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Local deformation patterns in Ti–6Al–4V under tensile, fatigue and dwell fatigue loading
International Journal of Fatigue 43 (2012) 111–119
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Local deformation patterns in Ti–6Al–4V under tensile, fatigue and dwell fatigue loading P.D. Littlewood ⇑, A.J. Wilkinson Department of Materials, University of Oxford, Park Road, Oxford, UK
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Article history: Received 31 October 2011 Received in revised form 2 March 2012 Accepted 4 March 2012 Available online 12 March 2012 Keywords: Strain Digital image correlation Fatigue Titanium alloys EBSD
a b s t r a c t We have used EBSD orientation mapping and digital image correlation-based strain mapping to investigate inhomogeneous deformation of Ti–6Al–4V in tension, fatigue and cold-dwell fatigue. Strong strain inhomogeneities were found in all loading modes and in each case the pattern of high and low strain is established relatively early in the tests. Comparing the orientation and strain maps shows that grain–grain interactions are the primary cause of strain concentration. Surface grains with the crystallographic c-axis parallel to the loading direction showed very low strain levels, and neighbouring grains showed exceptionally high strain levels. In both fatigue and dwell fatigue, these regions of high strain concentration were observed to act as sites for crack nucleation. Strain evolution was found to be significantly different in each loading mode; in particular, deformation in dwell fatigue appears to have similarities with creep deformation. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Because of their good strength-to-weight ratio, corrosion resistance and good fatigue performance, titanium alloys are extensively used for aerospace applications, so there is a large interest in optimising their performance in both static and cyclic loading applications. The most widely used Ti alloy is Ti–6Al–4V, an a–b alloy. Within the hcp a phase, plastic deformation primarily occurs through slip of dislocations with either hai or hc + ai Burgers vectors [1]. The hai Burgers vector is considerably shorter and so is energetically favoured and easier to move through the lattice. For the hai dislocations, slip is generally easiest on prism planes, but basal slip is also possible and often only requires slightly more stress [1–6]. The hc + ai dislocations slip on the pyramidal planes and have a considerably higher critical resolved shear stress [1,6]. Grains close to having the c-axis aligned to the direction of uniaxial tensile deformation are elastically stiffer [7,8]. They also have very low resolved shear stress on both the basal and prismatic hai slip systems, making them plastically hard. It can be expected that the presence of ‘‘hard’’ and ‘‘soft’’ grains will have a strong influence on the deformation behaviour of this material at the microstructural scale. Work by Bridier et al. [9] shows a relationship of both crystal orientation and local texture to the formation of fatigue cracks; in order to understand the underlying mechanisms, it is necessary to study the deformation
at the microstructural level. Transmission electron microscopy, and X-ray diffraction line profile analysis have been used to understand the local and global response of materials to deformation in terms of the accumulation of dislocations and other lattice defects during deformation including in Ti alloys [1,10–12]. More recently electron backscatter diffraction has provided a route for assessing the role of grain to grain interactions in this dislocation storage problem, including during tensile deformation of the Ti–6Al–4V studied here [13–16]. The strains themselves can be assessed at the grain and intragranular level by combining the EBSD technique with strain mapping by digital image correlation (DIC). Davidson’s pioneering work with the DISMAP system in the late 1980s and 1990s marks probably the earliest attempt to use digital image correlation methods to measure material deformation fields [17]. In recent years interest in the full field measurement of material deformation through DIC techniques has grown considerably and the method is becoming more widespread [18–29]. In this paper, we describe the application of this technique to the investigation of microstructure-scale deformation in Ti–6Al– 4V, and its combination with crystallographic information from EBSD to study the interaction between microstructural features and deformation behaviour. 2. Materials and experimental methods 2.1. Material, microstructure and texture
⇑ Corresponding author. Present address: Technical University of Denmark, Kgs. Lyngby, Denmark. Tel.: +45 42996855. E-mail address: [email protected] (P.D. Littlewood). 0142-1123/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2012.03.001
The experiments were conducted on rolled bar stock of Ti–6Al– 4V supplied by Rolls-Royce. This had first been pre-strained in the
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Fig. 1. Microstructure of rolled bar stock material, with primary a and grain boundary b highlighted.
ab temperature range, recrystallised in the b range, ab forged and then rolled from a 125 mm square cross section to a 75 mm diameter bar. Finally, it was annealed for 2 h at 700 °C to relieve residual stresses, and air cooled. This resulted in a microstructure composed primarily of globular a grains with small amounts of b primarily at the grain boundaries; the overall a fraction is over 95% with an average a grain size of 11 lm. Fig. 1 shows an optical image of the microstructure, which was etched using a solution of 3% HF and 30% HNO3 in water. This etch tends to predominantly attack the b phase and thus tends to increase the apparent b fraction to some extent. Samples were prepared for EBSD in two stages. Firstly, silicon carbide papers were used to give a flat surface and secondly, the samples were polished in a vibro-polisher using a solution of colloidal silica with 6% ammonia and 6% hydrogen peroxide on a neoprene ‘chem’ cloth. Polishing times between 12 and 18 h were generally found to be sufficient; it was also found that polishing by hand in the same solution for 10–15 min after the vibro-polishing increased the quality of EBSD patterns obtained.
2.2. Local deformation tracking by digital image correlation Tensile test specimens were machined by spark eroding to the dimensions shown in Fig. 2, with a rectangular cross section. To prepare specimens for deformation measurements, a region was marked with a coarse grid of 100 lm pitch, using a focused-ion beam (FIB). Fig. 3a shows an optical image of the coarse grid. EBSD scans were made of selected grid squares, and then the FIB was used to mark the scanned region with a pattern of random dots, as shown in Fig. 3b. Random ‘speckle’ pattern is a standard and widely accepted method for DIC measurements and avoids issues with the automated correlation failing to identify the correct grid within a regular repeating array pattern [29]. Three samples were prepared, and subjected to three different loading regimes. All mechanical testing was done on a Denison Mayes servohydraulic horizontal load frame using Instron wedge grips. The first sample underwent uniaxial tension at a loading rate of 5 105 mm s1 under crosshead control; an accurate extensometer was not available so strain rate control could not be used. The second was subjected to fatigue loading under load control with a peak stress of 900 MPa, a triangular waveform with frequency 0.5 Hz and a load ratio R = 0.1. As the tensile testing indicated a yield stress of approximately 850 MPa, this lies well within the low-cycle fatigue range. The final sample was loaded in dwell fatigue, with the same load profile as the fatigue loading but with the addition of a 2-min hold at peak load. Each test was interrupted at intervals and removed from load, and optical images were taken of the regions marked with the pattern of dots, then re-loaded and the test continued. In the case of the tensile test, re-loading was done at the same rate of crosshead movement as in the original loading. All samples in this study were unloaded for less than 1 h at a time for microscopic observation.
Once a series of images were obtained through a test, digital image correlation was used to measure the deformation of the marked region. This was done using StrainMaster DIC software, which divides a reference image (taken prior to the beginning of the test) into regions and uses a cross-correlation algorithm to identify the position of these regions in each subsequent image. From the shifts of these regions relative to the reference image, the strains in the region can be derived. An estimate of the error in this procedure was made by taking several different images of the same dot pattern as the sample was translated beneath the microscope. The cross-correlation analysis was then run with measurement noise being seen as fluctuations away from the known zero applied strain. Repeated trials give an average error of ±0.16% strain measured using 128 by 128 pixel cells. These 128 pixel cells are 3.4 lm across and the ±0.16% strain error corresponds to a spatial registration error of 5.6 nm. 3. Results 3.1. Tensile testing The tensile test was imaged at three strain levels: 2.2%, 8.0% and 13.1% (the failure strain). Due to the absence of a reliable extensometer, these values were obtained by averaging over the strain field measured by DIC. Fig. 4a shows an inverse pole figure map of the tracked region, and Fig. 4b–d shows maps of the strain component in the loading direction at all three macroscopic strain levels. The observed deformation shows strong inhomogeneity, with some points showing very high strain levels while others remain nearly undeformed. The deformation occurs in a pattern that appears to be established at the beginning of the test (before 2% strain) and continued until failure. In order to investigate the difference in strain evolution between points of high strain accumulation and low strain accumulation, several points were selected and the strain at these points was compared over the course of the test. Fig. 5a shows the strain map of the tracked region at failure with the selected points labelled, and Fig. 5b shows a plot of the strain at each of these points. This shows a roughly linear increase in strain level at the points of high strain accumulation, while some points accumulate essentially no strain at all. Throughout the test the strain concentration at the points of high strain remain 3–3.5 times higher than the average value. 3.2. Fatigue deformation The fatigue test was interrupted every 400 cycles for imaging, up to the point of failure at 6800 cycles. Fig. 6a shows an inverse pole figure map of this region, and Fig. 6b–e shows strain maps at some selected points in the course of the test. The overall strain levels measured are significantly lower than in the tensile case, with an average strain of 1% measured across the field at the end of the test. As with the tensile sample, the pattern of deformation appears to be established early (i.e. within the first block of cycling) across most of the tracked region, and intensifies as the test progresses. There is one feature of particular note in the lower-left part of the tracked region, which has accumulated a much higher level of strain than its surroundings, with this difference becoming extremely marked in the latter stages of the test. In order to investigate this further, the sample surface was re-polished to partly remove the dot pattern and allow other features to become visible. An optical image of the region after re-polishing is shown in Fig. 7. This reveals that a short fatigue crack has formed inside the tracked region, in the same position as the strain concentration. Some of the measured strain concentration, therefore,
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Fig. 2. (a) Coarse grid and (b) random dot pattern etched into sample surface by FIB.
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Fig. 3. Dimensions of test specimens with overall dimensions 50 mm 15 mm. All dimensions in mm.
must be due to the opening of the crack faces rather than to continued deformation of the material. Fig. 8a shows the strain map of the tracked region for this sample with some points of interest labelled, both within the crack region and in areas of high and low strain concentration away from the crack. Fig. 8b plots the evolution of strain at each of these points over the lifetime of the test. Due to the lower overall strain level, this plot is more sensitive to noise in the measurements. However, it appears to show a substantially different pattern of deformation. Here, a significant difference in strain levels between the high and low points appears to be established at the beginning of the test (i.e. in the first block of cycling). After this pattern has been established, the difference in strain rates between the regions of high and low strain drops significantly. This is in contrast to the monotonic tension test where the strain accumulation is essentially linear throughout the test. The one exception is the point within the cracked region, which accumulates strain at a significantly higher rate than the other tracked points once the test has exceeded approximately 4000 cycles. As the strains measured here are biased by the opening of the crack, it may be estimated that crack nucleation begins at around 4000 cycles. Before the crack had been initiated the high strain regions show strain concentrations of 2 compared to the mean, which is somewhat lower than for the monotonic deformation.
3.3. Dwell fatigue deformation Fig. 9a shows the inverse pole figure map for the sample tested in dwell fatigue, and Fig. 9b–d shows some selected strain maps across the lifetime of the sample (3200 cycles). As with the previous samples, the patterns of deformation are established early in the test and remain essentially unaltered at the end. The mean strain at failure was 5.4% within the tracked region, which is significantly higher than in normal fatigue, but lower than the tensile failure strain. A light re-polishing of the sample to remove the FIBed dot pattern revealed a small crack forming in the region of highest strain concentration, on the left-hand side of the tracked region. An SEM image of this region is shown in Fig. 10. As the crack seen here is smaller and the overall strains larger, the effect of the crack opening on the measured strains will be smaller, although not negligible. As with the previous samples, several points were selected and the strain evolution at these points was tracked. Fig. 11a shows the strain map from this region with the tracked points labelled, and Fig. 11b shows a plot of the strain evolution at these points. This loading mode shows a different pattern of deformation to both the tensile and normal fatigue modes. The form of strain evolution here appear similar to creep curves at each point, with an initial period of faster deformation, slowing into a longer period with
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Fig. 4. (a) Inverse pole figure map in sample normal direction and map of strain in loading direction at (b) 2.2% overall strain, (c) 8.0% overall strain and (d) 13.1% overall strain (failure) for tracked region of tensile sample.
Fig. 5. (a) Strain map for tensile sample with tracked points marked, and (b) chart showing strain accumulation at each point over the course of the test. Mean strain is also shown, with RMS deviation indicated by error bars.
near constant deformation rate before accelerating into a final faster deformation rate as failure is approached. This suggests that
room-temperature creep may be a significant deformation mode for this type of loading. Throughout the period with near constant
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Fig. 6. (a) Inverse pole figure map in sample normal direction and map of strain in loading direction at (b) 400 cycles, (c) 3200 cycles, (d) 4400 cycles and (e) 6800 cycles (failure) for tracked region of fatigue sample.
deformation rate the strain concentration at the ‘hot spots’ is 3.5, while a lower strain concentration factor of 1.8 is present in the
initial faster rate deformation, and a slight increase to 3.9 is noted in the final period of accelerated deformation.
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Fig. 7. Optical image of crack found in tracked region of fatigue sample.
4. Discussion 4.1. Relation of deformation patterns to microstructure In order to understand the effect of crystallographic anisotropy on the deformation behaviour of this material, it is necessary to have some measure of a grain’s resistance to deformation. For this study, the measure used is the maximum Schmid factor on all basal and prismatic hai slip systems. A low Schmid factor on all of these systems means that a grain is oriented with its c-axis nearly parallel to the loading direction, and thus there is low resolved shear on all a-type slip systems. This leaves only the hc + ai slip systems available, which have a much higher critical resolved shear stress [1,4–6], making it difficult to activate slip in these grains. Fig. 12 shows an overlay of the strain map from the tensile sample at 8% strain (colour) with a map of the Schmid factor for this region (greyscale, white = high Schmid factor). It can be seen that there are several areas where a grain with low Schmid factor corresponds to an area of low strain. Additionally, several regions of high strain correspond to grains with high Schmid factor which are loaded in series with grains having low Schmid factor. This suggests that grain-to-grain interactions are of high importance in the development of strain inhomogeneity. As the sample is strained, grains with low Schmid factor are unable to deform to accommodate the
macroscopic strain. In order to maintain compatibility, grains adjacent to these grains must undergo a high level of strain, leading to the observed strain concentrations. A similar pattern is seen in the other samples. Fig. 13 shows an overlay of the Schmid factor map and the strain map at failure for the fatigue sample. In particular, the crack which was observed occurs within a grain which is well-oriented for slip, with several poorly-oriented grains surrounding it. There is also a poorly-oriented grain directly below the cracked grain. The conflicting compatibility requirements have resulted in a very localised and intense shear band inside the soft grain, allowing the lower regions of the grain to remain relatively undeformed while the rest of the grain deforms to accommodate the poorly-oriented grains to its right. Further deformation has caused a crack to open along this band. This highlights the importance of grain interactions and strain inhomogeneities on the crack nucleation process. Fig. 14 shows the overlaid Schmid factor and strain maps for the dwell fatigue sample. As with the tension and fatigue samples, the main region of strain concentration and subsequent crack nucleation occurs in a group of grains well-oriented for slip, directly adjacent to a group of grains that are relatively poorly oriented for slip. The presence of strain concentration near poorly-oriented grains, and the presence of many well-oriented grains without strain concentration, suggests that this mechanism of ‘‘strain shedding’’ is the dominant factor in development of inhomogeneous strain, and is applicable to each of the three loading modes studied. 4.2. Strain evolution at ‘hot spots’ The plots of strain accumulation at selected points shown in Figs. 4, 7 and 10 show quite different evolution across the three samples. 4.2.1. Tensile test In the tensile test the points of high strain concentration increase in strain at a rate proportional to the average strain rate, while the points of lowest concentration accumulate essentially no strain. This is a straightforward illustration of the deformation shedding mechanism, as the grains that are poorly oriented are unable to activate any slip systems and neighbouring grains must deform at a higher rate so as to accommodate the imposed average strain. The strain concentration at the ‘hot spots’ is close to con-
Fig. 8. (a) Strain map for fatigue sample with tracked points marked, and (b) chart showing strain accumulation at each point over the course of the test. Mean strain is also shown, with RMS deviation indicated by error bars.
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Fig. 9. (a) Inverse pole figure map in sample normal direction and map of strain in loading direction at (b) 40 cycles, (c) 1600 cycles, and (d) 3200 cycles (failure) for tracked region of dwell fatigue sample.
gave strain concentrations of 2 at the strain maxima during plane strain compression testing to 8%. Efstathiou et al. [21] have worked on pure Ti looking at residual plastic strains after relatively small plastic deformations compared to those studied here. In the text they suggest strain concentrations of 2 occur near grain boundaries, but examination of some of their maps and strain histograms indicates that somewhat higher concentrations are present in the extreme locations, and that these are in line with values found here for larger strains in Ti–6Al–4V. An important point made by Efstathiou et al. is that the magnitude of the strain heterogeneities and therefore the extreme strains depends on the lengthscale used to assess the strain field as controlled by microscope resolution, marker distribution and image digitization (i.e. number of pixels).
Fig. 10. SEM image of crack found in tracked region of dwell fatigue sample.
stant throughout the test and reaches a values of 3.0 to 3.5 times the average value. In fcc Cu samples Kamaya et al. [27] found strain concentrations at a similar level 3 in Cu deformed to 3% strain in tension, while Tatschl and Kolednik [25] indicate a somewhat smaller strain concentration factor of 2 which was maintained throughout a tensile testing out to almost 10% strain. Earlier work by Raabe et al. [23] on a pseudo-2D aluminium microstructure also
4.2.2. Fatigue test The overall strain levels achieved are considerably lower in the fatigue test, and so are the levels of strain concentration. It is not clear whether the lower strain concentration at the hottest spots is an artefact of the relatively small number of grains that have been sampled or a real difference between monotonic and cyclic deformation. There is relatively little data in the literature with which to compare. El Bartali et al. [28] have used DIC to examine cyclic deformation at the microstructural level, but the duplex stainless steel and fully reversed strain controlled testing conditions limit quantitative comparison that can be made with the cur-
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Fig. 11. (a) Strain map for dwell fatigue sample with tracked points marked, and (b) chart showing strain accumulation at each point over the course of the test. Mean strain is also shown, with RMS deviation indicated by error bars.
Fig. 13. Overlay of Schmid factor and strain maps for tracked region of fatigue sample.
Fig. 12. Overlay of Schmid factor and strain maps for tracked region of tensile sample.
rent study. They found local strains at the 2% and +1.3% strain level occur within the ferritic (hard) and austenitic (soft) microstructure some three times higher than the imposed strain amplitude of 0.5%. The spatial location and point in the fatigue test when a near surface crack was formed was readily detected (see Fig. 7). Niendorf et al. [22] have also seen that deformation patterns are established early during fatigue and found that crack nucleation could be well predicted by the location of strain concentration. They observed much lower peak strains than were seen in this study; this is likely to be due to the lower ductility of TiAl alloys they were studying. This has some parallels with the use of DIC in studying the initiation and early growth of stress corrosion cracks in austenitic stainless steels by Rahimi et al. [24]. Once the crack has formed a large contribution to the apparent local strain is actually made by the opening of the crack.
4.2.3. Dwell fatigue test The dwell fatigue sample shows a pattern significantly different to the other two tests, with strain evolution resembling creep curves. Titanium alloys have been previously observed to be sensitive to creep at room temperature, and this experiment suggests that creep is a significant mode of deformation in dwell fatigue. This provides further evidence for the theory of dwell fatigue developed by Evans and Bache [30–32], who proposed the dominance of creep deformation in dwell fatigue. Bache et al. [33] used a similar technique, electron speckle pattern interferometry, to track deformation in a large grained form of the near a titanium alloy Ti 685 (Ti–6Al–5Zr–0.5Mo–0.25Si) in dwell fatigue. They observed strong strain localisation with patterns being established within the first few cycles of a test that ran for only 100 cycles to failure. Crack nucleation occurred within the regions showing the highest strains. Unfortunately the strain maps available do not allow quantification of the strain concentration. The work of Savage et al. [34] shows the profound effect of periods of unloading on the subsequent creep rate during creep tests with single prolonged interrupts. Ti–6Al samples with short range
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Fig. 14. Overlay of Schmid factor and strain maps for tracked region of dwell fatigue sample.
order, which may well be present in our air cooled Ti–6Al–4V samples, showed the strongest effects with the creep rates directly after an unload-reload event being 100 times faster than just before the unload. The transients seen after re-loading by Savage et al. lasted for several hours and so this accelerated creep is likely to persist through the entire 2 min hold of our dwell fatigue tests and thus contribute to the elevated deformation rate which is 107 s1 averaged over the entire test. 5. Conclusions Strain mapping at the microstructural scale using image correlation methods has been performed on Ti–6Al–4V under three different loading modes. Deformation is highly inhomogeneous, and follows patterns which are established at the beginning of loading. There is a strong link between grains with the c-axis nearly parallel to the loading and inhomogeneous deformation. Very low strain is seen in these grains, and regions of high strain are found in surrounding grains. Crack nucleation was observed in regions of high strain concentration in both fatigue and dwell fatigue loading. All three loading modes showed different patterns of strain evolution over time. In dwell fatigue, room-temperature creep was found to make a significant contribution to deformation. Acknowledgements This work was in part funded by EPSRC through Grant EP/ E044778/1, and PDL is grateful for receipt of a Clarendon Scholarship. We thank Rolls-Royce for materials and some financial support for PDL. References [1] Jones IP, Hutchinson WB. Stress–state dependence of slip in titanium–6A1–4V and other hcp metals. Acta Metall 1981;29(6):951–68. [2] Akhtar A. Basal slip and twinning in alpha-titanium single-crystals. Metall Trans 1975;6(5):1105–13. [3] Akhtar A, Teghtsoonian E. Prismatic slip in alpha-titanium single-crystals. Metall Trans A Phys Metall Mater Sci 1975;6(12):2201–8. [4] Churchman AT. The slip modes of titanium and the effect of purity on their occurrence during tensile deformation of single crystals. Proc Royal Soc Lond Ser A Math Phys Sci 1954;226(1165):216–26. [5] Conrad H. Effect of interstitial solutes on the strength and ductility of titanium. Prog Mater Sci 1981;26(2–4):123–404.
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Local deformation patterns in Ti–6Al–4V under tensile, fatigue and dwell fatigue loading P.D. Littlewood ⇑, A.J. Wilkinson Department of Materials, University of Oxford, Park Road, Oxford, UK
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Article history: Received 31 October 2011 Received in revised form 2 March 2012 Accepted 4 March 2012 Available online 12 March 2012 Keywords: Strain Digital image correlation Fatigue Titanium alloys EBSD
a b s t r a c t We have used EBSD orientation mapping and digital image correlation-based strain mapping to investigate inhomogeneous deformation of Ti–6Al–4V in tension, fatigue and cold-dwell fatigue. Strong strain inhomogeneities were found in all loading modes and in each case the pattern of high and low strain is established relatively early in the tests. Comparing the orientation and strain maps shows that grain–grain interactions are the primary cause of strain concentration. Surface grains with the crystallographic c-axis parallel to the loading direction showed very low strain levels, and neighbouring grains showed exceptionally high strain levels. In both fatigue and dwell fatigue, these regions of high strain concentration were observed to act as sites for crack nucleation. Strain evolution was found to be significantly different in each loading mode; in particular, deformation in dwell fatigue appears to have similarities with creep deformation. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Because of their good strength-to-weight ratio, corrosion resistance and good fatigue performance, titanium alloys are extensively used for aerospace applications, so there is a large interest in optimising their performance in both static and cyclic loading applications. The most widely used Ti alloy is Ti–6Al–4V, an a–b alloy. Within the hcp a phase, plastic deformation primarily occurs through slip of dislocations with either hai or hc + ai Burgers vectors [1]. The hai Burgers vector is considerably shorter and so is energetically favoured and easier to move through the lattice. For the hai dislocations, slip is generally easiest on prism planes, but basal slip is also possible and often only requires slightly more stress [1–6]. The hc + ai dislocations slip on the pyramidal planes and have a considerably higher critical resolved shear stress [1,6]. Grains close to having the c-axis aligned to the direction of uniaxial tensile deformation are elastically stiffer [7,8]. They also have very low resolved shear stress on both the basal and prismatic hai slip systems, making them plastically hard. It can be expected that the presence of ‘‘hard’’ and ‘‘soft’’ grains will have a strong influence on the deformation behaviour of this material at the microstructural scale. Work by Bridier et al. [9] shows a relationship of both crystal orientation and local texture to the formation of fatigue cracks; in order to understand the underlying mechanisms, it is necessary to study the deformation
at the microstructural level. Transmission electron microscopy, and X-ray diffraction line profile analysis have been used to understand the local and global response of materials to deformation in terms of the accumulation of dislocations and other lattice defects during deformation including in Ti alloys [1,10–12]. More recently electron backscatter diffraction has provided a route for assessing the role of grain to grain interactions in this dislocation storage problem, including during tensile deformation of the Ti–6Al–4V studied here [13–16]. The strains themselves can be assessed at the grain and intragranular level by combining the EBSD technique with strain mapping by digital image correlation (DIC). Davidson’s pioneering work with the DISMAP system in the late 1980s and 1990s marks probably the earliest attempt to use digital image correlation methods to measure material deformation fields [17]. In recent years interest in the full field measurement of material deformation through DIC techniques has grown considerably and the method is becoming more widespread [18–29]. In this paper, we describe the application of this technique to the investigation of microstructure-scale deformation in Ti–6Al– 4V, and its combination with crystallographic information from EBSD to study the interaction between microstructural features and deformation behaviour. 2. Materials and experimental methods 2.1. Material, microstructure and texture
⇑ Corresponding author. Present address: Technical University of Denmark, Kgs. Lyngby, Denmark. Tel.: +45 42996855. E-mail address: [email protected] (P.D. Littlewood). 0142-1123/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2012.03.001
The experiments were conducted on rolled bar stock of Ti–6Al– 4V supplied by Rolls-Royce. This had first been pre-strained in the
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Fig. 1. Microstructure of rolled bar stock material, with primary a and grain boundary b highlighted.
ab temperature range, recrystallised in the b range, ab forged and then rolled from a 125 mm square cross section to a 75 mm diameter bar. Finally, it was annealed for 2 h at 700 °C to relieve residual stresses, and air cooled. This resulted in a microstructure composed primarily of globular a grains with small amounts of b primarily at the grain boundaries; the overall a fraction is over 95% with an average a grain size of 11 lm. Fig. 1 shows an optical image of the microstructure, which was etched using a solution of 3% HF and 30% HNO3 in water. This etch tends to predominantly attack the b phase and thus tends to increase the apparent b fraction to some extent. Samples were prepared for EBSD in two stages. Firstly, silicon carbide papers were used to give a flat surface and secondly, the samples were polished in a vibro-polisher using a solution of colloidal silica with 6% ammonia and 6% hydrogen peroxide on a neoprene ‘chem’ cloth. Polishing times between 12 and 18 h were generally found to be sufficient; it was also found that polishing by hand in the same solution for 10–15 min after the vibro-polishing increased the quality of EBSD patterns obtained.
2.2. Local deformation tracking by digital image correlation Tensile test specimens were machined by spark eroding to the dimensions shown in Fig. 2, with a rectangular cross section. To prepare specimens for deformation measurements, a region was marked with a coarse grid of 100 lm pitch, using a focused-ion beam (FIB). Fig. 3a shows an optical image of the coarse grid. EBSD scans were made of selected grid squares, and then the FIB was used to mark the scanned region with a pattern of random dots, as shown in Fig. 3b. Random ‘speckle’ pattern is a standard and widely accepted method for DIC measurements and avoids issues with the automated correlation failing to identify the correct grid within a regular repeating array pattern [29]. Three samples were prepared, and subjected to three different loading regimes. All mechanical testing was done on a Denison Mayes servohydraulic horizontal load frame using Instron wedge grips. The first sample underwent uniaxial tension at a loading rate of 5 105 mm s1 under crosshead control; an accurate extensometer was not available so strain rate control could not be used. The second was subjected to fatigue loading under load control with a peak stress of 900 MPa, a triangular waveform with frequency 0.5 Hz and a load ratio R = 0.1. As the tensile testing indicated a yield stress of approximately 850 MPa, this lies well within the low-cycle fatigue range. The final sample was loaded in dwell fatigue, with the same load profile as the fatigue loading but with the addition of a 2-min hold at peak load. Each test was interrupted at intervals and removed from load, and optical images were taken of the regions marked with the pattern of dots, then re-loaded and the test continued. In the case of the tensile test, re-loading was done at the same rate of crosshead movement as in the original loading. All samples in this study were unloaded for less than 1 h at a time for microscopic observation.
Once a series of images were obtained through a test, digital image correlation was used to measure the deformation of the marked region. This was done using StrainMaster DIC software, which divides a reference image (taken prior to the beginning of the test) into regions and uses a cross-correlation algorithm to identify the position of these regions in each subsequent image. From the shifts of these regions relative to the reference image, the strains in the region can be derived. An estimate of the error in this procedure was made by taking several different images of the same dot pattern as the sample was translated beneath the microscope. The cross-correlation analysis was then run with measurement noise being seen as fluctuations away from the known zero applied strain. Repeated trials give an average error of ±0.16% strain measured using 128 by 128 pixel cells. These 128 pixel cells are 3.4 lm across and the ±0.16% strain error corresponds to a spatial registration error of 5.6 nm. 3. Results 3.1. Tensile testing The tensile test was imaged at three strain levels: 2.2%, 8.0% and 13.1% (the failure strain). Due to the absence of a reliable extensometer, these values were obtained by averaging over the strain field measured by DIC. Fig. 4a shows an inverse pole figure map of the tracked region, and Fig. 4b–d shows maps of the strain component in the loading direction at all three macroscopic strain levels. The observed deformation shows strong inhomogeneity, with some points showing very high strain levels while others remain nearly undeformed. The deformation occurs in a pattern that appears to be established at the beginning of the test (before 2% strain) and continued until failure. In order to investigate the difference in strain evolution between points of high strain accumulation and low strain accumulation, several points were selected and the strain at these points was compared over the course of the test. Fig. 5a shows the strain map of the tracked region at failure with the selected points labelled, and Fig. 5b shows a plot of the strain at each of these points. This shows a roughly linear increase in strain level at the points of high strain accumulation, while some points accumulate essentially no strain at all. Throughout the test the strain concentration at the points of high strain remain 3–3.5 times higher than the average value. 3.2. Fatigue deformation The fatigue test was interrupted every 400 cycles for imaging, up to the point of failure at 6800 cycles. Fig. 6a shows an inverse pole figure map of this region, and Fig. 6b–e shows strain maps at some selected points in the course of the test. The overall strain levels measured are significantly lower than in the tensile case, with an average strain of 1% measured across the field at the end of the test. As with the tensile sample, the pattern of deformation appears to be established early (i.e. within the first block of cycling) across most of the tracked region, and intensifies as the test progresses. There is one feature of particular note in the lower-left part of the tracked region, which has accumulated a much higher level of strain than its surroundings, with this difference becoming extremely marked in the latter stages of the test. In order to investigate this further, the sample surface was re-polished to partly remove the dot pattern and allow other features to become visible. An optical image of the region after re-polishing is shown in Fig. 7. This reveals that a short fatigue crack has formed inside the tracked region, in the same position as the strain concentration. Some of the measured strain concentration, therefore,
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Fig. 2. (a) Coarse grid and (b) random dot pattern etched into sample surface by FIB.
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Fig. 3. Dimensions of test specimens with overall dimensions 50 mm 15 mm. All dimensions in mm.
must be due to the opening of the crack faces rather than to continued deformation of the material. Fig. 8a shows the strain map of the tracked region for this sample with some points of interest labelled, both within the crack region and in areas of high and low strain concentration away from the crack. Fig. 8b plots the evolution of strain at each of these points over the lifetime of the test. Due to the lower overall strain level, this plot is more sensitive to noise in the measurements. However, it appears to show a substantially different pattern of deformation. Here, a significant difference in strain levels between the high and low points appears to be established at the beginning of the test (i.e. in the first block of cycling). After this pattern has been established, the difference in strain rates between the regions of high and low strain drops significantly. This is in contrast to the monotonic tension test where the strain accumulation is essentially linear throughout the test. The one exception is the point within the cracked region, which accumulates strain at a significantly higher rate than the other tracked points once the test has exceeded approximately 4000 cycles. As the strains measured here are biased by the opening of the crack, it may be estimated that crack nucleation begins at around 4000 cycles. Before the crack had been initiated the high strain regions show strain concentrations of 2 compared to the mean, which is somewhat lower than for the monotonic deformation.
3.3. Dwell fatigue deformation Fig. 9a shows the inverse pole figure map for the sample tested in dwell fatigue, and Fig. 9b–d shows some selected strain maps across the lifetime of the sample (3200 cycles). As with the previous samples, the patterns of deformation are established early in the test and remain essentially unaltered at the end. The mean strain at failure was 5.4% within the tracked region, which is significantly higher than in normal fatigue, but lower than the tensile failure strain. A light re-polishing of the sample to remove the FIBed dot pattern revealed a small crack forming in the region of highest strain concentration, on the left-hand side of the tracked region. An SEM image of this region is shown in Fig. 10. As the crack seen here is smaller and the overall strains larger, the effect of the crack opening on the measured strains will be smaller, although not negligible. As with the previous samples, several points were selected and the strain evolution at these points was tracked. Fig. 11a shows the strain map from this region with the tracked points labelled, and Fig. 11b shows a plot of the strain evolution at these points. This loading mode shows a different pattern of deformation to both the tensile and normal fatigue modes. The form of strain evolution here appear similar to creep curves at each point, with an initial period of faster deformation, slowing into a longer period with
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Fig. 4. (a) Inverse pole figure map in sample normal direction and map of strain in loading direction at (b) 2.2% overall strain, (c) 8.0% overall strain and (d) 13.1% overall strain (failure) for tracked region of tensile sample.
Fig. 5. (a) Strain map for tensile sample with tracked points marked, and (b) chart showing strain accumulation at each point over the course of the test. Mean strain is also shown, with RMS deviation indicated by error bars.
near constant deformation rate before accelerating into a final faster deformation rate as failure is approached. This suggests that
room-temperature creep may be a significant deformation mode for this type of loading. Throughout the period with near constant
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Fig. 6. (a) Inverse pole figure map in sample normal direction and map of strain in loading direction at (b) 400 cycles, (c) 3200 cycles, (d) 4400 cycles and (e) 6800 cycles (failure) for tracked region of fatigue sample.
deformation rate the strain concentration at the ‘hot spots’ is 3.5, while a lower strain concentration factor of 1.8 is present in the
initial faster rate deformation, and a slight increase to 3.9 is noted in the final period of accelerated deformation.
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Fig. 7. Optical image of crack found in tracked region of fatigue sample.
4. Discussion 4.1. Relation of deformation patterns to microstructure In order to understand the effect of crystallographic anisotropy on the deformation behaviour of this material, it is necessary to have some measure of a grain’s resistance to deformation. For this study, the measure used is the maximum Schmid factor on all basal and prismatic hai slip systems. A low Schmid factor on all of these systems means that a grain is oriented with its c-axis nearly parallel to the loading direction, and thus there is low resolved shear on all a-type slip systems. This leaves only the hc + ai slip systems available, which have a much higher critical resolved shear stress [1,4–6], making it difficult to activate slip in these grains. Fig. 12 shows an overlay of the strain map from the tensile sample at 8% strain (colour) with a map of the Schmid factor for this region (greyscale, white = high Schmid factor). It can be seen that there are several areas where a grain with low Schmid factor corresponds to an area of low strain. Additionally, several regions of high strain correspond to grains with high Schmid factor which are loaded in series with grains having low Schmid factor. This suggests that grain-to-grain interactions are of high importance in the development of strain inhomogeneity. As the sample is strained, grains with low Schmid factor are unable to deform to accommodate the
macroscopic strain. In order to maintain compatibility, grains adjacent to these grains must undergo a high level of strain, leading to the observed strain concentrations. A similar pattern is seen in the other samples. Fig. 13 shows an overlay of the Schmid factor map and the strain map at failure for the fatigue sample. In particular, the crack which was observed occurs within a grain which is well-oriented for slip, with several poorly-oriented grains surrounding it. There is also a poorly-oriented grain directly below the cracked grain. The conflicting compatibility requirements have resulted in a very localised and intense shear band inside the soft grain, allowing the lower regions of the grain to remain relatively undeformed while the rest of the grain deforms to accommodate the poorly-oriented grains to its right. Further deformation has caused a crack to open along this band. This highlights the importance of grain interactions and strain inhomogeneities on the crack nucleation process. Fig. 14 shows the overlaid Schmid factor and strain maps for the dwell fatigue sample. As with the tension and fatigue samples, the main region of strain concentration and subsequent crack nucleation occurs in a group of grains well-oriented for slip, directly adjacent to a group of grains that are relatively poorly oriented for slip. The presence of strain concentration near poorly-oriented grains, and the presence of many well-oriented grains without strain concentration, suggests that this mechanism of ‘‘strain shedding’’ is the dominant factor in development of inhomogeneous strain, and is applicable to each of the three loading modes studied. 4.2. Strain evolution at ‘hot spots’ The plots of strain accumulation at selected points shown in Figs. 4, 7 and 10 show quite different evolution across the three samples. 4.2.1. Tensile test In the tensile test the points of high strain concentration increase in strain at a rate proportional to the average strain rate, while the points of lowest concentration accumulate essentially no strain. This is a straightforward illustration of the deformation shedding mechanism, as the grains that are poorly oriented are unable to activate any slip systems and neighbouring grains must deform at a higher rate so as to accommodate the imposed average strain. The strain concentration at the ‘hot spots’ is close to con-
Fig. 8. (a) Strain map for fatigue sample with tracked points marked, and (b) chart showing strain accumulation at each point over the course of the test. Mean strain is also shown, with RMS deviation indicated by error bars.
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Fig. 9. (a) Inverse pole figure map in sample normal direction and map of strain in loading direction at (b) 40 cycles, (c) 1600 cycles, and (d) 3200 cycles (failure) for tracked region of dwell fatigue sample.
gave strain concentrations of 2 at the strain maxima during plane strain compression testing to 8%. Efstathiou et al. [21] have worked on pure Ti looking at residual plastic strains after relatively small plastic deformations compared to those studied here. In the text they suggest strain concentrations of 2 occur near grain boundaries, but examination of some of their maps and strain histograms indicates that somewhat higher concentrations are present in the extreme locations, and that these are in line with values found here for larger strains in Ti–6Al–4V. An important point made by Efstathiou et al. is that the magnitude of the strain heterogeneities and therefore the extreme strains depends on the lengthscale used to assess the strain field as controlled by microscope resolution, marker distribution and image digitization (i.e. number of pixels).
Fig. 10. SEM image of crack found in tracked region of dwell fatigue sample.
stant throughout the test and reaches a values of 3.0 to 3.5 times the average value. In fcc Cu samples Kamaya et al. [27] found strain concentrations at a similar level 3 in Cu deformed to 3% strain in tension, while Tatschl and Kolednik [25] indicate a somewhat smaller strain concentration factor of 2 which was maintained throughout a tensile testing out to almost 10% strain. Earlier work by Raabe et al. [23] on a pseudo-2D aluminium microstructure also
4.2.2. Fatigue test The overall strain levels achieved are considerably lower in the fatigue test, and so are the levels of strain concentration. It is not clear whether the lower strain concentration at the hottest spots is an artefact of the relatively small number of grains that have been sampled or a real difference between monotonic and cyclic deformation. There is relatively little data in the literature with which to compare. El Bartali et al. [28] have used DIC to examine cyclic deformation at the microstructural level, but the duplex stainless steel and fully reversed strain controlled testing conditions limit quantitative comparison that can be made with the cur-
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Fig. 11. (a) Strain map for dwell fatigue sample with tracked points marked, and (b) chart showing strain accumulation at each point over the course of the test. Mean strain is also shown, with RMS deviation indicated by error bars.
Fig. 13. Overlay of Schmid factor and strain maps for tracked region of fatigue sample.
Fig. 12. Overlay of Schmid factor and strain maps for tracked region of tensile sample.
rent study. They found local strains at the 2% and +1.3% strain level occur within the ferritic (hard) and austenitic (soft) microstructure some three times higher than the imposed strain amplitude of 0.5%. The spatial location and point in the fatigue test when a near surface crack was formed was readily detected (see Fig. 7). Niendorf et al. [22] have also seen that deformation patterns are established early during fatigue and found that crack nucleation could be well predicted by the location of strain concentration. They observed much lower peak strains than were seen in this study; this is likely to be due to the lower ductility of TiAl alloys they were studying. This has some parallels with the use of DIC in studying the initiation and early growth of stress corrosion cracks in austenitic stainless steels by Rahimi et al. [24]. Once the crack has formed a large contribution to the apparent local strain is actually made by the opening of the crack.
4.2.3. Dwell fatigue test The dwell fatigue sample shows a pattern significantly different to the other two tests, with strain evolution resembling creep curves. Titanium alloys have been previously observed to be sensitive to creep at room temperature, and this experiment suggests that creep is a significant mode of deformation in dwell fatigue. This provides further evidence for the theory of dwell fatigue developed by Evans and Bache [30–32], who proposed the dominance of creep deformation in dwell fatigue. Bache et al. [33] used a similar technique, electron speckle pattern interferometry, to track deformation in a large grained form of the near a titanium alloy Ti 685 (Ti–6Al–5Zr–0.5Mo–0.25Si) in dwell fatigue. They observed strong strain localisation with patterns being established within the first few cycles of a test that ran for only 100 cycles to failure. Crack nucleation occurred within the regions showing the highest strains. Unfortunately the strain maps available do not allow quantification of the strain concentration. The work of Savage et al. [34] shows the profound effect of periods of unloading on the subsequent creep rate during creep tests with single prolonged interrupts. Ti–6Al samples with short range
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Fig. 14. Overlay of Schmid factor and strain maps for tracked region of dwell fatigue sample.
order, which may well be present in our air cooled Ti–6Al–4V samples, showed the strongest effects with the creep rates directly after an unload-reload event being 100 times faster than just before the unload. The transients seen after re-loading by Savage et al. lasted for several hours and so this accelerated creep is likely to persist through the entire 2 min hold of our dwell fatigue tests and thus contribute to the elevated deformation rate which is 107 s1 averaged over the entire test. 5. Conclusions Strain mapping at the microstructural scale using image correlation methods has been performed on Ti–6Al–4V under three different loading modes. Deformation is highly inhomogeneous, and follows patterns which are established at the beginning of loading. There is a strong link between grains with the c-axis nearly parallel to the loading and inhomogeneous deformation. Very low strain is seen in these grains, and regions of high strain are found in surrounding grains. Crack nucleation was observed in regions of high strain concentration in both fatigue and dwell fatigue loading. All three loading modes showed different patterns of strain evolution over time. In dwell fatigue, room-temperature creep was found to make a significant contribution to deformation. Acknowledgements This work was in part funded by EPSRC through Grant EP/ E044778/1, and PDL is grateful for receipt of a Clarendon Scholarship. We thank Rolls-Royce for materials and some financial support for PDL. References [1] Jones IP, Hutchinson WB. Stress–state dependence of slip in titanium–6A1–4V and other hcp metals. Acta Metall 1981;29(6):951–68. [2] Akhtar A. Basal slip and twinning in alpha-titanium single-crystals. Metall Trans 1975;6(5):1105–13. [3] Akhtar A, Teghtsoonian E. Prismatic slip in alpha-titanium single-crystals. Metall Trans A Phys Metall Mater Sci 1975;6(12):2201–8. [4] Churchman AT. The slip modes of titanium and the effect of purity on their occurrence during tensile deformation of single crystals. Proc Royal Soc Lond Ser A Math Phys Sci 1954;226(1165):216–26. [5] Conrad H. Effect of interstitial solutes on the strength and ductility of titanium. Prog Mater Sci 1981;26(2–4):123–404.
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