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Statistical Void analysis from CT Imagery with Applications to Damage Evolution in an AM60B Magnesium Alloy Amy M. Waters, Harry E. Martz, Kenneth W. Dolan. , Lawrence Livermore National Laboratory Livermore, CA 94550 USA Mark F. Horstemeyer Lawrence Livermore National Laboratory Livermore, CA 94550 USA Permanent address Sandia National Laboratory, Livermore, CA 94550 Robert E. Green, Jr Lawrence Livermore National Laboratory Livermore, CA 94550 USA Permanent address Center for Nondestructive Evaluation, 102 Maryland Hall, The Johns Hopkins University, Baltimore MD 21218 Contact

ABSTRACT

Lawrence Livermore National Laboratory (LLNL) and Sandia National Laboratories (SNL) are collaborating on the development of new techniques to study damage evolution and growth in material specimens subjected to mechanical testing. These techniques include metallography, radiography, computed tomography (CT) and modeling. The material specimens being studied include cast magnesium and aluminum alloys, and forged stainless steel. In this paper we will concentrate on characterizing mechanically deformed magnesium alloy specimens using computed tomography. Several notched tensile magnesium specimens were uniaxially loaded to obtain different levels of deformation. Specimens were initially characterized by radiography and computed tomography to determine the preloaded state. Subsequent CT scans were performed at different failure load percentages. The CT volumetric data are being used to nondestructively measure void statistics in all three dimensions to determine the effect of void growth on the mechanical behavior of the magnesium alloy.

¹ This work is supported by and is performed under the auspices of the U.S. Department of Energy by the LLNL under contract W-7405-ENG-48

INTRODUCTION

In recent years, in an effort to comply with stricter environmental regulations, United States automobile manufacturers have increased efforts to research and develop automobile components made of cast light metals in order to decrease the weight of the vehicle. To improve the design and performance of these lighter components, it is necessary to understand the behavior of the material; in particular to understand the damage evolution that occurs when the material is loaded. This project focuses on understanding and quantifying damage evolution due to void growth and coalescence, and quantifying microstructure in three-dimensions (3-D) in a cast AM60B magnesium alloy at several loading conditions. The non-destructive inspection technique we have used is high spatial resolution X-ray computed tomography (CT).

MATERIALS

Tensile bars, obtained from the Institute of Magnesium Technology in Quebec, Canada, were cast AM60B magnesium alloy containing approximately 6% aluminum and 0.15% manganese by weight. The samples were cast using a cold chamber die casting machine with a 600-ton locking force and an injection temperature between 675 and 690 degrees Celsius. We obtained 3 tensile bars with 3 different notch radii (0.635, 0.794, and 1.27-cm) for a total of 9 tensile bars (samples H-23-25, G-23-25, and F-23-25). The average failure load for each notch radius was determined prior to this project by Westmoreland Mechanical Testing in Pennsylvania. Three tensile bars with a notch radius of 0.635-cm (samples H-23-25) were selected for analysis using the high spatial resolution CT system described below. The average failure load for sample H as determined by Westmoreland Mechanical Testing was 15293 N (s_ult = 207 MPa). The three samples were mechanically loaded at Sandia National Laboratories to 60% (9176 N), 87% (13304 N), 95-97% (14225-14835 N) of the failure load and eventually failure. CT data was acquired for the tensile bars after each loading and after failure.

EXPERIMENTAL TECHNIQUE

Initially the tensile bars were characterized using film radiography. Although some porosity was visible, the 3-D spatial information could not be determined from a single radiograph. CT technology is capable of retrieving complete 3-D information by acquiring multiple digital radiographic images, or projections, of an object at different angles and then mathematically reconstructing these projections using a computer. The final output is a 3-D map of the linear attenuation coefficient and gives the relative locations and dimensions of features within the object as well as external details [1,2]. We scanned each tensile bar after loading using the X-ray tomographic microscope (XTM), a high spatial resolution variant of CT described in detail elsewhere [3]. The radiation source was the 31-pole, X-ray wiggler beamline 10-2 at the Stanford Synchotron Radiation Laboratory (SSRL). The beamline energy was 25 keV, with the tensile bars mechanically rotated on a stage in front of an x-ray scintillating CdWO₄ single crystal of dimensions 25.0 x 25.0-mm² by 0.7-mm thick. The scintillator was optically coupled to a 12-bit CCD camera, with a resulting pixel size of 0.02368-mm. We acquired 360 projections over 180 degrees for each CT scan, which was approximately 1000 x 80 pixels (or approximately 23.7 x 1.9-mm²). Because of the limited height of the field of view, it was necessary to acquire multiple scans for each tensile bar, vertically translating the tensile bar between scans, since the notch region of the tensile bar was approximately 1-cm in height.

DATA REDUCTION AND ANALYSIS

After each sample was mechanically loaded a complete CT scan consisting of 4-6 vertical translations was acquired. Each set of projections was reconstructed on a Silicon Graphics Workstations using a Filtered Backprojection Algorithm (FBP) and successive scans were stacked to obtain 3-D CT volumes of approximate size 600 x 600 x 260 pixels³ (voxels). We acquired 5 complete CT scans for each tensile bar (60%, 87%, 93%, 95-97% and failure load). Representative CT slices for one tensile bar after loading to 60% of failure load are shown in Figure 1.

Fig 1: Representative CT slices from sample H24 at 60% of failure load. The image to the left is a CT slice through the y-axis (note that it consists of 6 separate CT scans stacked together), and the image on the right is a CT slice through the z-axis.

The 3-D CT volumes were segmented using a simple threshold, and then inverted and masked, resulting in a 3-D binary volume, with voids equal to 1, and material equal to 0. We performed a 3-D cluster analysis routine on the segmented volume which labeled connected voxels [4]. We then selected only those clusters containing more than 100 connected voxels for further statistical analysis. This corresponds to a minimum void volume of 1.33 x 10^-5 mm³, equivalent to a cube of dimension 0.110-mm (4.64 pixels) on a side. These voids were then selected and moved to a clean volume of identical size containing only the voids larger than 1.33 x 10^-5 mm³, where further analysis was performed. The centroid of each of these voids was calculated, and the 3-D nearest neighbor distance for each void was determined. Void size distributions and nearest neighbor distance distributions are shown in Figure 2 for one tensile bar after each loading.

Fig 2: Nearest neighbor distance distribution, and void size probability plots for one tensile bar (H24) after each loading. Note the shape of the distributions does not appear to change significantly with load.

Several additional statistical parameters were determined for each of the three tensile bars. Table 1 shows some void statistics calculated for one tensile bar at 4 loading conditions and failure.

Sample Number	Number of voids/mm3	Avg. void vol (mm3)	Median void vol (mm3)	Avg. Near. Neighbor Dist (mm)	Max Void vol (mm3)
H24-1 (60%)	0.394	0.00522 ± 0.00685	0.00244	0.687± 0.3978	0.04614
H24-2 (87%)	0.432	0.00602 ± 0.00985	0.00278	0.6593 ± 0.3525	0.09361
H24-3 (93%)	0.353	0.00632 ± 0.01218	0.00295	0.6754 ± 0.3778	0.13840
H24-4 (95%)	0.372	0.00664 ± 0.01473	0.00272	0.6795 ± 0.3976	0.13909
H24-5*(failure)	N/A	0.00597 ± 0.01652	0.00253	0.7097 ± 0.4215	0.19868
Table 1: Void statistics for sample H24 loaded and scanned 5 times. The minimum void volume used in this analysis was 1.33 x 10-5 mm3.

(*) This analysis was performed on a failed sample having two surfaces.

RESULTS AND DISCUSSION

Quantitative 3-D microstructural information for cast light metals can be obtained using computed tomography. Accumulation of damage during monotonic loading in ductile metals is almost always due to void nucleation, growth, and coalescence [5,6]. It is possible to see void nucleation, coalescence and growth trends from statistics such as average void size, number of voids, and maximum void size. For example, from Table 1, the number of voids per unit volume initially increases from 60% to 87% load and then decreases at 93% load, which, along with the increasing average void size, could indicate initial void nucleation and growth from 60% to 87%, followed by void coalescence at higher loads e.g., 93% load. Void growth is evident in the increasing maximum void size with increasing load. The average nearest neighbor distance does not seem to change dramatically during loading. This 3-D microstructural analysis can be applied to many different materials, and the statistical information from the experiment can be used to refine existing material models and the actual binary 3-D microstructure model may be meshed, and used as input to a finite element analysis code. In addition, it is also possible to track individual void behavior with time and mechanical loading. The CT data provides a very rich data set to be mined.

SUMMARY

We acquired 3-D CT data for 3 cast magnesium alloy tensile bars after 5 different loading conditions. This data was analyzed and several void statistics were obtained for one tensile bar at all 5 loading conditions. The void size and nearest neighbor distributions were obtained. Our preliminary analysis of the CT volume data reveals insight into better understanding of void nucleation, growth and coalescence in this magnesium alloy. The analysis is currently being performed on the remaining two tensile bars. This experimental technique may be used on a variety of different materials to further refine existing material models and eventually predict material behavior more accurately.

ACKNOWLEDGEMENTS

The authors would like to thank David Haupt and John Kinney, LLNL, for help with acquiring the XTM data, data analysis ideas and for providing cluster analysis code; Jean Renaud, IMT, Quebec, Canada, for providing the magnesium samples; Bonnie Antoun, Sandia National Laboratories, California, for acquiring tensile loading information; Jim Sudy, Westmoreland Mechanical Testing, Pennsylvania, for acquiring load failure data.

REFERENCES

1. Kak, A. C. and Slaney, M., Principles of Computerized Tomographic Imaging, New York: IEEE Press, 1988.
2. Herman, G. T., Image Reconstruction from Projections, Academic Press, 1980.
3. Kinney, J. H., and Nichols, M. C., "X-ray Tomographic Microscopy (XTM) using synchotron radiation", Ann Rev Mater Sci 22:121-152, 1992.
4. Hoshen, J., and Kopelman, R., "Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm", Phys Rev B 15:3438-3445, 1976.
5. Cocks, A. C. F., and Ashby, M. F., "On creep fracture by void growth", Prog Mater Sci 27:189-244, 1982.
6. Garrison, W. M., and Moody, N. R., "Ductile fracture", Phys Chem Solids 48:1035-1074, 1987.

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