AVERAGE AND GRAIN SPECIFIC STRAIN OF A COMPOSITE UNDER STRESS USING POLYCHROMATIC MICROBEAM X-RAYS

Transcription

1 AVERAGE AND GRAIN SPECIFIC STRAIN OF A COMPOSITE UNDER STRESS USING POLYCHROMATIC MICROBEAM X-RAYS 369 Hrishikesh A. Bale, 1 Jay C. Hanan, 1* Nobumichi Tamura 2 1 Mechanical and Aerospace Engineering, Oklahoma State University. Stillwater, OK, USA 2 Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA ABSTRACT Typically many grains are averaged to determine strains using X-ray diffraction. In a composite material, however, as the microstructure approaches the fiber diameter, approximations based on a few grains may be misleading. Polychromatic microbeam X-ray diffraction on beamline at the Advanced Light Source was used to observe relative strain and orientation within hundreds of grains of a metal matrix composite as a function of applied stress. Under polychromatic radiation, the sub-micron beam size was used to illuminate diffracting grains across a two-dimensional area associated with a single crystal fiber and many matrix grains. Due to the nature of poly-chromatic radiation, diffracting grains were observed throughout the two-dimensional area over many crystallographic orientations. The aluminum-matrix, sapphire-fiber sample was subjected to unidirectional in-situ applied stress until failure. Sub-grain and grain-to-grain strains from representative grains and the fiber are presented demonstrating the actual grain morphology and the respective strain states in the form of strain contours. INTRODUCTION Recent engineering advances in materials have led to developments in a variety of composites with a goal to achieve superior material properties such as high strength and toughness. Composites which consist of more than a single material, usually fibers of high strength materials embedded in a matrix, defy conventional assessment of the internal mechanical properties. Many macroscopic level experiments have been carried out to identify the residual stresses, the global strength, and the general material properties of composites. However, the complex internal interactions of the matrix and fiber, under conditions of loading, make complete understanding of composites a difficult task. Synchrotron X-ray diffraction (XRD) methods provide a powerful tool for examination beneath the surface of a composite that could help resolve the characteristic micromechanical behavior. Previous diffraction measurements were carried out on a macroscopic scale with large beam sizes and lower resolutions. [1, 2] Utilizing synchrotron based X-rays with high spatial resolution, experiments can now be carried out at a meso-scale ( µm) the scale of constituent matrix grains. A detailed picture of the grain-to-grain and grain-to-fiber interactions, under conditions of loading can be drawn in case of fiber-matrix composites. New measurements from a representative metal matrix composite reveal the power of the poly-chromatic microbeam XRD method. Sub-grain resolution and grain-to-grain strains identify some interesting mechanical properties of the matrix and fiber. * Corresponding author, Jay.Hanan@okstate.edu

2 This document was presented at the Denver X-ray Conference (DXC) on Applications of X-ray Analysis. Sponsored by the International Centre for Diffraction Data (ICDD). This document is provided by ICDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. All copyrights for the document are retained by ICDD. Usage is restricted for the purposes of education and scientific research. DXC Website ICDD Website -

3 METHOD The strain measurements have been carried out on beamline at the Advanced Light Source. A detailed description of the instrument has been published elsewhere [3]. A schematic of the experimental setup is shown in Figure 1. The aluminum matrix-sapphire fiber composite sample, gripped in the stress rig using Electrical Discharge Machined (EDM) adapters reinforced with epoxy, was mounted on a precision three-axis stage. The polychromatic X-ray beam from a bend magnet is focused to a size of 700 x 800 nm 2 using a pair of elliptically bent Kirkpatrick-Baez mirrors. The sample is scanned under the resulting submicron X-ray beam over a rectangular area of 0.3 mm x 0.5 mm forming a grid of 34x51 data points. At each step, the Laue pattern generated by the X-ray illuminated volume of the sample is collected using a Bruker SMART 6000 X-ray CCD detector. The reference lattice parameters for the sapphire was determined from a preliminary measurement performed on a single sapphire fiber with no load. The reference lattice parameters were then used to assess strain in the fiber in the composite. It was also used to refine the geometrical calibration parameters of the experiment. For the Al, we use as reference lattice parameters values for a pure bulk aluminum sample. 370 Figure 1 Schematic of beam line experiment at ALS. A load frame was used to control stress, σ, on the sample. Sample Preparation: A composite sample consisting of single crystal Al 2 O 3 (sapphire) 150 µm diameter fiber, surrounded by an aluminum alloy (A356) matrix was chosen for the analysis. The sample was prepared by quenching the A356 aluminum alloy from 700 o C around the single crystal fiber. During the quench, the fiber was held in place by slits at each end of a graphite mold. In order to dry the mold and reduce the thermal shock to the fiber, the mold was also heated to 700 o C. The molten aluminum alloy was poured into the hot mold. The alloy was allowed to surround the fiber prior to the final quench in room temperature water. This process can lead to void formation in the matrix. Multiple samples were reviewed using radiographic analysis to choose a representative sample. Wire EDM was used to cut the sample leaving the fiber at the center of a 600 µm square. Measurements: The composite sample was loaded in the axial direction in a set of two steps. Diffraction measurements were carried out prior to loading, which is the no applied stress case; however observation of residual strains was expected. Diffraction measurements under the stepped loading

4 condition were performed. Preliminary diffraction scans across and along the fiber axis allows precise determination of the position of the fiber relative to the diffractometer. Both polychromatic and monochromatic microbeam diffraction were used (see below). Strain analysis from XRD Laue Patterns: Indexing of the Laue pattern allows precise determination of the orientation of individual grains. The deviations of the spot positions with respect to their unstrained positions allow determination of the deviatoric strain. The accuracy of the deviatoric strain refinement depends on several factors: 1. The number of reflections used in the refinement procedure. With the parameter settings on BL733 at the ALS, the sapphire gives about 60 or more reflections, while the Al gives reflections. 2. The quality of the peak fitting. The sapphire fiber which experiences elastic deformation only, retains sharp peaks which are easy to fit using a 2D Lorentzian function, while Aluminum experiences plastic deformation both during processing and loading giving irregularly shaped peaks the fitting of which are more prone to errors. The strain accuracy on the aluminum is therefore worse than for the sapphire and was estimated at 2x Strain value accuracy depends on the geometrical calibration of CCD-sample distances and relative position of the CCD with respect to the X-ray beam. These calibration parameters have been least-square refined using a Laue pattern taken from an unstrained region of the sapphire fiber (bare non-loaded fiber). 4. For selected locations along the fiber, the energy (and thus the wavelength) of a specific reflection within the Laue pattern was measured to determine the absolute lattice spacing of the reflection. This was performed by inserting the 4-crystal monochromator into the beam (Figure 1) and scanning the energy while monitoring the reflection intensity on the CCD. The lattice spacing measurement combined with the deviatoric strain measurement allows calculating the complete strain tensor under the illuminated area. The above analysis was performed using the XMAS software package developed at the ALS. The core algorithm is based on a previous code developed at ORNL [4]. 371 Grain Sorting: The data collected from the experiment conducted under the Synchrotron beamline source contains the grain index number and the X and Y coordinates which are based on the Lab coordinates. Along with these, the data file also consists of the absolute stresses and strains, the deviatoric strains, angular orientation data, and diffracted intensity data. A histogram analysis (Figure 2) revealed the relative occurrence of various grains. Around 1200 orientations representing as many grains (or sub-grains) were observed. The prominent 20 which show up as significant and distinct grains were chosen for the analysis. Each individual grain among the 20 grains of interest was analyzed based on their morphologies, strain data, intensities, and orientation. The grains observed lie in the range of µm across. From this initial sorting, evident information of the individual grain morphologies and their uniqueness within the illuminated volume was observed. Each grain was separated based on crystallographic orientation and assigned a grain number. Many of the grains are not observed more than 30 times in the area of observation and have a

5 Y Axis Title X Axis Title Figure 2 Histogram of the Grains showing the frequency of appearance. small area. For the grains that have a large area (>100 µm across), the morphology, orientation, and relative strain was sufficient to identify individual grains at each applied stress. RESULTS Interpretation of the results begins with the preliminary step of indexing the Laue spots which are obtained on the CCD. Each set of Laue spots correspond to a particular grain among a huge number. Each specifically numbered grain along with the corresponding average strain values (axial strains ε xx ) over the entire area of each respective grain is presented in the chart below. The values of the strains are compared for the sample at a no applied stress condition and at applied stress. A serial number is used for convenience in labeling the grains. The grains were grouped at the two different load conditions and a graphic representation of the above chart is shown in Figure 3. The grain specific strains are useful in validating a model for the distribution of stress and strain resulting X-ray elastic constants. Early models such as the Voigt model or the Reuss model, which are based on uniform strain and stress respectively, could not be confirmed using these results [5, 6]. As seen in Figure 3, a substantial number of grains are stacked towards positive strain. Grain Counts * Grains at Load = 0 MPa Grains at Load = 80 MPa 5* 4*,7* 1,5 4,7 1* 0*,84* 9*,13* 0,9 13 3*,6*,8*,10*,16* 3,8,11 11*,14* Strain contours of typical grains revealing their uniqueness in shape is shown in Figure 4 (a-f). The contour plots on the left hand side, show the presence of initial residual strains. The contour plots on the right hand side include the resulting strains due to the application of stress. Contour plots of the fiber were also observed. The fiber location is across the bottom of Figure 4 at a depth of mm along the y-axis (for example below the dashed line in 4e). 12, Axial Strain ε XX ,10,15,16 Figure 3 Histogram of the strains observed in each grain at applied stress of 0MPa and 80MPa. 15* 372 Differences in the coefficient of thermal expansion of the aluminum matrix and the alumina fiber can result in the presence of potentially significant residual strains. Figure 5 shows the residual and applied stress in the fiber. Using a separate energy scan along the fiber axis, the actual strain

6 Axial Strains x Figure 4a) Grain #3 at 0MPa Figure 4b) Grain #3 at 80MPa Axial Strains x Figure 4c) Grain #6 at 0MPa Figure 4d) Grain #6 at 80MPa Figure 4e) Grain #14 at 0MPa Figure 4f) Grain #14 at 80MPa Axial Strains x referenced to a strain free reference in the fiber were observed. An average residual strain of x 10-3 was observed. In case of the Laue method, calibration of the sample position is an important issue. The energy scan gives the exact lattice spacing in the fiber. Calibration of the strains obtained from X-ray diffraction is based on the value of strains obtained from the energy scans. A 200µε relative error was observed based on the variation of these strains. This value of precision agrees with that

7 Axial Strain x Average strain x 10-3 Average strain -2.53x Axial Direction mm 0MPa 80MPa Figure 5 Axial strains present in the center of the fiber at no applied load. found in other experiments [3]. CONCLUSION The X-ray diffraction method has been used to look into the behavior at a sub micron level of an aluminum matrix with an embedded sapphire single crystal fiber. An overall perspective of the interactions of the grains within the matrix was obtained. The use of polychromatic light, unlike conventional techniques, presented an ability to acquire data from a greater number of grains than is available with monochromatic light. A major advantage of using this technique for strain measurement is that the morphology, orientation, and relative strain data is sufficient to identify individual grains at each applied stress. The technique provides a visual insight by two-dimensional representation of the grains contoured by strain. The current results, express the grains in a plane. The position of every grain in a volume by triangulation is under development and would enhance the applicability of this technique to composite micromechaincs. The distribution of the residual stresses in the matrix has been categorized, allowing a better visualization of the internal strain state in a typical metal matrix composite. 374 ACKNOWLEDGEMENTS The authors would like to acknowledge valuable discussions with E. Ustundag and R. Rogan. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH EDM was performed by Chris Teed of Accu-Wire EDM. REFERENCES [1] Hanan, J. C.; Ustundag, E.; Beyerlein, I. J.; Swift, G. A.; Almer, J. D.; Lineart, U.; Haeffner, D. R.; Microscale damage evolution and stress redistribution in Ti-SiC fiber composites. Acta. Mater 2003, 51 (14): [2] Hanan, J. C.; Mahesh, S.; Üstündag, E.; Beyerlein, I. J.; Clausen, B.; Brown, D. W.; Bourke, M. A. M.; Strain Evolution after Fiber Failure in a Single Fiber Metal Matrix Composite, 2005, Mater. Sci. and Eng. A. [3] MacDowell, A. A.; Celestre, R. S.; Tamura, N.; Spolenak, R.; Valek, B.; Brown, W. L.; Bravman, J. C.; Padmore, H. A.; Batterman, B. W.; Patel, J. R.; Nuclear Instruments and Methods in Physics Research A , 2001, [4] Chung, J.-S.; Ice, G. E.; Journal of Applied Physics, 1999, 86 (9) [5] Reuss, A.; Angew, Z.; Math. Mech., [6] Voigt, W.; Lehrbuch der Kristallphysik, 1889.