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Application of synchrotron X-ray diffraction and nanoindentation for the determination of residual stress fields around scratches
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Acta Materialia 59 (2011) 7508–7520 www.elsevier.com/locate/actamat
Application of synchrotron X-ray diffraction and nanoindentation for the determination of residual stress fields around scratches M.K. Khan a, M.E. Fitzpatrick a,⇑, S.V. Hainsworth b, A.D. Evans c, L. Edwards a,d a
Materials Engineering, The Open University, Milton Keynes MK7 6AA, UK Department of Engineering, University of Leicester, Leicester LE1 7RH, UK c Institut Laue Langevin, 6 Rue Jules Horowitz, F-38042 Grenoble, France d Institute of Materials Engineering, ANSTO, Locked Bag 2001, Kirrawee DC, Sydney, NSW 2234, Australia b
Received 23 May 2011; received in revised form 22 August 2011; accepted 22 August 2011 Available online 15 October 2011
Abstract Residual stresses and plastic deformation around scratches or scribe marks in ductile materials can affect fatigue life. Scratches of the order of tens of microns may convert into propagating cracks driven by tensile residual stresses at the scratch root. Probing such stresses on a small scale is experimentally challenging in engineering materials. Here we present results of a combined study using synchrotron X-ray diffraction and nanoindentation to determine the residual stresses around scratches in aluminium alloys. The extraction of residual stresses in metallic materials where there is work hardening is challenging using indentation methods, but a method is presented by which this has been achieved, and a good correlation is obtained between the results obtained using diffraction and nanoindentation. The advantage of synchrotron X-ray measurement is that it allows validation of the stresses at the same spatial scale as nanoindentation. It was found that scratches produced by a “ploughing” mechanism where there was significant plastic deformation beneath the scratch showed higher work hardening and tensile residual stresses than those produced by a “cutting” mechanism where there was little plastic deformation of the material. Little effect of fatigue cycling was seen on the peak stresses at the scratch tip. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nanoindentation; Synchrotron radiation; X-ray diffraction; Aluminium alloys; Residual stresses
1. Introduction The growth of fatigue cracks from small defects is of critical importance in the assessment of the integrity of aerospace structures. During operational service scratches, scribe marks and corrosion pits on fuselage structural areas may turn into propagating cracks owing to the use of thin, highly stressed sections to minimize airframe weight. The fatigue life for a scratch or a scribe mark is a function of the stress concentration around the root, which depends upon the depth and root radius of the scratch, the associated microstructure, the residual stress field, work hardening from plastic deformation, and any relaxation or redistribution of the residual stresses under fatigue loading. ⇑ Corresponding author. Tel.: +44 1908 653100; fax: +44 1908 653858.
E-mail address: m.e.fi[email protected] (M.E. Fitzpatrick).
Several investigations have been performed to address the issues associated with stress concentration and microstructural distortion around small damages [1–7], but a thorough understanding of the effect of the residual stress around scratches is yet to be obtained. Unfortunately, the ability to measure local residual stress–strain fields around a scratch is a difficult experimental problem due to the presence of localized high stress gradients around the scratch root. To probe such local residual stress fields experimental techniques are required that have spatial resolution of the order of a few microns, for which synchrotron X-ray diffraction is an ideal technique [8,9]. The high intensity of the X-rays and low beam divergence allows small gauge volumes to be defined in order to study stress fields existing over a range of hundreds of microns.
1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2011.08.034
M.K. Khan et al. / Acta Materialia 59 (2011) 7508–7520
Although synchrotron X-ray diffraction can be used to map local stress field and plasticity around scratches, to obtain good diffraction statistics the gauge volume must contain a sufficient number of grains. Owing to the large grain size of Al 2024-T351, a larger gauge volume will be required which will give an average value of stress within that gauge volume. Hence, a complementary technique is required which can map residual stress fields and local plasticity with a spatial resolution of 5–10 lm. Depth sensing indentation allows determination of mechanical properties at very low loads by driving an indenter into the material surface and subsequently recording the load–displacement data. As the indenter is driven into the material both elastic and plastic deformation processes occur. There have been various studies carried out on the sensitivity of nanoindentation load–displacement data to residual stress [10–13], as well as an investigation of how residual stress influences indentation creep [14]. The method provides a means to measure residual stress fields around small scale damage and to make a comparison with synchrotron X-ray diffraction results. Indentation load–displacement curves are sensitive to the presence of residual stress in the material being indented. Compared with the stress-free condition, to attain a particular indentation depth the maximum load of indentation Pmax increases for compressive residual stress and decreases for tensile residual stress, and there are corresponding changes to the slope of the loading and unloading curves obtained [10–13,15–20]. In an earlier study [21] we showed that the indentation maximum load Pmax changes by twice as much for an equibiaxial stress state (rxx = ryy – 0) compared with an equivalent uniaxial stress state (rxx – 0, ryy = 0), whilst pure shear (rxx = ryy – 0) does not produce any change in Pmax. For pure shear the increase in indentation maximum load for compressive stress in one axis negates the load decrease for tensile stress on the orthogonal axis [11,21]. This means that whenever a stressed region is indented both components of the in-plane stress play a part. The variation in load–displacement curves is sensitive to the individual components, but the overall response is not unique and varies depending on the overall in-plane residual stress state. Local residual stresses are generated by scratching, which will involve either “cutting” or “ploughing” of the material [22], with an associated degree of local work hardening of the material. The nanoindentation response will be affected by both the hardening and the residual stress field around a scratch. This problem of the convoluted response
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of a plastically deformed material and the presence of residual stresses requires a method to be developed for separation of the two effects for accurate calculation of residual stresses, and for this a comprehensive analytical model is required. In nanoindentation testing changes in response to the in-plane stress components rxx and ryy are obtained. There are some techniques from which individual stress components can be extracted if the ratio of stress components ryy/rxx is known [11,15,16], hence these methods require prior information on the stress components from some other measurement technique. In this paper we present the application of nanoindentation for the determination of residual stresses around scratches. A comparison of residual stresses from synchrotron X-rays and nanoindentation has been presented, and we believe this is the first instance of cross-comparison of nanoindentation-derived residual stresses with another experimental stress analysis technique at this spatial scale. The effect of fatigue loading on the relaxation of residual stresses has also been investigated. 2. Materials, specimens and experimental details 2.1. Material details Measurements were made on aluminium alloys 2024T351 and 5091. Although alloy 5091 is not used in the aerospace industry it is an ideal material for synchrotron X-ray measurement owing to its fine grain size (0.6 lm). This small grain size allows good diffraction data to be obtained even with a very small sampling gauge volume. The material properties are shown in Table 1. The grain size of Al 2024-T351 was determined by quantitative metallography and electron backscattered diffraction (EBSD) and was found to be 20 lm. The grains were equiaxed and showed a random orientation. 2.2. Specimen details For both materials 2 mm thick plates were used. Scratches were produced with diamond tipped cutting tools (designated A and B) with the nominal root radii and depths shown in Table 2. These two tools had been found, by chance, to give very different fatigue lives when used to scribe fatigue samples, despite having the same nominal specifications. Cross-sections of typical scratches using tools A and B are shown in Fig. 1 and the surface profiles are shown in
Table 1 Mechanical properties of Al 2024-T351 and AA 5091. Material
Composition (wt.%)
Elastic modulus (GPa)
Yield stress (MPa)
Strain hardening exponent
Al 2024T351 AA 5091
Cu 3.8–4.9, Mg 1.2–1.8, Mn 0.3–0.9, Zn 0.15 max, Cr 0.1 max, Si 0.05 max, Fe 0.5 max, balance Al Mg 4, Li 1.3, C 1.1, O 0.4, balance Al
72
360
0.1
78
448
0.065
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Table 2 Scratch marks produced. Sample
Material
Tool
Depth d (lm)
Root radius q (lm)
d/q
1 2 3 4 5 6 7 8 9 10 11 12 13
AA 5091 AA 5091 Al 2024 Al 2024 Al 2024 Al 2024 AA 5091 AA 5091 Al 2024 Al 2024 Al 2024 AA 5091 AA 5091
A B A A A A A A B B B B B
125 125 100 50 75 100 50 100 50 100 150 50 100
5 5 5 5 5 5 5 5 5 5 5 5 5
25 25 20 10 15 20 10 20 10 20 30 10 20
Fig. 2. Surface profiles of scratches in Al 2024-T351 using (a) tool A and (b) tool B.
plastic pads, is known as “ploughing”. In contrast, a very smooth scratch track was obtained for tool B, with very little deformed material around the scratch (Fig. 2b), so material removal was by a cutting action rather than by plastic deformation and displacement of material. 2.3. Synchrotron X-ray diffraction
Fig. 1. Cross-section of scratches. (a) Sample 1 (125 lm deep using tool A in 5091). (b) Sample 2 (125 lm deep using tool B in AA 5091). Note the “shoulder” on the left-hand side of the profile produced by tool A.
Fig. 2. For tool A the scratch cross-section was not symmetrical, as shown in Fig. 1a, and a “rough” scratch track with deformed material or debris around the scratch was observed, as shown in Fig. 2a. The scratching of the surface with this tool had clearly been associated with a large amount of plastic deformation and displacement of material, rather than a cutting action by which material is simply removed. This phenomenon, in which material is deposited around the edges of a scratch in the form of
In diffraction methods for strain measurement the interplanar atomic spacing is used as a strain gauge. Shifts in the Bragg diffraction peak give the strain for a particular set of hkl lattice planes. Synchrotron X-ray diffraction experiments were performed in the ID31 beam line of the European Synchrotron Radiation Facility (ESRF). A monochromatic X-ray beam is produced and the diffractometer uses a bank of nine detectors to measure diffracted intensity as a function of diffraction angle 2h. Each detector is preceded by an analyser crystal, which avoids any near surface pseudostrain effects due to partially filled gauge volumes. The sample was mounted on an xyz translation table. Monochromatic radiation of 60 keV was used, correspond˚ . The Al {3 1 1} reflection ing to a wavelength of 0.21 A was used, which gives the best representation of the
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Fig. 3. Strain axis definition relative to the scratch.
macroscopic elastic strain [23]. The diffraction angle 2h was 9.6°. The diffraction peak obtained was fitted assuming a Gaussian distribution function using LAMP (Large Array Manipulation Program) [24]. The geometry of the diffraction gauge volume depends upon the incident beam aperture, the aperture in front of the detector and the diffraction angle. Due to the very localized residual strain field associated with the scratches a very small gauge volume was used. Depending on the strain component being measured, gauge volume dimensions of between 50 and 150 lm were employed. One consequence of the low scattering angles obtained using high energy X-rays is an elongated gauge volume. The gauge volume was aligned such that the long axis was always parallel to the scratch, as in this direction the strain gradient can be assumed to be zero. Hence there was no significant averaging of the strain as a consequence of the elongated gauge volume. The components of the strains are defined in Fig. 3. The coordinate system was chosen with x = y = z = 0 at the scratch root tip and at the centre of the sample. Two components of the strains, exx and eyy, were measured for every scribe. As each scratch was long compared with its other two directions, a plane strain condition was assumed in which ezz = 0. The other possible assumption would be that of plane stress as the measured locations are reasonably close to the surface, however, in this paper only results for a plane strain assumption are presented. A reference value of the interplanar lattice spacing d0 was obtained from a region far from the scratch root which could be considered stress free. Surface scans were carried out for every scratch to find the exact position of its root. In principle, the Bragg line intensity starts from zero in air, rises rapidly as the diffraction volume enters the material, and reaches a maximum when the diffraction volume is fully immersed in the specimen. 2.4. Nanoindentation testing Indentations were carried out to 600 nm depth using an MTS (now Agilent) Nanoindenter XP system with a Berkovich indenter tip. The instrument was operated in contact stiffness mode (CSM), which allows the contact stiffness to be obtained at all points on the
Fig. 4. Array of indentations used in determining the nanoindentation response around the scratch.
load–displacement curve, and hardness and modulus can be obtained as functions of penetration depth. More details of the indentation testing of this material are available in a previous publication [25]. Indentations were made in an array around the scratch cross-section at 10 lm spacing. Load–displacement data was obtained for every indentation. Fig. 4 shows the arrangement of indentations in greater detail. Indentation in a notionally stress-free region was carried out far from the scratch root and 10 indentations were carried out in this region to reduce any scatter in the stress-free load–displacement curve. 2.5. Fatigue testing Al 2024-T351 four point bend fatigue samples of size 50 210 2 mm were prepared. Samples were tested in an MTS servo-hydraulic test system at a maximum stress of 200 MPa and constant load ratio R of 0.1. All tests were carried out at constant amplitude at a frequency of 5 Hz under load control. After fatigue cycling, indentation testing was conducted around the scratch roots in the same way as for the unfatigued samples.
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3. Results 3.1. Residual strains from synchrotron X-ray diffraction Fig. 5 shows the three stress components obtained from the measured strains for sample 1. ryy, transverse to the scratch, was the largest stress component, with a peak tensile residual stress of 180 MPa. The magnitudes of rxx and rzz were similar to each other but about half of the magnitude of ryy. For all stress components behind the scratch tip (negative x-direction) showed compressive residual stress. Fig. 6 shows the ryy stress component obtained from the measured strains for sample 2 (one strain component only is shown for brevity). ryy was again the highest stress component, with a peak tensile residual stress just below the scratch root of 100 MPa. The region behind the scratch tip was under low compressive residual stress. rxx and rzz showed similar profiles with a peak stress around half that of ryy. The results show that tool B produced a stress field with a smaller peak stress than tool A.
Fig. 6. ryy stress profile for sample 2, a 125 lm deep scratch in 5091 using tool B.
Fig. 7. ryy stress profile for sample 3, a 100 lm scratch in Al 2024-T351.
Fig. 7 shows the ryy stress component obtained from the measured strains for sample 3 (one strain component only is shown for brevity). Sample 3 was a similar scratch to sample 1 but in Al 2024-T351 and with a slightly smaller depth of 100 lm. Although information in a relatively small area was obtained, it was clear that a very similar stress field was present as for sample 1. The peak in tensile stress was found to be slightly ahead of the scratch root, probably because in this case a larger gauge volume was used and the measurement at x = 0 exactly at the scribe root showed an average value including stress from behind the root. A peak tensile stress of 180 MPa was found at x = +60 lm for ryy, which was the highest of the stress components. rxx and rzz showed similar profiles with a peak stress around half that of ryy, and a peak tensile stress of 90–100 MPa was found for these components. 3.2. Nanoindentation load–displacement curve analysis
Fig. 5. Stress profile for sample 1, a 125 lm deep scratch in 5091 using tool A for (a) ryy, (b) rxx and (c) rzz.
3.2.1. Sample 1 (125 m deep scratch in AA 5091 using tool A) Fig. 8 shows nanoindentation load–displacement curves for different locations ahead of the scratch tip. From synchrotron X-ray diffraction it was found that there were tensile stresses of around 180 MPa present around the
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Fig. 8. Nanoindentation load–displacement curves for sample 1 for positions ahead of the scratch tip.
scratch root. As a result, in principle the loading curves for the near scratch root region should have shifted downwards, but it can be seen that a mixed trend of upward and downward movement of the loading curves was obtained. This was due to the hard plastically deformed region around the scratch root for tool A [22]. A convoluted response of increased hardness (loading curve moves up) and high tensile stresses (loading curve moves down) was obtained. Hence, analysis of the peak load is insufficient for the extraction of residual stresses in cases where there has been differential hardening, and another parameter must be used [19], as changes in hardness will
always themselves affect the nanoindentation response. The detailed method for separation of this hardness increase from the residual stresses will be discussed later, in Section 4. 3.2.2. Sample 2 (125 m deep scratch in AA 5091 using tool B) Fig. 9 shows nanoindentation load–displacement curves obtained for sample 2 ahead of the scratch tip. It can be seen that near the scratch root all loading curves were below the stress-free loading curve. This was a clear indication that there were tensile residual stresses present below
Fig. 9. Nanoindentation load–displacement curve for sample 2 for positions ahead of the scratch tip.
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Fig. 10. Nanoindentation load–displacement curve for sample 3 for positions ahead of the scratch tip.
the scratch root. From synchrotron X-ray diffraction it was seen that around 100 MPa tensile residual stresses were present around the root of this scratch. From the full width at half maximum (FWHM) analysis for this scratch little work hardening was seen around the scratch [22] and it was observed that material removal was by a cutting process (see also Fig. 2b). In the absence of any work hardening around the scratch root it was evident that the variation in the loading curves was due to residual stresses. Altogether, the load–displacement curves successfully detected the presence of tensile residual stresses around the scratch root for this sample, in comparison with tool A, in which tensile residual stresses were not detectable in the highly plastically deformed regions. 3.2.3. Sample 3 (100 m deep scratch using tool A) Fig. 10 shows load–displacement curves obtained for sample 3 for different locations ahead of the scratch tip. It can be seen that at all locations the loading curves were above or equivalent to the stress-free loading curve. This scratch was created in Al 2024-T351 using tool A, which produces severe work hardening around the scratch root, and the indentation load–displacement curve again showed a dominant response due to hardening. The synchrotron Xray diffraction results show that high tensile stresses of around 180 MPa were present around the scratch root. 4. Extraction of residual stresses from nanoindentation load–displacement curves 4.1. Methodology There are various methods which have been developed to extract residual stresses from load–displacement curves
[10–13,15,16,19], however, these methods were developed with finite element studies and/or for relatively hard materials and to-date no study has been carried out on engineering alloys like aluminium, which may show pile-up even at small indentation loads [25–27] and for which the behaviour of the pile-up changes with the type and magnitude of the residual stress state. A different approach taken by Dean et al. was to examine the effect of residual stress on indentation creep [14]. A particular problem with engineering alloys like Al 2024-T351 is texture, in which grains of different orientation exhibit anisotropy in mechanical properties. Furthermore, hardening of the material associated with the scratching process studied here produces a convoluted response of a hard plastically deformed material and elastic residual stress field that requires separation for accurate calculation of residual stresses using nanoindentation, and for this a comprehensive analytical model is required. Finite element simulations have shown that if a compressive residual stress is applied during nanoindentation then the elastically recovered portion of the indentation displacement increases, and more of the deformation is elastically recovered [21]. When a tensile residual stress is applied the opposite occurs. This can be expressed by the ratio hf/hmax, where hf is the final indentation depth and hmax the maximum depth during indentation. The ratio hf/hmax is equivalent to the ratio of plastic work to total work Wp/Wt. Thus a relationship can be derived between the residual stress (or normalized residual stress) and the ratio Wp/Wt. This can be expressed by the equation: W p =W t ¼ a
rr þb rY
ð1Þ
M.K. Khan et al. / Acta Materialia 59 (2011) 7508–7520
where a and b are constants that depend upon the material, which in this case were derived from finite element modelling of the indentation process [21,28]. The ratio of total area of contact including pile-up Ac0 and the contact area from the Oliver–Pharr model Ac [29] can be related to the ratio of plastic to total work of indentation Wp/Wt [19] as: Ac0 Wp ¼a þb Ac Wt
ð2Þ
rr Ac0 ¼a þb rY Ac
Table 3 Slope and intercept values for Al 2024-T351 and AA 5091. Material
Coefficient Relation
Al 2024-T351 a b AA 5091
a b
and thus, by manipulation, we can obtain
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Ac0 /Ac and rr/rY
Ac0 /Ac and Wp/Wt
Compression 0.16 Tension 0.30 Compression 1.29 Tension 1.28
Compression 13.62 Tension 20.39 Compression 13.76 Tension 19.54
Compression 0.21 Tension 0.57 Compression 1.413 Tension 1.410
Compression 12.09 Tension 27.36 Compression 12.54 Tension 25.9
ð3Þ
where rY is the yield stress of the material. Once Ac0 is known then residual stress rr can be obtained from the relation in Eq. (3). Fuller details of the approach are given in Khan et al. [21]. 4.2. Amendments due to plastic deformation around scratches Application of any method for residual stress extraction from load–displacement curves is complicated when there has been hardening of the material. For a scratch there will be a change in hardness (and therefore Wp/Wt) around the scratch root and it will vary with position. Any change in Wp/Wt will be a convoluted response of the elastic residual stresses and hardening by plastic deformation of the material. For a material with only limited hardening this does not pose a significant problem to extracting residual stresses from nanoindentation, but Al 2024 used here hardens significantly and therefore we have had to develop a model for how the hardening can be separated from the effects of residual stress. For a general system, with no prior knowledge of the load history or likely residual stress distribution, a unique solution would be unobtainable. Here we have information from the synchrotron X-ray data to provide some calibration. For scratches with work hardening around the root Eq. (1) can be rewritten as: Ac0 Wp ¼a þ hardening þ b ð4Þ Ac Wt Here a new correction is defined which separates the effect of work hardening from the effect of residual stresses on the ratio of area contact: Ac0 Wp ¼a þbþ/ ð5Þ Ac Wt where ( = a hardening) is a correction factor which deconvolves work hardening from the effect of residual stress on the area contact ratio. Choosing a value of / is a very challenging problem. The actual increase in hardness at any point around the scratch root cannot be separated from the effect of tensile residual stresses. Additionally, the increase in hardness varies with position around the scratch root.
To accommodate these problems in the current analysis it has been assumed that the increase in hardness is due only to plastic deformation and that the hardening is uniform in a 50 lm region around the scratch root. For tool A the peak increase in hardness was 30% over the bulk hardness values [22]. This increase in hardness decreased Wp/Wt by 0.02. For tensile residual stress a was 20.4 (Table 3), so the correction factor can be obtained as: / ¼ a hardening / ¼ 20:4 0:02 ¼ 0:41
ð6Þ
So for tool A, which generates high work hardening, the correction factor for peak hardness was 0.41, whilst for tool B, which did not generate significant work hardening around the scratch root, this factor was considered to be zero. From Table 3 Eq. (4) can be rewritten as: Ac0 Wp ¼ 20:4 þ 19:64 þ / Ac Wt
ð7Þ
for tensile residual stresses, and Eq. (6) becomes: Ac0 Wp ¼ 20:4 þ 19:24 ðfor tool AÞ Ac Wt Ac0 Wp ¼ 20:4 þ 19:64 ðfor tool BÞ Ac Wt
ð8Þ ð9Þ
For compressive residual stresses no correction factor was developed because the expected stress field was predominantly tensile. Hence, Eq. (5) remained the same for compressive stresses: Ac0 Wp ¼ 13:62 þ 13:76 ðfor tools A and BÞ Ac Wt
ð10Þ
and then residual stress can be extracted based on the true contact area from the equations below. For tensile residual stresses: Ac0 rr ¼ 1:17 109 1:28 ð11Þ Ac rY For compressive residual stresses: Ac0 rr ¼ 2:2 109 1:3 Ac rY
ð12Þ
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A similar exercise can be repeated for AA 5091 for which the values a and b are presented in Table 3. A correction factor of 0.5 was used for this material. This method does have limitations in practice. The set of equations discussed above is based on the response to equibiaxial residual stresses, but the residual stress field obtained around the scratch root is not equibiaxial. The hardness increase may also not be constant, as assumed. Finally, the equations were derived from finite element modelling results in which indenter tip bluntness effects were not considered. 4.3. Reproducibility of the response The sensitivity of the nanoindentation load–displacement curves and the extraction of the residual stresses based on these curves are dependent upon the response of the material. The aluminium plates used in this study show some crystallographic texture, leading to anisotropy from grain to grain. A particularly interesting finding is that the grain to grain scatter in the nanoindentation result is significantly lower in the presence of a residual stress. Whenever a region of low residual stress (<50 MPa) is indented in Al 2024-T351 distinct load–displacement curves are obtained due to the different response of different grains, as shown in Fig. 11. When indents are made in a region with high residual stresses (>50 MPa) the load–displacement curves show much reduced scatter. The consequence of this is that high scatter in the residual stress values extracted from this approach can be attributed partly to zero or low residual stress. The peak residual stresses around the scratches are of the order of +100– 200 MPa in a very small region near the root of the scratch, and very quickly start to decrease away from the root.
Hence, it is expected from this observation that the near root regions are ideal for extraction of residual stresses from the model, and far from the root higher scatter in the data will be obtained. 4.4. Results from scratched samples 4.4.1. Sample 1 Fig. 12a shows residual stresses obtained from load–displacement curves in sample 1 for a very small region ±30 lm in the x-direction, and Fig. 12b shows the residual stress field from synchrotron X-ray diffraction for ±75 lm in the x-direction. The results show tensile stresses near the scratch root reducing with distance. There is remarkably good agreement with the synchrotron X-ray results (Fig. 12b), particularly given the assumptions required to extract the residual stresses from the nanoindentation data. Note also that the nature of the stress field in this case fortuitously acts in our favour; the nanoindentation response is insensitive to any direction dependence in the residual stresses, but the X-ray diffraction analysis has demonstrated that the stress field is biaxial (if not equibiaxial) in the plane on which the nanoindentation tests were performed. Due to the incapability of the nanoindentation-based technique to probe low residual stress values, regions far from the scratch root showed poor agreement with the synchrotron X-ray values. The synchrotron X-ray diffraction results were an average over the gauge volume and the nanoindentation results were for very localized regions, so to compare the results of synchrotron X-ray diffraction the average value of residual stress up to +50 lm was calculated and was found to be +163 MPa. This compares with +180 MPa from synchrotron X-ray diffraction, assuming plane strain.
Fig. 11. Residual stress values obtained using nanoindentation for Al 2024-T351 for regions of +30, +160 and +100 MPa.
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Fig. 12. Residual stress values for sample 1 obtained from (a) nanoindentation and (b) synchrotron X-ray diffraction.
4.4.2. Sample 2 Fig. 13a shows the residual stress field obtained from nanoindentation for a region ±35 lm in the x-direction around the scratch root, and Fig. 13b shows the residual stress field from the synchrotron X-ray diffraction for ±75 lm in the x-direction. It can again be seen that there is at least fair agreement between the stress fields obtained from both techniques, especially near the scratch root region. The average value of the stress from the two methods up to +50 lm at y = 0 was calculated and was found to be +77 MPa for nanoindentation, compared with +100 MPa from synchrotron X-ray diffraction, which was again in very good agreement. 4.4.3. Sample 3 For this sample the average value of stress up to +50 lm in the x-direction was +210 MPa. A maximum stress of +180 MPa was obtained from synchrotron X-ray diffraction, and the values were again in good agreement with each other. Table 4 shows a comparison of residual stresses obtained by synchrotron X-ray diffraction and nanoinden-
tation for all three samples. It can be seen that the nanoindentation-extracted residual stress values were in close agreement with the synchrotron results. The strain accuracy for the individual synchrotron X-ray results was better than 30le, giving a stress accuracy of better than ±10 MPa. For nanoindentation there is always point to point scatter in the results, although this is lower when the residual stress is higher (see Section 4.3); certainly a scatter of at least ±20 MPa can be expected. 4.4.4. Other samples Table 5 summarizes the results obtained from the other samples that were prepared and measured. It is seen that there is little dependence of the average stress below the scratch tip on the depth of the scratch. Most notably, the blunter tool A shows significantly higher levels of residual stress. 4.4.5. Effect of fatigue loading In a previous work [22] we showed that fatigue loading of samples containing scratches did not produce any measurable change in the nanoindentation hardness profile
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Fig. 13. Residual stress values for sample 2 obtained from (a) nanoindentation and (b) synchrotron X-ray diffraction.
Table 4 Comparison of residual stress results from synchrotron X-ray diffraction and nanoindentation. Sample
1 2 3
Residual stress (MPa) Synchrotron X-ray
Nanoindentation
+180 +100 +180
+163 +77 +210
Results are an average over the first 50 lm from the scratch tip.
ahead of the scratch tip. The measured residual stresses ahead of the tip are significant, particularly in the case of the relatively blunt tool A, although there is no direct correlation in this case between tensile residual stress ahead of the notch and a lower fatigue life, because of the additional effects of the work hardening induced by the tool, which appears to act to retard fatigue crack initiation. Any redistribution or relaxation of the residual stresses after fatigue cycling will strongly depend upon the applied
Table 5 Average residual stress in the first 50 lm from the scratch root for scratches of 5 lm root radius. Sample
Material
Tool
Depth d (lm)
Root radius q (lm)
d/q
Residual stress (MPa)
Average stress (MPa)
4 5 6 7 8 9 10 11 12 13
Al 2024-T351 Al 2024-T351 Al 2024-T351 AA 5091 AA 5091 Al 2024-T351 Al 2024-T351 Al 2024-T351 AA 5091 AA 5091
A A A A A B B B B B
50 75 100 50 100 50 100 150 50 100
5 5 5 5 5 5 5 5 5 5
10 15 20 15 15 10 20 30 15 15
+154 +160 +210 +155 +205 +120 +71 +67 +75 +73
+172 +172 +172 +172 +172 +81 +81 +81 +81 +81
M.K. Khan et al. / Acta Materialia 59 (2011) 7508–7520 Table 6 Details of the samples tested in fatigue. Sample
14 15 16 17 18 19 20 21
Scratch depth (lm)
Tool
50 50 50 75 100 100 100 100
A A A A A A B B
Fatigue cycles
Residual stress (MPa) Before fatigue
After fatigue
250,000 500,000 1250,000 500,000 250,000 500,000 100,000 200,000
+155 +155 +155 +160 +215 +215 +71 +71
+163 +178 +153 +134 +194 +158 +82 +93
loading. Boyce et al. [1,2] measured the residual stress field around foreign object damage (FOD) using synchrotron Xray diffraction and found that the initial residual stress around the damage was highly tensile and was 40% of the yield stress. They concluded that the initial residual stress state can decay significantly in fatigue depending upon the applied stress. For Ti–6Al–4V they obtained very little relaxation for 0.35rY, but for a higher applied stress of 0.54rY the relaxation reached 50%. They observed that decay of the residual stress state only occurred during the first cycle and subsequent cycles showed very little further relaxation. Hence, some scratches were tested which had already been loaded in fatigue. 50 210 2 mm four point bend samples were prepared. The span lengths between the top and bottom rollers were 35 and 70 mm, respectively. Samples were tested in an MTS servo-hydraulic test system at a maximum stress of 200 MPa and constant load ratio R of 0.1. All tests were at constant amplitude at a frequency of 5 Hz. In total, eight samples were tested in four point bend fatigue without being taken to failure (to preserve the scratches for nanoindentation testing). Table 6 shows details of the samples and the results obtained. Again, the results can be assumed to have an accuracy no better than ±20 MPa. It can be seen that for both tools, in general, no relaxation of residual stress occurred after fatigue cycles, even for scratches of larger depths. This is perhaps surprising given the relatively high applied stress, but may be a consequence of the local hardening in the case of tool A, and the relatively low induced stresses for the other tools studied. 5. Conclusions 1. Residual stresses have been determined around scratches in aluminium alloys using synchrotron X-ray diffraction and nanoindentation. The scratches were produced using different tools that caused different amounts of hardening and plastic damage. Experiments were performed on Al 2024 and also on fine grained 5091, which has advantages for the diffraction experi-
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ments, and similar results were obtained for both materials. Depending on the scratch depth and root radius, peak residual stresses up to 200 MPa were measured. The nanoindentation response shows lower scatter in the presence of residual stress, which is attributed to the effects of the residual stress negating local grain to grain scatter in the stress-free response. 2. It is necessary to deconvolute the effects of hardening and residual stress on the indentation response, and a technique to account for this has been proposed and demonstrated to provide good correlation with results obtained from synchrotron X-ray diffraction. 3. One tool in particular (tool A) had an irregular profile and scratched the material by a ploughing rather than by a cutting action. This tool produced higher tensile stresses and hardening around the scratch root than a sharper tool. 4. No significant effect of fatigue loading was seen on the residual stresses near the scratch tip as measured using nanoindentation, and this is attributed to the hardened layer near the scratch tip. Acknowledgements The synchrotron X-ray experiments were performed at the European Synchrotron Radiation Facility, Grenoble, and due acknowledgement is made for the provision of beam time on ID31. M.E.F. is supported by a grant through The Open University from The Lloyd’s Register Educational Trust, an independent charity working to achieve advances in transportation, science, engineering and technology education, training and research worldwide for the benefit of all. References [1] Boyce BL, Chen X, Hutchinson JW, Ritchie RO. Mech Mater 2001;33:441. [2] Boyce BL, Chen X, Peters JO, Hutchinson JW, Ritchie RO. Mater Sci Eng 2003;A349:48. [3] Oakley SY, Nowell D. Int J Fatigue 2007;29:69. [4] Peters JO, Boyce BL, Chen X, McNaney JM, Hutchinson JW, Ritchie RO. Eng Fract Mech 2002;13:1425. [5] Peters JO, Roder O, Boyce BL, Thompson AW, Ritchie RO. Metall Mater Trans 2000;31A:1571. [6] Ruschau JJ, Nicholas T, Thompson SR. Int J Impact Eng 2001;25:233. [7] Thompson SR, Ruschau JJ, Nicholas T. Int J Fatigue 2001;23:405. [8] Withers PJ. In: Fitzpatrick ME, Lodini A, editors. Analysis of residual stress by diffraction using neutron and synchrotron radiation. London: Taylor and Francis; 2003. [9] Steuwer A, Edwards L, Pratihar S, Ganguly S, Peel M, Fitzpatrick ME, et al. Nucl Instrum Methods Phys Res B Beam Interact Mater Atoms 2006;246:217. [10] Carlsson S, Larsson P-L. Acta Mater 2001;49:2179. [11] Lee YH, Kwon D. Acta Mater 2004;52:1555. [12] Suresh S, Giannakopoulos AE. Acta Mater 1998;46:5755. [13] Xu Z-H, Li X. Acta Mater 2005;53:1913. [14] Dean J, Aldrich-Smith G, Clyne TW. Acta Mater 2011;59:2749. [15] Lee YH, Ji WJ, Kwon D. Exp Mech 2004;44:55. [16] Lee YH, Kwon D. Scripta Mater 2003;49:459.
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Swadener JG, Taljat B, Pharr GM. J Mater Res 2001;16:2091. Tsui TY, Oliver WC, Pharr GM. J Mater Res 1996;11:752. Xu ZH, Li X. Philos Mag 2006;86:2835. Zhao M, Chen X, Yan J, Karlsson AM. Acta Mater 2006;54:2823. Khan MK, Fitzpatrick ME, Hainsworth SV, Edwards L. Comput Mater Sci 2011;50:2967. [22] Khan MK, Fitzpatrick ME, Hainsworth SV, Edwards L. Mater Sci Eng A 2009;527:297. [23] Clausen B, Lorentzen T, Leffers T. Acta Mater 1998;46:3087.
[24] Richard D, Ferrand M, Kearley GJ. J Neutron Res 1996;4:33. [25] Khan MK, Hainsworth SV, Fitzpatrick ME, Edwards L. J Mater Sci 2009;44:1006. [26] Bolshakov A, Pharr GM. J Mater Res 1998;13:1049. [27] Taljat B, Pharr GM. Int J Solids Struct 2004;41:3891. [28] Khan MK, Hainsworth SV, Fitzpatrick ME, Edwards L. Comput Mater Sci 2010;49:751. [29] Oliver WC, Pharr GM. J Mater Res 1992;7:1564.
Acta Materialia 59 (2011) 7508–7520 www.elsevier.com/locate/actamat
Application of synchrotron X-ray diffraction and nanoindentation for the determination of residual stress fields around scratches M.K. Khan a, M.E. Fitzpatrick a,⇑, S.V. Hainsworth b, A.D. Evans c, L. Edwards a,d a
Materials Engineering, The Open University, Milton Keynes MK7 6AA, UK Department of Engineering, University of Leicester, Leicester LE1 7RH, UK c Institut Laue Langevin, 6 Rue Jules Horowitz, F-38042 Grenoble, France d Institute of Materials Engineering, ANSTO, Locked Bag 2001, Kirrawee DC, Sydney, NSW 2234, Australia b
Received 23 May 2011; received in revised form 22 August 2011; accepted 22 August 2011 Available online 15 October 2011
Abstract Residual stresses and plastic deformation around scratches or scribe marks in ductile materials can affect fatigue life. Scratches of the order of tens of microns may convert into propagating cracks driven by tensile residual stresses at the scratch root. Probing such stresses on a small scale is experimentally challenging in engineering materials. Here we present results of a combined study using synchrotron X-ray diffraction and nanoindentation to determine the residual stresses around scratches in aluminium alloys. The extraction of residual stresses in metallic materials where there is work hardening is challenging using indentation methods, but a method is presented by which this has been achieved, and a good correlation is obtained between the results obtained using diffraction and nanoindentation. The advantage of synchrotron X-ray measurement is that it allows validation of the stresses at the same spatial scale as nanoindentation. It was found that scratches produced by a “ploughing” mechanism where there was significant plastic deformation beneath the scratch showed higher work hardening and tensile residual stresses than those produced by a “cutting” mechanism where there was little plastic deformation of the material. Little effect of fatigue cycling was seen on the peak stresses at the scratch tip. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Nanoindentation; Synchrotron radiation; X-ray diffraction; Aluminium alloys; Residual stresses
1. Introduction The growth of fatigue cracks from small defects is of critical importance in the assessment of the integrity of aerospace structures. During operational service scratches, scribe marks and corrosion pits on fuselage structural areas may turn into propagating cracks owing to the use of thin, highly stressed sections to minimize airframe weight. The fatigue life for a scratch or a scribe mark is a function of the stress concentration around the root, which depends upon the depth and root radius of the scratch, the associated microstructure, the residual stress field, work hardening from plastic deformation, and any relaxation or redistribution of the residual stresses under fatigue loading. ⇑ Corresponding author. Tel.: +44 1908 653100; fax: +44 1908 653858.
E-mail address: m.e.fi[email protected] (M.E. Fitzpatrick).
Several investigations have been performed to address the issues associated with stress concentration and microstructural distortion around small damages [1–7], but a thorough understanding of the effect of the residual stress around scratches is yet to be obtained. Unfortunately, the ability to measure local residual stress–strain fields around a scratch is a difficult experimental problem due to the presence of localized high stress gradients around the scratch root. To probe such local residual stress fields experimental techniques are required that have spatial resolution of the order of a few microns, for which synchrotron X-ray diffraction is an ideal technique [8,9]. The high intensity of the X-rays and low beam divergence allows small gauge volumes to be defined in order to study stress fields existing over a range of hundreds of microns.
1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2011.08.034
M.K. Khan et al. / Acta Materialia 59 (2011) 7508–7520
Although synchrotron X-ray diffraction can be used to map local stress field and plasticity around scratches, to obtain good diffraction statistics the gauge volume must contain a sufficient number of grains. Owing to the large grain size of Al 2024-T351, a larger gauge volume will be required which will give an average value of stress within that gauge volume. Hence, a complementary technique is required which can map residual stress fields and local plasticity with a spatial resolution of 5–10 lm. Depth sensing indentation allows determination of mechanical properties at very low loads by driving an indenter into the material surface and subsequently recording the load–displacement data. As the indenter is driven into the material both elastic and plastic deformation processes occur. There have been various studies carried out on the sensitivity of nanoindentation load–displacement data to residual stress [10–13], as well as an investigation of how residual stress influences indentation creep [14]. The method provides a means to measure residual stress fields around small scale damage and to make a comparison with synchrotron X-ray diffraction results. Indentation load–displacement curves are sensitive to the presence of residual stress in the material being indented. Compared with the stress-free condition, to attain a particular indentation depth the maximum load of indentation Pmax increases for compressive residual stress and decreases for tensile residual stress, and there are corresponding changes to the slope of the loading and unloading curves obtained [10–13,15–20]. In an earlier study [21] we showed that the indentation maximum load Pmax changes by twice as much for an equibiaxial stress state (rxx = ryy – 0) compared with an equivalent uniaxial stress state (rxx – 0, ryy = 0), whilst pure shear (rxx = ryy – 0) does not produce any change in Pmax. For pure shear the increase in indentation maximum load for compressive stress in one axis negates the load decrease for tensile stress on the orthogonal axis [11,21]. This means that whenever a stressed region is indented both components of the in-plane stress play a part. The variation in load–displacement curves is sensitive to the individual components, but the overall response is not unique and varies depending on the overall in-plane residual stress state. Local residual stresses are generated by scratching, which will involve either “cutting” or “ploughing” of the material [22], with an associated degree of local work hardening of the material. The nanoindentation response will be affected by both the hardening and the residual stress field around a scratch. This problem of the convoluted response
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of a plastically deformed material and the presence of residual stresses requires a method to be developed for separation of the two effects for accurate calculation of residual stresses, and for this a comprehensive analytical model is required. In nanoindentation testing changes in response to the in-plane stress components rxx and ryy are obtained. There are some techniques from which individual stress components can be extracted if the ratio of stress components ryy/rxx is known [11,15,16], hence these methods require prior information on the stress components from some other measurement technique. In this paper we present the application of nanoindentation for the determination of residual stresses around scratches. A comparison of residual stresses from synchrotron X-rays and nanoindentation has been presented, and we believe this is the first instance of cross-comparison of nanoindentation-derived residual stresses with another experimental stress analysis technique at this spatial scale. The effect of fatigue loading on the relaxation of residual stresses has also been investigated. 2. Materials, specimens and experimental details 2.1. Material details Measurements were made on aluminium alloys 2024T351 and 5091. Although alloy 5091 is not used in the aerospace industry it is an ideal material for synchrotron X-ray measurement owing to its fine grain size (0.6 lm). This small grain size allows good diffraction data to be obtained even with a very small sampling gauge volume. The material properties are shown in Table 1. The grain size of Al 2024-T351 was determined by quantitative metallography and electron backscattered diffraction (EBSD) and was found to be 20 lm. The grains were equiaxed and showed a random orientation. 2.2. Specimen details For both materials 2 mm thick plates were used. Scratches were produced with diamond tipped cutting tools (designated A and B) with the nominal root radii and depths shown in Table 2. These two tools had been found, by chance, to give very different fatigue lives when used to scribe fatigue samples, despite having the same nominal specifications. Cross-sections of typical scratches using tools A and B are shown in Fig. 1 and the surface profiles are shown in
Table 1 Mechanical properties of Al 2024-T351 and AA 5091. Material
Composition (wt.%)
Elastic modulus (GPa)
Yield stress (MPa)
Strain hardening exponent
Al 2024T351 AA 5091
Cu 3.8–4.9, Mg 1.2–1.8, Mn 0.3–0.9, Zn 0.15 max, Cr 0.1 max, Si 0.05 max, Fe 0.5 max, balance Al Mg 4, Li 1.3, C 1.1, O 0.4, balance Al
72
360
0.1
78
448
0.065
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Table 2 Scratch marks produced. Sample
Material
Tool
Depth d (lm)
Root radius q (lm)
d/q
1 2 3 4 5 6 7 8 9 10 11 12 13
AA 5091 AA 5091 Al 2024 Al 2024 Al 2024 Al 2024 AA 5091 AA 5091 Al 2024 Al 2024 Al 2024 AA 5091 AA 5091
A B A A A A A A B B B B B
125 125 100 50 75 100 50 100 50 100 150 50 100
5 5 5 5 5 5 5 5 5 5 5 5 5
25 25 20 10 15 20 10 20 10 20 30 10 20
Fig. 2. Surface profiles of scratches in Al 2024-T351 using (a) tool A and (b) tool B.
plastic pads, is known as “ploughing”. In contrast, a very smooth scratch track was obtained for tool B, with very little deformed material around the scratch (Fig. 2b), so material removal was by a cutting action rather than by plastic deformation and displacement of material. 2.3. Synchrotron X-ray diffraction
Fig. 1. Cross-section of scratches. (a) Sample 1 (125 lm deep using tool A in 5091). (b) Sample 2 (125 lm deep using tool B in AA 5091). Note the “shoulder” on the left-hand side of the profile produced by tool A.
Fig. 2. For tool A the scratch cross-section was not symmetrical, as shown in Fig. 1a, and a “rough” scratch track with deformed material or debris around the scratch was observed, as shown in Fig. 2a. The scratching of the surface with this tool had clearly been associated with a large amount of plastic deformation and displacement of material, rather than a cutting action by which material is simply removed. This phenomenon, in which material is deposited around the edges of a scratch in the form of
In diffraction methods for strain measurement the interplanar atomic spacing is used as a strain gauge. Shifts in the Bragg diffraction peak give the strain for a particular set of hkl lattice planes. Synchrotron X-ray diffraction experiments were performed in the ID31 beam line of the European Synchrotron Radiation Facility (ESRF). A monochromatic X-ray beam is produced and the diffractometer uses a bank of nine detectors to measure diffracted intensity as a function of diffraction angle 2h. Each detector is preceded by an analyser crystal, which avoids any near surface pseudostrain effects due to partially filled gauge volumes. The sample was mounted on an xyz translation table. Monochromatic radiation of 60 keV was used, correspond˚ . The Al {3 1 1} reflection ing to a wavelength of 0.21 A was used, which gives the best representation of the
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Fig. 3. Strain axis definition relative to the scratch.
macroscopic elastic strain [23]. The diffraction angle 2h was 9.6°. The diffraction peak obtained was fitted assuming a Gaussian distribution function using LAMP (Large Array Manipulation Program) [24]. The geometry of the diffraction gauge volume depends upon the incident beam aperture, the aperture in front of the detector and the diffraction angle. Due to the very localized residual strain field associated with the scratches a very small gauge volume was used. Depending on the strain component being measured, gauge volume dimensions of between 50 and 150 lm were employed. One consequence of the low scattering angles obtained using high energy X-rays is an elongated gauge volume. The gauge volume was aligned such that the long axis was always parallel to the scratch, as in this direction the strain gradient can be assumed to be zero. Hence there was no significant averaging of the strain as a consequence of the elongated gauge volume. The components of the strains are defined in Fig. 3. The coordinate system was chosen with x = y = z = 0 at the scratch root tip and at the centre of the sample. Two components of the strains, exx and eyy, were measured for every scribe. As each scratch was long compared with its other two directions, a plane strain condition was assumed in which ezz = 0. The other possible assumption would be that of plane stress as the measured locations are reasonably close to the surface, however, in this paper only results for a plane strain assumption are presented. A reference value of the interplanar lattice spacing d0 was obtained from a region far from the scratch root which could be considered stress free. Surface scans were carried out for every scratch to find the exact position of its root. In principle, the Bragg line intensity starts from zero in air, rises rapidly as the diffraction volume enters the material, and reaches a maximum when the diffraction volume is fully immersed in the specimen. 2.4. Nanoindentation testing Indentations were carried out to 600 nm depth using an MTS (now Agilent) Nanoindenter XP system with a Berkovich indenter tip. The instrument was operated in contact stiffness mode (CSM), which allows the contact stiffness to be obtained at all points on the
Fig. 4. Array of indentations used in determining the nanoindentation response around the scratch.
load–displacement curve, and hardness and modulus can be obtained as functions of penetration depth. More details of the indentation testing of this material are available in a previous publication [25]. Indentations were made in an array around the scratch cross-section at 10 lm spacing. Load–displacement data was obtained for every indentation. Fig. 4 shows the arrangement of indentations in greater detail. Indentation in a notionally stress-free region was carried out far from the scratch root and 10 indentations were carried out in this region to reduce any scatter in the stress-free load–displacement curve. 2.5. Fatigue testing Al 2024-T351 four point bend fatigue samples of size 50 210 2 mm were prepared. Samples were tested in an MTS servo-hydraulic test system at a maximum stress of 200 MPa and constant load ratio R of 0.1. All tests were carried out at constant amplitude at a frequency of 5 Hz under load control. After fatigue cycling, indentation testing was conducted around the scratch roots in the same way as for the unfatigued samples.
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3. Results 3.1. Residual strains from synchrotron X-ray diffraction Fig. 5 shows the three stress components obtained from the measured strains for sample 1. ryy, transverse to the scratch, was the largest stress component, with a peak tensile residual stress of 180 MPa. The magnitudes of rxx and rzz were similar to each other but about half of the magnitude of ryy. For all stress components behind the scratch tip (negative x-direction) showed compressive residual stress. Fig. 6 shows the ryy stress component obtained from the measured strains for sample 2 (one strain component only is shown for brevity). ryy was again the highest stress component, with a peak tensile residual stress just below the scratch root of 100 MPa. The region behind the scratch tip was under low compressive residual stress. rxx and rzz showed similar profiles with a peak stress around half that of ryy. The results show that tool B produced a stress field with a smaller peak stress than tool A.
Fig. 6. ryy stress profile for sample 2, a 125 lm deep scratch in 5091 using tool B.
Fig. 7. ryy stress profile for sample 3, a 100 lm scratch in Al 2024-T351.
Fig. 7 shows the ryy stress component obtained from the measured strains for sample 3 (one strain component only is shown for brevity). Sample 3 was a similar scratch to sample 1 but in Al 2024-T351 and with a slightly smaller depth of 100 lm. Although information in a relatively small area was obtained, it was clear that a very similar stress field was present as for sample 1. The peak in tensile stress was found to be slightly ahead of the scratch root, probably because in this case a larger gauge volume was used and the measurement at x = 0 exactly at the scribe root showed an average value including stress from behind the root. A peak tensile stress of 180 MPa was found at x = +60 lm for ryy, which was the highest of the stress components. rxx and rzz showed similar profiles with a peak stress around half that of ryy, and a peak tensile stress of 90–100 MPa was found for these components. 3.2. Nanoindentation load–displacement curve analysis
Fig. 5. Stress profile for sample 1, a 125 lm deep scratch in 5091 using tool A for (a) ryy, (b) rxx and (c) rzz.
3.2.1. Sample 1 (125 m deep scratch in AA 5091 using tool A) Fig. 8 shows nanoindentation load–displacement curves for different locations ahead of the scratch tip. From synchrotron X-ray diffraction it was found that there were tensile stresses of around 180 MPa present around the
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Fig. 8. Nanoindentation load–displacement curves for sample 1 for positions ahead of the scratch tip.
scratch root. As a result, in principle the loading curves for the near scratch root region should have shifted downwards, but it can be seen that a mixed trend of upward and downward movement of the loading curves was obtained. This was due to the hard plastically deformed region around the scratch root for tool A [22]. A convoluted response of increased hardness (loading curve moves up) and high tensile stresses (loading curve moves down) was obtained. Hence, analysis of the peak load is insufficient for the extraction of residual stresses in cases where there has been differential hardening, and another parameter must be used [19], as changes in hardness will
always themselves affect the nanoindentation response. The detailed method for separation of this hardness increase from the residual stresses will be discussed later, in Section 4. 3.2.2. Sample 2 (125 m deep scratch in AA 5091 using tool B) Fig. 9 shows nanoindentation load–displacement curves obtained for sample 2 ahead of the scratch tip. It can be seen that near the scratch root all loading curves were below the stress-free loading curve. This was a clear indication that there were tensile residual stresses present below
Fig. 9. Nanoindentation load–displacement curve for sample 2 for positions ahead of the scratch tip.
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Fig. 10. Nanoindentation load–displacement curve for sample 3 for positions ahead of the scratch tip.
the scratch root. From synchrotron X-ray diffraction it was seen that around 100 MPa tensile residual stresses were present around the root of this scratch. From the full width at half maximum (FWHM) analysis for this scratch little work hardening was seen around the scratch [22] and it was observed that material removal was by a cutting process (see also Fig. 2b). In the absence of any work hardening around the scratch root it was evident that the variation in the loading curves was due to residual stresses. Altogether, the load–displacement curves successfully detected the presence of tensile residual stresses around the scratch root for this sample, in comparison with tool A, in which tensile residual stresses were not detectable in the highly plastically deformed regions. 3.2.3. Sample 3 (100 m deep scratch using tool A) Fig. 10 shows load–displacement curves obtained for sample 3 for different locations ahead of the scratch tip. It can be seen that at all locations the loading curves were above or equivalent to the stress-free loading curve. This scratch was created in Al 2024-T351 using tool A, which produces severe work hardening around the scratch root, and the indentation load–displacement curve again showed a dominant response due to hardening. The synchrotron Xray diffraction results show that high tensile stresses of around 180 MPa were present around the scratch root. 4. Extraction of residual stresses from nanoindentation load–displacement curves 4.1. Methodology There are various methods which have been developed to extract residual stresses from load–displacement curves
[10–13,15,16,19], however, these methods were developed with finite element studies and/or for relatively hard materials and to-date no study has been carried out on engineering alloys like aluminium, which may show pile-up even at small indentation loads [25–27] and for which the behaviour of the pile-up changes with the type and magnitude of the residual stress state. A different approach taken by Dean et al. was to examine the effect of residual stress on indentation creep [14]. A particular problem with engineering alloys like Al 2024-T351 is texture, in which grains of different orientation exhibit anisotropy in mechanical properties. Furthermore, hardening of the material associated with the scratching process studied here produces a convoluted response of a hard plastically deformed material and elastic residual stress field that requires separation for accurate calculation of residual stresses using nanoindentation, and for this a comprehensive analytical model is required. Finite element simulations have shown that if a compressive residual stress is applied during nanoindentation then the elastically recovered portion of the indentation displacement increases, and more of the deformation is elastically recovered [21]. When a tensile residual stress is applied the opposite occurs. This can be expressed by the ratio hf/hmax, where hf is the final indentation depth and hmax the maximum depth during indentation. The ratio hf/hmax is equivalent to the ratio of plastic work to total work Wp/Wt. Thus a relationship can be derived between the residual stress (or normalized residual stress) and the ratio Wp/Wt. This can be expressed by the equation: W p =W t ¼ a
rr þb rY
ð1Þ
M.K. Khan et al. / Acta Materialia 59 (2011) 7508–7520
where a and b are constants that depend upon the material, which in this case were derived from finite element modelling of the indentation process [21,28]. The ratio of total area of contact including pile-up Ac0 and the contact area from the Oliver–Pharr model Ac [29] can be related to the ratio of plastic to total work of indentation Wp/Wt [19] as: Ac0 Wp ¼a þb Ac Wt
ð2Þ
rr Ac0 ¼a þb rY Ac
Table 3 Slope and intercept values for Al 2024-T351 and AA 5091. Material
Coefficient Relation
Al 2024-T351 a b AA 5091
a b
and thus, by manipulation, we can obtain
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Ac0 /Ac and rr/rY
Ac0 /Ac and Wp/Wt
Compression 0.16 Tension 0.30 Compression 1.29 Tension 1.28
Compression 13.62 Tension 20.39 Compression 13.76 Tension 19.54
Compression 0.21 Tension 0.57 Compression 1.413 Tension 1.410
Compression 12.09 Tension 27.36 Compression 12.54 Tension 25.9
ð3Þ
where rY is the yield stress of the material. Once Ac0 is known then residual stress rr can be obtained from the relation in Eq. (3). Fuller details of the approach are given in Khan et al. [21]. 4.2. Amendments due to plastic deformation around scratches Application of any method for residual stress extraction from load–displacement curves is complicated when there has been hardening of the material. For a scratch there will be a change in hardness (and therefore Wp/Wt) around the scratch root and it will vary with position. Any change in Wp/Wt will be a convoluted response of the elastic residual stresses and hardening by plastic deformation of the material. For a material with only limited hardening this does not pose a significant problem to extracting residual stresses from nanoindentation, but Al 2024 used here hardens significantly and therefore we have had to develop a model for how the hardening can be separated from the effects of residual stress. For a general system, with no prior knowledge of the load history or likely residual stress distribution, a unique solution would be unobtainable. Here we have information from the synchrotron X-ray data to provide some calibration. For scratches with work hardening around the root Eq. (1) can be rewritten as: Ac0 Wp ¼a þ hardening þ b ð4Þ Ac Wt Here a new correction is defined which separates the effect of work hardening from the effect of residual stresses on the ratio of area contact: Ac0 Wp ¼a þbþ/ ð5Þ Ac Wt where ( = a hardening) is a correction factor which deconvolves work hardening from the effect of residual stress on the area contact ratio. Choosing a value of / is a very challenging problem. The actual increase in hardness at any point around the scratch root cannot be separated from the effect of tensile residual stresses. Additionally, the increase in hardness varies with position around the scratch root.
To accommodate these problems in the current analysis it has been assumed that the increase in hardness is due only to plastic deformation and that the hardening is uniform in a 50 lm region around the scratch root. For tool A the peak increase in hardness was 30% over the bulk hardness values [22]. This increase in hardness decreased Wp/Wt by 0.02. For tensile residual stress a was 20.4 (Table 3), so the correction factor can be obtained as: / ¼ a hardening / ¼ 20:4 0:02 ¼ 0:41
ð6Þ
So for tool A, which generates high work hardening, the correction factor for peak hardness was 0.41, whilst for tool B, which did not generate significant work hardening around the scratch root, this factor was considered to be zero. From Table 3 Eq. (4) can be rewritten as: Ac0 Wp ¼ 20:4 þ 19:64 þ / Ac Wt
ð7Þ
for tensile residual stresses, and Eq. (6) becomes: Ac0 Wp ¼ 20:4 þ 19:24 ðfor tool AÞ Ac Wt Ac0 Wp ¼ 20:4 þ 19:64 ðfor tool BÞ Ac Wt
ð8Þ ð9Þ
For compressive residual stresses no correction factor was developed because the expected stress field was predominantly tensile. Hence, Eq. (5) remained the same for compressive stresses: Ac0 Wp ¼ 13:62 þ 13:76 ðfor tools A and BÞ Ac Wt
ð10Þ
and then residual stress can be extracted based on the true contact area from the equations below. For tensile residual stresses: Ac0 rr ¼ 1:17 109 1:28 ð11Þ Ac rY For compressive residual stresses: Ac0 rr ¼ 2:2 109 1:3 Ac rY
ð12Þ
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A similar exercise can be repeated for AA 5091 for which the values a and b are presented in Table 3. A correction factor of 0.5 was used for this material. This method does have limitations in practice. The set of equations discussed above is based on the response to equibiaxial residual stresses, but the residual stress field obtained around the scratch root is not equibiaxial. The hardness increase may also not be constant, as assumed. Finally, the equations were derived from finite element modelling results in which indenter tip bluntness effects were not considered. 4.3. Reproducibility of the response The sensitivity of the nanoindentation load–displacement curves and the extraction of the residual stresses based on these curves are dependent upon the response of the material. The aluminium plates used in this study show some crystallographic texture, leading to anisotropy from grain to grain. A particularly interesting finding is that the grain to grain scatter in the nanoindentation result is significantly lower in the presence of a residual stress. Whenever a region of low residual stress (<50 MPa) is indented in Al 2024-T351 distinct load–displacement curves are obtained due to the different response of different grains, as shown in Fig. 11. When indents are made in a region with high residual stresses (>50 MPa) the load–displacement curves show much reduced scatter. The consequence of this is that high scatter in the residual stress values extracted from this approach can be attributed partly to zero or low residual stress. The peak residual stresses around the scratches are of the order of +100– 200 MPa in a very small region near the root of the scratch, and very quickly start to decrease away from the root.
Hence, it is expected from this observation that the near root regions are ideal for extraction of residual stresses from the model, and far from the root higher scatter in the data will be obtained. 4.4. Results from scratched samples 4.4.1. Sample 1 Fig. 12a shows residual stresses obtained from load–displacement curves in sample 1 for a very small region ±30 lm in the x-direction, and Fig. 12b shows the residual stress field from synchrotron X-ray diffraction for ±75 lm in the x-direction. The results show tensile stresses near the scratch root reducing with distance. There is remarkably good agreement with the synchrotron X-ray results (Fig. 12b), particularly given the assumptions required to extract the residual stresses from the nanoindentation data. Note also that the nature of the stress field in this case fortuitously acts in our favour; the nanoindentation response is insensitive to any direction dependence in the residual stresses, but the X-ray diffraction analysis has demonstrated that the stress field is biaxial (if not equibiaxial) in the plane on which the nanoindentation tests were performed. Due to the incapability of the nanoindentation-based technique to probe low residual stress values, regions far from the scratch root showed poor agreement with the synchrotron X-ray values. The synchrotron X-ray diffraction results were an average over the gauge volume and the nanoindentation results were for very localized regions, so to compare the results of synchrotron X-ray diffraction the average value of residual stress up to +50 lm was calculated and was found to be +163 MPa. This compares with +180 MPa from synchrotron X-ray diffraction, assuming plane strain.
Fig. 11. Residual stress values obtained using nanoindentation for Al 2024-T351 for regions of +30, +160 and +100 MPa.
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Fig. 12. Residual stress values for sample 1 obtained from (a) nanoindentation and (b) synchrotron X-ray diffraction.
4.4.2. Sample 2 Fig. 13a shows the residual stress field obtained from nanoindentation for a region ±35 lm in the x-direction around the scratch root, and Fig. 13b shows the residual stress field from the synchrotron X-ray diffraction for ±75 lm in the x-direction. It can again be seen that there is at least fair agreement between the stress fields obtained from both techniques, especially near the scratch root region. The average value of the stress from the two methods up to +50 lm at y = 0 was calculated and was found to be +77 MPa for nanoindentation, compared with +100 MPa from synchrotron X-ray diffraction, which was again in very good agreement. 4.4.3. Sample 3 For this sample the average value of stress up to +50 lm in the x-direction was +210 MPa. A maximum stress of +180 MPa was obtained from synchrotron X-ray diffraction, and the values were again in good agreement with each other. Table 4 shows a comparison of residual stresses obtained by synchrotron X-ray diffraction and nanoinden-
tation for all three samples. It can be seen that the nanoindentation-extracted residual stress values were in close agreement with the synchrotron results. The strain accuracy for the individual synchrotron X-ray results was better than 30le, giving a stress accuracy of better than ±10 MPa. For nanoindentation there is always point to point scatter in the results, although this is lower when the residual stress is higher (see Section 4.3); certainly a scatter of at least ±20 MPa can be expected. 4.4.4. Other samples Table 5 summarizes the results obtained from the other samples that were prepared and measured. It is seen that there is little dependence of the average stress below the scratch tip on the depth of the scratch. Most notably, the blunter tool A shows significantly higher levels of residual stress. 4.4.5. Effect of fatigue loading In a previous work [22] we showed that fatigue loading of samples containing scratches did not produce any measurable change in the nanoindentation hardness profile
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Fig. 13. Residual stress values for sample 2 obtained from (a) nanoindentation and (b) synchrotron X-ray diffraction.
Table 4 Comparison of residual stress results from synchrotron X-ray diffraction and nanoindentation. Sample
1 2 3
Residual stress (MPa) Synchrotron X-ray
Nanoindentation
+180 +100 +180
+163 +77 +210
Results are an average over the first 50 lm from the scratch tip.
ahead of the scratch tip. The measured residual stresses ahead of the tip are significant, particularly in the case of the relatively blunt tool A, although there is no direct correlation in this case between tensile residual stress ahead of the notch and a lower fatigue life, because of the additional effects of the work hardening induced by the tool, which appears to act to retard fatigue crack initiation. Any redistribution or relaxation of the residual stresses after fatigue cycling will strongly depend upon the applied
Table 5 Average residual stress in the first 50 lm from the scratch root for scratches of 5 lm root radius. Sample
Material
Tool
Depth d (lm)
Root radius q (lm)
d/q
Residual stress (MPa)
Average stress (MPa)
4 5 6 7 8 9 10 11 12 13
Al 2024-T351 Al 2024-T351 Al 2024-T351 AA 5091 AA 5091 Al 2024-T351 Al 2024-T351 Al 2024-T351 AA 5091 AA 5091
A A A A A B B B B B
50 75 100 50 100 50 100 150 50 100
5 5 5 5 5 5 5 5 5 5
10 15 20 15 15 10 20 30 15 15
+154 +160 +210 +155 +205 +120 +71 +67 +75 +73
+172 +172 +172 +172 +172 +81 +81 +81 +81 +81
M.K. Khan et al. / Acta Materialia 59 (2011) 7508–7520 Table 6 Details of the samples tested in fatigue. Sample
14 15 16 17 18 19 20 21
Scratch depth (lm)
Tool
50 50 50 75 100 100 100 100
A A A A A A B B
Fatigue cycles
Residual stress (MPa) Before fatigue
After fatigue
250,000 500,000 1250,000 500,000 250,000 500,000 100,000 200,000
+155 +155 +155 +160 +215 +215 +71 +71
+163 +178 +153 +134 +194 +158 +82 +93
loading. Boyce et al. [1,2] measured the residual stress field around foreign object damage (FOD) using synchrotron Xray diffraction and found that the initial residual stress around the damage was highly tensile and was 40% of the yield stress. They concluded that the initial residual stress state can decay significantly in fatigue depending upon the applied stress. For Ti–6Al–4V they obtained very little relaxation for 0.35rY, but for a higher applied stress of 0.54rY the relaxation reached 50%. They observed that decay of the residual stress state only occurred during the first cycle and subsequent cycles showed very little further relaxation. Hence, some scratches were tested which had already been loaded in fatigue. 50 210 2 mm four point bend samples were prepared. The span lengths between the top and bottom rollers were 35 and 70 mm, respectively. Samples were tested in an MTS servo-hydraulic test system at a maximum stress of 200 MPa and constant load ratio R of 0.1. All tests were at constant amplitude at a frequency of 5 Hz. In total, eight samples were tested in four point bend fatigue without being taken to failure (to preserve the scratches for nanoindentation testing). Table 6 shows details of the samples and the results obtained. Again, the results can be assumed to have an accuracy no better than ±20 MPa. It can be seen that for both tools, in general, no relaxation of residual stress occurred after fatigue cycles, even for scratches of larger depths. This is perhaps surprising given the relatively high applied stress, but may be a consequence of the local hardening in the case of tool A, and the relatively low induced stresses for the other tools studied. 5. Conclusions 1. Residual stresses have been determined around scratches in aluminium alloys using synchrotron X-ray diffraction and nanoindentation. The scratches were produced using different tools that caused different amounts of hardening and plastic damage. Experiments were performed on Al 2024 and also on fine grained 5091, which has advantages for the diffraction experi-
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ments, and similar results were obtained for both materials. Depending on the scratch depth and root radius, peak residual stresses up to 200 MPa were measured. The nanoindentation response shows lower scatter in the presence of residual stress, which is attributed to the effects of the residual stress negating local grain to grain scatter in the stress-free response. 2. It is necessary to deconvolute the effects of hardening and residual stress on the indentation response, and a technique to account for this has been proposed and demonstrated to provide good correlation with results obtained from synchrotron X-ray diffraction. 3. One tool in particular (tool A) had an irregular profile and scratched the material by a ploughing rather than by a cutting action. This tool produced higher tensile stresses and hardening around the scratch root than a sharper tool. 4. No significant effect of fatigue loading was seen on the residual stresses near the scratch tip as measured using nanoindentation, and this is attributed to the hardened layer near the scratch tip. Acknowledgements The synchrotron X-ray experiments were performed at the European Synchrotron Radiation Facility, Grenoble, and due acknowledgement is made for the provision of beam time on ID31. M.E.F. is supported by a grant through The Open University from The Lloyd’s Register Educational Trust, an independent charity working to achieve advances in transportation, science, engineering and technology education, training and research worldwide for the benefit of all. References [1] Boyce BL, Chen X, Hutchinson JW, Ritchie RO. Mech Mater 2001;33:441. [2] Boyce BL, Chen X, Peters JO, Hutchinson JW, Ritchie RO. Mater Sci Eng 2003;A349:48. [3] Oakley SY, Nowell D. Int J Fatigue 2007;29:69. [4] Peters JO, Boyce BL, Chen X, McNaney JM, Hutchinson JW, Ritchie RO. Eng Fract Mech 2002;13:1425. [5] Peters JO, Roder O, Boyce BL, Thompson AW, Ritchie RO. Metall Mater Trans 2000;31A:1571. [6] Ruschau JJ, Nicholas T, Thompson SR. Int J Impact Eng 2001;25:233. [7] Thompson SR, Ruschau JJ, Nicholas T. Int J Fatigue 2001;23:405. [8] Withers PJ. In: Fitzpatrick ME, Lodini A, editors. Analysis of residual stress by diffraction using neutron and synchrotron radiation. London: Taylor and Francis; 2003. [9] Steuwer A, Edwards L, Pratihar S, Ganguly S, Peel M, Fitzpatrick ME, et al. Nucl Instrum Methods Phys Res B Beam Interact Mater Atoms 2006;246:217. [10] Carlsson S, Larsson P-L. Acta Mater 2001;49:2179. [11] Lee YH, Kwon D. Acta Mater 2004;52:1555. [12] Suresh S, Giannakopoulos AE. Acta Mater 1998;46:5755. [13] Xu Z-H, Li X. Acta Mater 2005;53:1913. [14] Dean J, Aldrich-Smith G, Clyne TW. Acta Mater 2011;59:2749. [15] Lee YH, Ji WJ, Kwon D. Exp Mech 2004;44:55. [16] Lee YH, Kwon D. Scripta Mater 2003;49:459.
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