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Experimental characterization and numerical modeling of thermo-mechanical properties of Al-B4C composites
Author’s Accepted Manuscript Experimental characterization and numerical modeling of thermo-mechanical properties of AlB4C composites Neeraj Kumar Sharma, R.K. Misra, Satpal Sharma www.elsevier.com/locate/ceri
PII: DOI: Reference:
S0272-8842(16)31719-9 http://dx.doi.org/10.1016/j.ceramint.2016.09.187 CERI13847
To appear in: Ceramics International Received date: 3 June 2016 Revised date: 6 September 2016 Accepted date: 27 September 2016 Cite this article as: Neeraj Kumar Sharma, R.K. Misra and Satpal Sharma, Experimental characterization and numerical modeling of thermo-mechanical properties of Al-B4C composites, Ceramics International, http://dx.doi.org/10.1016/j.ceramint.2016.09.187 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental characterization and numerical modeling of thermo-mechanical properties of Al-B4C composites Neeraj Kumar Sharmaa, R. K. Misraa,b & Satpal Sharmaa,b a
BML Munjal University, Gurgaon-122413, India
b
Gautam Buddha University, Greater Noida-201306
*Email: [email protected], Phone: +91-9717885162
Abstract This paper deals with the fabrication and characterization of thermo-mechanical properties of boron carbide reinforced aluminum matrix composites. The effective elastic moduli and effective coefficients of thermal expansion (CTEs) of 4, 8 and 12 vol% boron carbide reinforced aluminum matrix composites were measured experimentally. Object oriented finite element method (OOF) is used next to determine the effective material properties and the effects of microstructure morphologies, i.e., shape, size and orientation of reinforced particles and the presence of voids is analyzed. Different microstructures are constructed for finite element analysis using scanning electron microscopic images of composites. The results obtained from finite element modeling are compared with the experimental values.
Keywords: Metal matrix composites; Elastic Modulus; Thermal expansion; Finite element analysis; Elasto-plastic deformation.
1. Introduction In order to improve the strength, hardness, stiffness, chemical stability, thermal stability and wear deformation of metals, ceramics are often used as reinforcements. Ceramic particlereinforced metal matrix composites (CPMMCs) show excellent strength because of ceramic reinforcement and also demonstrate high toughness due to underlying metal matrix. Ceramics have stable properties at elevated temperatures therefore CPMMCs are often the only suitable choice in applications requiring operation with high temperatures, such as thermal barrier coatings, turbine blades, and internal combustion engines. Aluminum is widely used metal matrix in these composites due to its low cost, low density and ease of fabrication. The reinforcement used in CPMMCs should have high modulus to impart strength, comparable thermal expansion coefficient with metal matrix to reduce the development of residual stresses, and good wettability for uniform distribution and bonding among constituents.
Particle reinforced aluminium matrix composites with silicon carbide or alumina as reinforcement are studied extensively for their fabrication methods, mechanical and thermal properties and finite element analysis (FEM) [1-9]. However, CPMMCs with boron carbide as reinforcement are not studied in detail. Poor wettability and comparable densities of aluminum and boron carbide make it difficult to mix boron carbide well with aluminum. In order to overcome the wettability problem for B4C/Al composites, potassium fluorotitanate (K2TiF6) flux
has been used by few researchers [10,11]. Toptan et al. have reported the effects of Ti addition on the properties of Al-B4C composites [10]. Al-B4C composites were produced by casting route at 850°C and titanium-containing flux was used to overcome the wetting problem between B 4C and liquid aluminium metal. Rao et al. have produced functionally graded Al/B4C composites by flux assisted reaction synthesis followed by centrifugal casting [11]. As the density difference of boron carbide and molten aluminum are very close, the effect of centrifugal force during centrifugal casting on boron carbide distribution and hardness was also studied. Thirumalai et al. have fabricated the Al matrix hybrid composites reinforced with boron carbide (up to 12 wt%) and graphite (3 wt%). Magnesium (3 wt%) was added to the molten metal to improve wettability of reinforcements with aluminum [12].
Simulating the deformation behavior of CPMMCs is an important field relevant to a wide variety of applications. It can be used advantageously to optimize the composite’s microstructure to obtain the desired effective properties. Different analytical and finite element methods (FEM) have been applied [13-21] to predict the effective properties of composites. Thermomechanical behavior of composites is influenced by several parameters: the type of constituents, the reinforcement volume fraction and architecture, the plastic deformation of metal matrix and the thermal residual stresses generated out of mismatch of coefficient of thermal expansion (CTE) among constituents. In order to model the material microstructure, simpler geometries such as dilute or periodic distribution of particles, of spherical or ellipsoidal shape, in a homogenous matrix have been considered by many researchers [21-26]. However, it must be mentioned that the simpler geometries cannot represent the complex shaped
unsymmetrical reinforcement particles. Scanning Electron Microscope (SEM) is commonly used to study the material microstructure. SEM images of composites are used by many researchers to model the real microstructure of composites for FEM analysis. OOF software has been used to generate the finite element meshes from SEM images [14-19]. The advantage of using OOF is that the real microstructure of composites can be simulated; however the approach has not been fully explored. Apart from FE modeling, different analytical models such as: Hashin’s bounds [28] for effective elastic modulus, Turner model [29], Kerner model [30] and Schapery bounds [31] for effective CTE prediction are also used. These models cannot take into account the true microstructure of composites, plastic deformation of metal matrix and presence of voids.
In the present work, aluminum matrix composites, having 4, 8 and 12 vol% boron carbides are fabricated using squeeze liquid stir casting method. The structural (microstructure, porosity), mechanical (elastic moduli) and thermal properties (CTE) of the fabricated composites are then characterized at room temperature as well as at higher temperatures. Next, the effective properties are measured by OOF analysis and the effects of microstructural morphologies: shape, size, distribution, orientation of reinforced particles and the presence of voids are analyzed. The microstructures are generated from SEM images of composites for micromechanical modeling. OOF can conduct only linear elastic analysis, therefore, the finite element meshes generated using OOF are exported to commercial software Abaqus for elastoplastic analysis of composites. The effective CTEs and effective elastic moduli obtained from micromechanical modeling are compared with the experimental values.
2. Fabrication and Structural Characterization of Al-B4C composites 2.1 Sample Preparation
In order to prepare the composite’s samples, 99.5% pure aluminum ingots and boron carbide powder of 200 mesh size (Geepax, Delhi) was used. The composite specimens are fabricated with different volume contents of boron carbide: 4, 8 and 12 vol% using squeeze liquid stir casting method. In order to fabricate the composites, bottom pouring type stir casting furnace (see Fig. 1) is used. In this setup, two furnaces: a main heating furnace to melt the metal and a miniature furnace to preheat the reinforcement particles are mounted on the same setup.
Fig. 1. Bottom pouring type stir casting furnace for composite fabrication.
The aluminum ingots of weight 1 kg were melted in the main furnace, at temperature 800 ±50°C which is controlled by PID based on/off type controller. In order to increase the wettability of B4C in Al, two different additives: potassium fluorotitanate (K2TiF6) and magnesium, were used separately. The B4C powder was mixed with the same amount of K2TiF6 flux and the weighted quantity was preheated in the miniature furnace at temperature 200±25°C for 1 hr. In second case, 1 vol% magnesium was melted along with the weighted quantity of aluminum metal to improve wettability. The stirrer assembly consisting of twisted stainless steel blades with motorized upward/downward movement was used to stir the melt. The preheated mixture was introduced into the melt at a very slow rate when the vortex was
formed. The slurry was continuously stirred in the furnace for 10-15 minutes at variable speed from 400 to 900 rpm. The slurry was then transferred to the permanent mold by opening the path at the bottom of the main furnace. The pathway was also preheated to 650°C to avoid solidification of the melt. The permanent mold was connected to a piston, which was operated by a hydraulic power pack. The melt was pressed with 30 tons pressure by the piston and then allowed to cool down to room temperature.
The composite specimens produced using K2TiF6 flux was observed to have poor bonding between Al and boron carbide with non-uniform distribution of boron carbide particles in Al matrix. On the other hand, the composites produced using Mg additive demonstrated uniform mixing and strong bonding between Al and boron carbide and were used for further investigation in this study.
Fig. 2. Composite’s samples for various testing (a) Cylindrical ingot; (b) specimen for CTE test; (c) specimens for elastic modulus testing and (d) specimen for SEM images.
2.2 Microstructural Characterization
The processed samples of 10mm side cube (see Fig. 2), were cut and prepared for microstructural characterization. The sample’s surfaces were polished using 0.1μm diamond suspension particles. SEM images were taken using Backscattered (BS) and secondary electron (SE) detectors (Quanta 200, FEI). Fig. 3 (a) to (f) show selected but typical SE and BS images of the 4 vol%, 8 vol% and 12 vol% composites. In SE images of composites, the uniformly
distributed boron carbide particle in bright color can be observed, while the grey phase is aluminum. The dark colored region shows the presence of voids in samples which is resulted primarily due to the large difference in CTE values of aluminum and boron carbide.
Fig. 3. SEM micrograph of Al-B4C composites with 4, 8 and 12 vol% B4C, where (a), (c) and (e) are secondary electron images and (b), (d) and (f) are corresponding back scattered images.
3. Characterization of thermomechanical properties of Al-B4C composites 3.1 Elastic Modulus The effective elastic moduli of composite’s specimens are measured using High Temperature Creep Tester (BiSS Ltd.) The creep station is equipped with a high temperature furnace and high temperature extensometers for accurate strain measurement (see Fig. 4a). The threaded samples (M12) were prepared (see Fig. 2c) and the ratio of gauge length to diameter was kept as 4 (as per ASTM E21 and ASTM E8). The composites were tested in stroke mode at a rate of 0.1mm/min.
Fig. 4. (a) High temperature creep tester for elastic modulus measurement; (b) Elastic modulus for different volume contents of boron carbide and temperatures.
Fig. 4 shows the effective elastic modulus of 4, 8 and 12 vol% composites at room temperature as well as at 100°C and 200°C temperatures. It can be observed that the moduli increase continuously with the boron carbide reinforcement, since the elastic modulus of boron carbide is higher than aluminum. The decrease in elastic modulus with the increase of temperature is observed. It is due to the softening of aluminum metal matrix with the rise of temperature resulting in higher strain on the application of load.
3.2 Thermal Expansion
In order to measure the linear CTE of composites, cylindrical samples of 20mm length and 8mm diameter were prepared (see Fig. 2b). The linear coefficient of thermal expansion was measured using the horizontal differential dilatometer, (L75 PT, Linseis Instruments, IIT Roorkee). A variable force of 0.1-0.5 N was applied through the probe to ensure a perfect contact between the probe and the samples all times (see Fig. 5a). The samples were heated in the furnace at a rate of 5°C/min from room temperature (23°C) to 500°C as given by ASTM E831 standard. Changes in the lengths (μm) of the specimens were measured during heating. Thermal strains were obtained by taking the ratio of change in length to the initial length of the specimens.
The variation of thermal strain of composites with temperatures is shown in Fig. 5 (b). A gradual decrease in strain can be observed with the increase of reinforced boron carbide content from 4 vol% to 12 vol%. Further, the thermal strain increases linearly with the increases of temperature from 50° to 500°C. The linear coefficient of thermal expansion (CTE) is calculated by dividing the thermal strain with the temperature rise (∆T= T- Troom). Fig. 5(c) shows the CTE calculated at various temperatures for different samples. CTEs of composites decrease due to the reinforcement of boron carbide. This is expected since the boron carbide has significantly lower CTE of 3.2 μm/m°C [27, 28], when compared to that of Al99.5.
Fig. 5. (a) Differential dilatometer for CTE measurement; (b) Thermal strain and (c) Thermal expansion coefficient for different volume contents of boron carbide and temperatures.
4 Object Oriented Finite Element Analysis 4.1 Microstructure Simulation
In this section, the deformation behavior of Al-B4C composites is studied. The effective properties of composites are estimated using finite element method and the results obtained are compared with experimental values. The object oriented finite element method is used using the open source software OOF2 (NIST, USA). OOF2 works through the SEM images of composites and this way the explicit mathematical definition of microstructure boundary is not
necessary in this software unlike conventional FEMs [14-16]. This software first classifies the pixel groups of composite’s constituents based on the pixel color properties of SEM images. Once the microstructure is generated, the next task is to discretize the microstructure using finite element meshing. The imposed finite element mesh can be adapted using various subroutines so that it confines to the pixel boundary.
In Fig. 6, the SEM image of 4 vol% composite is shown. This image is discretized into four square regions by overlapping a grid over the image. These regions were used as the representative microstructures of 4 vol% composite. In Fig. 6b, the four microstructures used for OOF analysis is illustrated. Similarly, the microstructures of other composites (not shown here) are generated from their respective SEM images. The volume fractions of boron carbide particles and pores were measured from the SEM images of composites by estimating the number of pixels of each phase. In order to identify the pores, brightness and contrast of images were increased to differentiate between the black region, denoting pores and the gray regions, denoting Al in SE images. Table 1 shows the vol% of boron carbide and porosity present in four meshes of 4, 8 and 12 vol% composite. It can be observed that the volume fraction of boron carbide obtained from SEM image analysis varies slightly from the reinforced volume fraction of boron carbide. In case of 4 and 8 vol% composites the difference in measured and reinforced vol% of boron carbide is 0.18-1.4% and in case of 12 vol% composite the variation is 2-4.4%. Nevertheless, the measured volume fractions are relatively close to the reinforced volume fraction of boron carbide and the SEM images obtained are reasonably realistic in capturing the microstructural morphologies of composites.
Fig. 6. (a) SEM image of 4 vol% composite; (b) Four micrograph of 4 vol% composite and (c) corresponding OOF meshes.
Table 1: Volume fraction (% B4C) and porosity of the four FE meshes generated. OOF mesh-1
Vol %
OOF mesh-2
OOF mesh- 3
OOF mesh- 4
% B4C
% porosity
% B4C
% porosity
% B4C
% porosity
% B4C
% porosity
4
5.39
0.48
4.18
0.9
4.3
0.45
3.82
0.8
8
7.04
0.49
6.87
0.646
7.16
0.588
6.82
0.51
12
16.4
1.15
14.15
2.1
15.41
1.17
14.96
2.08
Table 2: The temperature dependence of elastic moduli E, Poisson’s ratio ν, and CTE of Al matrix and B4C reinforcement used for the modeling.
Temperature
Al99.5
B4C
E(MPa) Poisson's ratio CTE(µm/m°C) E(MPa) Poisson's ratio CTE(µm/m°C)
25
65200
0.336
21.1
50
63800
0.336
22
100
62700
0.336
23.8
200
58900
0.342
25.2
300
55800
0.345
26.9
400
50850
0.346
29.8
500
46300
0.3
31.3
448000
0.21
3.2
4.2 Boundary conditions The properties of boron carbide, used in present analysis, are obtained from literature [32,33] (see Table 2). The Al matrix was modeled as elasto-plastic material [34] and the initial
yield stress of aluminum is taken as 33 MPa (see Fig. 7). Boron carbide was modeled as linear elastic material. The OOF meshes are imported to commercial software ABAQUS and the effective elastic modulus and CTEs are measured. In order to measure the effective elastic modulus, the left side of mesh was fixed and the right side was prescribed a small displacement as: X(0, y) = 0; X(L, y) = 0.05 μm
(1)
The effective elastic modulus is computed by dividing the average stress (σxx) with the average strain (εxx) as: (2) In order to measure the effective CTEs of composites, OOF meshes were heated by 500°C above room temperature and the corresponding strain was measured in x and y direction from 50°C to 500°C. The average strain (εavg) was computed at different temperatures and the linear CTE was computed as: (3) Where ∆T= T- 23°C,
Fig. 7. Plastic strain at room temperature for Al99.5 [29].
4.3 Effective Elastic Modulus
Figure 8 shows the effective elastic modulus obtained from OOF analysis of four different microstructures of all three composites. The results obtained from hashin’s bounds [28] are also included. It can be observed that OOF predictions are in good agreement with the experimental values. Qualitatively similar results are obtained from different OOF meshes, however, the effects of the presence of pores and boron carbide particles in different microstructures of composites can be observed on their effective elastic modulus. It can be seen that mesh 1 of 4 vol% and 12 vol% composites show higher boron carbide content (see Table 1) and therefore have high elastic modulus. Mesh 1 and 4 of 12 vol% composite show highest porosity and therefore have lowest elastic modulus. Elastic modulus decreases with the increase of temperature due to the softening of Al matrix and plastic deformations with temperature rise.
Fig. 8. Effective elastic modulus predicted using OOF analysis and hashin’s bounds: (a) 4 vol% composite; (b) 8 vol% composite and (c) 12 vol% composite.
The measured elastic moduli do not fall in the range of upper and lower values of hashin’s bounds. It can be due to the presence of voids in composite’s microstructure which cannot be taken into account while applying the hashin’s bounds. Fig. 9 shows the local stress distribution (S11, MPa) in OOF microstructures for 4, 8 and 12 vol% composites at room temperature. The red colored region shows the high stress concentration in the composite’s microstructure. Boron carbide particles are subjected to high stresses due to their high elastic modulus. Furthermore, the high stress discontinuities can be observed at the interfaces of matrix and reinforcement, particularly at sharp corners or due to abrupt changes in shape of
particles, which could cause the debonding between the constituents. It can be observed that the maximum stress in composites microstructure is 51.5 MPa, 57.5 MPa and 89.6 MPa for 4, 8 and 12 vol% composites. The aluminum metal is subjected to low tensile stresses due to its low elastic modulus and elasto-plastic deformation behavior.
Fig. 9. Local stress distribution at room temperature(a) 4 vol% composite; (b) 8 vol% composite and (c) 12 vol% composite.
4.4 Thermal Expansion Coefficient
Fig. 10 compare the effective CTE measured using OOF and different analytical models from room temperature to 500°C temperature. In case of 12 vol% composite, OOF predicted CTEs are in good agreement with the measured values at all temperatures. However, in case of 4 & 8 vol% composites, OOF predicts slightly lower CTEs at 500°C temperature. The OOF predicted CTEs are differ from measured values by 3-6% in case of 4 and 8 vol% composites and 0.33-5% in case of 12 vol% composite. It can be observed that CTE is not influenced much for the measured presence of voids. Turner model [29] under predicts the CTE values, whereas, Kerner model [30] predicts slightly higher values at all temperatures. The consideration of perfect bonding among constituents in Turner model reduces the effective strain and thereby results in lower CTEs. The upper and lower bounds of schapery [31] are in good agreement with the experimental values at all temperatures.
Fig. 10. Effective CTE predicted using OOF analysis and analytical models: (a) 4 vol% composite; (b) 8 vol% composite and (c) 12 vol% composite.
Fig. 11. Equivalent plastic strain distribution in: (a) 4 vol% composite; (b) 8 vol% composite and (c) 12 vol% composite.
In Fig. 11 the equivalent plastic strain distribution for mesh 1 of all three composites is shown. It can be understood that the thermal expansion behavior of these composites is influenced by plastic deformation, since, the Al matrix starts yielding as the thermal stresses increase beyond its yield point. Fig. 12 shows the strain components for 12 vol% composite. The higher strain produced by Al matrix can be seen (deep yellow colored region), while, the light yellow colored region is majorly associated to boron carbide particles. In between these
two regions, the compression at few sites can be observed. This region is associated with voids. The metal matrix expanded into the voids on heating thereby causing the shrinkage of voids.
Fig. 12. Strain components E11 and E22 for 12 vol% composite at 500°C temperature.
5. Conclusion
Al-B4C composites are fabricated by reinforcing 4, 8 and 12 vol% boron carbide in Al matrix using squeeze casting method and their physical, thermal and thermomechanical behaviors are investigated.
In order to overcome the wettability problem for B4C/Al composites, two different additives: potassium fluorotitanate (K2TiF6) flux and magnesium were used. The composites produced using magnesium flux demonstrated strong bonding and homogenous distribution of
boron carbide particles. The effective CTEs and the effective elastic moduli are measured from composite’s specimens at room temperature as well as at high temperatures. The effective elastic modulus of composites decreases and the effective CTE increases with the increase of temperature.
The effective properties are also measured using FE modeling and analytical models and the results obtained are compared with the experimental values. The effects of microstructural characteristics, i.e., shape, size, distribution, orientation of reinforced particles, presence of porosities and temperatures are measured on the effective elastic modulus and CTE of composites using OOF. Microstructures of composites were constructed from the SEM images. The results obtained from OOF analysis are in good agreement with the experimental values. The porosity present in composites were characterize from image analysis of SEM images. We have observed that the effective elastic modulus is strongly influenced by the presence of porosity and boron carbide content, whereas, CTE is not much influenced for the measured porosity content. Turner model under predicts, whereas, the Kerner model over predicts the CTEs values. The bounds of schapery for CTE values are in good agreement with the experimental values. However, the hashin’s bounds could not predict well the effective elastic moduli, since, the elastic modulus is strongly influenced by the presence of voids.
OOF can be used advantageously to model the real microstructure of composites including the presence of voids. OOF conducts only linear elastic analysis, whereas, the thermomechanical behavior of metal matrix composites is strongly influenced by the plastic
deformation of metal matrix. Therefore, the OOF modeled microstructures were studied with the commercial software Abaqus to model the elasto-plastic deformation of metal matrix.
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PII: DOI: Reference:
S0272-8842(16)31719-9 http://dx.doi.org/10.1016/j.ceramint.2016.09.187 CERI13847
To appear in: Ceramics International Received date: 3 June 2016 Revised date: 6 September 2016 Accepted date: 27 September 2016 Cite this article as: Neeraj Kumar Sharma, R.K. Misra and Satpal Sharma, Experimental characterization and numerical modeling of thermo-mechanical properties of Al-B4C composites, Ceramics International, http://dx.doi.org/10.1016/j.ceramint.2016.09.187 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental characterization and numerical modeling of thermo-mechanical properties of Al-B4C composites Neeraj Kumar Sharmaa, R. K. Misraa,b & Satpal Sharmaa,b a
BML Munjal University, Gurgaon-122413, India
b
Gautam Buddha University, Greater Noida-201306
*Email: [email protected], Phone: +91-9717885162
Abstract This paper deals with the fabrication and characterization of thermo-mechanical properties of boron carbide reinforced aluminum matrix composites. The effective elastic moduli and effective coefficients of thermal expansion (CTEs) of 4, 8 and 12 vol% boron carbide reinforced aluminum matrix composites were measured experimentally. Object oriented finite element method (OOF) is used next to determine the effective material properties and the effects of microstructure morphologies, i.e., shape, size and orientation of reinforced particles and the presence of voids is analyzed. Different microstructures are constructed for finite element analysis using scanning electron microscopic images of composites. The results obtained from finite element modeling are compared with the experimental values.
Keywords: Metal matrix composites; Elastic Modulus; Thermal expansion; Finite element analysis; Elasto-plastic deformation.
1. Introduction In order to improve the strength, hardness, stiffness, chemical stability, thermal stability and wear deformation of metals, ceramics are often used as reinforcements. Ceramic particlereinforced metal matrix composites (CPMMCs) show excellent strength because of ceramic reinforcement and also demonstrate high toughness due to underlying metal matrix. Ceramics have stable properties at elevated temperatures therefore CPMMCs are often the only suitable choice in applications requiring operation with high temperatures, such as thermal barrier coatings, turbine blades, and internal combustion engines. Aluminum is widely used metal matrix in these composites due to its low cost, low density and ease of fabrication. The reinforcement used in CPMMCs should have high modulus to impart strength, comparable thermal expansion coefficient with metal matrix to reduce the development of residual stresses, and good wettability for uniform distribution and bonding among constituents.
Particle reinforced aluminium matrix composites with silicon carbide or alumina as reinforcement are studied extensively for their fabrication methods, mechanical and thermal properties and finite element analysis (FEM) [1-9]. However, CPMMCs with boron carbide as reinforcement are not studied in detail. Poor wettability and comparable densities of aluminum and boron carbide make it difficult to mix boron carbide well with aluminum. In order to overcome the wettability problem for B4C/Al composites, potassium fluorotitanate (K2TiF6) flux
has been used by few researchers [10,11]. Toptan et al. have reported the effects of Ti addition on the properties of Al-B4C composites [10]. Al-B4C composites were produced by casting route at 850°C and titanium-containing flux was used to overcome the wetting problem between B 4C and liquid aluminium metal. Rao et al. have produced functionally graded Al/B4C composites by flux assisted reaction synthesis followed by centrifugal casting [11]. As the density difference of boron carbide and molten aluminum are very close, the effect of centrifugal force during centrifugal casting on boron carbide distribution and hardness was also studied. Thirumalai et al. have fabricated the Al matrix hybrid composites reinforced with boron carbide (up to 12 wt%) and graphite (3 wt%). Magnesium (3 wt%) was added to the molten metal to improve wettability of reinforcements with aluminum [12].
Simulating the deformation behavior of CPMMCs is an important field relevant to a wide variety of applications. It can be used advantageously to optimize the composite’s microstructure to obtain the desired effective properties. Different analytical and finite element methods (FEM) have been applied [13-21] to predict the effective properties of composites. Thermomechanical behavior of composites is influenced by several parameters: the type of constituents, the reinforcement volume fraction and architecture, the plastic deformation of metal matrix and the thermal residual stresses generated out of mismatch of coefficient of thermal expansion (CTE) among constituents. In order to model the material microstructure, simpler geometries such as dilute or periodic distribution of particles, of spherical or ellipsoidal shape, in a homogenous matrix have been considered by many researchers [21-26]. However, it must be mentioned that the simpler geometries cannot represent the complex shaped
unsymmetrical reinforcement particles. Scanning Electron Microscope (SEM) is commonly used to study the material microstructure. SEM images of composites are used by many researchers to model the real microstructure of composites for FEM analysis. OOF software has been used to generate the finite element meshes from SEM images [14-19]. The advantage of using OOF is that the real microstructure of composites can be simulated; however the approach has not been fully explored. Apart from FE modeling, different analytical models such as: Hashin’s bounds [28] for effective elastic modulus, Turner model [29], Kerner model [30] and Schapery bounds [31] for effective CTE prediction are also used. These models cannot take into account the true microstructure of composites, plastic deformation of metal matrix and presence of voids.
In the present work, aluminum matrix composites, having 4, 8 and 12 vol% boron carbides are fabricated using squeeze liquid stir casting method. The structural (microstructure, porosity), mechanical (elastic moduli) and thermal properties (CTE) of the fabricated composites are then characterized at room temperature as well as at higher temperatures. Next, the effective properties are measured by OOF analysis and the effects of microstructural morphologies: shape, size, distribution, orientation of reinforced particles and the presence of voids are analyzed. The microstructures are generated from SEM images of composites for micromechanical modeling. OOF can conduct only linear elastic analysis, therefore, the finite element meshes generated using OOF are exported to commercial software Abaqus for elastoplastic analysis of composites. The effective CTEs and effective elastic moduli obtained from micromechanical modeling are compared with the experimental values.
2. Fabrication and Structural Characterization of Al-B4C composites 2.1 Sample Preparation
In order to prepare the composite’s samples, 99.5% pure aluminum ingots and boron carbide powder of 200 mesh size (Geepax, Delhi) was used. The composite specimens are fabricated with different volume contents of boron carbide: 4, 8 and 12 vol% using squeeze liquid stir casting method. In order to fabricate the composites, bottom pouring type stir casting furnace (see Fig. 1) is used. In this setup, two furnaces: a main heating furnace to melt the metal and a miniature furnace to preheat the reinforcement particles are mounted on the same setup.
Fig. 1. Bottom pouring type stir casting furnace for composite fabrication.
The aluminum ingots of weight 1 kg were melted in the main furnace, at temperature 800 ±50°C which is controlled by PID based on/off type controller. In order to increase the wettability of B4C in Al, two different additives: potassium fluorotitanate (K2TiF6) and magnesium, were used separately. The B4C powder was mixed with the same amount of K2TiF6 flux and the weighted quantity was preheated in the miniature furnace at temperature 200±25°C for 1 hr. In second case, 1 vol% magnesium was melted along with the weighted quantity of aluminum metal to improve wettability. The stirrer assembly consisting of twisted stainless steel blades with motorized upward/downward movement was used to stir the melt. The preheated mixture was introduced into the melt at a very slow rate when the vortex was
formed. The slurry was continuously stirred in the furnace for 10-15 minutes at variable speed from 400 to 900 rpm. The slurry was then transferred to the permanent mold by opening the path at the bottom of the main furnace. The pathway was also preheated to 650°C to avoid solidification of the melt. The permanent mold was connected to a piston, which was operated by a hydraulic power pack. The melt was pressed with 30 tons pressure by the piston and then allowed to cool down to room temperature.
The composite specimens produced using K2TiF6 flux was observed to have poor bonding between Al and boron carbide with non-uniform distribution of boron carbide particles in Al matrix. On the other hand, the composites produced using Mg additive demonstrated uniform mixing and strong bonding between Al and boron carbide and were used for further investigation in this study.
Fig. 2. Composite’s samples for various testing (a) Cylindrical ingot; (b) specimen for CTE test; (c) specimens for elastic modulus testing and (d) specimen for SEM images.
2.2 Microstructural Characterization
The processed samples of 10mm side cube (see Fig. 2), were cut and prepared for microstructural characterization. The sample’s surfaces were polished using 0.1μm diamond suspension particles. SEM images were taken using Backscattered (BS) and secondary electron (SE) detectors (Quanta 200, FEI). Fig. 3 (a) to (f) show selected but typical SE and BS images of the 4 vol%, 8 vol% and 12 vol% composites. In SE images of composites, the uniformly
distributed boron carbide particle in bright color can be observed, while the grey phase is aluminum. The dark colored region shows the presence of voids in samples which is resulted primarily due to the large difference in CTE values of aluminum and boron carbide.
Fig. 3. SEM micrograph of Al-B4C composites with 4, 8 and 12 vol% B4C, where (a), (c) and (e) are secondary electron images and (b), (d) and (f) are corresponding back scattered images.
3. Characterization of thermomechanical properties of Al-B4C composites 3.1 Elastic Modulus The effective elastic moduli of composite’s specimens are measured using High Temperature Creep Tester (BiSS Ltd.) The creep station is equipped with a high temperature furnace and high temperature extensometers for accurate strain measurement (see Fig. 4a). The threaded samples (M12) were prepared (see Fig. 2c) and the ratio of gauge length to diameter was kept as 4 (as per ASTM E21 and ASTM E8). The composites were tested in stroke mode at a rate of 0.1mm/min.
Fig. 4. (a) High temperature creep tester for elastic modulus measurement; (b) Elastic modulus for different volume contents of boron carbide and temperatures.
Fig. 4 shows the effective elastic modulus of 4, 8 and 12 vol% composites at room temperature as well as at 100°C and 200°C temperatures. It can be observed that the moduli increase continuously with the boron carbide reinforcement, since the elastic modulus of boron carbide is higher than aluminum. The decrease in elastic modulus with the increase of temperature is observed. It is due to the softening of aluminum metal matrix with the rise of temperature resulting in higher strain on the application of load.
3.2 Thermal Expansion
In order to measure the linear CTE of composites, cylindrical samples of 20mm length and 8mm diameter were prepared (see Fig. 2b). The linear coefficient of thermal expansion was measured using the horizontal differential dilatometer, (L75 PT, Linseis Instruments, IIT Roorkee). A variable force of 0.1-0.5 N was applied through the probe to ensure a perfect contact between the probe and the samples all times (see Fig. 5a). The samples were heated in the furnace at a rate of 5°C/min from room temperature (23°C) to 500°C as given by ASTM E831 standard. Changes in the lengths (μm) of the specimens were measured during heating. Thermal strains were obtained by taking the ratio of change in length to the initial length of the specimens.
The variation of thermal strain of composites with temperatures is shown in Fig. 5 (b). A gradual decrease in strain can be observed with the increase of reinforced boron carbide content from 4 vol% to 12 vol%. Further, the thermal strain increases linearly with the increases of temperature from 50° to 500°C. The linear coefficient of thermal expansion (CTE) is calculated by dividing the thermal strain with the temperature rise (∆T= T- Troom). Fig. 5(c) shows the CTE calculated at various temperatures for different samples. CTEs of composites decrease due to the reinforcement of boron carbide. This is expected since the boron carbide has significantly lower CTE of 3.2 μm/m°C [27, 28], when compared to that of Al99.5.
Fig. 5. (a) Differential dilatometer for CTE measurement; (b) Thermal strain and (c) Thermal expansion coefficient for different volume contents of boron carbide and temperatures.
4 Object Oriented Finite Element Analysis 4.1 Microstructure Simulation
In this section, the deformation behavior of Al-B4C composites is studied. The effective properties of composites are estimated using finite element method and the results obtained are compared with experimental values. The object oriented finite element method is used using the open source software OOF2 (NIST, USA). OOF2 works through the SEM images of composites and this way the explicit mathematical definition of microstructure boundary is not
necessary in this software unlike conventional FEMs [14-16]. This software first classifies the pixel groups of composite’s constituents based on the pixel color properties of SEM images. Once the microstructure is generated, the next task is to discretize the microstructure using finite element meshing. The imposed finite element mesh can be adapted using various subroutines so that it confines to the pixel boundary.
In Fig. 6, the SEM image of 4 vol% composite is shown. This image is discretized into four square regions by overlapping a grid over the image. These regions were used as the representative microstructures of 4 vol% composite. In Fig. 6b, the four microstructures used for OOF analysis is illustrated. Similarly, the microstructures of other composites (not shown here) are generated from their respective SEM images. The volume fractions of boron carbide particles and pores were measured from the SEM images of composites by estimating the number of pixels of each phase. In order to identify the pores, brightness and contrast of images were increased to differentiate between the black region, denoting pores and the gray regions, denoting Al in SE images. Table 1 shows the vol% of boron carbide and porosity present in four meshes of 4, 8 and 12 vol% composite. It can be observed that the volume fraction of boron carbide obtained from SEM image analysis varies slightly from the reinforced volume fraction of boron carbide. In case of 4 and 8 vol% composites the difference in measured and reinforced vol% of boron carbide is 0.18-1.4% and in case of 12 vol% composite the variation is 2-4.4%. Nevertheless, the measured volume fractions are relatively close to the reinforced volume fraction of boron carbide and the SEM images obtained are reasonably realistic in capturing the microstructural morphologies of composites.
Fig. 6. (a) SEM image of 4 vol% composite; (b) Four micrograph of 4 vol% composite and (c) corresponding OOF meshes.
Table 1: Volume fraction (% B4C) and porosity of the four FE meshes generated. OOF mesh-1
Vol %
OOF mesh-2
OOF mesh- 3
OOF mesh- 4
% B4C
% porosity
% B4C
% porosity
% B4C
% porosity
% B4C
% porosity
4
5.39
0.48
4.18
0.9
4.3
0.45
3.82
0.8
8
7.04
0.49
6.87
0.646
7.16
0.588
6.82
0.51
12
16.4
1.15
14.15
2.1
15.41
1.17
14.96
2.08
Table 2: The temperature dependence of elastic moduli E, Poisson’s ratio ν, and CTE of Al matrix and B4C reinforcement used for the modeling.
Temperature
Al99.5
B4C
E(MPa) Poisson's ratio CTE(µm/m°C) E(MPa) Poisson's ratio CTE(µm/m°C)
25
65200
0.336
21.1
50
63800
0.336
22
100
62700
0.336
23.8
200
58900
0.342
25.2
300
55800
0.345
26.9
400
50850
0.346
29.8
500
46300
0.3
31.3
448000
0.21
3.2
4.2 Boundary conditions The properties of boron carbide, used in present analysis, are obtained from literature [32,33] (see Table 2). The Al matrix was modeled as elasto-plastic material [34] and the initial
yield stress of aluminum is taken as 33 MPa (see Fig. 7). Boron carbide was modeled as linear elastic material. The OOF meshes are imported to commercial software ABAQUS and the effective elastic modulus and CTEs are measured. In order to measure the effective elastic modulus, the left side of mesh was fixed and the right side was prescribed a small displacement as: X(0, y) = 0; X(L, y) = 0.05 μm
(1)
The effective elastic modulus is computed by dividing the average stress (σxx) with the average strain (εxx) as: (2) In order to measure the effective CTEs of composites, OOF meshes were heated by 500°C above room temperature and the corresponding strain was measured in x and y direction from 50°C to 500°C. The average strain (εavg) was computed at different temperatures and the linear CTE was computed as: (3) Where ∆T= T- 23°C,
Fig. 7. Plastic strain at room temperature for Al99.5 [29].
4.3 Effective Elastic Modulus
Figure 8 shows the effective elastic modulus obtained from OOF analysis of four different microstructures of all three composites. The results obtained from hashin’s bounds [28] are also included. It can be observed that OOF predictions are in good agreement with the experimental values. Qualitatively similar results are obtained from different OOF meshes, however, the effects of the presence of pores and boron carbide particles in different microstructures of composites can be observed on their effective elastic modulus. It can be seen that mesh 1 of 4 vol% and 12 vol% composites show higher boron carbide content (see Table 1) and therefore have high elastic modulus. Mesh 1 and 4 of 12 vol% composite show highest porosity and therefore have lowest elastic modulus. Elastic modulus decreases with the increase of temperature due to the softening of Al matrix and plastic deformations with temperature rise.
Fig. 8. Effective elastic modulus predicted using OOF analysis and hashin’s bounds: (a) 4 vol% composite; (b) 8 vol% composite and (c) 12 vol% composite.
The measured elastic moduli do not fall in the range of upper and lower values of hashin’s bounds. It can be due to the presence of voids in composite’s microstructure which cannot be taken into account while applying the hashin’s bounds. Fig. 9 shows the local stress distribution (S11, MPa) in OOF microstructures for 4, 8 and 12 vol% composites at room temperature. The red colored region shows the high stress concentration in the composite’s microstructure. Boron carbide particles are subjected to high stresses due to their high elastic modulus. Furthermore, the high stress discontinuities can be observed at the interfaces of matrix and reinforcement, particularly at sharp corners or due to abrupt changes in shape of
particles, which could cause the debonding between the constituents. It can be observed that the maximum stress in composites microstructure is 51.5 MPa, 57.5 MPa and 89.6 MPa for 4, 8 and 12 vol% composites. The aluminum metal is subjected to low tensile stresses due to its low elastic modulus and elasto-plastic deformation behavior.
Fig. 9. Local stress distribution at room temperature(a) 4 vol% composite; (b) 8 vol% composite and (c) 12 vol% composite.
4.4 Thermal Expansion Coefficient
Fig. 10 compare the effective CTE measured using OOF and different analytical models from room temperature to 500°C temperature. In case of 12 vol% composite, OOF predicted CTEs are in good agreement with the measured values at all temperatures. However, in case of 4 & 8 vol% composites, OOF predicts slightly lower CTEs at 500°C temperature. The OOF predicted CTEs are differ from measured values by 3-6% in case of 4 and 8 vol% composites and 0.33-5% in case of 12 vol% composite. It can be observed that CTE is not influenced much for the measured presence of voids. Turner model [29] under predicts the CTE values, whereas, Kerner model [30] predicts slightly higher values at all temperatures. The consideration of perfect bonding among constituents in Turner model reduces the effective strain and thereby results in lower CTEs. The upper and lower bounds of schapery [31] are in good agreement with the experimental values at all temperatures.
Fig. 10. Effective CTE predicted using OOF analysis and analytical models: (a) 4 vol% composite; (b) 8 vol% composite and (c) 12 vol% composite.
Fig. 11. Equivalent plastic strain distribution in: (a) 4 vol% composite; (b) 8 vol% composite and (c) 12 vol% composite.
In Fig. 11 the equivalent plastic strain distribution for mesh 1 of all three composites is shown. It can be understood that the thermal expansion behavior of these composites is influenced by plastic deformation, since, the Al matrix starts yielding as the thermal stresses increase beyond its yield point. Fig. 12 shows the strain components for 12 vol% composite. The higher strain produced by Al matrix can be seen (deep yellow colored region), while, the light yellow colored region is majorly associated to boron carbide particles. In between these
two regions, the compression at few sites can be observed. This region is associated with voids. The metal matrix expanded into the voids on heating thereby causing the shrinkage of voids.
Fig. 12. Strain components E11 and E22 for 12 vol% composite at 500°C temperature.
5. Conclusion
Al-B4C composites are fabricated by reinforcing 4, 8 and 12 vol% boron carbide in Al matrix using squeeze casting method and their physical, thermal and thermomechanical behaviors are investigated.
In order to overcome the wettability problem for B4C/Al composites, two different additives: potassium fluorotitanate (K2TiF6) flux and magnesium were used. The composites produced using magnesium flux demonstrated strong bonding and homogenous distribution of
boron carbide particles. The effective CTEs and the effective elastic moduli are measured from composite’s specimens at room temperature as well as at high temperatures. The effective elastic modulus of composites decreases and the effective CTE increases with the increase of temperature.
The effective properties are also measured using FE modeling and analytical models and the results obtained are compared with the experimental values. The effects of microstructural characteristics, i.e., shape, size, distribution, orientation of reinforced particles, presence of porosities and temperatures are measured on the effective elastic modulus and CTE of composites using OOF. Microstructures of composites were constructed from the SEM images. The results obtained from OOF analysis are in good agreement with the experimental values. The porosity present in composites were characterize from image analysis of SEM images. We have observed that the effective elastic modulus is strongly influenced by the presence of porosity and boron carbide content, whereas, CTE is not much influenced for the measured porosity content. Turner model under predicts, whereas, the Kerner model over predicts the CTEs values. The bounds of schapery for CTE values are in good agreement with the experimental values. However, the hashin’s bounds could not predict well the effective elastic moduli, since, the elastic modulus is strongly influenced by the presence of voids.
OOF can be used advantageously to model the real microstructure of composites including the presence of voids. OOF conducts only linear elastic analysis, whereas, the thermomechanical behavior of metal matrix composites is strongly influenced by the plastic
deformation of metal matrix. Therefore, the OOF modeled microstructures were studied with the commercial software Abaqus to model the elasto-plastic deformation of metal matrix.
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