damage evolution in ti-sic unidirectional fiber … · fiber fractures in metal-matrix composites...

$: DAMAGE EVOLUTION IN Ti-SiC UNIDIRECTIONAL FIBER … · Fiber fractures in metal-matrix composites often initiate damage zones that grow until the composite ... fiber composite was$
DAMAGE EVOLUTION IN Ti-SiC UNIDIRECTIONAL FIBER COMPOSITES

Jay C. Hanan1, Geoffrey A. Swift1, Ersan Üstündag1, Irene J. Beyerlein2, Bjørn Clausen1, Jonathan D. Almer3, Ulrich Lienert3 and Dean R. Haeffner3

(1) Department of Materials Science, California Institute of Technology, Pasadena, CA 91125 (2) Materials Science and Technology Div., Los Alamos National Lab., Los Alamos, NM 87545

(3) Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439

ABSTRACT

Fiber fractures in metal-matrix composites often initiate damage zones that grow until the composite fails. To better understand the evolution of such damage from a micromechanics point of view, a model Ti-matrix/SiC-fiber composite was studied for the first time. Using high energy X-rays and a small sampling volume, the damage zone around a broken fiber was investigated. The growth of this zone was monitored in situ under applied tensile stress by measuring the responses of the fibers and the matrix. The diffraction data was compared to a modified shear lag model, which considers the elastic response of the matrix and the fibers. A comparison of the model and data shows a correlation on the trend of the data, while the nature of the damage region incurs discrepancies. Results indicate a need for further refinement of the model, revealing the necessity of incorporating such factors as residual stress in the system and plasticity in the matrix.

INTRODUCTION

The transfer of load from a broken fiber to the rest of a fiber-reinforced composite is one of the fundamental micromechanical processes determining strength. In order to predict strength, one needs to understand the details of this load transfer. In-situ measurements of strain can help validate and refine predictive modeling of strength in fiber composites. This study used synchrotron X-rays to investigate, for the first time, the evolution of in-situ strains in a damaged Ti-matrix/SiC-fiber composite. The diffraction results were compared to predictions from a micromechanics model [1]. This model accounts for the linear elastic co-deformation of fiber and matrix in unidirectional fiber composites containing any configuration of multiple fractures.

EXPERIMENTAL PROCEDURE

The studied composite system corresponds to the geometry presented in the mechanics model described in ref. [1]. It consisted of a single row of unidirectional SiC fibers (SCS-6, 140 µm diameter) in a Ti-6Al-4V matrix, prepared by a proprietary technique at 3M Corp. (St. Paul, MN 55144). Fig. 1 shows the schematic of a typical specimen. The fibers are uniformly spaced with an average center-to-center distance of about 240 µm. The area fraction of the fibers was 32%. On the specimen examined, a small region of the matrix was removed via acid etching (50% HF aqueous solution) to expose the SiC fibers. One fiber was subsequently broken in the exposed region, denoted “fiber 0”. The matrix was left intact around and behind the exposed region. A strain gage was attached measuring the applied macroscopic longitudinal strain (parallel to fibers) as well as that in the transverse direction (Fig. 1).

Copyright (c)JCPDS-International Centre for Diffraction Data 2002, Advances in X-ray Analysis, Volume 45. 251 ISSN 1097-0002

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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 – www.dxcicdd.com

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The samples were examined using 25 keV X-rays (wavelength, λ = 0.496 Å) at the 1-ID-C beam line, Advanced Photon Source. At this energy, the transmitted beam intensity is about 58% of the incident beam intensity. For an exponential decay in the transmitted beam intensity from the sample surface inward, the center of gravity of the sampling volume was calculated to be 91 µm from the surface facing the incoming beam. Therefore, these measurements are representative of the entire thickness of the sample.

A four-circle goniometer was used. The diffraction vector was along the fiber axis yielding longitudinal strain in the plane of the composite. The diffraction data was collected with a scintillator detector equipped with a Si (111) analyzer crystal. The X-ray beam size was defined by slits. A Si diode continuously monitored the transmitted beam intensity.

First, the location of the intact buried fibers immediately around the damage region was determined using absorption contrast and a 30 x 30 µm beam size. Fig. 2 shows the damage region and the location of the fibers around it. A reference spot on the sample was used to correct for shifts during loading. The greatest source of shifts came from the sample slipping at the grip region. A second calibration of position for each data point was the local absorption contrast. By translating the sample in the y direction, the position of the beam with respect to the center of the fiber was readily observed. Prior to each strain map, in order to assure that the fiber axis was aligned with the x-axis, this calibration procedure was performed at both extreme x positions of the region of interest.

To determine the effect of the broken fibers on the neighboring fibers and matrix regions, the damaged sample was scanned with a 90 x 90 µm2 beam (Fig. 1). Fits to individual reflections were performed using the method of least squares assuming a Lorentzian peak profile for each phase. The three nearest fibers adjacent to the broken fibers (no. 2, -1, and -2), the broken fibers (no. 0 and 1, the latter broke during the experiment), and the intervening matrix regions were scanned along fiber axes for a distance of 10 fiber diameters in each direction away from the break in 280 µm steps. Additionally, at 1.89 mm from the break, one

Figure 2. Absorption contrast image of the damageregion. The darker a region the higher the absorption.The damage region is evidenced by the bright regionnear the center of the image. The periodic change inintensity along y corresponds to the position of SiCfibers in the matrix. Some important fibers are labeled.

Strain Gage

Exposed

Fiber

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Grip

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σ,ε

σ,ε

Thickness, t = 0.20mm

L = 26.00mm

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Figure 1. Schematic showing the samplegeometry. Fibers are represented byblack lines between a gray matrix(illustration only – not to scale).


fiber and its adjacent matrix region were scanned at each load to obtain a measure of the in-situ applied far-field strain in the sample. Relative changes in the elastic lattice strains in the matrix and fibers were obtained by monitoring one reflection from the majority phases in each: (10⋅⋅⋅⋅2) from α-Ti and (220) from β-SiC. To reduce experimental errors, especially those due to specimen displacement, Si powder (NIST, Standard Reference Material 640a) was attached to the specimen as an internal standard. Displacement errors for each applied stress, which averaged about 30 µε, were subtracted from the measured strains.

In addition, nominally stress-free references of Ti and SiC were scanned. The XRD data from the references allowed the determination of the absolute values of strains in each component. The references were obtained by etching away one surface of the composite dissolving the matrix with a 25% HF acid aqueous solution to expose the fibers, which then easily separated because of thermal residual stresses. The Si standard powder was also placed on the surface of these reference samples.

The composite was stressed in tension using a custom-built load frame. A load cell on the frame was connected to a computer so that the applied load could be recorded simultaneously with the strain gage strains. The loading data was synchronized with the diffraction data.

RESULTS AND DISCUSSION

The transmitted beam intensity shows alignment of the fibers with the x-axis and clearly reveals the region of the matrix etched by HF (Fig. 2). Along with collecting the transmitted beam intensity, the intensity of α-Ti (11⋅⋅⋅⋅2) reflection was monitored using the 2θ detector set at 30.5°. The resulting plot gives the position of grains in the sample suitably oriented for diffraction (Fig. 3). As shown, the α-Ti (11⋅⋅⋅⋅2) map is highly discontinuous due to the large grain size found in the matrix (~29 µm). Similarly, an intensity map was collected from the matrix using the β−SiC (220) reflection (Fig. 4, this data was collected simultaneously with the data for Fig. 2). The nearly continuous nature of the SiC reflection reveals the drastic difference in grain size for the two phases (less than 1 µm for the fibers and about 29 µm for the matrix) [2,3].

The residual thermal strains were measured around the damage region under no applied load. The removal of the matrix around this area significantly relaxed the longitudinal residual strains in the fibers. The residual strains given by the far-field fiber (–1500 µε) approach the values at each extreme position measured along the fibers. Within the error of the measurement, these strains also agree with the bulk residual

Damage Zone Ti

Fibers

Figure 3. Map of α-Ti (11⋅2) reflection indicating the location of diffracting Ti grains. With a grain size of ~29 µm, few grains are oriented for diffraction at a given θ angle.


strains and those already quoted in literature [2,4]. Since the model [1] does not consider the residual strains, the residual strain data was subtracted from the total measured strains when stress was applied. Therefore, only the relative strains were used in the comparison of experimental data with model predictions.

Fig. 5 exhibits the model comparison with experimental data from the fibers. The fiber strains were normalized with respect to the far-field value. The dimensionless length [1] is given by ξ = (0.00304 µm-1)⋅x, where x is position along the fiber. It became obvious from the strain data [2] that two fibers were broken (no. 1 and 0) and this assumption was included in the model. This model also assumes the fibers are behaving as if the matrix is intact adjacent to the broken fibers. Overall, a reasonably good agreement is observed between the data

Figure 4. Map of β-SiC (220) reflection indicating the location of the buried fibers. The oval outlines the damage region.

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Figure 5. Comparison of strains from model predictions (designated by lines) and XRD data from fibers (symbols). The applied tensile stress varied between 430 and 410 MPa. Strains were normalized with respect to the applied far field value, εf = 2700 to 2600 µε. A typical error bar is shown beneath the data in graph (d).


and model predictions. However, a higher data density would have improved the comparison between the two around the damage zone. Note that the larger deviation in the strain profile along fiber no. 0 is likely due to the width of initial damage in the fiber.

Fig. 6 compares the model predictions with measured matrix strains. While experimental errors of less than 200 µε were found in the fibers, strain uncertainties of 100 µε to greater than 700 µε were observed in the matrix. In addition, not every location had diffracting matrix grains leading to a lower data density compared to fibers. This results from the relatively large grain size of the matrix compared to the sampling volume (the “graininess” problem). That means, at a given location, only a grain or two is likely contributing to the intensity of the (10⋅⋅⋅⋅2) reflection. As a result, the (10⋅⋅⋅⋅2) intensity varies tremendously accompanied with error in peak position. Furthermore, the strain values fluctuate due to intergranular effects. All of these observations confirm the difficulty of performing strain measurements on a scale comparable to grain size.

The experimental difficulties notwithstanding, the strain data from the matrix qualitatively agrees with model predictions. Its ability to collect strain data from both the fibers and the matrix provides XRD with an advantage compared to optical methods such as Raman and piezospectroscopy, methods that can usually investigate only the fibers (see e.g., [5]). With XRD it is possible to obtain a more complete description of the deformation in a fiber composite at length scales approaching those possible with optical methods.

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Figure 6. Comparison of strains from model predictions and XRD data for the matrix in various regions: a) the region between the two broken fibers (no. 0 and 1), b) the matrix region between an intact and broken fiber (no. –1 and 0), c) the matrix region between two intact fibers (no. –2 and –1), and d) also a region between an intact and broken fiber (no. 2 and 1). The applied tensile stress varied between 450 and 430 MPa. Strains were normalized with respect to the applied far field value, εm = 2340 to 2240 µε. The error bars denote the 95% confidence limits for the center position of the peak.


Several shortcomings of the micromechanics model were noted in this study. First, as mentioned above, it does not account for residual stresses/strains. Although the initial residual strains around the damage zone were measured and subtracted from the total strains under applied stress, it was implicitly assumed that these residual strains did not vary during loading. This assumption could be invalidated by any plastic deformation in the matrix. The macroscopic mechanical behavior of both the matrix and fibers was independently determined with XRD using a large sampling volume [2] and it was seen that global plasticity in the matrix did not commence below 500 MPa applied composite stress. This property would lower the probability of plastic deformation around the damage zone, but plastic deformation might still occur since some stress concentration was expected near the damage region. Another problem with the model was that it could not account for the half-removed matrix in the damage region. To eliminate these uncertainties, experiments were performed recently using an area detector [6]. For the new experiments, the step size was reduced to increase the data density and a well-defined damage zone was used in the form of a hole. This data is currently being analyzed while the micromechanics model is being improved. The results will be reported in a future publication.

SUMMARY

As an initial investigation of the micromechanical behavior of a model Ti-SiC composite using synchrotron radiation, notable results were obtained. The behavior of the composite under tensile loading was studied in both the fibers and the matrix, and the strains were compared to a modified shear-lag model. Considering the complicated residual strain profile, the model predictions are well within reason. While the model and data overall agree, there are a few instances where the assumptions break down and the predictions are inconsistent with the data. In the narrow region near the break where much activity is predicted, higher spatial resolution is necessary to better characterize the in-situ behavior. Nevertheless, this work has shown that the general behavior predicted by the model is evidenced in both the fiber and matrix of the composite.

ACKNOWLEDGMENTS

The authors are grateful to Dr. H. Deve at 3M Co. for providing the specimens and helpful discussions about the properties of the composites. This study was supported by the National Science Foundation (CAREER grant no. DMR-9985264) at Caltech and a Laboratory-Directed Research and Development Project (no. 2000043) at Los Alamos. The work at the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Basic Energy Sciences under contract no. W-31-109-ENG-38.

REFERENCES 1. I.J. Beyerlein and C.M. Landis, Mechanics of Materials, 31, 331-350 (1999). 2. J.C. Hanan, G.A. Swift, E. Üstündag, I.J. Beyerlein, B. Clausen, J.D. Almer, U. Lienert and D.R.

Haeffner, submitted to Metall. Mater. Trans. A (2001). 3. J.C. Hanan, E. Üstündag, I.C. Noyan, D.R. Haeffner and P.L. Lee, Adv. X-Ray Anal., 44 (2000). 4. P.J. Withers and A.P. Clarke, Acta Mater., 46 (18), 6585-6598 (1998). 5. J. He, I.J. Beyerlein and D.R. Clarke, J. Mech. Phys. Solids, 47, 465-502 (1999). 6. J.C. Hanan, G.A. Swift, E. Üstündag, I.J. Beyerlein, U. Lienert and D.R. Haeffner, unpublished results

(2001).


damage evolution in ti-sic unidirectional fiber … · fiber fractures in metal-matrix composites...

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