A Method of Measuring Stored Energy Macroscopically Using Statistically Stored Dislocations in Commercial Purity Aluminum

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1 A Method of Measuring Stored Energy Macroscopically Using Statistically Stored Dislocations in Commercial Purity Aluminum MITRA TAHERI, HASSO WEILAND, and ANTHONY ROLLETT Stored energy from plastic deformation in rolled aluminum has been quantified with both macroscopic and microscopic methods. Differential scanning calorimetry (DSC) and Microhardness tests were used to determine a value for stored energy based on energy released during recrystallization and resistance to plastic flow from the accumulated dislocation content, respectively. For a value of stored energy based only on geometrically necessary dislocations, orientation imaging microscopy (OIM) within a scanning electron microscope (SEM) was used and supported by transmission electron microscopy (TEM) observation of subgrain cell structure. A value for the average misorientation angle that could be associated with the TEM was obtained from the OIM data. The values of stored energy derived from the various analyses were found to be similar with slight overestimation from the OIM technique. Thus, the difference between the macroscopic and microscopic methods represented the statistically stored dislocations. I. INTRODUCTION IN order to measure the mobility of grain boundaries during recrystallization, it is imperative to quantify accurately the driving force for migration in the functional relationship V M P. It has long since been understood that the driving force for migration of boundaries during the process of recrystallization is the stored energy of cold work. In recent publications, stored energy has been measured as a driving force for recrystallization (in units of stress) in two primary ways: either directly via differential scanning calorimetry (DSC) [1,2,3] or indirectly with orientation imaging microscopy (OIM) [4 9] where stored energy is derived from some measure of orientation gradients. Though both methods have proved useful, measurements of the geometrically necessary dislocation content do not take into account all dislocations [9,10] that might contribute to the overall driving pressure, and, specifically, cannot measure the statistically stored dislocation density because of limitations in accuracy of orientation measurement and spatial resolution inherently not possible by OIM. Calorimetry [11,12] detects an energy change upon reaction, enthalpy, and so includes all the free, or statistically stored, and geometrically necessary dislocations that are eliminated during annealing. Orientation imaging microscopy, however, does have the capability of determining subgrain size and orientation within the limitations of the technique. Typical spatial and angular resolutions in automated electron backscattered diffraction (EBSD) systems are 0.1 m and 0.5 deg, MITRA TAHERI, formerly with the Department of Materials Science and Engineering, Carnegie Mellon University, is Postdoctoral Fellow, United States Naval Research Laboratory. HASSO WEILAND, Scientist, is with the Alcoa Technical Center, Alcoa Center, PA ANTHONY ROLLETT, Professor, is with the Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA Contact mitra.taheri@ gmail.com This article is based on a presentation made in the symposium entitled Processing and Properties of Structural Materials, which occurred during the Fall TMS meeting in Chicago, Illinois, November 9 12, 2003, under the auspices of the Structural Materials Committee. respectively. [4,5] This article attempts to quantify the stored energy values not only with these two methods, but also with transmission electron microscopy (TEM) for a more precise characterization of subgrain size. Vicker s microhardness was used to check the accuracy of the calorimetry results. Alloy 1050 was chosen for this study specifically for its low solute content. This, coupled with the high stacking fault energy of aluminum, and a moderately high homologous temperature for cold working, promotes the formation of subgrains in a single-phase microstructure. These characteristics are nearly optimum for the comparison of methods undertaken here. II. EXPERIMENTAL METHODS A. Differential Scanning Calorimetry Measurements of the total stored energy (i.e., stored energy arising from all dislocations) were performed using a Perkin- Elmer DSC-7 calorimeter (Perkin-Elmer, Wellesley, MA). This particular model is a power-compensated differential scanning calorimeter, with a feedback loop to maintain equal sample and reference temperatures during a heating experiment. The difference between the powers supplied to the two independently heated samples is recorded as a function of the reference temperature. [11] In these particular experiments, uniform samples of 0.2 mm 3 were punched out of 52-mm (0.2-in.) thick cold-rolled slabs of A These samples were placed directly in aluminum sample holders and heated from 50 C to 500 C at rates of 40 C/min, 50 C/min, and 60 C/min. B. Microhardness (H v ) Measurements Hardness measurements were performed using a ZWICK* *ZWICK is a trademark of Zwick/Roell, Zwick USA, Kennesaw, GA. Vicker s microhardness indenter; a total of six hardness indents were performed at different locations along the rolled sheet METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 37A, JANUARY

2 Table I. Calculation/Measurement Vicker s Microhardness Parameters Value Average of diamond indent diameters 0.5(d 1 d 2 ) d 30 m Alpha (constant) 0.5 Taylor factor, M 3.0 Angle 130 deg Load g Resulting hardness MPa Estimated flow stress MPa Shear modulus at 300 K 26 GPa Calculated stored energy MPa sample for the average value of hardness, where F is the applied load and d is the average diameter of the diamond indent: An approximate flow stress, which is taken as H v /3, was then used in the following relationship to yield an overall value stored energy, E D, where G is the shear modulus of the aluminum, M is the Taylor factor, and the constant is approximated as 0.5. [9,10] Table I shows the parameters that were used in Eqs. [1] and [2]. C. Orientation Imaging Microscopy (SEM) In order to characterize the driving pressure microscopically, the average subgrain diameter was calculated using EBSD within a PHILIPS* XL-40 field emission gun [1] [2] *PHILIPS is a trademark of Philips Electronic Instruments, Mahwah, NJ. scanning electron microscope (FEG SEM); TSL** OIM soft **TSL is a trademark of EDAX/TSL, Draper, UT. ware was used to derive grain sizes. The method is based on that of Humphreys and co-workers, [4 7] where an average misorientation, u, and an average subgrain diameter, D, are used in the Read Shockley relationship for the grain boundary energy, E D : E D 130 deg 2F sin 2 H V E D (H v/3 M a) 2 G cg m a u u m ba1 ln a u u m bbd where m and m are the values of boundary energy and misorientation characteristic of high-angle boundaries. Previous calculations following the work of Murr [13] yielded a value of J/m 2, which was used in the preceding relationship. Specifically, the EBSD scan reveals orientation gradients. Areas located within a single grain or macroscopic orientation also contain results in a number of discontinuous boundary segments, and are discussed at length in this analysis with respect to their contribution to stored energy. d 2 D [3] Table II. TSL Software Diameter and Misorientation Input/Output TSL Parameter Value Scan step size m Binned pattern size 4X4 Angle cutoff value 15 deg Calculated subgrain diameter* m Calculated average misorientation angle deg *A detailed view of subgrain delineation within the TSL software is shown in Fig. 7. Within these areas of similar orientation are orientation gradients, equivalent to low-angle boundaries. To calculate an average misorientation along these low-angle boundaries (subgrain boundaries), the TSL software was adapted to calculate the average misorientation for only those grains entirely bounded by misorientations greater than 15 deg; the misorientation determination simply refers to the minimum crystallographic misorientation associated with a line segment separating two measurement points in a scan; however, since the orientations at both points A and B separated by the line segment are known, the misorientation, g, associated with a line segment can be calculated using Eq. [4], where application of appropriate symmetry to find the minimum physical rotation is implied: g g A g T B The TSL software was used to calculate the circle equivalent diameter from the area of each grain. Table II provides a summary of the input and output data using the TSL software. D. Transmission Electron Microscopy Because of the (known) limits on resolving subgrains using OIM, [4 6,17] TEM was used to supplement the SEM results. Though orientations were not measured with TEM, a more accurate subgrain size was obtained. Bright-field images taken with a JEOL* transmission electron micro- *JEOL is a trademark of Japan Electron Optics Ltd., Tokyo. scope showed both geometrically necessary and statistically stored dislocations; the GNDs formed subgrains that were readily identifiable, facilitating the analysis of subgrain sizes. The boundaries in the images of the subgrain structures were hand traced and imported into SCION IMAGE** [4] **SCION IMAGE is a trademark of Scion Corporation, Frederick, MD. ( where they were skeletonized and then analyzed to extract the average grain diameter (Figure 1). The Scion image subgrain determination is not fully automated. The user may calculate area under the analyze particles option by number of pixels within a hand-traced grain; this area is in units calibrated according to the scale bar set by the actual micrograph (e.g., 67 pixels per 500 nm). In this experiment, the average grain area was obtained from three different micrographs (192 grains total), and an average circle-equivalent diameter of m was obtained. 20 VOLUME 37A, JANUARY 2006 METALLURGICAL AND MATERIALS TRANSACTIONS A

3 (a) (b) (c) Fig. 1 (a) TEM image (b) traced by hand and then (c) skeletonized using SCION IMAGE. III. RESULTS Nonisothermal heating of samples in the DSC yielded exothermic peaks upon recrystallization from which the stored energy was calculated from the peak area. [1 3,11,12] Peak areas were calculated by finding the area under the curve, where the cutoff temperatures were located at the most nearly linear areas before and after the peaks along the baseline. Note that the enthalpies associated with recrystallization are small by comparison to typical phase transformations. All the peaks associated with recrystallization were close to 350 C, as shown in the example in Figure 2, and their areas in MilliJoules were calculated using the baseline correction described in Figure 3; their respective standard deviations (difference from mean) are given in Table III. To check that the peak was indeed associated with recrystallization, DSC disk samples were analyzed using EBSD at temperatures of 25 C, 275 C, and 350 C, respectively, to mimic the heating evolution of as-rolled AA1050, recovery, and recrystallization. The results supported the DSC curve well as shown subsequently by confirming a recrystallization temperature of 350 C. Figure 4. The values in Table III were then averaged and divided by 1.11 mm 3, the volume of each DSC sample, to obtain a stored energy of MPa, which agrees well with the value of MPa obtained from the microhardness tests. With respect to microscopy, Figure 5 shows that the subgrains are not easily outlined in an EBSD image using the naked eye, nor can they be traced because of the frequent occurrence of incomplete boundaries around some subgrains. The TEM image (Figure 6), however, shows that each subgrain is easily identified and its border traced because of the different contrast mechanism(s). The values obtained using OIM yielded larger subgrain values than those observed in the TEM, as might be expected. Using the algorithm provided in the TSL software, the subgrain diameter was calculated as m; this contrasts with the value of m obtained with the Scion Image software analysis of the TEM images. The small difference is most likely a consequence of the limited spatial resolution of the EBSD technique, as discussed previously. Though the TSL software subgrain determination is fully automated whereas the Scion Image subgrain determination requires operator judgment in the preliminary identification and Fig. 2 Calorimetry scan at 60 C/min. Exothermic recrystallization peak (denoted by the arrow) is seen at 358 C. Fig. 3 Peak area calculation (magnified view of peak identified with arrow in Fig. 2). The shadowed area under the peak is enclosed by the three thin straight lines and flanked by the upper and lower temperature bounds of the exothermic reaction. Table III. Peak Area Values Heating rate 40 C/min 50 C/min 60 C/min Peak area (mj) 3.37 ( 0.12) 3.03 ( 0.22) 3.35 ( 0.10) tracing of subgrains, both methods use grain area (calculated using the number of data points within a grain) to calculate circle-equivalent diameters. Note that the average misorientation angle was also determined by EBSD. The value of deg reported previously excludes high-angle METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 37A, JANUARY

4 Fig. 4 Inverse pole figure maps of AA1050 DSC samples (from left to right in the upper row: as-rolled, 275 C, 350 C) showing partial recrystallization only at the highest temperature; magnified portions of two images in the lower row show the reduction of speckle in the images with increased temperature, denoting recrystallized grains interspersed in the deformed matrix for the specimen annealed to 350 C. Fig. 5 OIM boundary rotation angle map, showing only 15 to 180 deg misorientations (black lines) surrounding networks of low angle grain boundaries (LAGBs) (gray lines). The LAGBs tend not to form complete subgrain shapes and the subgrain structure is diffuse. boundaries and corresponds to the average subgrain diameter value of m reported in Table II. The difference in subgrain size between the two methods is simply a consequence of the fact that all subgrain boundaries are distin- Fig. 6 TEM bright-field micrograph of cold-rolled AA1050. Subgrains vary in size from 500 m to 2 m. 22 VOLUME 37A, JANUARY 2006 METALLURGICAL AND MATERIALS TRANSACTIONS A

5 Table IV. Comparison of Stored Energy Values (MPa) Microhardness DSC OIM TEM guishable in the TEM, whereas EBSD can only resolve boundaries with misorientations greater than about 1 deg. The overall stored energy values, in MPa, using the methods described previously, are compared in Table IV. A. Sources and Calculation of Error 1. Microhardness An overall stored energy average value of MPa was calculated using microhardness, and the variability was assessed from the measured indent lengths, d 1 and d 2. The value of 30 m that was used as d was the average of six indents with individual average d values of 29.75, 30.00, 31.50, 30.30, 30.00, and m. 2. Differential scanning calorimetry Errors in the calorimetry experiments were dominated by the calculations of peak area and were easily estimated (Table III). The choice of the initial and final temperatures, which equal the cutoff points for the automated integral calculation, requires non-utomatic operator intervention within the Pyris software (as shown in Figures 3 and 4), leading to variability in the peak area standard deviation. The operator must choose the temperatures that lie at the most nearly linear areas preceding and following the recrystallization peak, as stated in Section II. The values of the peak area did not fluctuate greatly, however; therefore, the three peak area values extrapolated were averaged to obtain one final peak area, which in turn was divided by the constant sample volume to obtain a stored energy. Because the sample volume remained constant throughout the experiments, the stored energy is MPa, where the variability was calculated from the upper and lower bounds of the peak area values. 3. Electron backscattered diffraction A distribution of misorentation angles and grain diameters was calculated from EBSD measurements using the TSL software; the plots of the number fraction (for a m EBSD scan) of misorentation angles and grains of a given size are shown in Figure 7. Rotation angles 15 deg and higher were left out of the calculation of the distribution for the number fraction of boundaries with a given misorentation angle. The distributions reveal a large fraction of small grains with extremely low angle boundaries. The spread in misorientation angle is much smaller than that of the grain size, with practically no angles greater than 2.0 deg, and an average misorientation angle of deg. The misorientation distribution is skewed to small sizes with 65 pct of boundaries having a misorientation angle of deg or less, 27 pct between deg and 1.13 deg, but a maximum measured misorientation angle of deg. By contrast, the spread in diameter was substantial, even though the majority of grains had a diameter between 0.27 and 5.53 m; the average grain diameter measured was m, and 50 pct were between and m. (a) (b) Fig. 7 Number fraction of (a) misorientation angles and (b) grain diameters for an EBSD scan of an as-rolled AA1050 sheet. 4. Transmission electron microscopy The variability of subgrain size in the TEM measurements is similar to that of a standard lognormal distribution. Figure 8 shows the distribution of grain Areas for the 192 grains that contributed to an average subgrain area of m 2 ( m diameter). The plot shows large variations, with a maximum area of m 2 (1.30- m diameter) and a minimum of m 2 ( m diameter). The average value corresponds with the mode of the distribution, at approximately 1.50 m 2. IV. DISCUSSION The results for the stored energy determined microscopically are consistent in magnitude with those of Huang and Humphreys, [7] who used a similar approach for an AlSi alloy with a higher, 70 pct reduction and determined a stored energy value of 0.13 MPa based on the average subgrain diameter. The energy values derived from DSC and hardness are significantly higher, however, than those based on subgrain measurements using EBSD and TEM. If the density METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 37A, JANUARY

6 Fig. 8 Distribution of grain areas for 192 skeletonized grains from TEM (top) and normalized distribution (bottom). of statistically stored dislocations were significant, one might expect the scanning electron microscopy to yield a lower stored energy than the microhardness or DSC methods because scanning electron microscopy/ TEM can only measure the geometrically necessary dislocations (GNDs). When one considers the absence of alloying in AA1050 that promotes the formation of subgrains, however, the statistically stored ( free ) dislocation density should be minimal. Values of stored energy calculated from microscopy that were more than 60 pct lower than those calculated from DSC or hardness, however, suggest that a non-negligible density of statistical dislocations was indeed present, prompting further analysis. The validity of the various methods for calculating diameter coupled with the Read Shockley equation is discussed thoroughly in the literature [4 7] and is a well-accepted method of estimating (sub-) grain size and therefore stored energy. Concerning EBSD data, there are many factors that can affect the subgrain size, including angular resolution limits, grain tolerance angle within the TSL software, and imaging capabilities specific to each microscope. As discussed by Humphreys, et al., [4,5,6] the occurrence of a nonindexed pattern at a grain boundary can skew the data significantly due to these points being lost and therefore an entire grain being lost, especially if the grain size is small. In this study, the average confidence index for the scan used was approximately 0.8, which is well above the widely accepted minimum of 0.1. The grain size was obtained by averaging all grain diameters; with a maximum grain size well above the calculated average in the TEM, the data were considered to be sufficiently accurate. The grain size distribution shows few grains above the calculated average of m. This suggests that a reasonable estimate of the grain size and average misorientation can be obtained with EBSD, provided that the spatial resolution and (average) confidence index are high enough. Recent research [4] suggests that in an FEG SEM/EBSD system, spatial resolution is roughly 50 to 150 nm. In this study, spatial resolution limits appeared to be 100 nm. As previously mentioned, an important restriction of the EBSD measurement is the misorientation limit. The sample used in this study was cold rolled, therefore containing a high density of subgrain-forming dislocations, surrounded by high angle grain boundaries (HAGBs). The lower limit of misorientation measurement using OIM is widely stated as 1 deg, which means that the subgrain size will be overestimated (and the stored energy underestimated) if the actual misorientations are smaller. The TEM measurements yield a 5 pct smaller grain diameter. Though this could be attributed to the small area that is examined in a TEM foil as well as the processing that a sample must undergo in order to be investigated via TEM, resolution is much higher in such an instrument. In this particular study, three TEM images, with a total of only 192 grains, were taken from different sections of the rolled AA1050 sample and then analyzed using Scion Image to calculate an average subgrain diameter. It was assumed that TEM is a much more accurate way to measure subgrain size simply because spatial resolution is much greater than that using an SEM. However, the average misorientation used in the context of EBSD maps may be a slight overestimation for the boundaries in the TEM images since it is reasonable to suppose that one can resolve boundaries at smaller misorientations then is practicable in EBSD/SEM. As shown in Figure 5, however, the 0 15 deg boundaries were visible in an EBSD scan, and comprised more than 80 pct of the total boundaries in the map. The algorithm provided in the TSL software is intended for analysis of annealed grain structures, which means that each grain must be completely enclosed by boundaries of the specified minimum misorientation. Boundaries contained within a grain that terminate within the grain, as commonly occur for low-angle boundaries, are therefore not included in the grain size estimate (as they would be for a line-intercept method). This effect is seen in Figure 9, where higher angle boundaries, heavy lines, surround areas containing irregular networks of low-angle boundaries. V. CONCLUSIONS 1. The methods laid out in this article are all reasonable methods of calculating stored energies in AA1050, as the relationship between the resulting values of stored energy and the amount of dislocations present were as expected: measurements of stored energy arising from both statistically stored dislocations and geometrically necessary dislocations (macroscopic) yielded a value approximately 67 pct larger than those of stored energy comprising solely geometrically necessary dislocations (microscopic). 2. The main limitation of EBSD appears to be the 1 deg misorientation lower limit on misorientation detection, which in turn affects the measurement of an accurate subgrain 24 VOLUME 37A, JANUARY 2006 METALLURGICAL AND MATERIALS TRANSACTIONS A

7 size; data cannot be collected for subgrains with a misorientation smaller than this limit. This limitation accounts for the discrepancy in the stored energy measured by both the TEM and SEM methods, and could account for the 5 pct larger value found in the TEM measurements. Direct measurement of an average misorientation angle is needed for TEM experiments for better comparison with diameter measured via Scion Image. ACKNOWLEDGMENTS This work was supported by a grant from the Alcoa Technical Center and by the MRSEC program of the National Science Foundation under Award No. DMR The authors thank Paula Kolek, Alcoa, for many useful discussions. The transmission electron microscopy images were acquired with the generous help of Paul Bagethun. REFERENCES 1. E. Woldt and D. Juul Jensen: Metall. Mater. Trans A, 1995, vol. 26A, pp R.A. Vandermeer and D. Juul Jensen: Metall. Mater. Trans A, 1995, vol. 26A, pp R.A. Vandermeer, D. Juul Jensen, and E. Woldt: Metall. Mater. Trans A, 1997, vol. 28A, pp F.J. Humphreys: J. Microsc., 1999, vol. 195, Part 3, pp F.J. Humphreys and I. Brough: J. Microsc., 1999, vol. 195, Part 1, pp F.J. Humphreys and M. Ferry: Mater. Sci. Technol., 1997, vol. 13, pp Y. Huang and F.J. Humphreys: Acta Mater., 1999, vol. 47 (7), pp T. Furu, R. Orsund, and E. Nes: Acta Metall. Mater., 1995, vol 43 (6), pp F.J. Humphreys and M. Hatherly: Recrystallization and Related Annealing Phenomena, Pergamon Press, Oxford, UK, G.E. Dieter: Mechanical Metallurgy, McGraw-Hill, Boston, MA, M.E. Brown: Introduction to Thermal Analysis: Techniques and Applications, Kluwer, Dordrecht, The Netherlands, G. Hohne, W. Hemminger, and H.J. Flammersheim: Differential Scanning Calorimetry, Springer, L.E. Murr: Interfacial Phenomena in Metals and Alloys, Addison- Wesley, Reading, MA, S.X. Mao, M. Zhao, and Z.L. Wang: Appl. Phys. Lett., 2003, vol. 83 (5), pp A.A. Volinsky, J. Vella, I.S. Adhihetty, V. Sarihan, L. Mercado, B.H. Yeung, and W.W. Gerberich: Mater. Res. Soc. Symp., 2001, vol. 649, p. Q T.-Y. Zhang, W.H. Xu, and M.H. Zhao: Acta Mater., 2004, vol. 52, pp O.R. Field, H. Weiland, and P. Bagethun: in The Integration of Material, Process and Product Design, N. Zabaros, R. Becker, L. Lalli, and S. Gosh, eds., BalKema Publishers, Lisse, The Netherlands, 1999, pp METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 37A, JANUARY