In-Situ Mechanical Testing for Characterizing StrainLocalization During Deformation at Elevated Temperatures

J.L. Walley & R. Wheeler & M.D. Uchic & M.J. Mills

Received: 19 November 2010 /Accepted: 7 April 2011# Society for Experimental Mechanics 2011

Abstract An experimental methodology has been developedto characterize local strain heterogeneities in alloys via in-situscanning electron microscope (SEM) based mechanicaltesting. Quantitative measurements of local strains as afunction of grain orientation, morphology and neighborhoodare crucial for mechanistic understanding and validation ofcrystal plasticity models. This study focuses on the technicalchallenges associated with performing creep tests at elevatedtemperatures ≤700°C in an SEM. Samples of nickel-basedsuperalloy Rene 104 were used for this study, but thetechnique is applicable to testing of any metal samples atelevated temperature. Electron beam lithography wasemployed to produce a suitable surface speckle pattern ofhafnium oxide to facilitate full field displacement measure-ments using a commercial software package. The specklepattern proved to have good thermal stability and providedexcellent contrast for image acquisition using secondary

electron imaging at elevated temperature. The specklepattern and microscope magnification were optimized toobtain the resolution necessary to discern strain localizationswithin grain interiors and along grain boundaries. Minimumstrain resolution due to SEM image distortions wasdetermined prior to tensile testing, and image integrationmethods were utilized to minimize imaging artifacts.Limitations due to the present specimen heating methodand potential solutions to these limitations are alsoaddressed.

Keywords Elevated temperature tension experiment .

Scanning electron microscopy . 2D digital imagecorrelation . Speckle pattern development .

Nickel-based superalloy

Introduction

One of the issues limiting the development of physics-based deformation models of polycrystalline materials isthe lack of experimental validation data that characterizeslocal strain variations at the grain size scale for relevantusage temperatures and loading conditions. Tests on singlecrystal samples can provide detailed information on the‘single grain’ mechanical behavior as a function ofcrystallographic orientation, but these methods often re-quire specialized sample preparation techniques and do notprovide direct information about the processes that allowfor strain transmission across grain boundaries [1, 2].Traditional tensile and creep tests on polycrystallinematerials characterize average properties but providelimited insight into local deformation behavior. Empiricalevidence describing the temporal development of localplastic flow is greatly desired. Therefore, novel experimen-

J.L. Walley (*) :M.J. MillsThe Ohio State University,477 Watts Hall, 2041 College Rd.,Columbus, OH 43210, USAe-mail: walley.7@osu.edu

M.J. Millse-mail: mills.108@osu.edu

R. WheelerUES, Inc.,4401 North Dayton-Xenia Rd.,Dayton, OH 45432, USAe-mail: Robert.Wheeler@wpafb.af.mil

M.D. UchicAir Force Research Laboratory, Materials & ManufacturingDirectorate, AFRL/RXLM, Wright Patterson AFB,Dayton, OH 45433, USAe-mail: Michael.Uchic@wpafb.af.mil

Experimental MechanicsDOI 10.1007/s11340-011-9499-7

tal techniques are being developed to characterize the grainand sub-grain scale deformation fields produced duringdeformation of polycrystalline materials.

Digital image correlation (DIC) methods that utilize opticalimaging are readily available for measuring macro-scaleplaner 2-D, and arbitrary 3-D, motion and deformation [3].DIC methods were proposed and developed in the early 80’s,and have since become widely accepted methods ofmeasuring surface displacements [3]. DIC uses a set ofalgorithms to correlate local displacements of a samplesurface between a reference image and subsequent imagesthat are collected during sample deformation [3, 4].Correlation occurs by dividing images into subsets andapplying a displacement vector to the deformed subset tominimize a normalized cross-correlation criterion (normal-ized sum of differences is an example) between thedeformed subset and the reference subset. Minimizing anormalized cross-correlation criterion allows for correctcorrespondence between images with slight variations ingray-scale intensity values, i.e. changes in optical lighting orinadequate dissipation of electrons in scanning electronmicroscopy (SEM) imaging. Often a speckle pattern isgenerated on the sample surface to provide a unique randompattern to optimize subset correlation. Optical imagingtechniques are applicable for characterizing sub-graindeformation heterogeneities in single crystal materialsand materials with very large grain sizes [5]. However,optical imaging methods can not provide the neededresolution to discern local displacements in fine grainedmaterials such as nickel-based superalloys. SEM imaginghas superior resolution as compared to optical microscopy,and techniques have been developed to use SEM tocharacterize strain heterogeneities on the 50–1000 μmgrain size scale [4, 6–10]. Work by Sutton and coworkershave examined many issues related to in-situ SEM-basedDIC analysis using a random speckle pattern [7, 8]. Theirstudies have shown that several SEM image distortionsmust be taken into consideration when evaluating smallamounts of strain accumulation, particularly signal noiseand random linear distortions due to beam rastering.Others have utilized a regular repeating grid pattern tocharacterize both room temperature deformation, by in-situ imaging [6], and elevated temperature deformation, byex-situ imaging [4, 9, 10]. Collectively, these studies haveshown that the primary limitations for developing an in-situ SEM-based elevated temperature strain mappingtechnique include developing a stable speckle pattern thatis of sufficient detail to achieve the desired resolutionwhile the sample is at temperature, developing techniquesto maintain specimen thermal stability, and limiting creepof the specimen while the images are being acquired.

This paper highlights the development of an in-situ,elevated-temperature tensile technique that operates in-

side of an SEM to characterize the local deformationbehavior in wrought nickel-based superalloys. Althoughthe methodology has been optimized for this one materialclass, it is generally applicable to testing a variety ofmaterials at elevated temperature. This work builds on theroom temperature experiments conducted by Sutton,while exploring the added complexities of conductingin-situ work at elevated temperature. The methodologydescribed herein includes a protocol for characterizing thegrain microstructure of samples prior to testing andcorrelating these features to the DIC measurements, thedevelopment of a high-resolution speckle patterningtechnique suitable for elevated temperature DIC measure-ments, identification and mitigation of issues related toboth image acquisition and stable uniform heating of thesample during testing, and demonstration of the methodvia creep at 700°C.

Experimental Procedures

Material

The material examined in this study is γ’-strengthenednickel-base superalloy Rene 104 (15wt% Cr,18.2% Co,3.8% Mo, 1.9% W, 1.4% Nb, 3.5% Al, 3.5% Ti, 2.7% Ta,0.03% C, 0.03% B, 0.05% Zr, balance Ni) [11]. Thematerial was heat treated above the γ’ solvus temperatureand aged to produce a microstructure consisting ofrelatively planar grain boundaries with an average grainsize of 32±4 μm and a bimodal γ’ distribution.

Sample Preparation

Flat dog-bone samples were prepared from the bulkusing electrical discharge machining. The dimensions ofthe gage section of the sample were as follows: a gagelength of 1.78 cm, and a rectangular cross-sectionnominally 0.31 cm × 0.081 cm. Prior to elevatedtemperature testing, samples were prepared for SEMimaging using conventional polishing techniques on anAllied Multiprep system, culminating with a finalvibratory polish using 0.02 μm colloidal silica. Afterpolishing, four microhardness indents were placed nearthe center of the gage section to define the four cornersof a 0.01 cm2 square. These hardness indents were used todefine the location where the speckle pattern wassubsequently deposited on the surface, and were alsouseful in coarse registration of microstructural images andelectron backscatter diffraction (EBSD) data with the localdisplacement maps. Next, the samples were characterizedvia EBSD mapping and a speckle pattern was depositedusing parameters described below. Once patterned, two

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type K thermocouples were spot welded onto the surfacealong the gage length on opposite sides of the patternedarea, as shown in Fig. 1.

Characterization Techniques

Electron backscatter diffraction (EBSD) mapping was usedto characterize both the grain size and grain orientation withrespect to the tensile axis. Mapping was conducted on anFEI ESEM XL-30 SEM outfitted with an EDAX TSLorientation image mapping system. Grains were defined asregions containing at least 5 contiguous data points, withless than 5° misorientation between adjacent data points.Twin boundaries of Σ3 orientation were not included ingrain size calculations.

Speckle Patterning

Correlated Solutions Inc. VIC-2D digital image correlationsoftware was used to analyze local deformation fields. TheDIC software produces optimum accuracy when theminimum speckle size is at least three pixels, and a greaternumber of speckles per grain produces a more detailedcharacterization of the strain distribution within each grain[3, 12]. With an average grain size of 32±4 μm, it wasdesired to make the subset size less than half the averagelinear grain size, ~10 μm. Image resolution was set at2048×1768. For an image to incorporate 15 grains acrossthe longest dimension the image, a resolution of 6.8 pixel/μmis required. Based on these resolution requirements and theminimum speckle size criteria mentioned above, a randompattern was generated using square speckles with a size rangebetween 0.45 and 0.7 μm. In addition to the random specklepattern, a regular repeating grid with node spacing of 10 μmwas added to allow for traditional grain boundary sliding

measurements [13]. The pattern also incorporated a set ofalpha-numeric markers every 200 μm in order to helpfacilitate locating particular regions within the 0.01 cm2

analysis area after testing. Electron beam (e-beam)lithography was used to fabricate the desired pattern. Thistechnique uses a focused scanning e-beam to locally exposephoto-resist on the sample surface, which results in a highlyrepeatable point-by-point constructed pattern [14]. Onceexposed, the resist is developed to remove the exposedresist and metal or dielectric is deposited onto the samplesurface. After deposition the developed resist is removedto reveal the pattern. Following standard clean roomprocedures, 950 k A4 PMMA resist was spin coated ontothe sample surface. Once coated, the sample was exposed at50 keV with an 800 uC/cm2 dose using a Vistec EBPG5000 e-beam lithography system. The resist was developedin a 1:3 mixture of methyl isobutyl ketone and isopropylalcohol. As previously mentioned, the location of thespeckle pattern on the sample surface was determined bythe microhardness indents placed on the surface beforeEBSD analysis, as shown in Fig. 2. A Denton 502Aevaporator was utilized to deposit a 100 nm thick layer ofhafnium oxide onto the surface. Once coated, the developedresist was lifted off the sample using an acetone bath,leaving the oxide speckles on the sample surface. Asecondary electron image of the speckle pattern is shownin Fig. 3.

Experimental Test Set-Up

An Ernest Fullam® tensile stage was used to perform thein-situ mechanical test. The stage can apply loads up to4448 N and provide measurements of both load andcrosshead displacement. The data acquisition systemprovided with the test frame was used to acquire load anddisplacement data every second. A molybdenum resistanceheater capable of heating to temperatures up to 1200°C wasused to heat the sample. The resistance heater is fastened tothe tensile frame using six alignment screws, and thesescrews allow the heater to be carefully positioned in directcontact with the backside of the specimen surface withoutimparting significant out-of-plane loads.

In order to characterize the performance of the test frameat elevated temperatures, a sample was subjected to variousthermal cycles to determine limitations of both the imagingsystem and the tensile stage. Elevated temperature imageacquisition capabilities of the SEM were assessed byimaging a specimen, which was incrementally heated to700°C at 100°C intervals. At each interval, the sample washeld at temperature for 3–5 min before backscatter (BSE)and secondary (SE) electron images were acquired. Thissame sample was also subjected to loading and unloading atdifferent rates from 0.01–0.003 mm/s (5.6×10−4–1.7×

Fig. 1 Schematic diagram showing the locations of the speckled area,two type K thermocouples located on the sample surface, and the sizeand placement of the resistance specimen heater with respect to thesample. The loading direction (F) is along the horizontal axis

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10−4 s−1) to determine the effect of strain rate on thethermal stability of the sample.

Elevated temperature testing was conducted in astepwise fashion in an attempt to minimize creep whileimaging. The sample was loaded in displacement control,at 0.003 mm/s, to 337 MPa and subsequently held inload control while a pair of images were acquired. Theseimages were used as the reference images for strainanalysis. The sample was further loaded in displacementcontrol, at the same rate, to 1100 MPa and held in loadcontrol for 35 min to allow for creep deformation. Notethat no images were acquired during creep loading. Afterthe prescribed period of time, the sample was unloadedin displacement control to 80% of peak load, and heldfor 5 min. During this second hold, secondary electronimages were acquired for DIC analysis. The sample wasreloaded to 1100 MPa and the sequence was repeated forthe duration of the experiment.

SEM operating parameters were as follows: 15 kVaccelerating voltage, image size of 2048×1768 pixels,and one of two imaging conditions: (a) a single scan at8 microsecond pixel dwell time, or (b) a pixel dwelltime of 1 microsecond, integrating eight frames. Bothimaging conditions correspond to a total image acqui-sition time of 32 seconds. Images were taken at 1000×magnification corresponding to an approximate pixelsize of 150 nm.

Correlated Solutions VIC-2D software was selected forconducting digital image correlation to determine localdisplacement and strain distributions. Analysis was con-ducted using 60×60 pixel (9×9 μm) subset size, and aspacing between subset centers of 3 pixels. No distortioncorrections were conducted for strain analysis. Lagrangianstrains were calculated using the VIC-2D post processingtab, using a 15 size decay filter. The subset size and spacingcan have a dramatic effect on the magnitude and distribu-tion of the calculated strain data; these effects were notaddressed in this paper, but should be optimized for theparticular imaging set-up.

Results

Microstructural Characterization

Distortions in the EBSD images did not allow for directoverlay of the data with BSE and SE images taken priorcreep testing. The use of a commercial SEM calibrationstandard showed that the lack of one-to-one correlationbetween the BSE/SE images and EBSD maps was causedby distortions in the EBSD data. For qualitative purposes,distortions in EBSD maps were corrected with imageprocessing software. First, the centers for the hardnessindents were used for a rough correlation, and thenparticular grain boundaries with high BSE contrast wereused to further match EBSD data with BSE images towithin pixel resolution. This qualitative alignment allows

Fig. 2 Inverse pole figure mapof the Rene 104 microstructureshowing the location of themicrohardness indents thatdefine the speckle patternregion. Colors represent grainorientation normal to the samplesurface as defined by thestereographic triangle inset inthe lower right corner of theimage

Fig. 3 SEM secondary electron image of the hafnium oxide specklepattern created by e-beam lithography. Also shown is the grid patternfor grain boundary sliding measurements and an alpha-numericmarker

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for direct overlay of the displacement and strain measure-ments with the EBSD maps.

Speckle Pattern

For both BSE and SE images, the hafnium oxidespeckles appear bright as compared to the nickel surface,as shown in the secondary electron image in Fig. 3.Therefore, care was taken during image acquisition tooptimize image brightness and contrast to insure that thegrey level distribution was not saturated due to thepresence of very bright speckles on the dark background.This improved the quality of the image correlation as theVIC-2D correlation works best when the speckle patternproduces a random grayscale pattern at the subset scale.For this work, the subset area was on the order of 81 μm2,which encompasses several speckles in each subset.

Experimental Limitations

High temperature imaging

In order to determine the best imaging conditions for hightemperature DIC testing, a series of incremental heatingexperiments were performed at 100°C intervals up to amaximum temperature of 750°C. One of the findings fromthese experiments was that BSE imaging was only possibleto about 300°C, above which thermal radiation significantlydegraded the image; this observation is consistent withother studies [15, 16]. By comparison, secondary electronimages showed only minimal degradation in quality up to750°C. For prolonged exposure to temperatures at andabove 700°C, white lines appeared in the SE images thatdegraded the quality of the image. These imaging artifactswere removed by placing an aluminum foil heat shieldbetween the SE detector and the specimen heater. This heatshield limited radiative heat transfer to the secondaryelectron detector, enabling the use of the secondary electronimaging for these elevated temperature experiments.

Images during creep testing were acquired at regulartime intervals. The load was reduced to 80% of the testingcondition (880 MPa for 1100 MPa testing condition). Theseunloading intervals were dependent on the expected creeprate as extrapolated from traditional testing, i.e. shorterintervals for faster creep rates and longer intervals forslower creep rates. Intervals were determined based on thedesire for enough strain accumulation to occur that eachinterval provided unique strain data. A valuable timeinterval was determined by estimating the required lengthof time needed such that the average strain would increaseby more than three times the noise limits. For thisexperiment, a 20% drop in applied load arrested creepdeformation during imaging, for slow strain rate experi-

ments this unloading might not be necessary and for higherstrain rates the unloading during imaging would need tobe more dramatic and should be determined for eachmaterial type. Assuming uniform deformation, the max-imum creep rate above which a stress drop would berequired can be calculated as a function of imagingparameters and noise in the calculated strain data,discussed below. For this experimental set-up that wouldbe approximately 4×10−5s−1, but since deformation is notuniform and can vary dramatically it would be expected thatthis is not a conservative estimate.

Specimen thermal stability

During the initial assessment of the test frame performance,loading and unloading of a sample with two weldedthermocouples showed that displacement rates of 0.01 and0.005 mm/s produced substantial and repeatable fluctua-tions in the sample temperature. The source of thesefluctuations is tentatively linked to changes in the totalcontact surface area of the backside of the specimen and theresistance heater during testing. When the displacement ratewas reduced to 0.003 mm/s, these thermal fluctuations wereeliminated, presumably because the response time for thethermal controller and substrate heater is commensuratewith the variation in contact that may occur during the testat lower strain rate. Since a goal of the present investigationis to study time-dependent deformation processes, testing atslower strain rates is not a severe limitation.

The two thermocouples on the sample surface allowedfor the measurement of a possible thermal gradient alongthe gage length due to improper alignment of the resistanceheater and the specimen surface. The temperatureacquisition equipment was calibrated to within ±2°C.Therefore, the two thermocouples on the sample surfaceshould read the same value, within ±4°C, if the specimenheater is properly aligned relative to the sample surface.A sample was heated to 700°C prior to tensile testing tovalidate that the heater was evenly contacting thespecimen surface. In an iterative fashion, the specimenheater was tilted until the two thermocouples read within7°C of each other.

In-Situ Strain Mapping

VIC-2D calibration and distortion corrections

As previously mentioned in the introduction, the study bySutton and coworkers showed that SEM images containseveral linear distortions that can limit the resolution ofimage correlation displacement measurements [7, 8]. Aconclusion from that study was that conducting integratedimage scans eliminates the linear distortions seen when

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correlating single scan images taken at 5000× magnifica-tion, while at 200× magnification these linear distortionswere not observed. In an effort to characterize theperformance of the SEM used in our study, at the particularmagnification of interest (1000×), pairs of images of thesame region of the sample were first acquired at roomtemperature with zero load without moving the sampleusing both a single scan with an 8 microsecond dwell timeand an eight image integrated scan at 1 microsecond dwelltime. Analysis of these images using VIC-2D DIC providesa base-line estimation of the image distortions caused bythe SEM optics. It can be seen in Fig. 4(a) and (b) that nolinear distortions in the displacement noise were visiblewith either imaging condition. A histogram of the noiseintensity data, for both imaging condition, indicates that theu and v displacement noise fields have a Gaussian intensitydistribution with standard deviations presented in Table 1. Itcan be seen from Table 1 and Fig. 4 data bars that theintegrated imaging conditions produced a smaller standarddeviation in the intensity of the noise distributions. Byintegrating eight images using the same frame time, thestandard deviation of the random noise in both the u and vdisplacement measurements decreased by 25–50%, andtherefore integrated scans were used for the remainder ofthis study. Fourier transform of the data indicates that thehorizontal (u) and vertical (v) displacement noise are alsospatially random, with no linear image distortions visible inFig. 4(b). The Fourier transform of the calculated strainfields indicates that the strain noise is not completelyspatially random, but has a preferred orientation withrespect to the straining direction. The noise is ellipticalwith the long axis perpendicular to the direction of thestrain calculated. Note that for all images the loadingdirection is along the horizontal axis.

Following the room temperature measurements, a similarexperiment was performed at 700°C, the sample was pre-loaded to a stress well below the proportional limit(337 MPa) and pairs of integrated images were acquired.Since the pair of images was acquired at the same stresslevel, the mean strain value should be zero. The horizontaland vertical displacement fields show similar characteristicsto the room temperature measurements, having a Gaussianintensity distribution and a random spatial distribution, withstandard deviation in the intensity presented in Table 1. Thestandard deviation (noise) in the displacement data at700°C is larger than the data collected at roomtemperature, as shown in Table 1. Fourier transforms ofthe strain data indicate that the spatial distributions of thestrains are not completely random. There is a slight,preferred orientation of the maxima and minima of thedata. Instead of being circular in nature, the extrema areslightly elliptical with the major axis of the ellipse alignedperpendicular to the strain measurement direction: vertical

for exx, forty five degrees from horizontal for exy, andvertical for eyy as seen in Fig. 5. This is consistent with thestrain data calculated at room temperature, and indicatesthat the method of calculating strain causes somepreferential alignment of the noise measurements.

Preliminary elevated temperature data

Bulk stress–strain data was calculated from the crossheaddisplacement measurements and is presented in Fig. 6, itcan be seen that at the first load drop at which images wereacquired the sample had experienced 1.45±0.02% strain.When the elastic portion of the strain below the DICpreload stress is subtracted from this value, it indicates thatthe average strain measured by DIC measurements wouldbe 1.28±0.02%.

Figure 7(b) shows the results of digital image correlation(DIC) analysis between the image taken at the preloadstress (337 MPa) and an image taken after a 35 min hold at1100 MPa. The average tensile strain from the DICmeasurements was 1.48±0.07%, which is in good agree-ment with the bulk data calculated from crossheaddisplacement, but may indicate that a larger area might beneeded for better correlation. The maps in Fig. 7(b–d),along with the inverse pole figure map in Fig. 7(a), provideinsight into the propensity for strain localization/inhomo-geneity at elevated temperature. The magnitude of the highand low exx and eyy strain measurements shown respec-tively in Fig. 7(b) and (d) are far greater than the standarddeviation of the random noise calculated for theses imagingconditions, as discussed above. Regions of high exx strainare often associated with grain boundaries, as shown inFig. 7(b). These regions often correlate with cracks thatform after even larger deformations, as discussed below.Regions of highly negative vertical strain, eyy, routinelycorrelate to regions near those containing highly positivehorizontal strain, exx, which is consistent with the need tomaintain constant volume during plastic deformation. Theexy data [Fig. 7(c)] indicates that regions of highlylocalized shear, either positive or negative, tend tocorrelate with grain boundaries in this sample. In general,strain inhomogeneity appears on a scale similar to thegrain size of the material, which is consistent with theanisotropic deformation response of superalloys as afunction of crystal orientation [17].

A magnified region of the deformed sample (from thetop left corner of the microstructure presented in Fig. 7) isshown in Fig. 8. Several small cracks have been identifiedwith arrows in Fig. 8(a). Several of these cracks and slipsteps correlate with high angle grain boundary locations,which are superimposed from the EBSD map presented inFig. 8(b). The high angle grain boundary at the upper righthand corner of this region has cracked. Correlating with

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Fig. 4 horizontal (U) and vertical (V) displacement fields of a sample imaged at room temperature at 1000× magnification for (a) 8 μs dwell timewith one scan and (b) 1 μs dwell time with eight integrated scans. The exx eyy fields for 1 μs dwell (c) show a slightly nonrandom distribution

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Fig. 8(c), which displays the strain localizations measuredby the DIC software, indicates that the crack in this grainboundary is due to a localization of tensile strain, exx. Thereis also large principle strain in the grain near the center ofthe field of view in Fig. 8(c), it can be seen that thisdeformation is associated with the twins in the grain. Largeshear strains are also observed in the region presented inFig. 8(b). The Schmid factors for <110> {111} and <112>{111} slip systems are shown in Fig. 8(e) and (f),respectively. Operation of both of these slip systems havebeen previously reported [17, 18], and are expected to bothbe active when deformation occurs at this strain rate. It isinteresting that the influence of the annealing twinboundary in the central grain is manifested in the shearstrain pattern [Fig. 8(b)]. In general, there is not a clearcorrelation between Schmid factors and plastic strainlocalizations based on these initial experiments.

Discussion

The present study demonstrates the feasibility of conduct-ing in-situ SEM deformation studies in temperature andstrain rate regimes relevant to high temperature structuralmaterials. The correlation between localized deformationand microstructural features was assessed by correlatingEBSD analysis of grain shape and orientation with DICdeformation maps. Yet to be resolved technical issuesrelated to the application of this technique are as follows:distortions in the EBSD data, and intensity and spatialresolution limitations of the DIC analysis due to both thespeckle pattern and noise associated with elevated temper-ature testing. In this section we will discuss in detail theseissues and how they can be mitigated in future work.

The major limitation for implementing the datacollected into computational models is the EBSD spatialdistortions. The current method relies on manualmanipulation of the image maps created by EBSDsoftware and does not provide an adequate method for

transforming the raw data into a useful form. A methodto remove distortion in the raw data is needed beforecorrelation of crystallographic orientation with DIC.This issue can be resolved through careful applicationof the following techniques. First, care should be takenwhen aligning the specimen in the SEM chamber toensure the sample surface is first truly perpendicular tothe electron column before tilting to precisely for EBSDanalysis. Verification of the tilting angle can be doneusing the crystallographic relationships of a singlecrystal silicon sample placed on the sample surface[19]. Further, the scans should be conducted at sufficientmagnification to eliminate distortion due to excessivebeam shifting. Finally, the scans must be stitched togetherto provide a continuous data set for the entire region ofinterest, this can be done using an open source Matlabcode such as the AnyStitch program [20].

Intensity resolution and spatial resolution are the twoprimary issues associated with resolving strain. Intensityresolution is primarily a function of imaging specifica-tions [8]. The intensity resolution is limited by theability of DIC to recognize the shift of a speckle by apixel width, therefore the relative focus of each speckleis important. The FEI microscope used in this studyperforms image integration by creating a single imagewhere the final pixel intensity is the average intensity ateach pixel for the set of collected images. If thespecimen drifts during image collection, the speckleedges blur substantially, leading to significant degrada-tion of the image. Therefore, while the image integra-tion technique can minimize signal noise, the blurringof the speckle edges often limits the ultimate resolutionthat can be practically achieved using DIC. Onepotential method for maximizing the signal-to-noiseratio while minimizing the effects of specimen drift isto employ a pattern matching algorithm to align thesequence of images, thus eliminating systematic andrandom drift effects prior to image integration.

Spatial resolution of the full-field data is dependent onthe image subset step size used for analysis, smaller stepsizes will yield higher spatial resolution. For a givenspeckle pattern and image resolution there is a minimumstep size and in-turn maximum spatial resolution. Using astep size smaller than this minimum size will yieldinadequate correlation as each subset will not contain aunique speckle distribution, and will therefore not containthe requisite random grayscale. Thus, for a given imageresolution, a higher speckle density will allow for a smallerstep size. For a given image resolution there exists amaximum speckle density above which Moiré fringesoccurs. This Moiré effect obscures unique speckles andcauses a breakdown in the ability to conduct DIC. If the

Table 1 List of standard deviations for the noise in the displacementand strain measurements for single and integrated images taken atroom temperature and 700°C

Standard deviation

u v exx eyy exy(pixel) (pixel) (%) (%) (%)

single scan 20°C 0.053 0.044 0.142 0.121 0.086

integrated scan 20°C 0.028 0.030 0.073 0.075 0.054

integrated scan 700°C 0.046 0.069 0.079 0.157 0.080

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region of interest is analyzed using a single image, there isa trade-off between having the necessary spatial resolutionto provide details on local displacement events and havingthe necessary field of view to observe multiple displace-ment events. A method for overcoming this paradox is toacquire overlapping images at high magnification with highspeckle density to create an image montage. Such amontage will eliminate the paradox as long as imageaberrations are minimized or corrected. Merging multipleimage sets to acquire a larger field of view has been done

with optical DIC techniques and would be applicable toSEM based imaging techniques [5].

The shape of each speckle is also a factor for spatialresolution of DIC techniques. Previous work conductedby Biery et al. concluded that the orientation of squarespeckles effects vertical resolution of strain mappingtechnique as the rastering method of SEM imageformation is continuous in the horizontal (or scan)direction and discrete in the vertical direction [6]. Bieryobserved that when the edges of square speckles arealigned with the beam scan direction the vertical resolu-tion was limited by the number of scan lines. Rotating thesquare pixels an arbitrary amount so that speckle edgeswere not parallel to the scan direction increased thevertical resolution. Round speckles would eliminate thealignment issue associated with square speckles. Unfortu-nately, e-beam lithography patterning using a 25 nm stepsize on a square grid can not accommodate roundspeckles. The data collected in this study show a largerstandard deviation in the eyy data than the exx and exydata. The limited spatial resolution in the y-directionmight be caused by speckle alignment. The e-beamlithography technique provides the valuable ability totailor the speckle shape and density. New patterns areunder development to gain a better understanding of howthese variables can be tailored to optimize the DICdisplacement calculations.

The technical issues addressed above are independent oftesting temperature. The additional complexity of operating atelevated temperatures increases the standard deviation in thedisplacements by almost 2 times as compared with thosecalculated from room temperature images. This could indicatethat this technique has limited application for measuring verysmall strains (e.g. for elastic modulus measurements), butshould not limit the ability to use this technique to observe

Fig. 6 Bulk stress–strain data showing the preload stress and stressdrop during creep when images for DIC were acquired

Fig. 5 Noise in the strain measurements as calculated from a pair of images (each with 1 μs dwell, eight image integration) at 700°C and337 MPa. The loading direction is horizontal

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trends between regions of higher deformation and themicrostructural features controlling them.

Inter-granular and intra-granular strain localizationswere observable with this technique. At the particularstress examined, strains associated both with grainboundaries and grain interiors were detected. The surfacestrain measurements often correlated directly with surfaceslip steps and grain-scale cracks. Overall, there is not aclear correlation between local strain level and Schmidfactor, which may indicate the importance of interactinggrain neighborhoods in determining the local stress andstrain development. There appears to be evidence ofgrain boundary sliding, the extent of which is still beinganalyzed, which is consistent with conclusions previous-ly reported by Soula et al. [9]. This is particularly

interesting since these were observed in spite of thesignificantly larger stress levels, and in turn strain rates,imposed in the present study. Nevertheless, the presenttechnique yields a direct correlation between 2-D localizeddeformation behavior and microstructure. As such, it is apowerful tool for examining how deformation behavior iscontrolled by a variety of characteristics, including: grainboundary character, 3-D boundary orientation relative tothe stress axis (using subsequent FIB sectioning to revealboundary orientations [21]) and second phase/impuritycontent (using FIB/TEM analysis [22]). The technique hasthe potential to provide valuable information that can beutilized to validate microstructure-sensitive, computationalmodels of deformation that are being concurrently developedfor these superalloys.

Fig. 7 (a) inverse pole figure map overlaying the speckle pattern and measurement of (b) tensile strain in the x-direction (c) shear strain and (d)tensile strain in the y-direction. The sample was loaded in creep along the horizontal direction in the image at a stress of 1100 MPa for 35 min

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Fig. 8 (a) visible cracks and slip steps on the sample surface correlate with (b) high angle and twin boundaries. The principle (c) and shear (d)strain localizations measured by DIC also correlate with regions near grain boundaries with no clear correlation between strain localization andSchmid Factors for {111} slip systems in (e) <110> or (f) <112> slip directions, high values of Schmid factor indicate easy deformation. Loadingdirection, σ, is horizontal

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Conclusion

The present study has demonstrated a high temperature in-situtesting methodology that can produce high resolution full-field deformation maps which are ultimately applicable tophysics-based crystal plasticity models. The novel patterningtechnique developed in this study provides adequate contrastin secondary electron imaging mode to facilitate digitalimage correlation. Further work is needed to address issuesof spatial and intensity resolutions of the strain measurementif elastic modulus measurements are required, but these donot limit the ability of the present procedure to distinguishtrends in deformation behavior as a function of micro-structural features.

Preliminary strain data indicates that strain localization inRene 104 occurs most often along grain boundaries.While it isnot yet fully understood how orientation, misorientation, andgrain size influence the strain distributions, it is conceivablethat these factors may contribute to particular boundarieshaving high strain localizations while others do not.

The methodology described in the paper has demon-strated that adequate strain and spatial resolution can beobtained with an in-situ elevated temperature technique.The full field data collected can provide significant insightinto both intra- and inter-granular deformation mechanismsin nickel-base superalloys at service-relevant temperaturesand strain rates, and can ultimately be applied to other alloysystems and testing temperatures.

Acknowledgements This work is funded by the Air Force ResearchLaboratory (AFRL) STW-21 program FA9550-09-1-0014. The supportreceived from the Materials &Manufacturing Directorate of the Air ForceResearch Laboratory has been instrumental for the development of the in-situ tensile frame. The authors would like to thank Aimee Price of theOhio State University Institute for Materials Research and OSUNanotech West Laboratory for her invaluable assistance with develop-ment on the lithography techniques for the speckle patterning.

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