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SiC ceramic matrix composites using Raman spectroscopy
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Original Article
Residual stress measurements in melt infiltrated SiC/SiC ceramic matrix composites using Raman spectroscopy ⁎
Kaitlin Kollinsa,b, , Craig Przybylaa, Maher S. Amerb a b
Air Force Research Labs, WPAFB, OH, 45433, United States Department of Mechanical and Materials Engineering, Wright State University, Dayton, OH, 45435, United States
A R T I C L E I N F O
A B S T R A C T
Keywords: Ceramic matrix composites Residual stress Raman spectroscopy Silicon expansion
Raman spectroscopy was utilized to characterize the chemical composition and residual stresses formed in melt infiltrated SiC/SiC CMCs during processing. Stresses in SiC fibers, in SiC chemical vapor (CVI) infiltrated matrix, in SiC melt infiltrated matrix, and in free silicon were measured for two different plates of CMCs. Stresses in the free silicon averaged around 2 GPa in compression, while stresses in the matrix SiC were 1.45 GPa in tension. The SiC CVI phase had stresses ranging between 0.9 GPa and 1.2 GPa in tension and the SiC fibers experienced stresses of .05–0.7 GPa in tension. These results were validated with the proposed model of the system. While the mismatch in the coefficients of thermal expansion between the constituents contributes to the overall residual stress state, the silicon expansion upon solidification was found to be the major contributor to residual stresses within the composite.
1. Introduction SiC/SiC ceramic matrix composites (CMCs) are promising materials for replacing Ni-base super-alloys in high temperature applications as they exhibit as much as 1/3rd the density while maintaining sufficient strength and creep resistance to operate at significantly higher temperatures (i.e. > 1000 °C) [1,2]. Changes in processing of SiC/SiC CMCs has shown to significantly impact the mechanical performance of the composite, including the tensile strength and peak strain, affecting the composite toughness and creep resistance; the observed correlation was attributed to differences in porosity, residual stresses, and the formation of silica glass during processing [2,3]. Because of the mismatch in coefficients of thermal expansion of the various constituent phases and the high processing temperature employed in the processing of SiC/SiC CMCs, significant residual stresses can develop in these types of composites upon cooldown from the processing temperature. During processing, the two plates in the study here were subject to a melt infiltration process, in which molten silicon was infiltrated into a fiber preform containing SiC particulate. This process results in a certain amount of residual unreacted silicon dispersed throughout the composite structure. Silicon falls in the category of crystals with an open cubic lattice structure that increase their interatomic distance by large amounts upon solidification from a liquid. Hence, severe stresses develop if the crystal cannot expand freely upon solidification [4]. Residual stresses in the matrix may be beneficial in
⁎
some cases. For example, compressive residual stresses present within the matrix will help to inhibit early crack growth in the composite similar to the desired effect of the residual stress induced by shot peening in metals Previous work has performed using Raman spectroscopy to characterize residual stresses in multiphase ceramic composites. Residual stresses in reaction bonded silicon carbide (RBSiC) samples, containing no fibers, produced from the melt infiltration process were studied as a function of their unreacted silicon [5]. Within the unreacted silicon, residual stresses of up to 2 GPa in compression were reported, with tensile residual stresses in the SiC reaching 2.3 GPa. Higher compressive residual stresses were measured in the samples containing lower amounts of silicon, with lower tensile residual stresses. A follow-up study was conducted on matrix material away from fibers in 0/90 laminate HiPerComp CMCs produced by GE [6]. The matrix material in the composite had a silicon volume fraction of 20 percent. Compressive stresses ranging from 2.4 to 3.1 GPa were reported for the silicon, and tensile stresses of 0.24 to 0.75 GPa in tension were measured for SiC within the matrix [6]. In this paper, two different variants of melt infiltrated SiC/SiC CMCs are characterized via Raman spectroscopy. Like the previously cited study in a similar material, the residual stresses in the matrix material is measured. Additionally, unlike the previous study, micro-Raman residual stress measurements are performed in the immediate neighborhood on and around the SiC fibers. Also, unique to the materials studied
Corresponding author at: Air Force Research Labs, WPAFB, OH, 45433, United States. E-mail address: [email protected] (K. Kollins).
https://doi.org/10.1016/j.jeurceramsoc.2018.02.013 Received 2 January 2018; Received in revised form 31 January 2018; Accepted 5 February 2018 0955-2219/ Published by Elsevier Ltd.
Please cite this article as: Kollins, K., Journal of the European Ceramic Society (2018), https://doi.org/10.1016/j.jeurceramsoc.2018.02.013
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here is a SiC layer deposited around the fiber preform via a chemical vapor infiltration (CVI) process, which was also characterized using Raman spectroscopy. The coupling of these stresses in these various material constituents is considered and a simple model is proposed to model the residual stresses in these materials around the SiC fibers.
Table 1 Wavenumber and shift to stress conversion factors.
2. Experimental setup
Constituent
Fingerprint Raman Peak Position (cm−1)
Shift to Stress Conversion Factor C (cm−1/GPa)
Silicon Cubic SiC Peak 1 Cubic SiC Peak 2
515.3 796 [40] 973 [40]
1.88 ± 0.05 [21] 3.53 ± 0.21 [41] 4.28 ± 0.22 [41]
2.1. Material
ωo−ωs = σR * C
Two plates of continuous SiC fiber reinforced SiC matrix CMCs were investigated. In both plates, the fibers were woven into a five-harness satin weave preform. Plate 1 contained Sylramic fibers, while Plate 2 contained Sylramic-iBN fibers. The plates went through similar processing steps, with exception to an extra processing step for Plate 2 in which the preform first went through a thermal treatment that forces excess boron to diffuse to the surface of the fibers that then interacts with a nitrogen-rich environment, creating an in-situ boron nitride (iBN) fiber coating around the fibers [7,8]. It has been shown that by diffusing the boron to the surface, the tensile strength of the fiber is retained and the creep resistance and oxidation resistance are improved [2,8,9]. Also, the iBN coating helps to avoid direct contact between fibers, as well as avoiding silica glass formation that is detrimental to the mechanical properties. Both preforms then went through chemical vapor infiltration (CVI) of boron nitride followed by a CVI SiC layer and then a preceramic polymer containing SiC particulate was infiltrated into remaining porosity at room temperature. Next the preceramic polymer is pyrolyzed resulting in a carbon rich matrix. Then, molten silicon, at 1415 °C, is melt-infiltrated (MI) into the fiber preform and reacts with excess carbon to form a predominantly silicon carbide matrix with minimal porosity [9]. To characterize local volume fraction fluctuations, a point counting method [10] was employed to determine the volume fraction of the constituents within each plate. In this method, an appropriate grid size was found through convergence studies, and then overlaid onto representative images of the microstructure. Wherever a grid intersection occurred, the point was evaluated to determine the phase of the material. The BN fiber coatings were not considered during point counting, as their volume fraction is minimal. If a grid point landed in the middle of a fiber coating and fiber, the point was counted as a fiber. Tensile testing was performed on two dogbone specimens for each plate at room temperature at Honeywell Advanced Composites in 2002. Thee samples were 154 mm in length and were 2 mm thick and had a gage section 18 mm long by 8 mm wide.
(1)
The conversion factors for β silicon carbide and silicon were previously determined in the literature and are shown in Table 1. However, due to the presence of boron doping in the silicon, the standard stress free peak position of 520.5 cm−1 for silicon could not be used. The stress free peak position of the doped silicon was found experimentally by using samples ground into fine powders. The measured peak position is listed in Table 1, and the peak can also be seen in Fig. 2 plotted against the silicon standard and silicon measured within the composite. While the silicon natural Raman active band is typically a symmetric triplet, the silicon peak is asymmetric in the samples presented. This is likely due to a Fano resonance effect that has been observed before due to boron doping [15,16]. The silicon peaks were curve fit with a Fano profile, while the β SiC peaks were fit with Lorentzian profiles. The presence of β SiC was confirmed by the peak profile [17]. Although the shift to stress conversion factor used in this work is based on the literature values for pure silicon, boron doping of the silicon may have affected this value as well. Implications of the effect of boron doping on the stress conversion factor will be considered in Section III with the results. It is important to note that for SiC, the absorption coefficient at the laser wavelength used in this study, 514 nm, is 13.98 cm−1 [18]. This will give a penetration depth of 715 microns for SiC. On the other hand, the penetration depth for silicon is only 1 μm with an absorption coefficient of 9877 cm−1 at 514 nm [19]. When observing the results, SiC and Si may be present in the same location on the Raman maps. This is due to Si being detected directly beneath SiC on the surface. Another consideration that must be made in the case of these composites is Raman’s inability to characterize residual stresses in the boron nitride coatings between the fiber and matrix material. The boron nitride fluoresces under the laser, causing the Raman signal at the fiber coatings to become distorted and uninterpretable. Raman spectra were collected using a Renishaw Raman Spectrometer equipped with a 514.5 nm excitation Ar+ laser, a 1800 line/mm grating, and a back depleted CCD for data collection. Laser power at the sample was kept below 2 mW to avoid sample heating. A long working distance 50x objective was employed to focus the laser beam on the sample and to collect the Raman scattered light in a backscattering setup. Raman maps were collected using a motorized stage with a step size of 1 μm. The data collected was then imported into a MATLAB® program which calculates the local chemical composition and residual stress maps of the area analyzed. Specifically, this output was calculated based on the integrated intensity and wavenumber shift, respectively, for both Si and SiC. Data were taken from both areas within the matrix and around fibers surrounded in matrix material in the middle of the fiber tows, as shown in Fig. 1. Several Raman maps were collected and analyzed to obtain data representative of the entire sample.
2.2. Raman spectroscopy 12 × 2 mm samples were sectioned from as-manufactured specimens. The samples were polished to a 1 μm finish using diamond grinding disks. Samples were ultrasonically cleaned in solvent to avoid contamination. Micro-Raman spectroscopy was utilized to investigate local chemical compositions and residual stresses, which likely significantly influence SiC/SiC composite mechanical properties. Micro-Raman spectroscopy is a nondestructive technique that is employed to measure the various fundamental vibration modes in a material [11]. By following the “fingerprint” of the Raman active modes of different materials within the investigated sample, accurate measurements of chemical composition can be obtained from the peak integrated intensity. As the exact position of the peak and its shift depends on local stress, the average of the trace of the stress tensor in the sample can be accurately measured with a 1 μm spatial resolution [12,13]. A shift from the known, stress free wavenumber indicates a residual stress within the material [14]. The residual stress (σR) can be calculated from the measured peak position (ωs) and the stress free peak position (ωo) using a shift to stress conversion factor (C) , as seen in Equation 1:
2.3. Scanning electron microscopy A 12 × 2 mm sample was polished to a 1 μm finish using diamond grinding disks. The sample was cleaned with solvents to avoid contamination. Silicon within the matrix was studied with a Zeiss GeminiSEM 500 using Oxford EDS to quantify the amount of boron dopant within the melt infiltrated silicon. The voltage was at 5.00 kV 2
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Table 2 Volume fraction of Plates 1 and 2.
Plate 1 Plate 2
SiC Particulate
MI Silicon
CVI SiC
Fiber
Porosity
.23 .18
.12 .11
.19 .22
.41 .46
.05 .03
Table 3 Room temperature macro-mechanical properties of investigated samples. Sample
Tensile strength (MPa)
Strain to failure (%)
Yield Strength (MPa)
Elastic Modulus (GPa)
Plate 1 Plate 2
271 ± 21 425 ± 25
0.29 ± 0.03 0.56 ± 0.02
157 ± 8 165 ± 15
200 ± 9 199 ± 1
Fig. 1. Optical micrograph showing fiber and matrix areas studied.
3.2. Micro-Raman spectroscopy mapping
with a 20 μm aperture.
Fig. 3 and 4 depict the Raman mapping results for both SiC and Si distribution and their residual stress around Sylramic fiber in Plate 1 and the Sylramic-iBN fiber in Plate 2, respectively. The distribution maps are derived from the integrated peak areas in the Raman spectrum. As mentioned, when using Raman spectroscopy to measure stress, the stated residual stress values are the average of the trace of the stress tensor. The Raman maps show that Plate 2 has higher residual tensile stress in the fiber and higher residual stress in the SiC than Plate 1. Also, the local area studied in Plate 1 has much higher unreacted silicon content, with similar residual compressive stress in the silicon as Plate 2. As seen in Table 4, for Plate 1, the residual stress in fiber reaches a maximum of + 1.87 GPa, +2.58 GPa in the SiC CVI coating, and + 3.05 GPa in the SiC matrix. In the silicon, however, the residual stress maximum is around −2.97 GPa. In Plate 2, the maximum residual stress in the fiber
3. Results 3.1. Material properties The volume fraction of each phase constituent is listed in Table 2. Silicon content is estimated at 12% in Plate 1 and 11% in Plate 2, which is in good agreeance with literature [20]. The averaged mechanical testing results for two samples from each plate are shown in Table 3. From this, it is seen that the differences between the boron nitride fiber coatings of these SiC/SiC CMCs has a large impact on the composite tensile strength and strain to failure while it does not dramatically affect the composite stiffness or proportional limit.
Fig. 2. Silicon spectra taken from Si standard (centered at 520.5 cm−1), from within composite (centered at 518 cm−1), and from powder (centered at 515.3 cm−1).
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Fig. 3. Silicon carbide and unreacted silicon distributions as well as residual stresses around the Sylramic fibers as measured by micro-Raman spectroscopy in a 30 μm × 30 μm map in Plate 1.
Fig. 4. Silicon carbide and unreacted silicon distributions as well as residual stresses around the Sylramic-iBN fibers as measured by micro-Raman spectroscopy in Plate 2.
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Table 4 Raman stress measurements for Plate 1 and plate 2.
Plate 1 Plate 2
SiC Fiber Average Stress (GPa)
SiC Fiber Maximum Stress (GPa)
SiC CVI Coating Average Stress (GPa)
SiC CVI Coating Maximum Stress (GPa)
SiC Matrix Average Stress (GPa)
SiC Matrix Maximum Stress (GPa)
Free Silicon Average Stress (GPa)
Free Silicon Maximum Stress (GPa)
0.50 ± 0.11 0.69 ± 0.10
1.87 1.81
0.93 ± 0.05 1.24 ± 0.07
2.58 2.72
1.46 ± 0.08 1.45 ± 0.05
3.05 3.02
−2.04 ± 0.07 −1.96 ± 0.04
−2.97 −2.99
from Raman spectroscopy. It is important to note that the value of such stress will depend on the volume of the affected zone compared to the volume of the silicon pools. Specifically, the larger the ratio of the SiC volume over the silicon volume, or VSiC/VSi, the lower the developed internal pressure. Shown in Fig. 6a, the fiber and surrounding matrix material can be modeled as concentric spheres. The Si bulk modulus, kSi, is estimated to be 73.2 GPa (0.75 of the room temperature value of 97.6 GPa) [23–26] near 1400 °C and the SiC bulk modulus is 235 GPa [27]. Substituting these values into Eq. 4 yields a value for VSiC / VSi = 4.14 . The silicon spherical pool will be under hydrostatic pressure with a stress tensor in the form of; Fig. 5. A schematic and a micrograph showing the Cartesian axes system used in stress analysis.
σSi =
reaches + 1.81 GPa, +2.72 GPa in the SiC CVI coating, and + 3.02 GPa in the SiC matrix. In Si, the residual stress is found to at a maximum of around −2.99 GPa. The shift to stress conversion factor used to calculate the residual stresses in the silicon phases is for pure silicon. However, the silicon phase in this composite is doped with boron. This dopant may have an effect on the shift to stress conversion factor. From elemental analysis, the atomic percent of boron within the silicon of the material studied here was 1.40 at%. For this study, it is assumed that the dopant concentration of boron is low enough to have minimal effect on the stress conversion factor; therefore, the shift to stress conversion factor for pure Silicon of 1.88 cm−1/GPa from the literature was employed [21].
σSiC =
(d 2 + d 2 ) σrr = pi ⎡ 0 2 2i ⎤ ⎢ (d 0 −di ) ⎥ ⎣ ⎦
(2)
where ΔV is the change in volume from liquid to solid, Vo is the volume at room temperature, and ρ represents the densities at 1410 °C and at room temperature. Substituting for the density values of liquid silicon at the melting point, 2.55 g/cm3, and in the solid state at room temperature, 2.33 g/cm3, leads to a volumetric expansion of 9.4% upon cooldown. Realizing that the expanding silicon is surrounded by a matrix of SiC, the final increase in the silicon volume must equal the shrinkage in SiC volume within the affected zone. Hence,
VSiC ⎡ P ⎤ P + ⎢ kSiC ⎦ ⎥ VSi ⎣ kSi
(6)
(7)
Another source of residual stresses in the matrix is thermal residual stresses (TRS) due to the mismatch in the coefficients of thermal expansion (CTEs) between the silicon and silicon carbide. Using the CTE values listed in Table 5 and calculating the TRS in both silicon and silicon carbide resulted in small values in the range of 0.03 GPa. Such values are negligible compared to the stress values resulted from the silicon expansion upon solidification. Realizing the Raman measurements under such stress state would yield a value representing the average of the tensor trace [29–32], we realize that our average measurements of -2.0 GPa in the free silicon in the matrix are near the theoretical calculations of −2.11 GPa, confirming that the affected zone around the unreacted silicon has a diameter that extends to 3.45 times that of the silicon pool size.
Fig. 5 depicts an optical micrograph and a schematic representing the SiC/SiC CMC investigated and the Cartesian axes system considered in our discussion and theoretical calculation of the expected residual stresses. The volume expansion of silicon can be estimated according to the equation as [4,22]:
0.094 =
0 0 − 3.0 GPa 0 0 + 3.54 0 0 + 3.54
The radial stresses calculated in Eq. 6 are calculated at the interface using elastic theory treatment of thick-walled spherical pressure vessel equation with an internal pressure (pi), internal diameter (di), and external diameter (do) according to Eq. 7 [28]:
4.1. Residual stresses in the matrix due to silicon solidification expansion
eSi × VSi = eSiC × VSiC
(5)
In this case, for VSiC / VSi = 4.14 , the outer diameter (do) of the affected spherical zone must be 3.45 the internal diameter (di), and, hence, the stress tensor at the Si/SiC interface will be;
4. Model development
−ρ ρ ΔV = 1410° C RT Vo ρRT
− 3.0 0 0 GPa − 3.0 0 0 − 3.0 0 0
4.2. Residual stresses around the fibers In addition to stresses resulting from silicon solidification around the Sylramic and Sylramic-iBN fibers, the large difference in CTE of the composite constituents will also contribute to the developed residual stresses in processed composite. In this case, we modeled the fiber area studied as 4 concentric cylinders as shown in Fig. 6b. Knowing that the fiber diameter is 10 μm, the thickness of the CVI-SiC coating around the fibers was measured experimentally using high resolution optical microscopy and was found to be 4.4 μm. The area of the SiC matrix in the model was determined by the volume fraction of the local areas studied, and backed out to have an 18.1 μm thickness. The silicon cylinder thickness was varied to
(3)
(4)
Where, e is volumetric strain, k is the bulk modulus, V is the volume, and P is the maximum measured silicon stress, obtained to be −3 GPa 5
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Fig. 6. Schematics showing the geometry used to model residual stresses around a) an unreacted silicon pool embedded in the SiC matrix away from the fiber, and b) an unreacted silicon pool next to a fiber.
Table 5 Properties of Si, SiC and sylramic fibers.
αf ΔT −
Material
CTE (10−6/°C)
Elastic modulus (GPa)
Poisson’s Ratio
Si At 1400ºC Cubic SiC CVI SiC Sylramic Fiber Sylramic-iBN Fiber
2.69 [42]
165 [23] 123.75 [23–26] 390 [44] 380 [45] 400 [46–48] 400 [46–48]
0.27 [43]
2.77 [22] 4.6 [45] 5.4 [9] 5.4 [9]
Pf PSi PCVI PSiC = = = ASi ESi Af Ef ACVI ECVI ASiC ESiC
PCVI P PSiC = αSi ΔT − Si = αSiC ΔT − ACVI ECVI ASi ESi ASiC ESiC
And the forces equilibrium condition necessitates that;
Pf = PSi + PCVI + PSiC
0.17 [44] n/a 0.17 [47,48] 0.17 [47,48]
(11)
By solving these equations, the axial stresses due to silicon expansion can be calculated, as shown in Fig. 7. These stresses, the residual thermal stresses and the total approximated residual stresses are presented and compared to the measured stresses in Table 6. 5. Discussion On the microscale, extremely high stresses in the GPa range are measured with Raman spectroscopy. This is consistent with measurements noted in previous studies [5,6]. When not accounting for silicon expansion upon crystallization, and only considering thermal residual stresses, the predicted stresses are much lower than that measured with Raman spectroscopy. However, with the additional consideration of the silicon expansion, the predicted values are much closer to those measured. The model presented in Fig. 7 shows the stresses of constituents within the composite as a function of silicon volume fraction. First, we will consider values at 11.5% silicon content, as this is the average volume fraction between the two plates. The values from the model are presented in Table 6. The model supports the compressive and tensile trends of each constituent. Also, the high GPa magnitudes measured are supported by the model as well.
(8)
Also, the force equilibrium condition in the fiber axial direction necessitates that;
PSi = Pf + PCVI + PSiC
= αCVI ΔT −
(10)
represent an increasing volume fraction. As mentioned, the volumetric expansion of silicon can be estimated as 9.4%. The 9.4% expansion can be divided by 3 to calculate an axial expansion of 3%, or 0.03. Assuming a perfect interfacial adhesion between all cylinders, equilibrium conditions due to 0.03 axial expansion of the silicon upon solidification can be expressed as Eq. 8.
0.03−
Pf Af Ef
(9)
To account for the thermal residual stresses developing upon cooling the composite from 1410ºC to room temperature, considered to be 25 °C, equilibrium conditions can be expressed as;
Fig. 7. Residual stress model as a function of Silicon volume fraction.
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Table 6 Approximated and measured residual stresses.
Calculated Silicon Expansion Stresses (at 11% Si volume fraction) Calculated Thermal Residual Stresses (at 11% Si volume fraction) Total Approximation Measured: Plate 1 Measured: Plate 2
Fiber Stress (GPa)
Silicon Stress (GPa)
SiC CVI Stress (GPa)
SiC Matrix Stress (GPa)
+0.19 +0.47 +0.66 +0.50 +0.69
−1.92 +0.006 −1.91 −2.04 −1.96
+0.19 +.34 +0.53 +0.93 +1.24
+1.55 +0.14 +1.69 +1.46 +1.45
Table 7 Summary of average measured stresses in silicon and SiC of various materials. Material (silicon content)
Fibers
Geometry
Si Stress (GPa)
SiC Matrix Stress (GPa)
RBSiC [5] (24 ± 1% of material) RBSiC [5] (42 ± 1% of material) GE HiPerComp [6] (20% of MI matrix) Honeywell Plate 1 (11% of composite, 34% of MI matrix) Honeywell Plate 2 (12% of composite, 38% of MI matrix)
none none SiC, type not stated Sylramic Sylramic-iBN
n/a n/a [0/90]2s 5HSW [0/90/0]sym 5HSW [0/90/0]sym
−1.92 −1.76 −2.72 −2.04 −1.96
2.15 2.28 0.50 1.46 1.45
± ± ± ± ±
0.20 0.25 0.36 0.07 0.04
± ± ± ± ±
0.38 0.36 0.33 0.08 0.05
Acknowledgements
Specifically, values presented for the silicon and SiC matrix particulate are within a range of around 10 percent for both plates. However, the values measured for the Sylramic fiber in Plate 1 are off by nearly 25%. Such reductions in the measured stresses have been shown to be direct results of interfacial adhesion and fiber fragmentation within the composite [33–39]. However, this phenomenon is more likely attributed to a relief of the stresses near the weak BN interface between the fiber and the CVI SiC. Under these length scales, it would be unlikely that fragmentation within the SiC fiber would occur. As mentioned, the Sylramic-iBN fibers in Plate 2 have an additional processing step that diffuses excess boron in the fiber to the surface. This change in fiber composition could result in the difference of measured residual stresses within the fibers, and is not represented in the model. Second, we see that the model shows an increase in residual stresses in all constituents with increases in silicon content. However, Wing, Esmonde-White, & Halloran noted in their RBSiC study that increasing silicon content resulted in a decrease of compressive stress in the silicon and increase in the SiC tensile stresses [5]. A summary of the results can be seen in Table 7. It is important to note that these materials did not contain any fibers, and therefore would behave differently than the model. Unfortunately, the silicon content does not vary greatly in the two Honeywell plates in this study (difference of 1% by point counting). As such, the average silicon and SiC stress values are nearly the same for the two plates. It would be imperative to study materials that have undergone the same processing conditions with varying silicon volume fractions to either verify or deny the proposed model.
The authors acknowledge support of this work by the Air Force Office of Scientific Research, task # 14RX06COR with David Stargel and Jim Fillerup as the program managers. Kaitlin Kollins recognizes the US Air Force Pathways Program for sponsorship of her time. We would also like to thank Jennifer Pierce of UDRI for her help and support on many aspects of this work, as well as Dr. Nick Pagano for his guidance and advice. Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi: https://doi.org/10.1016/j.jeurceramsoc.2018. 02.013. References [1] N.P. Bansal, J. Lamon, Ceramic matrix composites, Materials, Modeling and Technology, John Wiley & Sons, 2014. [2] J.A. DiCarlo, H.-M. Yun, G.N. Morscher, R.T. Bhatt, SiC/SiC composites for 1200°C and above, in: N.P. Bansal (Ed.), Handbook of Ceramic Composites, Springer US, Boston, MA, 2005, pp. 77–98. [3] J.C.M. Li, Microstructure and Properties of Materials: (Volume 2), World Scientific, (2000). [4] E. Billig, Some defects in crystals grown from the melt. I. defects caused by thermal stresses, Mathematical and Physical Sciences, Proceedings of the Royal Society of London. Series A, 235 1956, pp. 37–55 (1200). [5] B.L. Wing, F. Esmonde-White, J. Halloran, Microstress in reaction-bonded SiC from crytallization expansion of silicon, J. Am. Ceram. Soc. 99 (11) (2016) 3705–3711. [6] B.L. Wing, J.W. Halloran, Microstress in the matrix of a melt-infiltrated SiC/SiC ceramic matrix composite, J. Am. Ceram. Soc. 100 (2017) 5286–5294. [7] N.E. Dowling, Mechanical Behavior of Materials, Pearson, 2012. [8] J.A. DiCarlo, H.M. Yun, New High-Performance SiC Fiber Developed for Ceramic Composites, NASA, Cleveland, OH, 2002, p. 3. [9] J.A. DiCarlo, H.M. Yun, SiC/SiC composites for 1200 C and above, Handbook of Ceramic Composites, Springer, USA, 2005, pp. 33–52. [10] A. International, A.S.T.M, E562-11, Standard Test Method for Determining Volume Fraction by Systematic Manual Point Count, (2011) , West Conschocken, PA www. astm.org. [11] P. Vandenabeele, Practical Raman Spectroscopy: an Introduction, Wiley, Chichester, West Sussex, United Kingdom, 2013. [12] M.S. Amer, Raman Spectroscopy, Fullerenes, and Nanotechnology, Royal Society of Chemistry, Cambridge, UK, 2010. [13] M.S. Amer, Raman Spectroscopy Applications in Soft Matter, Wiley-Blackwell, New York, 2009. [14] G. Gouadec, S. Karlin, J. Wu, M. Parlier, P. Colomban, Physical chemistry and mechanical imaging of ceramic-fibre-reinforced ceramic- or metal-matrix composites, Compos. Sci. Technol. 61 (3) (2001) 383–388. [15] M. Momose, M. Hirasaka, Y. Furukawa, Raman spectroscopic study on boron-doped silicon nanoparticles, Vib. Spectrosc. 72 (2014) 62–65. [16] R. Gajić, D. Braun, F. Kuchar, A. Golubović, R. Korntner, H. Löschner, J. Butschke, R. Springer, F. Letzkus, Boron-content dependence of Fano resonances in p-type silicon, J. Phys. Condens. Matter 15 (17) (2003) 2923.
6. Conclusion Residual stresses were measured in commercial woven SiC/SiC ceramic matrix composites by utilizing Raman spectroscopy. High microstresses were measured and supported by the developed model. Average stresses in the fibers ranged from 0.5 to 0.69 GPa in tension. Both the SiC CVI and SiC particulate matrix were also in tension, with the SiC matrix being slightly higher at 1.45 GPa and the SiC CVI ranging from 0.93 to 1.24 GPa on average. The melt infiltrated silicon has high compressive residual stresses of about 2 GPa. When considering the magnitudes produced by modeling the silicon expansion and thermal expansions, the free silicon expansion is the more dominant phenomena causing the high residual stresses in the composite. The proposed model suggests that an increasing silicon volume fraction will result in an increase of residual stresses amongst all of the constituents in the composite.
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integrated circuits, Semicond. Sci. Technol. 11 (2) (1996) 139. [33] M. Amer, M. Koczak, C. Galiotis, L. Schadler, Environmental degradation studies of the interface in single-filament graphite/epoxy composites using laser Raman spectroscopy, Adv. Compos. Lett. 3 (1) (1994) 17–20. [34] M.S. Amer, L.S. Schadler, Micromechanical behavior of graphite/epoxy composites - part I: the effect of fiber sizing, Sci. Eng. Compos. Mater. 7 (1–2) (1998) 81–113. [35] M.S. Amer, L.S. Schadler, Micromechanical behavior of graphite/epoxy composites - part II: Interfacial durability, Sci. Eng. Compos. Mater. 7 (1–2) (1998) 115–149. [36] H.D. Wagner, M.S. Amer, L.S. Schadler, Residual compression stress profile in highmodulus carbon fiber embedded in isotactic polypropylene by micro-Raman spectroscopy, Appl. Compos. Mater. 7 (4) (2000) 209–217. [37] M.S. Amer, Raman spectroscopy investigations of functionally graded materials and inter-granular mechanics, Int. J. Solids Struct. 42 (2) (2005) 751–757. [38] L.S. Schadler, M. Koczak, M.S. Amer, Environmental effects on interfacial behavior in graphite/epoxy single-fiber and multi-fibers composites, in: L. Drazal, R. Opila, N. Peppas, C. Shutte (Eds.), Polymer/Inorganic Interfaces II, MRS, 1995, pp. 155–166. [39] M.S. Amer, Raman spectroscopy and molecular simulation investigations of adsorption on the surface of single-walled carbon nanotubes and nanospheres, J. Raman Spectrosc. 38 (6) (2007) 721–727. [40] W.L. Zhu, J.L. Zhu, S. Nishino, G. Pezzotti, Spatially resolved Raman spectroscopy evaluation of residual stresses in 3C-SiC layer deposited on Si substrates with different crystallographic orientations, Appl. Surf. Sci. 252 (6) (2006) 2346–2354. [41] J.F. DiGregorio, T.E. Furtak, Analysis of residual stress in 6H-SiC particles within Al2O3/SiC composites through Raman spectroscopy, J. Am. Ceram. Soc. 75 (7) (1992) 1854–1857. [42] C.A. Swenson, Recommended values for the thermal expansivity of silicon from 0 to 1000 K, J. Phys. Chem. Ref. Data 12 (2) (1983) 179–182. [43] P. Hess, Laser diagnostics of mechanical and elastic properties of silicon and carbon films, Appl. Surf. Sci. 106 (1996) 429–437. [44] T.D. Gulden, Mechanical properties of polycrystalline β-sic, J. Am. Ceram. Soc. 52 (11) (1969) 585–590. [45] S.K. Mital, B.A. Bednarcyk, S.M. Arnold, J. Lang, Modeling of melt-infiltrated SiC/ SiC composite properties, NASA, Hanover, MD (2009). [46] H. Mei, Measurement and calculation of thermal residual stress in fiber reinforced ceramic matrix composites, Compos. Sci. Technol. 68 (15–16) (2008) 3285–3292. [47] P.L.N. Murthy, S.K. Mital, J.A. DiCarlo, Characterizing the properties of a woven SiC/SiC composite using W-CEMCAN computer code, NASA (1999) 20. [48] S.K. Mital, B.A. Bednarcyk, S.M. Arnold, J. Lang, Modeling of melt-infi ltrated SiC/ SiC composite properties, NASA (2009) 20.
[17] Y. Ward, R.J. Young, R.A. Shatwell, Application of Raman microscopy to the analysis of silicon carbide monofilaments, J. Mater. Sci. 39 (22) (2004) 6781–6790. [18] C.W.G. Derst, K.L. Bhatia, W. Kratschmer, S. Kalbitzer, Optical properties of SiC for crystalline/amorphous pattern fabrication, Appl. Phys. Lett. 54 (18) (1989) 1722–1724. [19] G.E. Jellison Jr., Optical functions of silicon determined by two-channel polarization modulation ellipsometry, Opt. Mater. 1 (1) (1992) 41–47. [20] J.A. Dicarlo, H.M. Yun, G.N. Morscher, R.T. Bhatt, SiC/SiC composites for 1200 C and above, Handbook of Ceramic Composites, Springer, US, 2005, pp. 77–98. [21] E. Anastassakis, A. Cantarero, M. Cardona, Piezo-Raman measurements and anharmonic parameters in silicon and diamond, Phys. Rev. B 41 (11) (1990) 7529–7535. [22] G.A. Slack, S.F. Bartram, Thermal expansion of some diamondlike crystals, J. Appl. Phys. 46 (1) (1975) 89–98. [23] M.A. Hopcroft, W.D. Nix, T.W. Kenny, What is the Young’s Modulus of silicon? J. Microelectromech. Syst. 19 (2) (2010) 229–238. [24] S. Koun, Temperature dependence of Young's Modulus of silicon, Jpn. J. Appl. Phys. 52 (8R) (2013) 088002. [25] C.-H. Cho, Characterization of Young’s modulus of silicon versus temperature using a “beam deflection” method with a four-point bending fixture, Curr. Appl. Phys. 9 (2) (2009) 538–545. [26] G. Ouyang, M.X. Gu, S.Y. Fu, C.Q. Sun, W.G. Zhu, Determination of the Si-Si bond energy from the temperature dependence of elastic modulus and surface tension, EPL (Europhys. Lett.) 84 (6) (2008) 66005. [27] Silicon carbide (SiC) bulk modulus, Youngs modulus, shear modulus, in: O. Madelung, U. Rössler, M. Schulz (Eds.), Group IV Elements, IV-IV and III-V Compounds. Part a - Lattice Properties, Springer Berlin Heidelberg, Berlin, Heidelberg, 2001, pp. 1–7. [28] D.R. Moss, Pressure Vessel Design Manual, Elsevier Science, 2004. [29] P.A. Gustafson, S.J. Harris, A.E. O’Neill, A.M. Waas, Measurement of biaxial stress states in silicon using micro-Raman spectroscopy, J. Appl. Mech. 73 (5) (2006) 745–751. [30] P.J. Mcnally, J.W. Curley, M. Bolt, A. Reader, T. Tuomi, R. Rantama¨ki, A.N. Danilewsky, I. De Wolf, Monitoring of stress reduction in shallow trench isolation CMOS structures via synchrotron X-ray topography, electrical data and raman spectroscopy, J. Mater. Sci.: Mater. Electron. 10 (5) (1999) 351–358. [31] K.-S. Chen, Techniques in residual stress measurement for MEMS and their applications, in: C.T. Leondes (Ed.), MEMS/NEMS: Handbook Techniques and Applications, Springer US, Boston, MA, 2006, pp. 1252–1328. [32] I. De Wolf, Micro-Raman spectroscopy to study local mechanical stress in silicon
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Journal of the European Ceramic Society journal homepage: www.elsevier.com/locate/jeurceramsoc
Original Article
Residual stress measurements in melt infiltrated SiC/SiC ceramic matrix composites using Raman spectroscopy ⁎
Kaitlin Kollinsa,b, , Craig Przybylaa, Maher S. Amerb a b
Air Force Research Labs, WPAFB, OH, 45433, United States Department of Mechanical and Materials Engineering, Wright State University, Dayton, OH, 45435, United States
A R T I C L E I N F O
A B S T R A C T
Keywords: Ceramic matrix composites Residual stress Raman spectroscopy Silicon expansion
Raman spectroscopy was utilized to characterize the chemical composition and residual stresses formed in melt infiltrated SiC/SiC CMCs during processing. Stresses in SiC fibers, in SiC chemical vapor (CVI) infiltrated matrix, in SiC melt infiltrated matrix, and in free silicon were measured for two different plates of CMCs. Stresses in the free silicon averaged around 2 GPa in compression, while stresses in the matrix SiC were 1.45 GPa in tension. The SiC CVI phase had stresses ranging between 0.9 GPa and 1.2 GPa in tension and the SiC fibers experienced stresses of .05–0.7 GPa in tension. These results were validated with the proposed model of the system. While the mismatch in the coefficients of thermal expansion between the constituents contributes to the overall residual stress state, the silicon expansion upon solidification was found to be the major contributor to residual stresses within the composite.
1. Introduction SiC/SiC ceramic matrix composites (CMCs) are promising materials for replacing Ni-base super-alloys in high temperature applications as they exhibit as much as 1/3rd the density while maintaining sufficient strength and creep resistance to operate at significantly higher temperatures (i.e. > 1000 °C) [1,2]. Changes in processing of SiC/SiC CMCs has shown to significantly impact the mechanical performance of the composite, including the tensile strength and peak strain, affecting the composite toughness and creep resistance; the observed correlation was attributed to differences in porosity, residual stresses, and the formation of silica glass during processing [2,3]. Because of the mismatch in coefficients of thermal expansion of the various constituent phases and the high processing temperature employed in the processing of SiC/SiC CMCs, significant residual stresses can develop in these types of composites upon cooldown from the processing temperature. During processing, the two plates in the study here were subject to a melt infiltration process, in which molten silicon was infiltrated into a fiber preform containing SiC particulate. This process results in a certain amount of residual unreacted silicon dispersed throughout the composite structure. Silicon falls in the category of crystals with an open cubic lattice structure that increase their interatomic distance by large amounts upon solidification from a liquid. Hence, severe stresses develop if the crystal cannot expand freely upon solidification [4]. Residual stresses in the matrix may be beneficial in
⁎
some cases. For example, compressive residual stresses present within the matrix will help to inhibit early crack growth in the composite similar to the desired effect of the residual stress induced by shot peening in metals Previous work has performed using Raman spectroscopy to characterize residual stresses in multiphase ceramic composites. Residual stresses in reaction bonded silicon carbide (RBSiC) samples, containing no fibers, produced from the melt infiltration process were studied as a function of their unreacted silicon [5]. Within the unreacted silicon, residual stresses of up to 2 GPa in compression were reported, with tensile residual stresses in the SiC reaching 2.3 GPa. Higher compressive residual stresses were measured in the samples containing lower amounts of silicon, with lower tensile residual stresses. A follow-up study was conducted on matrix material away from fibers in 0/90 laminate HiPerComp CMCs produced by GE [6]. The matrix material in the composite had a silicon volume fraction of 20 percent. Compressive stresses ranging from 2.4 to 3.1 GPa were reported for the silicon, and tensile stresses of 0.24 to 0.75 GPa in tension were measured for SiC within the matrix [6]. In this paper, two different variants of melt infiltrated SiC/SiC CMCs are characterized via Raman spectroscopy. Like the previously cited study in a similar material, the residual stresses in the matrix material is measured. Additionally, unlike the previous study, micro-Raman residual stress measurements are performed in the immediate neighborhood on and around the SiC fibers. Also, unique to the materials studied
Corresponding author at: Air Force Research Labs, WPAFB, OH, 45433, United States. E-mail address: [email protected] (K. Kollins).
https://doi.org/10.1016/j.jeurceramsoc.2018.02.013 Received 2 January 2018; Received in revised form 31 January 2018; Accepted 5 February 2018 0955-2219/ Published by Elsevier Ltd.
Please cite this article as: Kollins, K., Journal of the European Ceramic Society (2018), https://doi.org/10.1016/j.jeurceramsoc.2018.02.013
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here is a SiC layer deposited around the fiber preform via a chemical vapor infiltration (CVI) process, which was also characterized using Raman spectroscopy. The coupling of these stresses in these various material constituents is considered and a simple model is proposed to model the residual stresses in these materials around the SiC fibers.
Table 1 Wavenumber and shift to stress conversion factors.
2. Experimental setup
Constituent
Fingerprint Raman Peak Position (cm−1)
Shift to Stress Conversion Factor C (cm−1/GPa)
Silicon Cubic SiC Peak 1 Cubic SiC Peak 2
515.3 796 [40] 973 [40]
1.88 ± 0.05 [21] 3.53 ± 0.21 [41] 4.28 ± 0.22 [41]
2.1. Material
ωo−ωs = σR * C
Two plates of continuous SiC fiber reinforced SiC matrix CMCs were investigated. In both plates, the fibers were woven into a five-harness satin weave preform. Plate 1 contained Sylramic fibers, while Plate 2 contained Sylramic-iBN fibers. The plates went through similar processing steps, with exception to an extra processing step for Plate 2 in which the preform first went through a thermal treatment that forces excess boron to diffuse to the surface of the fibers that then interacts with a nitrogen-rich environment, creating an in-situ boron nitride (iBN) fiber coating around the fibers [7,8]. It has been shown that by diffusing the boron to the surface, the tensile strength of the fiber is retained and the creep resistance and oxidation resistance are improved [2,8,9]. Also, the iBN coating helps to avoid direct contact between fibers, as well as avoiding silica glass formation that is detrimental to the mechanical properties. Both preforms then went through chemical vapor infiltration (CVI) of boron nitride followed by a CVI SiC layer and then a preceramic polymer containing SiC particulate was infiltrated into remaining porosity at room temperature. Next the preceramic polymer is pyrolyzed resulting in a carbon rich matrix. Then, molten silicon, at 1415 °C, is melt-infiltrated (MI) into the fiber preform and reacts with excess carbon to form a predominantly silicon carbide matrix with minimal porosity [9]. To characterize local volume fraction fluctuations, a point counting method [10] was employed to determine the volume fraction of the constituents within each plate. In this method, an appropriate grid size was found through convergence studies, and then overlaid onto representative images of the microstructure. Wherever a grid intersection occurred, the point was evaluated to determine the phase of the material. The BN fiber coatings were not considered during point counting, as their volume fraction is minimal. If a grid point landed in the middle of a fiber coating and fiber, the point was counted as a fiber. Tensile testing was performed on two dogbone specimens for each plate at room temperature at Honeywell Advanced Composites in 2002. Thee samples were 154 mm in length and were 2 mm thick and had a gage section 18 mm long by 8 mm wide.
(1)
The conversion factors for β silicon carbide and silicon were previously determined in the literature and are shown in Table 1. However, due to the presence of boron doping in the silicon, the standard stress free peak position of 520.5 cm−1 for silicon could not be used. The stress free peak position of the doped silicon was found experimentally by using samples ground into fine powders. The measured peak position is listed in Table 1, and the peak can also be seen in Fig. 2 plotted against the silicon standard and silicon measured within the composite. While the silicon natural Raman active band is typically a symmetric triplet, the silicon peak is asymmetric in the samples presented. This is likely due to a Fano resonance effect that has been observed before due to boron doping [15,16]. The silicon peaks were curve fit with a Fano profile, while the β SiC peaks were fit with Lorentzian profiles. The presence of β SiC was confirmed by the peak profile [17]. Although the shift to stress conversion factor used in this work is based on the literature values for pure silicon, boron doping of the silicon may have affected this value as well. Implications of the effect of boron doping on the stress conversion factor will be considered in Section III with the results. It is important to note that for SiC, the absorption coefficient at the laser wavelength used in this study, 514 nm, is 13.98 cm−1 [18]. This will give a penetration depth of 715 microns for SiC. On the other hand, the penetration depth for silicon is only 1 μm with an absorption coefficient of 9877 cm−1 at 514 nm [19]. When observing the results, SiC and Si may be present in the same location on the Raman maps. This is due to Si being detected directly beneath SiC on the surface. Another consideration that must be made in the case of these composites is Raman’s inability to characterize residual stresses in the boron nitride coatings between the fiber and matrix material. The boron nitride fluoresces under the laser, causing the Raman signal at the fiber coatings to become distorted and uninterpretable. Raman spectra were collected using a Renishaw Raman Spectrometer equipped with a 514.5 nm excitation Ar+ laser, a 1800 line/mm grating, and a back depleted CCD for data collection. Laser power at the sample was kept below 2 mW to avoid sample heating. A long working distance 50x objective was employed to focus the laser beam on the sample and to collect the Raman scattered light in a backscattering setup. Raman maps were collected using a motorized stage with a step size of 1 μm. The data collected was then imported into a MATLAB® program which calculates the local chemical composition and residual stress maps of the area analyzed. Specifically, this output was calculated based on the integrated intensity and wavenumber shift, respectively, for both Si and SiC. Data were taken from both areas within the matrix and around fibers surrounded in matrix material in the middle of the fiber tows, as shown in Fig. 1. Several Raman maps were collected and analyzed to obtain data representative of the entire sample.
2.2. Raman spectroscopy 12 × 2 mm samples were sectioned from as-manufactured specimens. The samples were polished to a 1 μm finish using diamond grinding disks. Samples were ultrasonically cleaned in solvent to avoid contamination. Micro-Raman spectroscopy was utilized to investigate local chemical compositions and residual stresses, which likely significantly influence SiC/SiC composite mechanical properties. Micro-Raman spectroscopy is a nondestructive technique that is employed to measure the various fundamental vibration modes in a material [11]. By following the “fingerprint” of the Raman active modes of different materials within the investigated sample, accurate measurements of chemical composition can be obtained from the peak integrated intensity. As the exact position of the peak and its shift depends on local stress, the average of the trace of the stress tensor in the sample can be accurately measured with a 1 μm spatial resolution [12,13]. A shift from the known, stress free wavenumber indicates a residual stress within the material [14]. The residual stress (σR) can be calculated from the measured peak position (ωs) and the stress free peak position (ωo) using a shift to stress conversion factor (C) , as seen in Equation 1:
2.3. Scanning electron microscopy A 12 × 2 mm sample was polished to a 1 μm finish using diamond grinding disks. The sample was cleaned with solvents to avoid contamination. Silicon within the matrix was studied with a Zeiss GeminiSEM 500 using Oxford EDS to quantify the amount of boron dopant within the melt infiltrated silicon. The voltage was at 5.00 kV 2
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Table 2 Volume fraction of Plates 1 and 2.
Plate 1 Plate 2
SiC Particulate
MI Silicon
CVI SiC
Fiber
Porosity
.23 .18
.12 .11
.19 .22
.41 .46
.05 .03
Table 3 Room temperature macro-mechanical properties of investigated samples. Sample
Tensile strength (MPa)
Strain to failure (%)
Yield Strength (MPa)
Elastic Modulus (GPa)
Plate 1 Plate 2
271 ± 21 425 ± 25
0.29 ± 0.03 0.56 ± 0.02
157 ± 8 165 ± 15
200 ± 9 199 ± 1
Fig. 1. Optical micrograph showing fiber and matrix areas studied.
3.2. Micro-Raman spectroscopy mapping
with a 20 μm aperture.
Fig. 3 and 4 depict the Raman mapping results for both SiC and Si distribution and their residual stress around Sylramic fiber in Plate 1 and the Sylramic-iBN fiber in Plate 2, respectively. The distribution maps are derived from the integrated peak areas in the Raman spectrum. As mentioned, when using Raman spectroscopy to measure stress, the stated residual stress values are the average of the trace of the stress tensor. The Raman maps show that Plate 2 has higher residual tensile stress in the fiber and higher residual stress in the SiC than Plate 1. Also, the local area studied in Plate 1 has much higher unreacted silicon content, with similar residual compressive stress in the silicon as Plate 2. As seen in Table 4, for Plate 1, the residual stress in fiber reaches a maximum of + 1.87 GPa, +2.58 GPa in the SiC CVI coating, and + 3.05 GPa in the SiC matrix. In the silicon, however, the residual stress maximum is around −2.97 GPa. In Plate 2, the maximum residual stress in the fiber
3. Results 3.1. Material properties The volume fraction of each phase constituent is listed in Table 2. Silicon content is estimated at 12% in Plate 1 and 11% in Plate 2, which is in good agreeance with literature [20]. The averaged mechanical testing results for two samples from each plate are shown in Table 3. From this, it is seen that the differences between the boron nitride fiber coatings of these SiC/SiC CMCs has a large impact on the composite tensile strength and strain to failure while it does not dramatically affect the composite stiffness or proportional limit.
Fig. 2. Silicon spectra taken from Si standard (centered at 520.5 cm−1), from within composite (centered at 518 cm−1), and from powder (centered at 515.3 cm−1).
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Fig. 3. Silicon carbide and unreacted silicon distributions as well as residual stresses around the Sylramic fibers as measured by micro-Raman spectroscopy in a 30 μm × 30 μm map in Plate 1.
Fig. 4. Silicon carbide and unreacted silicon distributions as well as residual stresses around the Sylramic-iBN fibers as measured by micro-Raman spectroscopy in Plate 2.
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Table 4 Raman stress measurements for Plate 1 and plate 2.
Plate 1 Plate 2
SiC Fiber Average Stress (GPa)
SiC Fiber Maximum Stress (GPa)
SiC CVI Coating Average Stress (GPa)
SiC CVI Coating Maximum Stress (GPa)
SiC Matrix Average Stress (GPa)
SiC Matrix Maximum Stress (GPa)
Free Silicon Average Stress (GPa)
Free Silicon Maximum Stress (GPa)
0.50 ± 0.11 0.69 ± 0.10
1.87 1.81
0.93 ± 0.05 1.24 ± 0.07
2.58 2.72
1.46 ± 0.08 1.45 ± 0.05
3.05 3.02
−2.04 ± 0.07 −1.96 ± 0.04
−2.97 −2.99
from Raman spectroscopy. It is important to note that the value of such stress will depend on the volume of the affected zone compared to the volume of the silicon pools. Specifically, the larger the ratio of the SiC volume over the silicon volume, or VSiC/VSi, the lower the developed internal pressure. Shown in Fig. 6a, the fiber and surrounding matrix material can be modeled as concentric spheres. The Si bulk modulus, kSi, is estimated to be 73.2 GPa (0.75 of the room temperature value of 97.6 GPa) [23–26] near 1400 °C and the SiC bulk modulus is 235 GPa [27]. Substituting these values into Eq. 4 yields a value for VSiC / VSi = 4.14 . The silicon spherical pool will be under hydrostatic pressure with a stress tensor in the form of; Fig. 5. A schematic and a micrograph showing the Cartesian axes system used in stress analysis.
σSi =
reaches + 1.81 GPa, +2.72 GPa in the SiC CVI coating, and + 3.02 GPa in the SiC matrix. In Si, the residual stress is found to at a maximum of around −2.99 GPa. The shift to stress conversion factor used to calculate the residual stresses in the silicon phases is for pure silicon. However, the silicon phase in this composite is doped with boron. This dopant may have an effect on the shift to stress conversion factor. From elemental analysis, the atomic percent of boron within the silicon of the material studied here was 1.40 at%. For this study, it is assumed that the dopant concentration of boron is low enough to have minimal effect on the stress conversion factor; therefore, the shift to stress conversion factor for pure Silicon of 1.88 cm−1/GPa from the literature was employed [21].
σSiC =
(d 2 + d 2 ) σrr = pi ⎡ 0 2 2i ⎤ ⎢ (d 0 −di ) ⎥ ⎣ ⎦
(2)
where ΔV is the change in volume from liquid to solid, Vo is the volume at room temperature, and ρ represents the densities at 1410 °C and at room temperature. Substituting for the density values of liquid silicon at the melting point, 2.55 g/cm3, and in the solid state at room temperature, 2.33 g/cm3, leads to a volumetric expansion of 9.4% upon cooldown. Realizing that the expanding silicon is surrounded by a matrix of SiC, the final increase in the silicon volume must equal the shrinkage in SiC volume within the affected zone. Hence,
VSiC ⎡ P ⎤ P + ⎢ kSiC ⎦ ⎥ VSi ⎣ kSi
(6)
(7)
Another source of residual stresses in the matrix is thermal residual stresses (TRS) due to the mismatch in the coefficients of thermal expansion (CTEs) between the silicon and silicon carbide. Using the CTE values listed in Table 5 and calculating the TRS in both silicon and silicon carbide resulted in small values in the range of 0.03 GPa. Such values are negligible compared to the stress values resulted from the silicon expansion upon solidification. Realizing the Raman measurements under such stress state would yield a value representing the average of the tensor trace [29–32], we realize that our average measurements of -2.0 GPa in the free silicon in the matrix are near the theoretical calculations of −2.11 GPa, confirming that the affected zone around the unreacted silicon has a diameter that extends to 3.45 times that of the silicon pool size.
Fig. 5 depicts an optical micrograph and a schematic representing the SiC/SiC CMC investigated and the Cartesian axes system considered in our discussion and theoretical calculation of the expected residual stresses. The volume expansion of silicon can be estimated according to the equation as [4,22]:
0.094 =
0 0 − 3.0 GPa 0 0 + 3.54 0 0 + 3.54
The radial stresses calculated in Eq. 6 are calculated at the interface using elastic theory treatment of thick-walled spherical pressure vessel equation with an internal pressure (pi), internal diameter (di), and external diameter (do) according to Eq. 7 [28]:
4.1. Residual stresses in the matrix due to silicon solidification expansion
eSi × VSi = eSiC × VSiC
(5)
In this case, for VSiC / VSi = 4.14 , the outer diameter (do) of the affected spherical zone must be 3.45 the internal diameter (di), and, hence, the stress tensor at the Si/SiC interface will be;
4. Model development
−ρ ρ ΔV = 1410° C RT Vo ρRT
− 3.0 0 0 GPa − 3.0 0 0 − 3.0 0 0
4.2. Residual stresses around the fibers In addition to stresses resulting from silicon solidification around the Sylramic and Sylramic-iBN fibers, the large difference in CTE of the composite constituents will also contribute to the developed residual stresses in processed composite. In this case, we modeled the fiber area studied as 4 concentric cylinders as shown in Fig. 6b. Knowing that the fiber diameter is 10 μm, the thickness of the CVI-SiC coating around the fibers was measured experimentally using high resolution optical microscopy and was found to be 4.4 μm. The area of the SiC matrix in the model was determined by the volume fraction of the local areas studied, and backed out to have an 18.1 μm thickness. The silicon cylinder thickness was varied to
(3)
(4)
Where, e is volumetric strain, k is the bulk modulus, V is the volume, and P is the maximum measured silicon stress, obtained to be −3 GPa 5
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Fig. 6. Schematics showing the geometry used to model residual stresses around a) an unreacted silicon pool embedded in the SiC matrix away from the fiber, and b) an unreacted silicon pool next to a fiber.
Table 5 Properties of Si, SiC and sylramic fibers.
αf ΔT −
Material
CTE (10−6/°C)
Elastic modulus (GPa)
Poisson’s Ratio
Si At 1400ºC Cubic SiC CVI SiC Sylramic Fiber Sylramic-iBN Fiber
2.69 [42]
165 [23] 123.75 [23–26] 390 [44] 380 [45] 400 [46–48] 400 [46–48]
0.27 [43]
2.77 [22] 4.6 [45] 5.4 [9] 5.4 [9]
Pf PSi PCVI PSiC = = = ASi ESi Af Ef ACVI ECVI ASiC ESiC
PCVI P PSiC = αSi ΔT − Si = αSiC ΔT − ACVI ECVI ASi ESi ASiC ESiC
And the forces equilibrium condition necessitates that;
Pf = PSi + PCVI + PSiC
0.17 [44] n/a 0.17 [47,48] 0.17 [47,48]
(11)
By solving these equations, the axial stresses due to silicon expansion can be calculated, as shown in Fig. 7. These stresses, the residual thermal stresses and the total approximated residual stresses are presented and compared to the measured stresses in Table 6. 5. Discussion On the microscale, extremely high stresses in the GPa range are measured with Raman spectroscopy. This is consistent with measurements noted in previous studies [5,6]. When not accounting for silicon expansion upon crystallization, and only considering thermal residual stresses, the predicted stresses are much lower than that measured with Raman spectroscopy. However, with the additional consideration of the silicon expansion, the predicted values are much closer to those measured. The model presented in Fig. 7 shows the stresses of constituents within the composite as a function of silicon volume fraction. First, we will consider values at 11.5% silicon content, as this is the average volume fraction between the two plates. The values from the model are presented in Table 6. The model supports the compressive and tensile trends of each constituent. Also, the high GPa magnitudes measured are supported by the model as well.
(8)
Also, the force equilibrium condition in the fiber axial direction necessitates that;
PSi = Pf + PCVI + PSiC
= αCVI ΔT −
(10)
represent an increasing volume fraction. As mentioned, the volumetric expansion of silicon can be estimated as 9.4%. The 9.4% expansion can be divided by 3 to calculate an axial expansion of 3%, or 0.03. Assuming a perfect interfacial adhesion between all cylinders, equilibrium conditions due to 0.03 axial expansion of the silicon upon solidification can be expressed as Eq. 8.
0.03−
Pf Af Ef
(9)
To account for the thermal residual stresses developing upon cooling the composite from 1410ºC to room temperature, considered to be 25 °C, equilibrium conditions can be expressed as;
Fig. 7. Residual stress model as a function of Silicon volume fraction.
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Table 6 Approximated and measured residual stresses.
Calculated Silicon Expansion Stresses (at 11% Si volume fraction) Calculated Thermal Residual Stresses (at 11% Si volume fraction) Total Approximation Measured: Plate 1 Measured: Plate 2
Fiber Stress (GPa)
Silicon Stress (GPa)
SiC CVI Stress (GPa)
SiC Matrix Stress (GPa)
+0.19 +0.47 +0.66 +0.50 +0.69
−1.92 +0.006 −1.91 −2.04 −1.96
+0.19 +.34 +0.53 +0.93 +1.24
+1.55 +0.14 +1.69 +1.46 +1.45
Table 7 Summary of average measured stresses in silicon and SiC of various materials. Material (silicon content)
Fibers
Geometry
Si Stress (GPa)
SiC Matrix Stress (GPa)
RBSiC [5] (24 ± 1% of material) RBSiC [5] (42 ± 1% of material) GE HiPerComp [6] (20% of MI matrix) Honeywell Plate 1 (11% of composite, 34% of MI matrix) Honeywell Plate 2 (12% of composite, 38% of MI matrix)
none none SiC, type not stated Sylramic Sylramic-iBN
n/a n/a [0/90]2s 5HSW [0/90/0]sym 5HSW [0/90/0]sym
−1.92 −1.76 −2.72 −2.04 −1.96
2.15 2.28 0.50 1.46 1.45
± ± ± ± ±
0.20 0.25 0.36 0.07 0.04
± ± ± ± ±
0.38 0.36 0.33 0.08 0.05
Acknowledgements
Specifically, values presented for the silicon and SiC matrix particulate are within a range of around 10 percent for both plates. However, the values measured for the Sylramic fiber in Plate 1 are off by nearly 25%. Such reductions in the measured stresses have been shown to be direct results of interfacial adhesion and fiber fragmentation within the composite [33–39]. However, this phenomenon is more likely attributed to a relief of the stresses near the weak BN interface between the fiber and the CVI SiC. Under these length scales, it would be unlikely that fragmentation within the SiC fiber would occur. As mentioned, the Sylramic-iBN fibers in Plate 2 have an additional processing step that diffuses excess boron in the fiber to the surface. This change in fiber composition could result in the difference of measured residual stresses within the fibers, and is not represented in the model. Second, we see that the model shows an increase in residual stresses in all constituents with increases in silicon content. However, Wing, Esmonde-White, & Halloran noted in their RBSiC study that increasing silicon content resulted in a decrease of compressive stress in the silicon and increase in the SiC tensile stresses [5]. A summary of the results can be seen in Table 7. It is important to note that these materials did not contain any fibers, and therefore would behave differently than the model. Unfortunately, the silicon content does not vary greatly in the two Honeywell plates in this study (difference of 1% by point counting). As such, the average silicon and SiC stress values are nearly the same for the two plates. It would be imperative to study materials that have undergone the same processing conditions with varying silicon volume fractions to either verify or deny the proposed model.
The authors acknowledge support of this work by the Air Force Office of Scientific Research, task # 14RX06COR with David Stargel and Jim Fillerup as the program managers. Kaitlin Kollins recognizes the US Air Force Pathways Program for sponsorship of her time. We would also like to thank Jennifer Pierce of UDRI for her help and support on many aspects of this work, as well as Dr. Nick Pagano for his guidance and advice. Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi: https://doi.org/10.1016/j.jeurceramsoc.2018. 02.013. References [1] N.P. Bansal, J. Lamon, Ceramic matrix composites, Materials, Modeling and Technology, John Wiley & Sons, 2014. [2] J.A. DiCarlo, H.-M. Yun, G.N. Morscher, R.T. Bhatt, SiC/SiC composites for 1200°C and above, in: N.P. Bansal (Ed.), Handbook of Ceramic Composites, Springer US, Boston, MA, 2005, pp. 77–98. [3] J.C.M. Li, Microstructure and Properties of Materials: (Volume 2), World Scientific, (2000). [4] E. Billig, Some defects in crystals grown from the melt. I. defects caused by thermal stresses, Mathematical and Physical Sciences, Proceedings of the Royal Society of London. Series A, 235 1956, pp. 37–55 (1200). [5] B.L. Wing, F. Esmonde-White, J. Halloran, Microstress in reaction-bonded SiC from crytallization expansion of silicon, J. Am. Ceram. Soc. 99 (11) (2016) 3705–3711. [6] B.L. Wing, J.W. Halloran, Microstress in the matrix of a melt-infiltrated SiC/SiC ceramic matrix composite, J. Am. Ceram. Soc. 100 (2017) 5286–5294. [7] N.E. Dowling, Mechanical Behavior of Materials, Pearson, 2012. [8] J.A. DiCarlo, H.M. Yun, New High-Performance SiC Fiber Developed for Ceramic Composites, NASA, Cleveland, OH, 2002, p. 3. [9] J.A. DiCarlo, H.M. Yun, SiC/SiC composites for 1200 C and above, Handbook of Ceramic Composites, Springer, USA, 2005, pp. 33–52. [10] A. International, A.S.T.M, E562-11, Standard Test Method for Determining Volume Fraction by Systematic Manual Point Count, (2011) , West Conschocken, PA www. astm.org. [11] P. Vandenabeele, Practical Raman Spectroscopy: an Introduction, Wiley, Chichester, West Sussex, United Kingdom, 2013. [12] M.S. Amer, Raman Spectroscopy, Fullerenes, and Nanotechnology, Royal Society of Chemistry, Cambridge, UK, 2010. [13] M.S. Amer, Raman Spectroscopy Applications in Soft Matter, Wiley-Blackwell, New York, 2009. [14] G. Gouadec, S. Karlin, J. Wu, M. Parlier, P. Colomban, Physical chemistry and mechanical imaging of ceramic-fibre-reinforced ceramic- or metal-matrix composites, Compos. Sci. Technol. 61 (3) (2001) 383–388. [15] M. Momose, M. Hirasaka, Y. Furukawa, Raman spectroscopic study on boron-doped silicon nanoparticles, Vib. Spectrosc. 72 (2014) 62–65. [16] R. Gajić, D. Braun, F. Kuchar, A. Golubović, R. Korntner, H. Löschner, J. Butschke, R. Springer, F. Letzkus, Boron-content dependence of Fano resonances in p-type silicon, J. Phys. Condens. Matter 15 (17) (2003) 2923.
6. Conclusion Residual stresses were measured in commercial woven SiC/SiC ceramic matrix composites by utilizing Raman spectroscopy. High microstresses were measured and supported by the developed model. Average stresses in the fibers ranged from 0.5 to 0.69 GPa in tension. Both the SiC CVI and SiC particulate matrix were also in tension, with the SiC matrix being slightly higher at 1.45 GPa and the SiC CVI ranging from 0.93 to 1.24 GPa on average. The melt infiltrated silicon has high compressive residual stresses of about 2 GPa. When considering the magnitudes produced by modeling the silicon expansion and thermal expansions, the free silicon expansion is the more dominant phenomena causing the high residual stresses in the composite. The proposed model suggests that an increasing silicon volume fraction will result in an increase of residual stresses amongst all of the constituents in the composite.
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