour and its statistical properties on a coarse grained version of a different pure titanium were also investigated under rotating bending and the results were compared with those on a fine grained version of this titanium in a previous report s. Based on the experimental results obtained, the following issues are discussed: 1. the effect of grain size on growth rate; 2. the statistical aspects of small crack growth; 3. the relationship between stage I cracking and grain size; 4. the size of MSSC. MATERIALS AND PROCEDURES The materials used in this study were two different pure titaniums, TP35H and TB35C (JIS: Japanese

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Effect of grain size on crack growth in Ti: K. Tokaji et al. Table 1 Chemical compositions of the two materials tested

RESULTS

(wt %) Material

H

O

N

Fe

Ti

TP35H TB35C

0.0005 0.0019

0.101 0.095

0.005 0.008

0.006 0.043

bal.

Industrial Standards), which were supplied as 10 mm thick plate and 13 mm diameter bar respectively. The latter material is the same as in a previous repor¢. The chemical compositions are listed in Table 1. Plate-type specimens of 5 mm minimum width and 4 mm thickness and round bar specimens of 8 mm diameter and 10 mm gauge length were machined from the above materials, and were employed for fatigue experiments under axial loading and rotating bending respectively. Specimens were mechanically polished by emery paper and then electropolished in order to facilitate the observation of small crack growth. Subsequently, plate-type specimens were annealed at 700°C for 1 h and 850°C for 10 h in vacuum, and the latter heat treatment was also applied to round bar specimens. The average grain size d obtained by these heat treatments was 27 ~m (fine grain, FG) and 90/zm (coarse grain, CG) for plate-type specimens (TP35H), and 115/xm (CG) for round bar specimens (TB35C). The mechanical properties are given in Table 2. For comparison, the results on the FG material (d = 73/zm) in TB35C are also shown in the table. A 49 kN closed-loop electrohydraulic testing machine (frequency f = 10 Hz) and a 98 N m rotating bending testing machine (f = 33 Hz) were used for axial loading (R = - 1 ) and rotating bending (R = - 1 ) fatigue tests respectively, at room temperature in laboratory air. Small crack growth was monitored by replicating the surface of the specimens. After testing, crack length was measured by an optical microscope with the aid of an image-processing system, in which the length projected onto the direction perpendicular to the specimen axis was used as crack length. The fracture surfaces were examined under a scanning electron microscope (SEM). The stress intensity factors were calculated using the analytical solutions6 by Newman and Raju for axial loading and by Shiratori et al. 7 for rotating bending.

Fatigue strength Under both loading conditions, fatigue strengths in the FG material were higher than those in the CG material. The fatigue limits tr, in the FG and CG materials were 210 MPa and 130 MPa under axial loading and 240 MPa and 220 MPa under rotating bending respectively. Crack initiation Cracks were always generated within grains, irrespective of grain size and loading condition. Crack appearances immediately after initiation in the CG material are shown in Figure 1, revealing a linear morphology because of the planar slip nature of the material. While intense slip bands are seen under axial loading within and around the grains in which cracks are initiated, this is not the case under rotating bending. Small crack growth behaviour As an example, Figure 2 shows the macroscopic appearances of crack growth in both the FG and CG materials under axial loading. The early growth after crack initiation is strongly affected by the microstructure, and subsequently cracks tend to grow gradually to the direction perpendicular to the loading axis. It can be seen in the figure that cracks in the CG material exhibit a more complicated path, with remarkable deflections and branchings, compared with those in the FG material8. These macroscopic features in crack growth were also observed under rotating bending. The growth rates, da/dN, under axial loading are presented in Figure 3a as a function of the maximum stress intensity factor K .... ; crack depth a was obtained from the measurements of surface crack length 2c by assuming the aspect ratio a/c = 1. For the sake of comparison, the relationships da/dN vs AK and da/ dN vs effective stress intensity factor range AKeff for large cracks are represented in the figure. In the FG material, the growth rates at trmax = 290 MPa are considerably higher than large cracks over the whole Kma x regime tested, but at trmax = 230 MPa, small cracks grow faster only in the low Kmax regime or the small-crack regime. However, in the CG material, the growth rates at O'max 180 MPa and 170 MPa are similar and are higher than for large cracks, particularly in the low Kmax regime. A further important point to be noted in the figure is that small cracks in the CG material tend to grow faster than those in the FG =

Table 2 Mechanical properties of the heat-treated specimens

Material

Grain size, d (/.Lm)

0.2% proof stress, ~ro.2 (MPa)

Tensile strength, o'B (MPa)

Breaking strength on final area, trT (MPa)

Elongation, ~ (%)

Reduction of area, (%)

TP35H

27 90

284 311

411 397

736 646

39 41

60 60

TB35C

73 115

324 246

434 383

776 863

28 39

57 69

572

Fatigue, 1994, Vol 16, November

Effect of grain size on crack growth in Ti: K. Tokaji et al.

Figure 1 Cracks immediately after initiation in coarse-grained material: (a) axial loading (tr = 170 MPa); (b) rotating bending (tr = 240 MPa)

tO

Figure 2 Macroscopic appearances of small fatigue crack growth under axial loading: (a) fine-grained material (tr = 230 MPa); (b) coarsegrained material (tr = 170 MPa)

material at stresses that are considered to be nominally elastic. Crack closure was monitored for small crack growth at O'max = 290 MPa in the FG material and at o-max ---- 180 MPa and 170 MPa in the CG material by measuring the displacement between two Vickers hardness indentations straddling the crack 9. Consequently, no crack closure was detected in the stress vs displacement relationships, indicating that the cracks were fully open throughout cycling at the above stresses. Based on the crack closure measurements, the growth data for small cracks are plotted in Figure 3b in terms of AK~ff, as AK~ff = 2Kmax. It can be seen that the da/dN vs AK~ff relationships for small cracks are coincident with those for large cracks in the high AKeff regime or large-crack regime, indicating that the enhanced crack growths seen in Figure 3a can be attributed to the reduction in crack closure. At o-max = 290 MPa in the FG material, macroscopic plastic deformation may take place because the maximum stress exceeds the proof stress of the

material (o'0.2 = 284 MPa). Also, at O'max = 180 MPa and 170 MPa in the CG material, cyclic plastic deformation seems to occur extensively, as many grains with intense slip bands were seen around the crack. In these situations, elastic-plastic parameters such as the J-integral should be used to characterize the crack growth behaviour. However, Figure 3b suggests that such plastic deformation at the above stresses can affect only crack closure behaviour, and thus small crack growth can be correlated with large cracks by taking crack closure into account. Similar results have been reported by the authors on a low-carbon steel 1°. The most important aspect in Figure 3b is the enhanced growth behaviour observed at AKeff ~< 7 MPa m ~ in the FG material and at AKeff ~< 6 MPa m i in the CG material. This may be attributed to a different growth mechanism from that for large cracks, because the depths of stage I facets observed correspond approximately to the crack sizes calculated from the above AKeff values, as will be discussed later.

Fatigue, 1994, Vol 16, November

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Effect of grain size on crack growth in Ti: K. Tokaji et el.

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i~ 7

(a) ~/dN vsK~.;(b) da/dN vsAK~ff The relationships between da/dN and /
Coarse grain

Fatigue, 1994, Vol 16, N o v e m b e r

1

b

2 3 4 5 10 20 30 50 Maximum stress intensity factor Kmax MPa~

Figure 4 Relationships between da/dN and Kmaa of coarse-grained

material under rotating bending: (a) tr = 250 MPa and 230 MPa; (b) tr = 240 MPa

Effect of grain size on crack growth in Ti: K. Tokaji et al. growth behaviour of small cracks is very similar to that under axial loading (Figure 3a) and in the FG material 5, i.e. small cracks grow much faster than large cracks, especially in the low Kmax regime, and with the increase in /
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An interesting point to be seen in the figure is the similar dependence of 77 on a/d in both materials; the 7/values are almost constant at large a/d, but increase with decreasing a/d at a/d ~< 3. In this region, the r/

Fatigue,

1994,

Vol

16,

November

575

Effect of grain size on crack growth in Ti: K. Tokaji et al. values are smaller in the CG material than in the FG material, reflecting a lower frequency of transient decreases or arrests in growth rate in the CG material.

Effect of microstructure and stage I cracking The relationship between surface growth rate, dc/ dN, and surface crack length in the CG material is shown in Figure 8a. For comparison, the result in the FG material is also given in Figure 8b. These results are a different expression of the growth behaviour in the low Kmax regime in Figure 4b and Figure 5. It can be clearly seen that transient decreases or arrests in growth rate often take place at 2c ~< 880/xm and 2c ~< 550 ~m in the CG and FG materials respectively. A close examination of the relationship between the crack path and the microstructure showed that such variations are related to the blocking effect of grain boundaries and crack deflections. The extent and

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u

I0 -3 o u~ ~-'~ E

Coarse grain o=240MPa (I0 specimens) R=-I

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10-4 ~- ,a

frequency of the variations are less remarkable in the CG material. This trend was also observed under axial loading. It can therefore be concluded that the effect of microstructure on small crack growth is significantly smaller in the CG material than in the FG material 8, independent of loading condition. Fractographic examination of fracture surfaces revealed featureless and flat facets at the crack initiation site in all the specimens studied under rotating bending. These facets are considered to be stage I cracks because they were inclined at approximately 45 ° to the loading axis. Similar facets were observed under axial loading. The stage I facet depths, a~, in the CG material obtained under rotating bending are represented in Figure 9 as a function of applied stress, together with the results in the FG material. In the CG material, the ai values at tr = 240 MPa are between 100/zm and 190 ~m, and are somewhat larger than the average grain size ( d = 115/zm). The ai values at or= 2 5 0 M P a and 230 MPa are 180 tzm and 90/~m respectively, and they correspond to the upper and lower bounds of the scatter in the ai values at o" = 240 MPa, indicating an influence of the applied stress. On the other hand, the a~ values at or = 250 MPa in the FG material tend to deviate towards smaller depth when compared with those in the CG material. Under axial loading, furthermore, the a~ values were found to be 30-100/~m in the FG material and 116-228/~m in the CG material. Thus stage I crack depths appear to be strongly dependent on grain size rather than stress level. DISCUSSION

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c

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0.6

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0.8

Dependence of crack growth rate on grain size As shown in Figures 3-5, the effect of grain size on growth rate was observed in the low Kmax regime or

mm

a

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b Figure 8 Effect of microstructure on crack growth rate under rotating bending: (a) coarse-grained material (tr = 240 MPa); (b) fine-grained material (or = 250 MPa) 576

Fatigue, 1994, Vol 16, N o v e m b e r

I

0

mm

2OO

i

i

i

I t 250

Stress amplitude

i 0

I

I 300

MPa

Stage I facet depth as a function of applied stress in coarse- and fine-grained materials under rotating bending

Figure 9

Effect of grain size on crack growth in Ti: K. Tokaji et al. small-crack regime, and small cracks in the CG material tended to grow faster than those in the FG material. This may be attributed to the lower frequency of transient decreases or arrests in growth rate resulting from the effect of microstructural barriers such as grain boundaries and crack deflections (Figure 8). The differences in the effect of microstructure between the FG and CG materials can be explained as follows. 1. The decreases or arrests in growth rate at grain boundaries depend on both the crack-driving force and the blocking effect of the grain boundary. The latter is mainly due to the misorientation between grains and is considered to be independent of grain size. For example, as the crack tip reaches the first grain boundary, the absolute crack size is larger in the CG material than in the FG material; thus the crack driving force becomes larger in the CG material. This leads to a much smaller effect of microstructure in the CG material. 2. As the same crack size is assumed in both materials, the number of grain boundaries that the crack crosses is lower in the CG material. Thus decreases or arrests in growth rate would take place with statistically lower frequencies in the CG material. 3. Frequently, small deflections in crack path induce more remarkable fluctuations in growth rate than large deflections. This is supported by a crystallographic study on microstructurally small crack growth in 3%Si iron n.

Relationship between stage 1 crack and grain size In this section, the relationship between a~ and d will be discussed. The statistics of the extreme values were used to examine the relationship between a~ and the maximum size of d. The cumulative probability of the maximum grain size dj . . . . (j = 1-20), obtained from measurements in 20 unit areas So (0.281 mm 2 in the FG material and 0.248 mm 2 in the CG material), was plotted on an extreme probability paper, and then the maximum grain size contained in a single specimen, d...... was deduced from the return period T corresponding to the surface area S of a specimen (S = 249.2 mm2) 12. The obtained dm.... values are 430 ~m and 310/~m in the CG and FG materials respectively, and are much greater than the a I values shown in Figure 9. The fact that each at value does not correspond to d . . . . . indicates that crack initiation is not dependent on grain size only. This is quite reasonable, because the grain orientation is more important for crack initiation and the maximum grain would have an extremely low probability of a favourable orientation for crack initiation. The a~ values in the CG and FG materials under rotating bending were plotted on log-normal probability paper together with d. The results are shown in Figure 10. Also included are the distributions of half-maximum grain sizes, din,x/2. The reason why dmax/2 was considered is that as grains on the specimen surface face the free surface, their average depths are thought to correspond to half grain size. As previously mentioned, the a~ values are almost in the order of d, but the distributions tend to deviate towards slightly larger sizes of d independent of grain size. It is found that there is a close correspondence in the distributions between the ai and dmax/2 values in the CG material.

99

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Figure 10 Distribution of stage ! hcet depths in coarse- and finegrained materials plotted on log-normal probability paper

The correspondence in the FG material is somewhat less convincing, but still feasible. From the above discussion, cracks are initiated within relatively large grains that satisfy a specific crystallographic condition for crack initiation, and the distribution of stage I crack depths can be estimated from the maximum value distribution of grain sizes. The authors have indicated that the transition from stage I to stage II was characterized by Kmax in an aluminium alloy 13. In pure titanium, however, it is apparent that the transition is strongly dominated by microstructural factors rather than mechanical factors.

Microstructurally small crack and grain size Small cracks whose growth rates are strongly affected by microstructure are termed microstructurally small cracks. Their maximum sizes, 2Cm, are obtained from Figure 8 as 880/zm and 550/xm in the CG and FG materials respectively. These sizes are slightly larger than the maximum sizes that were evaluated for each of ten specimens (690 ~tm and 450/~m in the CG and FG materials). However, considering the uncertainty or the error in determining 2Cm, the sizes of 880/.~m and 550/~m can be regarded as 2Cn~.The crack depths obtained from these sizes are 392 ~m and 245/xm in the CG and FG materials respectively, and they coincide with the depths obtained from a/d = 3. In pure titanium, therefore, as the relative size of microstructurally small cracks is not dependent on grain size, one can estimate their absolute size from the average grain size of the material. Fatigue, 1994, Vol 16, November

577

Effect of grain size on crack growth in Ti: K. Tokaji et al. The above depths of microstructurally small cracks tend to be larger than the stage I facet depths (Figure 10), suggesting that growth after the transition from stage I to stage II is still influenced by the microstructure. This may be attributed to the limited slip systems in the present material. Finally, it is worth noting that the 2Cm value (or am) has an important meaning as the limiting crack length (or depth) above which AKeff-based linear elastic fracture mechanics (LEFM) is applicable. Therefore, it is necessary to obtain the 2Cm values for a wide variety of materials. The relationship between 2cm and d is given elsewhere for seven different materials, including pure titanium TM,

7. The coefficients of variation in growth rate were significantly large at a/d ~< 3 (a = crack depth, d = average grain size); they were smaller in coarsegrained material than in fine-grained material, reflecting a much smaller effect of the microstructure. The crack depths obtained from a/d = 3 corresponded to the size of microstructurally small cracks. Therefore it was found that the size of microstructurally small cracks can be obtained from the average grain size. ACKNOWLEDGEMENTS The authors wish to thank Messrs T. Ochi and Y. Yato for assistance in the experiments.

CONCLUSIONS 1. Under both axial loading and rotating bending, small cracks grew faster than large cracks, in particular in a small-crack regime, independent of grain size. As the data were plotted in terms of the effective stress intensity factor AKeft (after allowing for crack closure), the growth rates for small cracks were correlated with those for large cracks in a large-crack regime, while small cracks still exhibited enhanced growth rates in a smallcrack regime. 2. In a small-crack regime, small cracks in coarsegrained material showed faster growth rates than those in fine-grained material. 3. The decreases or arrests in growth rate due to grain boundaries and crack deflections were less remarkable in coarse-grained material than in finegrained material. 4. The depths of stage I facets were less than the maximum grain sizes contained in a single specimen estimated by the statistics of the extreme values, but their distributions corresponded to the maximum value distributions of grain size. 5. The transition from stage I to stage II was strongly dominated by microstructural factors rather than mechanical factors. 6. The scatter in growth rate followed log-normal distributions independent of grain size.

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Fatigue, 1994, Vol 16, November

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6 7 8 9

10 11 12 13 14

Robinson, J.L. and Beevers, C.J. Met. Sci. J. 1973, 7, 153 Walker, N. and Beevers, C.J. Fatigue Eng Mater. Struct. 1979 1, 135 Ward-Close, C.M. and Beevers, C.J. Metall. Trans. 1980, I1A, 1007 Ogawa, T., Tokaji, K. and Kameyama, Y. J. Soc. Mater. Sci. Jpn 1989, 38(432), 1026 (in Japanese) Tokaji, K., Ogawa, T., Kameyama, Y. and Kato, Y. In 'Proceedings Fatigue 90' Honolulu, Hawaii, (Eds H. Kitagawa and T. Tanaka), Materials and Component Engineering Publications, 1990, Vol. 2, pp. 1091-1096 Newman, J.C. Jr In ASTM STP687, American Society for Testing and Materials, 1979, pp. 16-42 Shiratori, M., Miyosbi, T., Sakai, Y. and Zhang, G.R. Trans. Jpn Soc. Mech. Eng. 1987, 53(488), 889 (in Japanese). James, M.N. and Sharpe, W.N. Jr Fatigue Fract. Eng. Mater. Struct. 1989, 12(4), 347 Tokaji, K., Ogawa, T., Osako, S. and Harada, Y. In 'Proceedings of Fatigue 87' Charlottesville, VA, (Eds R.O. Ritchie and E.A. Starke Jr.), Engineering Materials Advisory Services Ltd, 1987, Vol. 1, pp. 313-322 Tokaji, K., Ogawa, T. and Aoki, T. Fatigue Fract. Eng. Mater. Struct. 1990, 13, 31 Tokaji, K., Ogawa, T. and Okamoto, R. J. Soc. Mater. Sci. Jpn 1991, 40(457), 1310 (in Japanese) Murakami, Y. and Usuki, H. Int. J. Fatigue 1989, 11(5), 299 Tokaji, K., Ogawa, T. and Kameyama, Y. Fatigue Fract. Eng. Mater. Struct. 1990, 13(4), 411 Tokaji, K. and Ogawa, T. In 'Short Fatigue Cracks' (Eds K.J. Miller and E.R. de los Rios), Mechanical Engineering Publications Ltd, 1992, pp. 85-99