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Multiscale fatigue crack observations on Ti–6Al–4V
International Journal of Fatigue 33 (2011) 710–718
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Multiscale fatigue crack observations on Ti–6Al–4V Bernd Oberwinkler ⇑, Anton Lettner, Wilfried Eichlseder Montanuniversität Leoben, Chair of Mechanical Engineering, Franz-Josef-Straße 18, Leoben 8700, Austria
a r t i c l e
i n f o
Article history: Received 2 August 2010 Received in revised form 17 November 2010 Accepted 30 November 2010 Available online 4 December 2010 Keywords: Titanium base alloys Fatigue Crack initiation Crack growth Microstructure
a b s t r a c t The fatigue process of dynamic loaded materials can generally be classified in four stages, namely crack initiation, short crack growth, long crack growth and rupture. A continuous fracture mechanical description of the crack growth stages under consideration of the crack initiation phase was the aim of this research. The fatigue behavior of forged Ti–6Al–4V with three different microstructures were thereby characterized on the basis of multiscale fatigue crack observations on electrolytically polished hourglass specimens loaded in the finite life region. The gathered crack propagation data was compared with single-edge bending long crack growth curves. It was determined that the crack initiation phase accounts for less than 5% of the total lifetime. Depending on the (a + b)-content, the fatigue behavior is dominated either by primary a-grain size (equiaxed-type microstructures) or colony length of the (a + b)-lamellae (bimodal-type microstructures). Transcrystalline crack propagation was observed for all microstructures. The comparison of the multiscale fatigue crack growth rates with single-edge bending long crack growth curves revealed that the short crack growth behavior is the extension of the Paris-region of the long crack growth curve, and can be fitted with a power law for lifetime estimation. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The fatigue process of dynamic loaded materials can generally be classified in four stages: crack initiation, short crack growth, long crack growth and rupture. Depending on the material (inhomogeneities, etc.) and on the loading (low cycle or high cycle fatigue region), the fraction of these different stages varies with respect to the total lifetime. Usually, these stages are analyzed either separately (e.g., in crack growth experiments) or holistically in the classical stress- or strain-based approaches (S/N- or e/N-curves). Separate analyses lead to a better understanding of the involved mechanisms of the respective stages. Crack growth results can further be used for lifetime estimation of defectafflicted materials (inhomogeneities, e.g. pores, act as initial cracks) based on fracture mechanical methods. The holistic S/N- or e/N-approaches (the specimens are thereby tested until failure) enable a lifetime estimation of defect-free materials based on local stresses or strains. To gain a better understanding of the complete fatigue process, it is necessary to perform multiscale fatigue crack observation experiments from crack initiation to failure. Furthermore, the gathered data of such continuous experiments is the basis for a fracture mechanical based lifetime estimation of components manufactured from defect-free materials, such as the titanium base alloy Ti–6Al–4V. This is a promising approach to include the influence of variable amplitude loading ⇑ Corresponding author. Tel.: +43 38424021466. E-mail address: [email protected] (B. Oberwinkler). 0142-1123/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2010.11.024
and sequence effects in a lifetime estimation in further research. Currently used S/N- or e/N-approaches are not able to include such effects without enormous testing amount for calibration of non-linear damage accumulation methods. As mentioned before, the different fatigue stages are usually analyzed separately, and especially for Ti–6Al–4V a lot of literature data is available. Bridier et al. [1] performed strain-controlled fatigue tests on bimodal Ti–6Al–4V in the finite life region for determination of the crack initiation mechanisms. They noted that in primary a-grains, the prismatic slip is more easily activated than the basal one. All cracks were found to form across primary a-grains either on prismatic or basal planes. Most of the observed prismatic cracks remained restricted to the initial primary a-grain and were parallel to straight and regularly spaced slip bands. Conversely, basal cracks at the same number of cycles had already propagated through the surrounding microstructure. Their results revealed that prismatic crack formation involves a classical surface roughening mechanism. In the case of basal systems, it is quite different. The crack formation in the finite life region requires a combination of a high Schmid factor and a high elastic stiffness, inducing a high tensile stress normal to the basal plane. Ivanova et al. [2] tested equiaxed and bimodal Ti–6Al–4V in the finite life and high cycle fatigue regime. In the finite life region, they found crack initiation at the a/b interface and within the primary a-phase. In contrast, in the high cycle fatigue region the fatigue cracks initiated solely in a-grains. In the equiaxed microstructure, the cracks started thereby at the a/a grain boundary. Field emission microscopy of the crack initiation site revealed a
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fan-shaped pattern on the grain surface, which is characteristic for cleavage-type fracture, cf. [3]. The percentage of life spent for crack initiation was below 30% in the finite life region and over 80% in the high cycle fatigue region. Knobbe et al. [4] analyzed fatigue crack initiation and microstructurally short crack growth in mill-annealed Ti–6Al–4V in the high cycle fatigue region. They found that the fatigue cracks initiate preferentially at grain or phase boundaries. More initial fatigue cracks were determined in the lamellar (a + b)-phase. The initiated cracks grow intercrystalline; even in lamellae. Wagner and Gregory [5] studied the crack growth behavior of microstructurally short respectively long cracks in coarse lamellar and fine equiaxed microstructures. They ascertained that the coarse lamellar microstructure exhibits a worse short crack growth behavior but – owing to the additional crack growth resistance contributions of crack front geometry and crack closure – a slower long crack propagation compared to the fine equiaxed microstructure. Furthermore, they reported a decrease of long crack growth rate with increasing a-grain size owing to the same crack growth resistance contributions mentioned before. Similar findings are reported by Lütjering and Gysler [6] and Peters et al. [7]. Gray and Lütjering [8] also observed that coarsening the equiaxed grain size reduces the fatigue crack propagation rates of Ti– 6Al–4V at low stress ratios. They attributed the influence of grain size and the increase in fatigue crack propagation resistance with decreasing stress ratio to roughness-induced crack closure. Furthermore, they found that the coarse lamellar microstructure possesses (in comparison to equiaxed microstructures) the highest resistance to fatigue crack propagation owing to roughnessinduced crack closure. Nakajima et al. [9] investigated the early stage of crack growth in mill-annealed Ti–6Al–4V on notched flat specimens (stress ratio R = 0.1). They found that the analyzed fatigue crack initiated as a stage I crack in an a-grain at the notch root surface. The incipient crack grows under 45° to the maximum tensile stress axis. It was also revealed that the small fatigue crack changed its propagation direction at the grain boundary. They supposed that crack closure develops fast, owing to the relatively large a-grains with planar slip characteristics. These literature results enable a deep insight into the individual fatigue stages. However, to gain a better understanding of the holistic fatigue process in respect of microstructure and to generate the basis for fracture mechanical lifetime estimation of defect-free materials such as Ti–6Al–4V, continuous multiscale fatigue crack observation (MFCO) experiments are necessary. In this research, the crack initiation, short and long crack growth in Ti– 6Al–4V with three different microstructures were hence continuously characterized according to the method presented by Wagner and Lütjering [10]. Additionally, separate long crack growth experiments on single-edge bending (SEB) specimens served as a reference.
2. Material characterization The material used for this research work has been provided by Böhler Schmiedetechnik GmbH & Co KG (Austria) in the form of heat-treated Ti–6Al–4V V-shape and side-pressed pancake forgings, respectively. Due to the chosen forging temperature (between 900 °C and 930 °C) no crystallographic texture occurs in the microstructure [11]. This has been approved with X-ray diffraction (XRD) and electron backscatter diffraction (EBSD) measurements. Different types of microstructures were achieved by subsequent heat treatments (mill-annealing, solution treating, recrystallization-annealing). Additional information regarding the forging processes and heat treatments can be found in [12,13]. The analysis of the different microstructures was done with a light optical microscope. The metallographic sections were therefore grinded, polished and etched. The microstructure becomes thereby visible in a light optical microscope, whereby the a-phase appears bright and the b-phase appears dark. The mill-annealed V-shape (MAV) shows a typical mill-annealed microstructure (Fig. 1a). Mill-annealing does not cause complete recrystallization and therefore leads to a distinct texture of the primary a-grain shapes, representative of the forging process. The solution treating of the pancakes (STP) causes a bimodal microstructure (Fig. 1b). The recrystallization-annealing of the pancakes (RAP) results in a coarse equiaxed microstructure (Fig. 1c). The microstructures were characterized with respect to primary a-grain size ap, colony length Col of the (a + b)-lamellae and (a + b)-content Ca+b, cf. Table1. Depending on the (a + b)-content, the microstructures can be classified in equiaxed-type (Ca+b 6 20%) and bimodal-type (Ca+b P 25%), cf. [12,19]. This classification was confirmed in the present work and will be discussed below. The mill-annealed and recrystallization-annealed microstructures are hence equiaxedtype, the solution treated microstructure is bimodal-type.
3. Experimental procedure The characterization of the long crack growth behavior was done with V-notched single-edge bending (SEB) specimens under four-point-bending loading (cf. ASTM E647 [14]) at a Rumul Cracktronic resonant testing rig with a frequency of approximately 140 Hz. The crack length was measured with the potential drop method, cf. Fig. 2. Temperature compensation was done with a
Table 1 Microstructural characterization of the analyzed materials. Material
Abbr.
ap (lm)
Ca+b (%)
Col. (lm)
V-shape mill-annealed Pancake solution treated Pancake recryst.-annealed
MAV STP RAP
8.7 8.9 10.3
20.3 50.9 0
9.2 16.1 –
Fig. 1. Micrographs of the analyzed materials.
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and plasticity-induced crack closure can hence be neglected. The measured data points were fitted with a purpose four-parametric equation introduced in [13].
rpl ¼
Fig. 2. Scheme of the potential drop method.
Pt100 resistance temperature sensor fixed at the specimens near the crack. The measurements were performed at ambient air with room temperature at a stress ratio R (ratio of minimum and maximum stress or stress intensity factor, respectively) of 1. The stress intensity factor range DK was derived according to linear elastic fracture mechanics for all stress ratios, cf. Eq. (1), where Dr is the applied stress range, a the crack length and Y the appropriate geometry factor according to Murakami [15].
pffiffiffiffiffiffi DK ¼ Dr paY
ð1Þ
p The measurements were finished at 80 MPa m due to testing rig limitations regarding maximum stress intensity factor range. At least two specimens were tested for each microstructure. The test procedure was constant DK-testing for crack initiation up to a crack length of 6 mm, DK-decreasing testing from the Paris-region down to the threshold and subsequent DK-increasing testing with constant bending moment from the Paris-regime to fracture or testing rig limit. Carboni et al. [16] reported that this testing method could lead to non-conservative threshold values, mainly due to plasticity-induced crack closure. Therefore, the size of the plastic zone after the constant DK-testing was determined with both, FE analysis and estimation according to Irwin (e.g., [17]) for the plain strain state, Eq. (2), where KI is the applied stress intensity factor, ry the yield stress and t the Poisson ratio. The applied parameters for the Irwin estimation are in the case of Ti–6Al–4V t = 0.3 and ry 900 MPa (depending on microstructure, the 0.2%yield-strength varies from 880 MPa for RAP, over 900 MPa for STP to 925 MPa for MAV). It was observed that the size of the plastic zone is in the near-threshold region in the range of the grain size
K 2I 2pr2y
ð1 2mÞ2
ð2Þ
The multiscale fatigue crack observations (MFCO) were performed according to the method presented by Wagner and Lütjering [10]. Thereby, round hourglass fatigue test specimens (gauge diameter 6 mm, usually used for S/N-curve experiments) were electrolytically polished to get a smooth surface and to remove residual stresses from machining. For crack initiation, the polished specimens (d 5.85 mm) were loaded under rotating bending (R = 1, ambient air and room temperature) with a stress amplitude of 750 MPa for 4000 load cycles. After this predefined crack initiation phase, the specimens were etched for visualization of the microstructure and for accentuation of the initiated cracks. For evaluation of the crack length with a confocal laser-scanning microscope, crack opening was necessary. Therefore, a pretensioning device was designed for static loading of the round specimens during the microscopy, cf. Fig. 3. The initiated cracks were searched on eight positions (every 45°) on the specimens. Over 50 initiated cracks were found on each position on a specimen. Therefore, several cracks were selected randomly to get a sum of approximately 80 cracks per specimen for the observation of the crack growth. Then the fatigue tests were continued at the same stress level and interrupted after a given number of cycles (DN = 1000) for measurement of the crack propagation. This procedure was repeated until failure of the specimens. The mill-annealed microstructure resulted in a lifetime of 16,800 load cycles. A higher lifetime of 21,400 load cycles was determined for the solution treated microstructure. Recrystallization-annealing led, compared to the other microstructures, to an anomalous low fatigue life of 10,700 load cycles, which stands in contrast to rotating bending test results on machined hourglass specimens of the same batch, cf. [12,13] or [19]. 4. Discussion The single-edge bending tests revealed long crack growth down to propagation rates of 1012 m/cycle, cf. Fig. 12, which was also reported by Stanzl-Tschegg [18]. Above crack growth rates of approximately 107 m/cycle, the investigated microstructures show almost the same crack propagation behavior. The mill-annealed microstructure leads to an anomalous high crack growth rate in the region between 109 m/cycle and 107 m/cycle. The multiscale fatigue crack observation (MFCO) results performed on rotating bending specimens were analyzed with respect to crack initiation and crack propagation behavior. In the
Fig. 3. FE-model (l), pretensioning device (r).
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mill-annealed microstructure (Ca+b = 20%), about 60% of the cracks initiated in (a + b)-phase. The higher (a + b)-content of the solution treated microstructure (Ca+b = 51%) increases the percentage of initial cracks in (a + b)-phase to 80%. The crack initiation in the recrystallization-annealed material have to take place in a-phase, as no (a + b)-phase is present due to the heat treatment. A significantly larger amount of initiated cracks was determined in the recrystallization-annealed microstructure. It can hence be assumed, that the primary a-grains are strengthen with increasing (a + b)-content; maybe by alloying elements partitioning effects. These findings confirm the classification in equiaxed-type (Ca+b 6 20%, the primary a-grain size dominates the fatigue behavior) and bimodal-type (Ca+b P 25%, the colony length of the (a + b)-phase correlates with the fatigue strength) microstructures discussed in [12,19]. The comparison of the initial crack lengths after 4000 load cycles (stress amplitude 750 MPa) is shown in Fig. 4. It was assumed that the crack length distribution follows a Weibull-curve. The peak value of the initial crack length distribution correlates with the microstructural parameters primary a-grain size or colony length. The crack initiation phase in the equiaxed-type microstructures (Ca+b 6 20%) of the recrystallization-annealed pancakes and mill-annealed V-shapes is dominated by the primary a-grain size. The ratio of initial crack length (peak value of the Weibull-distribution) and the primary a-grain size is 1.7 for both equiaxed-type microstructures. In bimodal-type microstructures (Ca+b P 25%, e.g. the microstructure of STP), crack initiation occurs primarily in (a + b)-phase. The initial crack length can hence be linked with the colony length. The ratio of this microstructural size and initial crack length is again 1.7, analogical to the findings for the equiaxed-type microstructures. This value of 1.7 indicates that the observed ‘‘initial cracks’’ were already propagated into adjacent grains. This causes a shift of the Weibull-distributions to longer crack lengths. It is remarkable that the recrystallization-annealed microstructure exhibits a relatively large portion (12%) of noticeably longer cracks. This behavior will be discussed below. The crack length distributions were separated for a- and (a + b)-phase, Fig. 5. It was observed that the crack length distributions in both phases are very similar for the mill-annealed microstructure. In contrast, the distributions for the solution treated pancake are significantly different. Thereby, the distribution of the initial cracks in the a-phase exhibits a maximum at a crack length approximating the primary a-grain size. This means that they were not significantly propagated after 4000 load cycles. However, those cracks which initiated in (a + b)-phase were considerably longer owing to two facts: the colony length is larger
Fig. 4. Initial crack length distributions.
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Fig. 5. Initial crack length distributions separated for a- and (a + b)-phase.
than the primary a-grain size and the initial cracks were already propagated. The orientation of the initial cracks with regard to the load direction is presented in Fig. 6. It was determined that the separation in a- and (a + b)-phase does not affect these distributions. It has to be mentioned that the crack orientation can only be measured at the surface (2D information). Therefore, the unknown third (radial) dimension has to be included theoretically in the advisements regarding crack initiation, considering the texturefree material with a huge amount of grains in the highest loaded region. Schmid’s law (see, e.g. [20]) is given in Eq. (3); the according delineation is shown in Fig. 7. Thereby, u is the angle between the normal vector n of a cutting plane (slip plane) and the load direction, k the angle between slip direction d and load direction, F the applied force, and m the so-called Schmid factor. The vectors n and d have to be perpendicular. This leads to the following inequation for the Schmid factor: 0 6 |m| 6 0.5. The maximum possible shear stress smax is hence half the applied normal stress r.
s ¼ r cos k cos u ¼ r m
ð3Þ
The maximum shear stress plane (u = 45°) is drawn in Fig. 7. It can be observed, that surface cracks which lay on the maximum shear stress plane are able to exhibit orientations from 45° up to 90° with respect to the load direction. From a continuum mechanical point of
Fig. 6. Initial crack orientations with respect to loading direction.
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Fig. 8. Crack growth behavior in mill-annealed Ti–6Al–4V.
Fig. 7. Possible surface crack orientations for maximum shear stress.
view, it can be assumed that every orientation between 45° and 90° has the same probability to occur. If the crack initiation is solely shear stress controlled, the distribution of the crack orientation should approximate a value as plotted in Fig. 6. Thereby the percentage of cracks with orientations 645° was subtracted for each material; the residual percentages should then be uniformly distributed on the orientations 46–90°. It was observed that both equiaxed-type materials (V-shape MA and pancake RA) follow their ideal distributions for pure shear stress induced crack initiation (maximum deviation 10%). In contrast, the solution treated pancake shows a maximum at orientations between 76° and 90°. This reveals that some fatigue cracks (20%) also initiate under maximum normal stress, which is just possible at orientations close to 90°. The crack growth observations after the crack initiation phase started at a microstructurally short scale (crack lengths approximate the grain size) and ended at a long crack scale (crack lengths >1 mm) due to failure of the rotating bending specimens. Linear elastic fracture mechanics, cf. Eq. (1), were used for determination of the applied stress intensity factor range. The thereby used geometry factor Y = 0.75 was an average of the proposed values of De Freitas and François [21] and Murakami [15]. This approach was used for easy and continuous comparability of short and long crack growth, even in the region where linear elastic fracture mechanics usually loose its validity (crack length a < 150 lm, cf. [22]). The crack growth behavior of these cracks was compared with those of single-edge bending long cracks for each microstructure. Figs. 8 and 9 depict such a comparison for the mill-annealed and solution treated microstructure, respectively. It was observed, that the crack growth behavior of the microstructurally short cracks meets the extension of the Paris-region determined with single-edge bending specimens. Several cracks were observed, which did not grow during the last 1000 load cycles. It can be assumed, that those non-propagating cracks, which stopped at stress intensity factors higher than the long crack growth threshold, would continue to grow after certain load cycles. This behavior can be attributed to the analysis method;
Fig. 9. Crack growth behavior in solution treated Ti–6Al–4V.
the growth of larger cracks occurs increasingly beneath the surface, but the crack size can only be measured directly at the surface. Intermittent crack stopping was determined for several microstructurally short cracks at and beneath the threshold. This behavior is caused by microstructurally barriers, e.g. grain or phase boundaries. It was observed that the threshold of the short cracks p p lies in the region of 4–5 MPa m. Beneath 4 MPa m, just nonp propagating cracks were determined, above 5 MPa m, each analyzed crack grew at least for a while. Figs. 10 and 11 show confocal laser scanning micrographs of microstructurally short cracks (the loading direction in these pictures is vertical) in mill-annealed respectively solution treated Ti–6Al–4V after certain load cycles. The crack tips are thereby marked with arrows. The thicker regions of the cracks represent the initial cracks after 4000 load cycles, enlarged by the performed etching. It can be assumed that the influence of the etching (crack tip blunting, reduced crack closure, etc.) on the crack growth behavior can be neglected after the first crack extension. Transcrystalline crack growth was observed. A relatively large scatter of crack growth rates in the short crack region was determined independent from material, owing to the significant influence of local microstructure on the crack propagation of microstructurally short cracks. It is hence important to analyze an adequate amount of microstructurally short cracks to get a meaningful average crack growth behavior. The experimental
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Fig. 10. Crack growth observations for mill-annealed Ti–6Al–4V.
Fig. 11. Crack growth observations for solution treated Ti–6Al–4V.
crack growth data gathered in MFCO tests was fitted with a power law consistent with the Paris-law for long cracks, Eq. (4), and compared with the single-edge bending long crack growth behavior, Fig. 12 and Table 2.
da ¼ C DK m dN
ð4Þ
Table 2 Fitting parameters for the multiscale fatigue crack observation experiments. Parameter
V-shape MA
Pancake ST
Pancake RA
p C (m/(Cyc. MPa m)) m (–)
5.34E11 2.06
1.57E11 2.34
1.36E11 2.36
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The higher average crack growth rates of the mill-annealed microstructure, which were observed in single-edge bending tests, were confirmed with the MFCO experiments. Striation dimension measurements were performed on scanning electron microscopy pictures of the SEB fracture surfaces. The crack growth rate within an a-grain was thereby determined to be more than a decade higher than the global crack growth rate at this position (lower Parisregion). This means that the crack formation within an a-grain consumes approximately 98% of the time for crack propagation on the scale of the average grain size. However, it can be assumed that the elongated a-grains of the mill-annealed microstructures lead for the same time of crack formation to an approximately two times higher crack propagation distance and hence crack growth rate. It is believed that this is the reason for the anomalous high crack growth rates of the mill-annealed microstructure. The cycles to failure Nf consist of the cycles spent for crack initiation Ni and the cycles of crack growth Ng, Eq. (5). The combination and integration (from initial crack length a0 to failure-causing crack length af) of Paris law, Eq. (4), and basic equation of the linear elastic fracture mechanics, Eq. (1), provides an estimation of the cycles consumed for crack growth Ng, Eq. (6). The average fitting parameters determined in MFCO experiments (Table 2) were used for calculation of the consumed crack growth cycles. As initial crack length a0, the mean primary a-grain size (for MAV) or mean colony length (for STP) plus according standard deviation was chosen, as the larger grains of the grain size distribution will be the limiting factor with respect to the fatigue life. However, it was observed that the failure-causing cracks were not initiated in extraordinarily large grains. Therefore the standard deviation was added once (this means that 84% of the grains are smaller than this value) and not twice (this would mean that already 98% of the grains are smaller than this value) to the mean grain size to achieve the initial crack length. Nevertheless, this is an assumption, and should be proofed in additional MFCO experiments. The crack initiation cycles were further determined by subtracting the crack growth cycles from the cycles to failure. The measured cycles to failure Nf, the calculated crack growth cycles Ng, and the crack initiation cycles Ni for the solution treated respectively mill-annealed microstructures are summarized in Table 3.
Nf ¼ Ni þ Ng
Ng ¼
Z
ð5Þ
af
a0
lower than those of the V-shape mill-annealed microstructure. However, crack initiation is considerably easier in the recrystallization-annealed material. Not only the length of the initial cracks was thereby anomalously large, also the quantity of initial cracks was significantly higher, what may be attributed to the unknown effect (possibly notch effect) of the interstice phase between the primary a-grains of the recrystallization-annealed material (cf. Fig. 1) or to alloying elements partitioning effects in microstructures with (a + b)-phase. Furthermore, a statistical influence may be the reason for this crack initiation behavior after 4000 load cycles (cf. Fig. 4). The crack initiation is easier directly at the surface (as in the case of the electrolytically polished specimens) than underneath the surface (as in the case of the machined specimens with compressive residual stresses in the surface layer). In combination with the fact that fatigue cracks initiate easier in the primary a-grains of the recrystallization-annealed microstructure (interstice notch effect, alloying elements partitioning effects, etc.), it is more likely that adjacent initiated cracks with similar orientations can coalesce during the initiation stage and form ‘‘super cracks’’ with crack lengths up to five times larger than the average ‘‘initial’’ cracks. Additionally, the absence of the (a + b)-phase and hence phase boundaries can promote this behavior. The same mechanism can
1 C Y Drm ðpaÞ0:5m m
da
ð6Þ
A crack initiation phase of approximately 3% of the total lifetime was determined for both mill-annealed and solution treated microstructure. This ties in well with the findings of other authors (e.g., [1,2]) regarding cleavage-type crack initiation in Ti–6Al–4V, and with the loading in the finite life region. It is hence possible to predict the fatigue lifetime solely based on the microstructurally characteristic dimension (a-grain size or colony length) and MFCO crack growth curves. The electrolytically polished specimen with the recrystallization-annealed microstructure exhibited an anomalous low finite life fatigue strength (Nf = 10,700 for ra = 750 MPa) compared to the fatigue tests of machined specimens tested in prior research, cf. [12,13] or [19]. The multiscale crack growth data showed no irregularity, cf. Fig. 12. An initial crack length on the scale of the grain size leads to a calculated lifetime slightly higher than those of the solution treated microstructure, what corresponds to the fatigue tests on machined specimens. The microhardness of the primary a-grains of the mill-annealed and recrystallization-annealed microstructures was measured and compared. The microhardness of the primary a-grains of pancake recrystallization-annealed was determined to be insignificantly
Fig. 12. Comparison of single-edge bending and multiscale fatigue crack observation experiments.
Fig. 13. Coalescing cracks and grains with multiple crack initiations in recrystallization-annealed Ti–6Al–4V.
B. Oberwinkler et al. / International Journal of Fatigue 33 (2011) 710–718 Table 3 Separation of the cycles to failure in crack initiation and crack growth cycles.
a
Material
Initial crack length, a0 (lm)
Nf (–)
Ng (–)
Ni (–)
V-shape MA Pancake ST Pancake RA
16.0 22.4 15.5
16,800 21,400 10,700
16,170 20,900 10,380a
630 (4%) 500 (2%) 320a (3%)
Assumption: Ni = 0.03 Nf, Ng = Nf Ni.
Fig. 14. Crack growth behavior in recrystallization-annealed Ti–6Al–4V.
be responsible for faster crack growth than the measured average crack growth rate. Fig. 13 (vertical loading direction) shows two adjacent cracks (ca. 50 lm spacing) after 5000 load cycles, which coalesced during additional 5000 load cycles, resulting in an abrupt and enormous increase of crack length. Furthermore, multiple crack initiation within one grain on parallel slip bands can be observed in this picture; a side effect of the easy crack initiation. Assuming that the crack initiation phase accounts for 3% of the total lifetime, Table 3, an increase of the fitting parameter C by a factor of 2.5 is necessary (cf. Fig. 14, adapted crack growth fit compared to average crack growth fit) to meet the measured cycles to failure with the crack growth calculations. This does not reflect the physical mechanism, but is an easy, first attempt to describe the crack growth rate. However, in machined specimens, where compressive residual stresses are present at the surface, crack initiation takes place underneath the surface, what significantly impedes the crack initiation. This could considerably reduce the probability of coalescing cracks to a level where they do not play a role. Additional MFCO experiments should be performed on the recrystallization-annealed material, to clarify the crack initiation stage and crack coalescence more in detail, by decreasing the initial load cycles prior to the first microscopy and using smaller increments for the measurement of the crack extension. 5. Conclusion Multiscale fatigue crack observations and long crack growth tests were performed on Ti–6Al–4V with three different microstructures. The analyses of the gathered data regarding crack initiation and crack growth revealed several interesting findings. The transition from equiaxed- (primary a-grain size controlled) to bimodal-type (colony length controlled) fatigue behavior occurs at a relatively low (a + b)-content of 20%.
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Based on linear elastic fracture mechanics, the average short crack growth rate is in accordance with the extension of the Paris-region of long crack growth data. The short crack growth threshold was determined to lay in the p p region of 4–5 MPa m. Beneath 4 MPa m, just non-propagating p cracks were determined, above 5 MPa m each analyzed crack grew at least for a while. Based on the determined crack growth data and on the characteristically microstructural dimension, the cycles consumed for crack initiation were approximated. With respect to the total lifetime of the used fatigue test specimens, the crack initiation phase accounts only for approximately 3%. This ties in well with the findings of other authors (e.g., [1,2]) regarding cleavagetype crack initiation in Ti–6Al–4V, and with the chosen loading in the finite life region. The mill-annealed microstructure leads to the fastest crack propagation of the analyzed microstructures. It can be assumed, that this behavior is caused by the grain shape texture (elongated primary a-grains) due to incomplete recrystallization during mill-annealing. An anomalously low fatigue strength was determined for the recrystallization-annealed Ti–6Al–4V. However, the observed crack growth rates are similar to those of the solution treated microstructure. It was assumed, that the easier crack initiation in the recrystallization-annealed material (eventually caused by alloying elements partitioning effects) leads to a high probability of crack coalescence. If the crack initiation is impeded by subsurface crack initiation due to (e.g., machining-induced) compressive residual stresses in the surface layer, this behavior can be repressed, resulting in significantly higher finite life fatigue strength. The applied multiscale fatigue crack observation (MFCO) technique is suitable for the characterization of the crack initiation and crack growth phase. It is possible to predict the fatigue lifetime solely based on the microstructurally characteristic dimension (a-grain size or colony length) and MFCO crack growth curves. With respect to the recrystallization-annealed material, additional MFCO experiments should be performed for clarification of crack initiation and crack coalescence by decreasing the initial load cycles prior to the first microscopy and using smaller increments for the measurement of the crack extension. Further research should also address the fatigue behavior in the high cycle fatigue region. Therefore, a mini rotating bending test rig is currently developed at our institute based on the experiences of the presented research work, which operates directly at the confocal laser-scanning microscope (no mounting and dismounting of the specimen for loading/observation necessary) and which is compatible to our scanning electron microscope. Acknowledgements The authors would like to thank the Austrian Federal Ministry for Transport, Innovation and Technology, the Austrian Federal Ministry of Economics and Labor, and the Austrian Research Promotion Agency for funding of this research work in the framework of the FFG’s BRIDGE program. The support by Böhler Schmiedetechnik GmbH & Co KG is much valued. References [1] Bridier F, Villechaise P, Mendez J. Slip and fatigue crack formation processes in an a/b titanium alloy in relation to crystallographic texture on different scales. Acta Mater 2008;56:3951–62. [2] Ivanova SG, Biederman RR, Sisson Jr RD. Investigations of fatigue crack initiation in Ti–6Al–4V during tensile–tensile fatigue. J Mater Eng Perform 2002;11:226–31.
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[3] Henry G. Fractography and microfractography, vol. 5. Düsseldorf, Germany: Verlag Stahleisen; 1979. p. 445. [4] Knobbe H, Köster P, Christ H-J, Fritzen C-P, Riedler M. Initiation and propagation of short fatigue cracks in forged Ti6Al4V. Proc Eng 2010;2:931–40. [5] Wagner L, Gregory JK. Ermüdung von Titanlegierungen. In: Peters M, Leyens C, editors. Titan und Titanlegierungen. WILEY-VCH Verlag; 2007. p. 163–96. ISBN:978-3-527-30539-1. [6] Lütjering G, Gysler A. Fatigue. In: Lütjering G, Zwicker U, Bunk W, editors. Titanium ‘84 – science and technology, vol. 4. DGM; 1985. p. 2065–83. [7] Peters M, Gysler A, Lütjering G. Influence of microstructure on the fatigue behavior of Ti–6Al–4V. In: Kimura H, Izumi O, editors. Titanium ‘80 – science and technology, vol. 3. Japan: TMS–AIME; 1980. p. 1777–86. [8] Gray III GT, Lütjering G. The effect of microstructure and stress ratio on fatigue crack propagation behavior of Ti–6Al–4V. In: Lütjering G, Zwicker U, Bunk W, editors. Titanium ‘84 – science and technology, vol. 4. DGM; 1985. p. 2251–8. [9] Nakajima K, Terao K, Miyata T. The effect of microstructure on fatigue crack propagation of a + b titanium alloys in-situ observation of short fatigue crack growth. Mater Sci Eng A 1998;A243:176–81. [10] Wagner L, Lütjering G. Propagation of small fatigue cracks in Ti alloys. In: Lacombe P, Tricot R, Béranger G, editors. Titanium ‘88 – science and technology, vol. 1. Les Ulis Cedex, France; 1988. p. 345–50. [11] Lütjering G. Influence of processing on microstructure and mechanical properties of (a + b) titanium alloys. Mater Sci Eng, A 1998;A243:32–45. [12] Oberwinkler B. Fatigue-proof and damage tolerant lightweight design of Ti– 6Al–4V forgings. Doctoral thesis, Montanuniversität Leoben; 2010.
[13] Oberwinkler B, Riedler M, Eichlseder W. Importance of local microstructure for damage tolerant light weight design of Ti–6Al–4V forgings. Int J Fatigue 2010;32:808–14. [14] ASTM E647. Standard test method for measurement of fatigue crack growth rates. West Conshohocken, PA, USA: ASTM International; 2008. [15] Murakami Y. Stress intensity factors handbook, vol. 2. Pergamon Press; 1987. ISBN:0-08-034809-2. [16] Carboni M, Patriarca L, Regazzi D. Determination of DKth by compression precracking in a structural steel. J ASTM Int 2009;6(9). [17] McClintock FA, Irwin GR. Plasticity aspects of fracture mechanics. In: Fracture toughness testing and its applications, ASTM STP 381. ASTM; 1964. p. 84–113. [18] Stanzl-Tschegg S. Fatigue crack growth and thresholds at ultrasonic frequencies. Int J Fatigue 2006;28:1456–64. [19] Oberwinkler B, Riedler M, Eichlseder W. Light weight design of Ti–6Al–4V forgings, Titanium 2009, Hawaii, USA. In: 25th Annual conference proceedings. International Titanium Association; 2009. [20] Gottstein G. Physikalische Grundlagen der Materialkunde. 2nd ed. Berlin: Springer; 2001. ISBN:3-540-41961-6. [21] De Freitas M, François D. Analysis of fatigue crack growth in rotary bend specimens and railway axles. Fatigue Fract Eng Mater Struct 1995;18(2):171–8. [22] Tokaji K, Ogawa T, Harada Y, Ando Z. Limitations of linear elastic fracture mechanics in respect of small fatigue cracks and microstructure. Fatigue Fract Eng Mater Struct 1986;9(1):1–14.
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Multiscale fatigue crack observations on Ti–6Al–4V Bernd Oberwinkler ⇑, Anton Lettner, Wilfried Eichlseder Montanuniversität Leoben, Chair of Mechanical Engineering, Franz-Josef-Straße 18, Leoben 8700, Austria
a r t i c l e
i n f o
Article history: Received 2 August 2010 Received in revised form 17 November 2010 Accepted 30 November 2010 Available online 4 December 2010 Keywords: Titanium base alloys Fatigue Crack initiation Crack growth Microstructure
a b s t r a c t The fatigue process of dynamic loaded materials can generally be classified in four stages, namely crack initiation, short crack growth, long crack growth and rupture. A continuous fracture mechanical description of the crack growth stages under consideration of the crack initiation phase was the aim of this research. The fatigue behavior of forged Ti–6Al–4V with three different microstructures were thereby characterized on the basis of multiscale fatigue crack observations on electrolytically polished hourglass specimens loaded in the finite life region. The gathered crack propagation data was compared with single-edge bending long crack growth curves. It was determined that the crack initiation phase accounts for less than 5% of the total lifetime. Depending on the (a + b)-content, the fatigue behavior is dominated either by primary a-grain size (equiaxed-type microstructures) or colony length of the (a + b)-lamellae (bimodal-type microstructures). Transcrystalline crack propagation was observed for all microstructures. The comparison of the multiscale fatigue crack growth rates with single-edge bending long crack growth curves revealed that the short crack growth behavior is the extension of the Paris-region of the long crack growth curve, and can be fitted with a power law for lifetime estimation. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The fatigue process of dynamic loaded materials can generally be classified in four stages: crack initiation, short crack growth, long crack growth and rupture. Depending on the material (inhomogeneities, etc.) and on the loading (low cycle or high cycle fatigue region), the fraction of these different stages varies with respect to the total lifetime. Usually, these stages are analyzed either separately (e.g., in crack growth experiments) or holistically in the classical stress- or strain-based approaches (S/N- or e/N-curves). Separate analyses lead to a better understanding of the involved mechanisms of the respective stages. Crack growth results can further be used for lifetime estimation of defectafflicted materials (inhomogeneities, e.g. pores, act as initial cracks) based on fracture mechanical methods. The holistic S/N- or e/N-approaches (the specimens are thereby tested until failure) enable a lifetime estimation of defect-free materials based on local stresses or strains. To gain a better understanding of the complete fatigue process, it is necessary to perform multiscale fatigue crack observation experiments from crack initiation to failure. Furthermore, the gathered data of such continuous experiments is the basis for a fracture mechanical based lifetime estimation of components manufactured from defect-free materials, such as the titanium base alloy Ti–6Al–4V. This is a promising approach to include the influence of variable amplitude loading ⇑ Corresponding author. Tel.: +43 38424021466. E-mail address: [email protected] (B. Oberwinkler). 0142-1123/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2010.11.024
and sequence effects in a lifetime estimation in further research. Currently used S/N- or e/N-approaches are not able to include such effects without enormous testing amount for calibration of non-linear damage accumulation methods. As mentioned before, the different fatigue stages are usually analyzed separately, and especially for Ti–6Al–4V a lot of literature data is available. Bridier et al. [1] performed strain-controlled fatigue tests on bimodal Ti–6Al–4V in the finite life region for determination of the crack initiation mechanisms. They noted that in primary a-grains, the prismatic slip is more easily activated than the basal one. All cracks were found to form across primary a-grains either on prismatic or basal planes. Most of the observed prismatic cracks remained restricted to the initial primary a-grain and were parallel to straight and regularly spaced slip bands. Conversely, basal cracks at the same number of cycles had already propagated through the surrounding microstructure. Their results revealed that prismatic crack formation involves a classical surface roughening mechanism. In the case of basal systems, it is quite different. The crack formation in the finite life region requires a combination of a high Schmid factor and a high elastic stiffness, inducing a high tensile stress normal to the basal plane. Ivanova et al. [2] tested equiaxed and bimodal Ti–6Al–4V in the finite life and high cycle fatigue regime. In the finite life region, they found crack initiation at the a/b interface and within the primary a-phase. In contrast, in the high cycle fatigue region the fatigue cracks initiated solely in a-grains. In the equiaxed microstructure, the cracks started thereby at the a/a grain boundary. Field emission microscopy of the crack initiation site revealed a
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fan-shaped pattern on the grain surface, which is characteristic for cleavage-type fracture, cf. [3]. The percentage of life spent for crack initiation was below 30% in the finite life region and over 80% in the high cycle fatigue region. Knobbe et al. [4] analyzed fatigue crack initiation and microstructurally short crack growth in mill-annealed Ti–6Al–4V in the high cycle fatigue region. They found that the fatigue cracks initiate preferentially at grain or phase boundaries. More initial fatigue cracks were determined in the lamellar (a + b)-phase. The initiated cracks grow intercrystalline; even in lamellae. Wagner and Gregory [5] studied the crack growth behavior of microstructurally short respectively long cracks in coarse lamellar and fine equiaxed microstructures. They ascertained that the coarse lamellar microstructure exhibits a worse short crack growth behavior but – owing to the additional crack growth resistance contributions of crack front geometry and crack closure – a slower long crack propagation compared to the fine equiaxed microstructure. Furthermore, they reported a decrease of long crack growth rate with increasing a-grain size owing to the same crack growth resistance contributions mentioned before. Similar findings are reported by Lütjering and Gysler [6] and Peters et al. [7]. Gray and Lütjering [8] also observed that coarsening the equiaxed grain size reduces the fatigue crack propagation rates of Ti– 6Al–4V at low stress ratios. They attributed the influence of grain size and the increase in fatigue crack propagation resistance with decreasing stress ratio to roughness-induced crack closure. Furthermore, they found that the coarse lamellar microstructure possesses (in comparison to equiaxed microstructures) the highest resistance to fatigue crack propagation owing to roughnessinduced crack closure. Nakajima et al. [9] investigated the early stage of crack growth in mill-annealed Ti–6Al–4V on notched flat specimens (stress ratio R = 0.1). They found that the analyzed fatigue crack initiated as a stage I crack in an a-grain at the notch root surface. The incipient crack grows under 45° to the maximum tensile stress axis. It was also revealed that the small fatigue crack changed its propagation direction at the grain boundary. They supposed that crack closure develops fast, owing to the relatively large a-grains with planar slip characteristics. These literature results enable a deep insight into the individual fatigue stages. However, to gain a better understanding of the holistic fatigue process in respect of microstructure and to generate the basis for fracture mechanical lifetime estimation of defect-free materials such as Ti–6Al–4V, continuous multiscale fatigue crack observation (MFCO) experiments are necessary. In this research, the crack initiation, short and long crack growth in Ti– 6Al–4V with three different microstructures were hence continuously characterized according to the method presented by Wagner and Lütjering [10]. Additionally, separate long crack growth experiments on single-edge bending (SEB) specimens served as a reference.
2. Material characterization The material used for this research work has been provided by Böhler Schmiedetechnik GmbH & Co KG (Austria) in the form of heat-treated Ti–6Al–4V V-shape and side-pressed pancake forgings, respectively. Due to the chosen forging temperature (between 900 °C and 930 °C) no crystallographic texture occurs in the microstructure [11]. This has been approved with X-ray diffraction (XRD) and electron backscatter diffraction (EBSD) measurements. Different types of microstructures were achieved by subsequent heat treatments (mill-annealing, solution treating, recrystallization-annealing). Additional information regarding the forging processes and heat treatments can be found in [12,13]. The analysis of the different microstructures was done with a light optical microscope. The metallographic sections were therefore grinded, polished and etched. The microstructure becomes thereby visible in a light optical microscope, whereby the a-phase appears bright and the b-phase appears dark. The mill-annealed V-shape (MAV) shows a typical mill-annealed microstructure (Fig. 1a). Mill-annealing does not cause complete recrystallization and therefore leads to a distinct texture of the primary a-grain shapes, representative of the forging process. The solution treating of the pancakes (STP) causes a bimodal microstructure (Fig. 1b). The recrystallization-annealing of the pancakes (RAP) results in a coarse equiaxed microstructure (Fig. 1c). The microstructures were characterized with respect to primary a-grain size ap, colony length Col of the (a + b)-lamellae and (a + b)-content Ca+b, cf. Table1. Depending on the (a + b)-content, the microstructures can be classified in equiaxed-type (Ca+b 6 20%) and bimodal-type (Ca+b P 25%), cf. [12,19]. This classification was confirmed in the present work and will be discussed below. The mill-annealed and recrystallization-annealed microstructures are hence equiaxedtype, the solution treated microstructure is bimodal-type.
3. Experimental procedure The characterization of the long crack growth behavior was done with V-notched single-edge bending (SEB) specimens under four-point-bending loading (cf. ASTM E647 [14]) at a Rumul Cracktronic resonant testing rig with a frequency of approximately 140 Hz. The crack length was measured with the potential drop method, cf. Fig. 2. Temperature compensation was done with a
Table 1 Microstructural characterization of the analyzed materials. Material
Abbr.
ap (lm)
Ca+b (%)
Col. (lm)
V-shape mill-annealed Pancake solution treated Pancake recryst.-annealed
MAV STP RAP
8.7 8.9 10.3
20.3 50.9 0
9.2 16.1 –
Fig. 1. Micrographs of the analyzed materials.
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and plasticity-induced crack closure can hence be neglected. The measured data points were fitted with a purpose four-parametric equation introduced in [13].
rpl ¼
Fig. 2. Scheme of the potential drop method.
Pt100 resistance temperature sensor fixed at the specimens near the crack. The measurements were performed at ambient air with room temperature at a stress ratio R (ratio of minimum and maximum stress or stress intensity factor, respectively) of 1. The stress intensity factor range DK was derived according to linear elastic fracture mechanics for all stress ratios, cf. Eq. (1), where Dr is the applied stress range, a the crack length and Y the appropriate geometry factor according to Murakami [15].
pffiffiffiffiffiffi DK ¼ Dr paY
ð1Þ
p The measurements were finished at 80 MPa m due to testing rig limitations regarding maximum stress intensity factor range. At least two specimens were tested for each microstructure. The test procedure was constant DK-testing for crack initiation up to a crack length of 6 mm, DK-decreasing testing from the Paris-region down to the threshold and subsequent DK-increasing testing with constant bending moment from the Paris-regime to fracture or testing rig limit. Carboni et al. [16] reported that this testing method could lead to non-conservative threshold values, mainly due to plasticity-induced crack closure. Therefore, the size of the plastic zone after the constant DK-testing was determined with both, FE analysis and estimation according to Irwin (e.g., [17]) for the plain strain state, Eq. (2), where KI is the applied stress intensity factor, ry the yield stress and t the Poisson ratio. The applied parameters for the Irwin estimation are in the case of Ti–6Al–4V t = 0.3 and ry 900 MPa (depending on microstructure, the 0.2%yield-strength varies from 880 MPa for RAP, over 900 MPa for STP to 925 MPa for MAV). It was observed that the size of the plastic zone is in the near-threshold region in the range of the grain size
K 2I 2pr2y
ð1 2mÞ2
ð2Þ
The multiscale fatigue crack observations (MFCO) were performed according to the method presented by Wagner and Lütjering [10]. Thereby, round hourglass fatigue test specimens (gauge diameter 6 mm, usually used for S/N-curve experiments) were electrolytically polished to get a smooth surface and to remove residual stresses from machining. For crack initiation, the polished specimens (d 5.85 mm) were loaded under rotating bending (R = 1, ambient air and room temperature) with a stress amplitude of 750 MPa for 4000 load cycles. After this predefined crack initiation phase, the specimens were etched for visualization of the microstructure and for accentuation of the initiated cracks. For evaluation of the crack length with a confocal laser-scanning microscope, crack opening was necessary. Therefore, a pretensioning device was designed for static loading of the round specimens during the microscopy, cf. Fig. 3. The initiated cracks were searched on eight positions (every 45°) on the specimens. Over 50 initiated cracks were found on each position on a specimen. Therefore, several cracks were selected randomly to get a sum of approximately 80 cracks per specimen for the observation of the crack growth. Then the fatigue tests were continued at the same stress level and interrupted after a given number of cycles (DN = 1000) for measurement of the crack propagation. This procedure was repeated until failure of the specimens. The mill-annealed microstructure resulted in a lifetime of 16,800 load cycles. A higher lifetime of 21,400 load cycles was determined for the solution treated microstructure. Recrystallization-annealing led, compared to the other microstructures, to an anomalous low fatigue life of 10,700 load cycles, which stands in contrast to rotating bending test results on machined hourglass specimens of the same batch, cf. [12,13] or [19]. 4. Discussion The single-edge bending tests revealed long crack growth down to propagation rates of 1012 m/cycle, cf. Fig. 12, which was also reported by Stanzl-Tschegg [18]. Above crack growth rates of approximately 107 m/cycle, the investigated microstructures show almost the same crack propagation behavior. The mill-annealed microstructure leads to an anomalous high crack growth rate in the region between 109 m/cycle and 107 m/cycle. The multiscale fatigue crack observation (MFCO) results performed on rotating bending specimens were analyzed with respect to crack initiation and crack propagation behavior. In the
Fig. 3. FE-model (l), pretensioning device (r).
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mill-annealed microstructure (Ca+b = 20%), about 60% of the cracks initiated in (a + b)-phase. The higher (a + b)-content of the solution treated microstructure (Ca+b = 51%) increases the percentage of initial cracks in (a + b)-phase to 80%. The crack initiation in the recrystallization-annealed material have to take place in a-phase, as no (a + b)-phase is present due to the heat treatment. A significantly larger amount of initiated cracks was determined in the recrystallization-annealed microstructure. It can hence be assumed, that the primary a-grains are strengthen with increasing (a + b)-content; maybe by alloying elements partitioning effects. These findings confirm the classification in equiaxed-type (Ca+b 6 20%, the primary a-grain size dominates the fatigue behavior) and bimodal-type (Ca+b P 25%, the colony length of the (a + b)-phase correlates with the fatigue strength) microstructures discussed in [12,19]. The comparison of the initial crack lengths after 4000 load cycles (stress amplitude 750 MPa) is shown in Fig. 4. It was assumed that the crack length distribution follows a Weibull-curve. The peak value of the initial crack length distribution correlates with the microstructural parameters primary a-grain size or colony length. The crack initiation phase in the equiaxed-type microstructures (Ca+b 6 20%) of the recrystallization-annealed pancakes and mill-annealed V-shapes is dominated by the primary a-grain size. The ratio of initial crack length (peak value of the Weibull-distribution) and the primary a-grain size is 1.7 for both equiaxed-type microstructures. In bimodal-type microstructures (Ca+b P 25%, e.g. the microstructure of STP), crack initiation occurs primarily in (a + b)-phase. The initial crack length can hence be linked with the colony length. The ratio of this microstructural size and initial crack length is again 1.7, analogical to the findings for the equiaxed-type microstructures. This value of 1.7 indicates that the observed ‘‘initial cracks’’ were already propagated into adjacent grains. This causes a shift of the Weibull-distributions to longer crack lengths. It is remarkable that the recrystallization-annealed microstructure exhibits a relatively large portion (12%) of noticeably longer cracks. This behavior will be discussed below. The crack length distributions were separated for a- and (a + b)-phase, Fig. 5. It was observed that the crack length distributions in both phases are very similar for the mill-annealed microstructure. In contrast, the distributions for the solution treated pancake are significantly different. Thereby, the distribution of the initial cracks in the a-phase exhibits a maximum at a crack length approximating the primary a-grain size. This means that they were not significantly propagated after 4000 load cycles. However, those cracks which initiated in (a + b)-phase were considerably longer owing to two facts: the colony length is larger
Fig. 4. Initial crack length distributions.
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Fig. 5. Initial crack length distributions separated for a- and (a + b)-phase.
than the primary a-grain size and the initial cracks were already propagated. The orientation of the initial cracks with regard to the load direction is presented in Fig. 6. It was determined that the separation in a- and (a + b)-phase does not affect these distributions. It has to be mentioned that the crack orientation can only be measured at the surface (2D information). Therefore, the unknown third (radial) dimension has to be included theoretically in the advisements regarding crack initiation, considering the texturefree material with a huge amount of grains in the highest loaded region. Schmid’s law (see, e.g. [20]) is given in Eq. (3); the according delineation is shown in Fig. 7. Thereby, u is the angle between the normal vector n of a cutting plane (slip plane) and the load direction, k the angle between slip direction d and load direction, F the applied force, and m the so-called Schmid factor. The vectors n and d have to be perpendicular. This leads to the following inequation for the Schmid factor: 0 6 |m| 6 0.5. The maximum possible shear stress smax is hence half the applied normal stress r.
s ¼ r cos k cos u ¼ r m
ð3Þ
The maximum shear stress plane (u = 45°) is drawn in Fig. 7. It can be observed, that surface cracks which lay on the maximum shear stress plane are able to exhibit orientations from 45° up to 90° with respect to the load direction. From a continuum mechanical point of
Fig. 6. Initial crack orientations with respect to loading direction.
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Fig. 8. Crack growth behavior in mill-annealed Ti–6Al–4V.
Fig. 7. Possible surface crack orientations for maximum shear stress.
view, it can be assumed that every orientation between 45° and 90° has the same probability to occur. If the crack initiation is solely shear stress controlled, the distribution of the crack orientation should approximate a value as plotted in Fig. 6. Thereby the percentage of cracks with orientations 645° was subtracted for each material; the residual percentages should then be uniformly distributed on the orientations 46–90°. It was observed that both equiaxed-type materials (V-shape MA and pancake RA) follow their ideal distributions for pure shear stress induced crack initiation (maximum deviation 10%). In contrast, the solution treated pancake shows a maximum at orientations between 76° and 90°. This reveals that some fatigue cracks (20%) also initiate under maximum normal stress, which is just possible at orientations close to 90°. The crack growth observations after the crack initiation phase started at a microstructurally short scale (crack lengths approximate the grain size) and ended at a long crack scale (crack lengths >1 mm) due to failure of the rotating bending specimens. Linear elastic fracture mechanics, cf. Eq. (1), were used for determination of the applied stress intensity factor range. The thereby used geometry factor Y = 0.75 was an average of the proposed values of De Freitas and François [21] and Murakami [15]. This approach was used for easy and continuous comparability of short and long crack growth, even in the region where linear elastic fracture mechanics usually loose its validity (crack length a < 150 lm, cf. [22]). The crack growth behavior of these cracks was compared with those of single-edge bending long cracks for each microstructure. Figs. 8 and 9 depict such a comparison for the mill-annealed and solution treated microstructure, respectively. It was observed, that the crack growth behavior of the microstructurally short cracks meets the extension of the Paris-region determined with single-edge bending specimens. Several cracks were observed, which did not grow during the last 1000 load cycles. It can be assumed, that those non-propagating cracks, which stopped at stress intensity factors higher than the long crack growth threshold, would continue to grow after certain load cycles. This behavior can be attributed to the analysis method;
Fig. 9. Crack growth behavior in solution treated Ti–6Al–4V.
the growth of larger cracks occurs increasingly beneath the surface, but the crack size can only be measured directly at the surface. Intermittent crack stopping was determined for several microstructurally short cracks at and beneath the threshold. This behavior is caused by microstructurally barriers, e.g. grain or phase boundaries. It was observed that the threshold of the short cracks p p lies in the region of 4–5 MPa m. Beneath 4 MPa m, just nonp propagating cracks were determined, above 5 MPa m, each analyzed crack grew at least for a while. Figs. 10 and 11 show confocal laser scanning micrographs of microstructurally short cracks (the loading direction in these pictures is vertical) in mill-annealed respectively solution treated Ti–6Al–4V after certain load cycles. The crack tips are thereby marked with arrows. The thicker regions of the cracks represent the initial cracks after 4000 load cycles, enlarged by the performed etching. It can be assumed that the influence of the etching (crack tip blunting, reduced crack closure, etc.) on the crack growth behavior can be neglected after the first crack extension. Transcrystalline crack growth was observed. A relatively large scatter of crack growth rates in the short crack region was determined independent from material, owing to the significant influence of local microstructure on the crack propagation of microstructurally short cracks. It is hence important to analyze an adequate amount of microstructurally short cracks to get a meaningful average crack growth behavior. The experimental
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Fig. 10. Crack growth observations for mill-annealed Ti–6Al–4V.
Fig. 11. Crack growth observations for solution treated Ti–6Al–4V.
crack growth data gathered in MFCO tests was fitted with a power law consistent with the Paris-law for long cracks, Eq. (4), and compared with the single-edge bending long crack growth behavior, Fig. 12 and Table 2.
da ¼ C DK m dN
ð4Þ
Table 2 Fitting parameters for the multiscale fatigue crack observation experiments. Parameter
V-shape MA
Pancake ST
Pancake RA
p C (m/(Cyc. MPa m)) m (–)
5.34E11 2.06
1.57E11 2.34
1.36E11 2.36
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The higher average crack growth rates of the mill-annealed microstructure, which were observed in single-edge bending tests, were confirmed with the MFCO experiments. Striation dimension measurements were performed on scanning electron microscopy pictures of the SEB fracture surfaces. The crack growth rate within an a-grain was thereby determined to be more than a decade higher than the global crack growth rate at this position (lower Parisregion). This means that the crack formation within an a-grain consumes approximately 98% of the time for crack propagation on the scale of the average grain size. However, it can be assumed that the elongated a-grains of the mill-annealed microstructures lead for the same time of crack formation to an approximately two times higher crack propagation distance and hence crack growth rate. It is believed that this is the reason for the anomalous high crack growth rates of the mill-annealed microstructure. The cycles to failure Nf consist of the cycles spent for crack initiation Ni and the cycles of crack growth Ng, Eq. (5). The combination and integration (from initial crack length a0 to failure-causing crack length af) of Paris law, Eq. (4), and basic equation of the linear elastic fracture mechanics, Eq. (1), provides an estimation of the cycles consumed for crack growth Ng, Eq. (6). The average fitting parameters determined in MFCO experiments (Table 2) were used for calculation of the consumed crack growth cycles. As initial crack length a0, the mean primary a-grain size (for MAV) or mean colony length (for STP) plus according standard deviation was chosen, as the larger grains of the grain size distribution will be the limiting factor with respect to the fatigue life. However, it was observed that the failure-causing cracks were not initiated in extraordinarily large grains. Therefore the standard deviation was added once (this means that 84% of the grains are smaller than this value) and not twice (this would mean that already 98% of the grains are smaller than this value) to the mean grain size to achieve the initial crack length. Nevertheless, this is an assumption, and should be proofed in additional MFCO experiments. The crack initiation cycles were further determined by subtracting the crack growth cycles from the cycles to failure. The measured cycles to failure Nf, the calculated crack growth cycles Ng, and the crack initiation cycles Ni for the solution treated respectively mill-annealed microstructures are summarized in Table 3.
Nf ¼ Ni þ Ng
Ng ¼
Z
ð5Þ
af
a0
lower than those of the V-shape mill-annealed microstructure. However, crack initiation is considerably easier in the recrystallization-annealed material. Not only the length of the initial cracks was thereby anomalously large, also the quantity of initial cracks was significantly higher, what may be attributed to the unknown effect (possibly notch effect) of the interstice phase between the primary a-grains of the recrystallization-annealed material (cf. Fig. 1) or to alloying elements partitioning effects in microstructures with (a + b)-phase. Furthermore, a statistical influence may be the reason for this crack initiation behavior after 4000 load cycles (cf. Fig. 4). The crack initiation is easier directly at the surface (as in the case of the electrolytically polished specimens) than underneath the surface (as in the case of the machined specimens with compressive residual stresses in the surface layer). In combination with the fact that fatigue cracks initiate easier in the primary a-grains of the recrystallization-annealed microstructure (interstice notch effect, alloying elements partitioning effects, etc.), it is more likely that adjacent initiated cracks with similar orientations can coalesce during the initiation stage and form ‘‘super cracks’’ with crack lengths up to five times larger than the average ‘‘initial’’ cracks. Additionally, the absence of the (a + b)-phase and hence phase boundaries can promote this behavior. The same mechanism can
1 C Y Drm ðpaÞ0:5m m
da
ð6Þ
A crack initiation phase of approximately 3% of the total lifetime was determined for both mill-annealed and solution treated microstructure. This ties in well with the findings of other authors (e.g., [1,2]) regarding cleavage-type crack initiation in Ti–6Al–4V, and with the loading in the finite life region. It is hence possible to predict the fatigue lifetime solely based on the microstructurally characteristic dimension (a-grain size or colony length) and MFCO crack growth curves. The electrolytically polished specimen with the recrystallization-annealed microstructure exhibited an anomalous low finite life fatigue strength (Nf = 10,700 for ra = 750 MPa) compared to the fatigue tests of machined specimens tested in prior research, cf. [12,13] or [19]. The multiscale crack growth data showed no irregularity, cf. Fig. 12. An initial crack length on the scale of the grain size leads to a calculated lifetime slightly higher than those of the solution treated microstructure, what corresponds to the fatigue tests on machined specimens. The microhardness of the primary a-grains of the mill-annealed and recrystallization-annealed microstructures was measured and compared. The microhardness of the primary a-grains of pancake recrystallization-annealed was determined to be insignificantly
Fig. 12. Comparison of single-edge bending and multiscale fatigue crack observation experiments.
Fig. 13. Coalescing cracks and grains with multiple crack initiations in recrystallization-annealed Ti–6Al–4V.
B. Oberwinkler et al. / International Journal of Fatigue 33 (2011) 710–718 Table 3 Separation of the cycles to failure in crack initiation and crack growth cycles.
a
Material
Initial crack length, a0 (lm)
Nf (–)
Ng (–)
Ni (–)
V-shape MA Pancake ST Pancake RA
16.0 22.4 15.5
16,800 21,400 10,700
16,170 20,900 10,380a
630 (4%) 500 (2%) 320a (3%)
Assumption: Ni = 0.03 Nf, Ng = Nf Ni.
Fig. 14. Crack growth behavior in recrystallization-annealed Ti–6Al–4V.
be responsible for faster crack growth than the measured average crack growth rate. Fig. 13 (vertical loading direction) shows two adjacent cracks (ca. 50 lm spacing) after 5000 load cycles, which coalesced during additional 5000 load cycles, resulting in an abrupt and enormous increase of crack length. Furthermore, multiple crack initiation within one grain on parallel slip bands can be observed in this picture; a side effect of the easy crack initiation. Assuming that the crack initiation phase accounts for 3% of the total lifetime, Table 3, an increase of the fitting parameter C by a factor of 2.5 is necessary (cf. Fig. 14, adapted crack growth fit compared to average crack growth fit) to meet the measured cycles to failure with the crack growth calculations. This does not reflect the physical mechanism, but is an easy, first attempt to describe the crack growth rate. However, in machined specimens, where compressive residual stresses are present at the surface, crack initiation takes place underneath the surface, what significantly impedes the crack initiation. This could considerably reduce the probability of coalescing cracks to a level where they do not play a role. Additional MFCO experiments should be performed on the recrystallization-annealed material, to clarify the crack initiation stage and crack coalescence more in detail, by decreasing the initial load cycles prior to the first microscopy and using smaller increments for the measurement of the crack extension. 5. Conclusion Multiscale fatigue crack observations and long crack growth tests were performed on Ti–6Al–4V with three different microstructures. The analyses of the gathered data regarding crack initiation and crack growth revealed several interesting findings. The transition from equiaxed- (primary a-grain size controlled) to bimodal-type (colony length controlled) fatigue behavior occurs at a relatively low (a + b)-content of 20%.
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Based on linear elastic fracture mechanics, the average short crack growth rate is in accordance with the extension of the Paris-region of long crack growth data. The short crack growth threshold was determined to lay in the p p region of 4–5 MPa m. Beneath 4 MPa m, just non-propagating p cracks were determined, above 5 MPa m each analyzed crack grew at least for a while. Based on the determined crack growth data and on the characteristically microstructural dimension, the cycles consumed for crack initiation were approximated. With respect to the total lifetime of the used fatigue test specimens, the crack initiation phase accounts only for approximately 3%. This ties in well with the findings of other authors (e.g., [1,2]) regarding cleavagetype crack initiation in Ti–6Al–4V, and with the chosen loading in the finite life region. The mill-annealed microstructure leads to the fastest crack propagation of the analyzed microstructures. It can be assumed, that this behavior is caused by the grain shape texture (elongated primary a-grains) due to incomplete recrystallization during mill-annealing. An anomalously low fatigue strength was determined for the recrystallization-annealed Ti–6Al–4V. However, the observed crack growth rates are similar to those of the solution treated microstructure. It was assumed, that the easier crack initiation in the recrystallization-annealed material (eventually caused by alloying elements partitioning effects) leads to a high probability of crack coalescence. If the crack initiation is impeded by subsurface crack initiation due to (e.g., machining-induced) compressive residual stresses in the surface layer, this behavior can be repressed, resulting in significantly higher finite life fatigue strength. The applied multiscale fatigue crack observation (MFCO) technique is suitable for the characterization of the crack initiation and crack growth phase. It is possible to predict the fatigue lifetime solely based on the microstructurally characteristic dimension (a-grain size or colony length) and MFCO crack growth curves. With respect to the recrystallization-annealed material, additional MFCO experiments should be performed for clarification of crack initiation and crack coalescence by decreasing the initial load cycles prior to the first microscopy and using smaller increments for the measurement of the crack extension. Further research should also address the fatigue behavior in the high cycle fatigue region. Therefore, a mini rotating bending test rig is currently developed at our institute based on the experiences of the presented research work, which operates directly at the confocal laser-scanning microscope (no mounting and dismounting of the specimen for loading/observation necessary) and which is compatible to our scanning electron microscope. Acknowledgements The authors would like to thank the Austrian Federal Ministry for Transport, Innovation and Technology, the Austrian Federal Ministry of Economics and Labor, and the Austrian Research Promotion Agency for funding of this research work in the framework of the FFG’s BRIDGE program. The support by Böhler Schmiedetechnik GmbH & Co KG is much valued. References [1] Bridier F, Villechaise P, Mendez J. Slip and fatigue crack formation processes in an a/b titanium alloy in relation to crystallographic texture on different scales. Acta Mater 2008;56:3951–62. [2] Ivanova SG, Biederman RR, Sisson Jr RD. Investigations of fatigue crack initiation in Ti–6Al–4V during tensile–tensile fatigue. J Mater Eng Perform 2002;11:226–31.
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