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(Ti,W)C composites
Int. Journal of Refractory Metals and Hard Materials 36 (2013) 167–173
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Int. Journal of Refractory Metals and Hard Materials journal homepage: www.elsevier.com/locate/IJRMHM
Prediction and analysis of microstructural effects on fabrication of ZrB2/(Ti,W)C composites Bin Li a,⁎, Hong Wang b a b
Department of Mechanical Engineering, Luoyang Institute of Science and Technology, Luoyang 471023, Henan Province, PR China Luoyang Institute of Science and Technology, Luoyang 471023, Henan Province, PR China
a r t i c l e
i n f o
Article history: Received 13 April 2012 Accepted 21 August 2012 Keywords: Zirconium diboride (Ti,W)C compounds Composites Hot-pressing
a b s t r a c t Zirconium diboride matrix composites are strengthened by incorporating (Ti,W)C into the matrix ceramic. Cellular automata models were used to predict the microstructural effects on the ceramic materials. ZrB2/ (Ti,W)C composites were fabricated and then analyzed via X-ray diffraction. The effects of the (Ti,W)C compounds on microstructures of zirconium diboride matrix materials were also determined. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Ultrahigh-temperature composites are of particular interest because of their unique combination of high refractoriness, high electrical and thermal conductivities, and chemical inertness against molten metals [1,2]. Zirconium diboride (ZrB2) is one of the most important boride materials. It has a very high melting point, high hardness, high elastic modulus, good electrical conductivity, and excellent chemical resistance against HCl, HF, other nonferrous metals, cryolite, and nonbasic slags. It is used in the electrolytic production of aluminum because of its superior cathode quality compared with carbon [3–5]. ZrB2 is also used in foundries, in refractory industries, and in steel refining, or as an additive for cutting tools, which is a new application of TiB2 [6,7]. ZrB2 also has potential applications in the aerospace industry such as material for the leading edges of hypersonic aerospace vehicles and of reusable re-entry spacecrafts [8,9]. ZrB2 has an advantage over titanium diboride because it does not have many stable intermediate phases [10]. ZrB2 materials can be prepared via powdering, forming, and hot-pressing fabrication processes. The driving force for sintering is the reduction in surface free energy. This reduction is achieved through the diffusion of materials. Many factors affect material transport and exhalation of pores. Hence, the hot-pressing fabrication is a highly complicated process. In this method, a compact structure is fabricated from fine powders at temperatures below the melting
⁎ Corresponding author. Tel.: +86 15937911896. E-mail address: [email protected] (B. Li). 0263-4368/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijrmhm.2012.08.011
point of the main constituent to obtain sufficient energy to form interparticle bonds [11]. Various models that simulate the microstructures formed during hot-pressing fabrication have been reported. These models can be categorized as multistage kinetics Monte Carlo, vertex, front-tracking, phase-field, and cellular automata (CA) models [12,13]. Compared with Monte Carlo simulations, the CA method is relatively flexible and effective in simulating different physical systems. Theoretical principles and experimental parameters can be readily incorporated within the CA simulation through appropriate transformation functions [14]. Models that use partial differential equations are based on a global or macroscopic approach. On the other hand, CA models are deduced from the microscopic description of the particle behavior in the system. The development and use of CA models have considerably increased with the availability of powerful computers [15]. Simulations with this method allow behavior modeling of complicated mechanical systems at the mesoscopic scale. The CA model is used to simulate crack generation and development in heterogeneous materials (e.g., concrete) under different modes of mechanical loading [16] and to investigate the friction process [17]. The CA method can also be used in predicting microstructural effects on ceramic materials [18]. The major challenge in the preparation of ZrB2-based materials is densification. To improve the material properties and obtain higher densification at relatively lower hot pressing temperatures, techniques such as particulate incorporation, which is an effective method in material research [19,20], can be used. Rangaraj et al. [21] obtained a ZrB2–ZrC composite via the reactive hot pressing of a Zr and boron carbide mixture at 1600 °C and 40 MPa. Among these additives, silicon carbide is the most common because it enhances the strength and oxidation resistance of ZrB2 ceramics [22,23]. Mishra et al. [24] reported
168
B. Li, H. Wang / Int. Journal of Refractory Metals and Hard Materials 36 (2013) 167–173
that the oxygen present on ZrB2 surfaces hinders densification. Through the addition of TiC and C, they achieved a 94% relative density via pressureless sintering at 1800 °C under an Ar atmosphere. (Ti,W)C may be the most widely known tungsten carbide because of its exceptional hardness and superior wear resistance. The application for (Ti,W)C carbide combined with binders is currently being investigated. This composite powder has been successfully used as a master alloy in molten steel [25–27]. However, reports on the application of (Ti,W)C carbide in strengthening ZrB2 materials are scarce. In this investigation, different amounts of (Ti,W)C carbide were added to ZrB2 ceramic materials. The CA models were then used to predict the microstructural effects on the ceramic materials. The effects of (Ti,W)C compounds on the densification rate, mechanical properties, and microstructures of ZrB2 materials were also analyzed. 2. Model description and calculation Finite element calculation with CA models theoretically can take into account the ceramic material constitutive equation and phase distribution, and the basic features of a cellular automaton are the following: (i) it consists of a discrete number of sites called cells, which constitute a two or three-dimensional lattice; (ii) each cell is associated with a specific local neighborhood; (iii) each cell is characterized by parameters that can take discrete or continuous values; and (iv) finally, the above parameters change with a time-like variable according to some deterministic rules; the latter depend only on the present states of the cell considered and its neighborhood [28–30]. Simulated ceramic specimen is divided into elements of finite size interacting with each other. These elements represent particles or grains in ceramic material. An aggregate of equivolumic grains of two phases A and B is submitted to plane strain deformation. Each grain in the considered material section is associated with one cell of a two-dimensional cellular automaton in Fig. 1. For simplification, each grain is further assumed to have exactly the same number, n, of first neighbors. For n = 6 or n = 8, the automaton can thus be represented by a hexagonal or square lattice, respectively. To model an infinite aggregate by a finite lattice, the upper and lower edges of the array must be thought first to fit together to form a cylinder; then the left and right ends of the latter are to be linked up, thus building a torus. This classical procedure is equivalent to assuming periodic boundary conditions for the automaton.
(a)
(b) 4
3
2
5
(β)
1
6
7
8
Although the model can be extended to the case of nonlinear viscous materials, the two phases A and B are assumed here to be isotropic, incompressible, and linearly viscous (or, alternatively, linearly elastic and incompressible, by substituting the strains εij to the strain rates ε_ ij ): sij ¼ kϕ ε_ ij
ð1Þ
where sij and ε_ ij denote the deviatoric stress and strain rate, and the subscript ϕ stands for A or B. Throughout this paper, phase A will be considered as the “harder” one, so the viscosity ratio ∑ = kB / kA ranges between 0 and 1. The grains are assumed to be cylinders of axis x3 perpendicular to the plane (x1, x2) in which deformation is confined. Their sections in that plane are ellipses of semiaxes a and b, parallel to x1 and x2, respectively. The material is submitted to plane strain deformation along the symmetry axes x1 and x2 ( ε_ 11 þ ε_ 22 ¼ 0; ε_ 33 ¼ ε_ 13 ¼ ε_ 23 ¼ ε_ 12 ¼ 0). In a first step of localization, the strain rate associated with any cell (β) of the automaton is calculated from Gilormini's results [31], by considering in turn each grain as an inclusion embedded in its neighborhood. Neglecting the orthotropic anisotropy of the overall material, which is likely to be induced by the shape of the grains (morphological anisotropy), the strain rate ε_ c11 ¼ −ε_ c22 of (c) can be written in the form: c ∞ ε_ 11 ¼ ρδc ε_ 11 ∞
ð2Þ ∞
where ε_ 11 ¼ −ε_ 22 is the remote prescribed strain rate and ρ is a normalization constant (i.e. independent of the cell considered). The localization factor 6c has been derived explicitly by Gilormini [32]: δc ¼
λ2c
ðλc þ 1Þ2 þ 2 kc =k λc þ 1
ð3Þ
where λc = b / a is the aspect ratio of the grain; kc is its viscosity (kc = kA or kB); and k is an average viscosity of its neighborhood. To derive these quantities from Eq. (3), it is first necessary to determine the average viscosity k of the neighborhood. Three possible choices are proposed and compared in the following: (i) k is the arithmetic average of the viscosities associated with the n cells of the neighborhood; (ii) k is the harmonic average of the viscosities associated with the cells of the neighborhood, i.e. 1 / k is the arithmetic average of the inverses of these viscosities; (iii) k is calculated from a self-consistent model extended over the neighborhood under consideration. In agreement with Eq. (3), which assumes that the matrix is isotropic, k is considered here as independent of the aspect ratios and respective positions of the grains in the neighborhood. The con c stant ρ is calculated such that the average strain rate ε_ 11 is equal to the prescribed one ε_ ∞11 , from where: c ε_ 11 ¼
δc ∞ ε_ : hδc i 11
ð4Þ
In a second step, an averaging procedure is applied to derive the overall deviatoric stress:
(c) 3
4
2
5 (β) 6
1 7
8
c hk δ i ∞ ∞ s11 ¼ s11 ¼ c c ε_ 11 ¼ kε_ 11 hδc i
where k is the viscosity of the aggregate along direction x1 or x2. Introducing now the volume fraction f = fA of phase A, the above equation can be written in the equivalent form: x¼
Fig. 1. Cellular automaton model of grain embedded with its neighborhood for calculation. (a) Three-dimensional cellular automaton model in numerical simulations; (b) two-dimensional cellular automaton model in numerical simulations; (c) the automaton represented by squares for the grain which has eight neighbors.
ð5Þ
k f hδA i þ ð1−f ÞΣhδB i ¼ kA f hδA i þ ð1−f ÞhδB i
ð6Þ
Where bδA> and b δB> are the average values of the localization factors pertaining to the A and B grains, respectively. It can be easily
B. Li, H. Wang / Int. Journal of Refractory Metals and Hard Materials 36 (2013) 167–173
shown that the overall viscosity kCL predicted by the proposed cell model always lies between the uniform stress (static) and uniform strain rate (Taylor) bounds: kS ≤ kCL ≤ kT
ð7Þ
where 1 / kS = bl / kc> and kT = bkc>. Moreover, it will be shown in the next section that narrower bounds can be found for kCL under more restrictive assumptions. It is worth emphasizing that the localization and averaging methods employed here ensure that the averages of both the strain rates and deviatoric stresses are equal to their overall counterparts, whatever the aspect ratios λc of the grains [33]. The hydrostatic pressure in an inclusion for the geometry and boundary conditions presently considered has also been derived in an explicit form when applied to cell (β), and this gives ð8Þ
where p∞ is the remote pressure. Thus bpc> and p∞ are generally unequal c ∞ (and so are the stresses b σ11 > and σ11 ) according to the cell model, unless λc =1 for all grains. This contrasts with the two-phase self-consistent approach, where λc =λ is generally assumed to be the same for all grains. In that special case, the average pressure can be written as: ð9Þ
where kSC is the predicted overall viscosity. In another special case, since the neighborhood of any grain consists of the whole material in the self-consistent scheme, k =kSC, which leads to bpc>=p∞. _ c associated with cell (β) Finally, the plastic work rate density w and the average work rate density is D E D E _ c i ¼ 2 kc δ2c = δ2c · ε ∞11 2 hw
ð10Þ
which is less than (or equal to) _ ∞ i ¼ 2k ε∞11 2 ¼ 2ðhkc δc i=hδc iÞ· ε∞11 2 : hw
ð11Þ
_ c i≤w _ ∞ whatever the aspect ratios of the Since 〈kcδc2〉 ≤ 〈kcδc〉〈δc〉, hw grains. In order to analyze the uniform distribution for microstructural grains, it is assumed that the grains are equiaxed, i.e. λc = 1 for any cell of the array. Furthermore, the size of the aggregate is infinite and the two kinds of constituents, A and B, are randomly and uniformly distributed. The following analytical derivations are given for plane strain deformation; however, their extension to the three-dimensional case is straightforward. The probability for any cell (of the A or B type) to have exactly p cells of type A within its neighborhood is n! n p n−p p n−p f ð1−f Þ f ð1−f Þ ¼ p P!ðn−P Þ!
ZW0 ZW10 ZW20 ZW30 ZW40
possible reaction
ΔGθT
Result
1 2 3 4 5 6
ZrB2 + TiC = ZrC + TiB2 ZrO2 + TiC = ZrC + TiO2 ZrO2 + WC = ZrC + WO2 2ZrB2 + 3 N2 = 2ZrN + 4BN ZrO2 + N2 = ZrN + NO2 2ZrO2 + N2 = 2ZrN + 2O2
+25,688 +123,230 — — +702,595 +1,075,799
No occurrence
where f is the volume fraction of phase A. The average values of the localization factors associated with the A and B grains are then hδA i ¼
n X
V ðpÞδA ðpÞ and hδB i ¼
n X
V ðpÞδB ðpÞ
ð13Þ
p¼0
where δA(p) and δB(p) are the localization factors pertaining to a cell A or cell B surrounded by exactly p cells of type A. 3. Experimental procedure The raw material used for the matrix is ZrB2, which has a ZrB2 content of 92.2% ± 0.1% by volume and a ZrO2 content of 7.8% ± 0.1% by volume, according to the manufacturer's information. The average particle size is approximately 1.7 μm. (Ti,W)C (99% purity 99%) is a solid-solution powder with an average grain size of approximately 0.8 μm. Four different volume fractions of (Ti,W)C (10, 20, 30, and 40 vol.%) were used in designing ZrB2/(Ti,W)C materials. The compositions of the ZrB2 matrix ceramics are shown in Table 1. The suffixes in ZW0, ZW10, ZW20, ZW30, and ZW40 represent the (Ti,W)C volume content. For example, in AZ0, the (Ti,W)C volume content is zero. The original ZrB2 powders were refined via wet ball milling with cemented carbide balls in alcohol for 150 h to reduce the particle size. The combined (Ti,W)C and refined ZrB2 powders were then dispersed in an ultrasonic oscillator (HS10260D, Shanghai Troody Analytical Instrument Co., Ltd., China) to prevent material agglomeration in the subsequent step. The (Ti,W)C and refined ZrB2 powders were then mixed with cemented carbide balls in alcohol via wet ball milling for 300 h to obtain a homogeneous mixture. The slurry was dried at 150 °C in a vacuum oven (ZK-82A, Shanghai Silong Scientific Instrument Co., Ltd., China) and then screened using a 0.1 mm aperture sieve. Following the forming stage, the compacted powders were filled into a graphite die via uniaxial hot pressing in an N2 atmosphere at 1800 °C (30 °C·min−1) and at a pressure of 35 MPa for 40 min to produce a disk. X-ray diffraction (XRD) analysis (BRUKER AXS D8 ADVANCE, Bruker Axis Corporation, Germany) was performed to
ZrB2 TiC WC ZrO2
1200 1000
ð12Þ
Table 1 Starting compositions of hot pressed composites. Specimen
Code
CPS/(S-1)
2 ∞ 1−λ2 kSC − k hpc i ¼ p∞ − ε_ 11 2 3 1þλ
V ðpÞ ¼
Table 2 The possible reaction in sintering ZW series ceramic materials at 1800 °C.
p¼0
2 2 ∞ 1−λc kc δc pc ¼ p∞ − ε_ 11 −k 2 3 1 þ λc hδc i
169
800 600 400
Composition (vol.%) (Ti,W)C
ZrB2
ZrO2
0 10 20 30 40
92.2 82.98 73.76 64.54 55.32
7.8 7.02. 6.24 5.46 4.68
200 0 20
30
40
50
60
70
2θ/(o) Fig. 2. X-ray diffraction phase analysis of ZW30 specimen.
80
170
B. Li, H. Wang / Int. Journal of Refractory Metals and Hard Materials 36 (2013) 167–173
identify the crystal phases after sintering. The microstructure of the polished and fracture surfaces were examined via scanning electron microscopy (SEM, HITACHI S-570, Hitachi Corporation, Japan). 4. Results and discussion Based on the Gibbs free energy function, the standard reaction Gibbs free energy can be calculated using θ
ΔG
T
¼ ΔH
θ
′ 298 −TΔΦ T
ð14Þ
θ
where ΔH 298 is the thermal effect of the standard reaction at room temperature (J); T is the sintering temperature (absolute tempera′ ture, K); and ΔΦ T is the Gibbs free energy function (J·K −1) of the reaction. The reaction cannot proceed when ΔGθ T > 0, whereas the θ reaction occurs when ΔG T b0. Table 2 shows the possible reactions during the sintering of the ZW series of ceramic materials at 1800 °C. “—” indicates that the reaction product cannot be formed at this temperature. Based on Table 2, the reaction or product is not formed in Reactions (3) and (4) at 1800 °C, with exception for them, other reactions cannot occur. The X-ray diffraction results for the ZW30 specimen (Fig. 2) show the presence of ZrB2, WC, TiC, and ZrO2 phases. Thus, the standard reaction Gibbs energy can be used for analyzing chemical compatibility.
×2,000
10 µm
Fig. 4. SEM micrograph of the fracture surface of monolithic ZrB2.
Fig. 2 shows that the composite contains a large amount of ZrO2 despite its moderate content in the starting powder. This increase in ZrO2 content may be due to oxidation during long-term milling (150 and 300 h).
(a)
(b)
(c)
(d)
Fig. 3. Simulated microstructure of ZW series ceramic composite at 1800 °C. The series ceramics are: (a) ZW0; (b) ZW10; (c) ZW20; (d) ZW30, respectively.
B. Li, H. Wang / Int. Journal of Refractory Metals and Hard Materials 36 (2013) 167–173
×2,000
171
in Fig. 4; the fracture surfaces of ZW10, ZW20, ZW30, and ZW40 are shown in Figs. 5–8, respectively. In Fig. 6, the black areas in No. 1 are ZrB2 and ZrO2, as identified via energy-dispersive X-ray spectroscopy; the white areas in No. 3 are (Ti,W)C compounds; and the junction in No. 2 contains ZrB2 and (Ti,W)C. The results above show significant microstructural differences among the composites. The fracture mode of monolithic ZrB2 is primarily intergranular, and the mean grain size is approximately 15 μm. The addition of (Ti,W)C compounds results in the formation of finer and more homogeneous composite microstructures. The fracture mode remains intergranular with the incorporation of 10 and 20 vol.% (Ti,W)C compounds (Figs. 5 and 6, respectively). However, the fracture mode becomes a combination of transgranular and intergranular failures as the concentration of (Ti,W)C compounds reaches 30 vol.% (Fig. 7). Further addition of (Ti,W)C compounds results in a primarily intergranular fracture mode, accompanied by a small percentage of transgranular failure (Fig. 8). The WC and TiC particles are uniformly distributed throughout the microstructure (Fig. 7). The size of the ZrB2 grains range from 4 μm to 5 μm and is considerably smaller than that of the monolithic ZrB2 grains. In Fig. 6, the bond strength of the grains increases when the fracture mode is a combination of transgranular and intergranular failures. In other words, the fracture mode changes from intergranular to a combination of transgranular and intergranular failures. The change is mainly due to the strengthening of the grain boundaries of the composites as a result of the addition of moderate amounts of (Ti,W)C compounds. This transformation causes a significant increase in the bending strength and fracture toughness. As previously mentioned, the mean grain size of monolithic ZrB2 is approximately 15 μm, whereas those of ZW10, ZW20, ZW30, and ZW40 are approximately 10, 8, 5, and 7 μm, respectively. The grain size of monolithic ZrB2 is larger than those of the composites strengthened by (Ti,W)C compounds under identical conditions. This result indicates that the addition of (Ti,W)C compounds prevents the abnormal growth
10 µm
Fig. 5. SEM micrograph of the fracture surface of ZW10 ceramic composite.
The initial microstructure was formed via a normal grain growth algorithm. The primary grains and the newly formed grains have an orientation which was randomly set in the program. Fig. 3 shows the simulated microstructure of the ZW series of ceramic composites at 1800 °C. For comparison, all simulated microstructures were based on the same initial microstructure. To simulate the experimental observations accurately, the mean diameter of the starting grains in the calculation was set to around 15 μm. Figs. 4–8 show significant microstructural differences among the composites. The relative density increased with increasing percentage of (Ti,W)C compounds, whereas the mean grain size decreased from 15 μm to 7 μm. The SEM photomicrograph of the fracture surface of monolithic ZrB2 sintered for 40 min at 1800 °C under a 35 MPa pressure is shown
a 3
2 1
×2,000
b
c
10 µm
d
Fig. 6. (a) SEM micrograph of the fracture surface of ZW20 ceramic composite; (b) EDX energy spectrum diagram of area 1 ; (c) EDX energy spectrum diagram of area 2; (d) EDX energy spectrum diagram of area 3.
172
B. Li, H. Wang / Int. Journal of Refractory Metals and Hard Materials 36 (2013) 167–173
transgranular
This change increases the bending strength and fracture toughness. One reason is that the grain boundaries of the composites are strengthened. The other is that the addition of (Ti,W)C compounds prevents the abnormal growth of ZrB2 grains in the composites. When the amount of (Ti,W)C exceeds 30 vol.%, the densification becomes more difficult, and the mechanical properties of the composites decrease.
intergranular Acknowledgements
×2,000
10 µm
Fig. 7. SEM micrograph of the fracture surface of ZW30 ceramic composite.
of ZrB2 grains in the composites [25]. When the amount of (Ti,W)C was increased to 40 vol.% (Fig. 8), the bonds between grains become weaker than those in ZW30, which resulted in lower densification and weaker mechanical properties compared with those of ZW30. Thus, the addition of a moderate amount of (Ti,W)C compounds results in the formation of finer and more homogeneous composite microstructures as well as stronger bonds between grains. Based on the simulations and on the experimental analyses, the addition of 30 vol.% (Ti,W)C compounds results in higher performance compared with those of other amounts. 5. Conclusions ZrB2/(Ti,W)C composites were fabricated via hot-pressing technology. Cellular automata models were then used to predict the microstructural effects on ceramic materials. Particular attention was given to the effect of the addition of (Ti,W)C compounds on the microstructure. The following conclusions were drawn from the results: 1. Simulations using CA models show significant microstructural differences among the composites. The relative density increased with the increasing percentage of (Ti,W)C compounds, whereas the mean grain size decreased from 15 μm to 7 μm; 2. The addition of (Ti,W)C compounds results in the formation of finer and more homogeneous composite microstructures. 3. The fracture mode becomes a combination of transgranular and intergranular failures when the amount of (Ti,W)C reaches 30 vol.%.
×2,000
10 µm
Fig. 8. SEM micrograph of the fracture surface of ZW40 ceramic composite.
The work described in this paper is supported by the National Natural Science Foundation of China (No. 51105188), the Natural Science Foundation of Education Department of Henan Province (No. 12B460016), and the Development Program for Science and Technology of Luoyang. References [1] Fahrenholtz WG, Hilmas GE, Zhang SC, Zhu S. Pressureless sintering of zirconium diboride: particle size and additive effects. J Am Ceram Soc 2008;91(5):1398-404. [2] Mishra SK, Das SK, Pathak LC. Sintering behaviour of self-propagating high temperature synthesised ZrB2–Al2O3 composite powder. Mater Sci Eng, A 2006;426(1–2): 229-34. [3] Li B, Deng JX, Li YS. Oxidation behavior and mechanical properties degradation of hot-pressed Al2O3/ZrB2/ZrO2 ceramic composites. Int J Refract Met Hard Mater 2009;27(4):747-53. [4] Monteverde F. The addition of SiC particles into a MoSi2-doped ZrB2 matrix: effects on densification, microstructure and thermo-physical properties. Mater Chem Phys 2009;113(2–3):626-33. [5] Kim KH, Shim KB. The effect of lanthanum on the fabrication of ZrB2–ZrC composites by spark plasma sintering. Mater Charact 2003;50(1):31-7. [6] Millet P, Hwang T. Preparation of TiB2 and ZrB2. Influence of a mechano-chemical treatment on the borothermic reduction of titania and zirconia. J Mater Sci 1996;31(2):351-5. [7] Shew B-Y, Huang J-L. Investigation of chemical reactions in TiB2/Si3N4 composites. Mater Sci Eng, A 1992;159(1):127-33. [8] Parthasarathy TA, Rapp RA, Opeka M, Kerans RJ. A model for the oxidation of ZrB2, HfB2 and TiB2. Acta Mater 2007;55(17):5999-6010. [9] Opeka MM, Talmy IG, Wuchina EJ, Zaykoski JA, Causey SJ. Mechanical, thermal, and oxidation properties of refractory hafnium and zirconium compounds. J Eur Ceram Soc 1999;19(13–14):2405-14. [10] Zhang SC, Hilmas GE, Fahrenholtz WG. Pressureless sintering of ZrB2–SiC ceramics. J Am Ceram Soc 2008;91(1):26-32. [11] Hu P, Guolin W, Wang Z. Oxidation mechanism and resistance of ZrB2–SiC composites. Corros Sci 2009;51(11):2724-32. [12] Raabe D, Becker RC. Coupling of a crystal plasticity finite-element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminium. Modell Simul Mater Sci 2000;8:445. [13] Chen W, Brouwers HJH, Shui Z. Three-dimensional computer modeling of slag cement hydration. J Mater Sci 2007;42(23):9595-610. [14] Brown S, Bruce N. Three-dimensional cellular automaton models of microstructural evolution during solidification. J Mater Sci 1995;30(5):1144-50. [15] Mitchell M, Crutchfield JP, Das R. Evolving cellular automata with genetic algorithms: a review of recent work; 1996. [16] Psakhie SG, Horie Y, Ostermeyer GP, Korostelev SY, Smolin AY, Shilko EV, et al. Movable cellular automata method for simulating materials with mesostructure. Theor Appl Fract Mech 2001;37(1–3):311-34. [17] Österle W, Dörfel I, Prietzel C, Rooch H, Cristol-Bulthé AL, Degallaix G, et al. A comprehensive microscopic study of third body formation at the interface between a brake pad and brake disc during the final stage of a pin-on-disc test. Wear 2009;267(5): 781-8. [18] Österle W, Dmitriev AI, Kloß H. Possible impacts of third body nanostructure on friction performance during dry sliding determined by computer simulation based on the method of movable cellular automata. Tribol Int 2012;48:128-36. [19] Mishra SK, Pathak L. Effect of carbon and titanium carbide on sintering behaviour of zirconium diboride. J Alloys Compd 2008;465(1–2):547-55. [20] Monteverde F, Guicciardi S, Bellosi A. Advances in microstructure and mechanical properties of zirconium diboride based ceramics. Mater Sci Eng, A 2003;346(1–2): 310-9. [21] Rangaraj L, Suresha SJ, Divakar C, Jayaram V. Low-temperature processing of ZrB2–ZrC composites by reactive hot pressing. Metall Mater Trans A 2008;39(7):1496-505. [22] Chamberlain AL, Fahrenholtz WG, Hilmas GE. Reactive hot pressing of zirconium diboride. J Eur Ceram Soc 2009;29(16):3401-8. [23] Chamberlain AL, Fahrenholtz WG, Hilmas GE. Pressureless sintering of zirconium diboride. J Am Ceram Soc 2006;89(2):450-6. [24] Mishra SK, Das SK. Sintering and microstructural behaviour of SHS produced zirconium diboride powder with the addition of C and TiC. Mater Lett 2005;59(27): 3467-70. [25] Saidi A, Barati M. Production of (W, Ti)C reinforced Ni–Ti matrix composites. J Mater Process Technol 2002;124(1–2):166-70.
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Int. Journal of Refractory Metals and Hard Materials journal homepage: www.elsevier.com/locate/IJRMHM
Prediction and analysis of microstructural effects on fabrication of ZrB2/(Ti,W)C composites Bin Li a,⁎, Hong Wang b a b
Department of Mechanical Engineering, Luoyang Institute of Science and Technology, Luoyang 471023, Henan Province, PR China Luoyang Institute of Science and Technology, Luoyang 471023, Henan Province, PR China
a r t i c l e
i n f o
Article history: Received 13 April 2012 Accepted 21 August 2012 Keywords: Zirconium diboride (Ti,W)C compounds Composites Hot-pressing
a b s t r a c t Zirconium diboride matrix composites are strengthened by incorporating (Ti,W)C into the matrix ceramic. Cellular automata models were used to predict the microstructural effects on the ceramic materials. ZrB2/ (Ti,W)C composites were fabricated and then analyzed via X-ray diffraction. The effects of the (Ti,W)C compounds on microstructures of zirconium diboride matrix materials were also determined. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Ultrahigh-temperature composites are of particular interest because of their unique combination of high refractoriness, high electrical and thermal conductivities, and chemical inertness against molten metals [1,2]. Zirconium diboride (ZrB2) is one of the most important boride materials. It has a very high melting point, high hardness, high elastic modulus, good electrical conductivity, and excellent chemical resistance against HCl, HF, other nonferrous metals, cryolite, and nonbasic slags. It is used in the electrolytic production of aluminum because of its superior cathode quality compared with carbon [3–5]. ZrB2 is also used in foundries, in refractory industries, and in steel refining, or as an additive for cutting tools, which is a new application of TiB2 [6,7]. ZrB2 also has potential applications in the aerospace industry such as material for the leading edges of hypersonic aerospace vehicles and of reusable re-entry spacecrafts [8,9]. ZrB2 has an advantage over titanium diboride because it does not have many stable intermediate phases [10]. ZrB2 materials can be prepared via powdering, forming, and hot-pressing fabrication processes. The driving force for sintering is the reduction in surface free energy. This reduction is achieved through the diffusion of materials. Many factors affect material transport and exhalation of pores. Hence, the hot-pressing fabrication is a highly complicated process. In this method, a compact structure is fabricated from fine powders at temperatures below the melting
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point of the main constituent to obtain sufficient energy to form interparticle bonds [11]. Various models that simulate the microstructures formed during hot-pressing fabrication have been reported. These models can be categorized as multistage kinetics Monte Carlo, vertex, front-tracking, phase-field, and cellular automata (CA) models [12,13]. Compared with Monte Carlo simulations, the CA method is relatively flexible and effective in simulating different physical systems. Theoretical principles and experimental parameters can be readily incorporated within the CA simulation through appropriate transformation functions [14]. Models that use partial differential equations are based on a global or macroscopic approach. On the other hand, CA models are deduced from the microscopic description of the particle behavior in the system. The development and use of CA models have considerably increased with the availability of powerful computers [15]. Simulations with this method allow behavior modeling of complicated mechanical systems at the mesoscopic scale. The CA model is used to simulate crack generation and development in heterogeneous materials (e.g., concrete) under different modes of mechanical loading [16] and to investigate the friction process [17]. The CA method can also be used in predicting microstructural effects on ceramic materials [18]. The major challenge in the preparation of ZrB2-based materials is densification. To improve the material properties and obtain higher densification at relatively lower hot pressing temperatures, techniques such as particulate incorporation, which is an effective method in material research [19,20], can be used. Rangaraj et al. [21] obtained a ZrB2–ZrC composite via the reactive hot pressing of a Zr and boron carbide mixture at 1600 °C and 40 MPa. Among these additives, silicon carbide is the most common because it enhances the strength and oxidation resistance of ZrB2 ceramics [22,23]. Mishra et al. [24] reported
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that the oxygen present on ZrB2 surfaces hinders densification. Through the addition of TiC and C, they achieved a 94% relative density via pressureless sintering at 1800 °C under an Ar atmosphere. (Ti,W)C may be the most widely known tungsten carbide because of its exceptional hardness and superior wear resistance. The application for (Ti,W)C carbide combined with binders is currently being investigated. This composite powder has been successfully used as a master alloy in molten steel [25–27]. However, reports on the application of (Ti,W)C carbide in strengthening ZrB2 materials are scarce. In this investigation, different amounts of (Ti,W)C carbide were added to ZrB2 ceramic materials. The CA models were then used to predict the microstructural effects on the ceramic materials. The effects of (Ti,W)C compounds on the densification rate, mechanical properties, and microstructures of ZrB2 materials were also analyzed. 2. Model description and calculation Finite element calculation with CA models theoretically can take into account the ceramic material constitutive equation and phase distribution, and the basic features of a cellular automaton are the following: (i) it consists of a discrete number of sites called cells, which constitute a two or three-dimensional lattice; (ii) each cell is associated with a specific local neighborhood; (iii) each cell is characterized by parameters that can take discrete or continuous values; and (iv) finally, the above parameters change with a time-like variable according to some deterministic rules; the latter depend only on the present states of the cell considered and its neighborhood [28–30]. Simulated ceramic specimen is divided into elements of finite size interacting with each other. These elements represent particles or grains in ceramic material. An aggregate of equivolumic grains of two phases A and B is submitted to plane strain deformation. Each grain in the considered material section is associated with one cell of a two-dimensional cellular automaton in Fig. 1. For simplification, each grain is further assumed to have exactly the same number, n, of first neighbors. For n = 6 or n = 8, the automaton can thus be represented by a hexagonal or square lattice, respectively. To model an infinite aggregate by a finite lattice, the upper and lower edges of the array must be thought first to fit together to form a cylinder; then the left and right ends of the latter are to be linked up, thus building a torus. This classical procedure is equivalent to assuming periodic boundary conditions for the automaton.
(a)
(b) 4
3
2
5
(β)
1
6
7
8
Although the model can be extended to the case of nonlinear viscous materials, the two phases A and B are assumed here to be isotropic, incompressible, and linearly viscous (or, alternatively, linearly elastic and incompressible, by substituting the strains εij to the strain rates ε_ ij ): sij ¼ kϕ ε_ ij
ð1Þ
where sij and ε_ ij denote the deviatoric stress and strain rate, and the subscript ϕ stands for A or B. Throughout this paper, phase A will be considered as the “harder” one, so the viscosity ratio ∑ = kB / kA ranges between 0 and 1. The grains are assumed to be cylinders of axis x3 perpendicular to the plane (x1, x2) in which deformation is confined. Their sections in that plane are ellipses of semiaxes a and b, parallel to x1 and x2, respectively. The material is submitted to plane strain deformation along the symmetry axes x1 and x2 ( ε_ 11 þ ε_ 22 ¼ 0; ε_ 33 ¼ ε_ 13 ¼ ε_ 23 ¼ ε_ 12 ¼ 0). In a first step of localization, the strain rate associated with any cell (β) of the automaton is calculated from Gilormini's results [31], by considering in turn each grain as an inclusion embedded in its neighborhood. Neglecting the orthotropic anisotropy of the overall material, which is likely to be induced by the shape of the grains (morphological anisotropy), the strain rate ε_ c11 ¼ −ε_ c22 of (c) can be written in the form: c ∞ ε_ 11 ¼ ρδc ε_ 11 ∞
ð2Þ ∞
where ε_ 11 ¼ −ε_ 22 is the remote prescribed strain rate and ρ is a normalization constant (i.e. independent of the cell considered). The localization factor 6c has been derived explicitly by Gilormini [32]: δc ¼
λ2c
ðλc þ 1Þ2 þ 2 kc =k λc þ 1
ð3Þ
where λc = b / a is the aspect ratio of the grain; kc is its viscosity (kc = kA or kB); and k is an average viscosity of its neighborhood. To derive these quantities from Eq. (3), it is first necessary to determine the average viscosity k of the neighborhood. Three possible choices are proposed and compared in the following: (i) k is the arithmetic average of the viscosities associated with the n cells of the neighborhood; (ii) k is the harmonic average of the viscosities associated with the cells of the neighborhood, i.e. 1 / k is the arithmetic average of the inverses of these viscosities; (iii) k is calculated from a self-consistent model extended over the neighborhood under consideration. In agreement with Eq. (3), which assumes that the matrix is isotropic, k is considered here as independent of the aspect ratios and respective positions of the grains in the neighborhood. The con c stant ρ is calculated such that the average strain rate ε_ 11 is equal to the prescribed one ε_ ∞11 , from where: c ε_ 11 ¼
δc ∞ ε_ : hδc i 11
ð4Þ
In a second step, an averaging procedure is applied to derive the overall deviatoric stress:
(c) 3
4
2
5 (β) 6
1 7
8
c hk δ i ∞ ∞ s11 ¼ s11 ¼ c c ε_ 11 ¼ kε_ 11 hδc i
where k is the viscosity of the aggregate along direction x1 or x2. Introducing now the volume fraction f = fA of phase A, the above equation can be written in the equivalent form: x¼
Fig. 1. Cellular automaton model of grain embedded with its neighborhood for calculation. (a) Three-dimensional cellular automaton model in numerical simulations; (b) two-dimensional cellular automaton model in numerical simulations; (c) the automaton represented by squares for the grain which has eight neighbors.
ð5Þ
k f hδA i þ ð1−f ÞΣhδB i ¼ kA f hδA i þ ð1−f ÞhδB i
ð6Þ
Where bδA> and b δB> are the average values of the localization factors pertaining to the A and B grains, respectively. It can be easily
B. Li, H. Wang / Int. Journal of Refractory Metals and Hard Materials 36 (2013) 167–173
shown that the overall viscosity kCL predicted by the proposed cell model always lies between the uniform stress (static) and uniform strain rate (Taylor) bounds: kS ≤ kCL ≤ kT
ð7Þ
where 1 / kS = bl / kc> and kT = bkc>. Moreover, it will be shown in the next section that narrower bounds can be found for kCL under more restrictive assumptions. It is worth emphasizing that the localization and averaging methods employed here ensure that the averages of both the strain rates and deviatoric stresses are equal to their overall counterparts, whatever the aspect ratios λc of the grains [33]. The hydrostatic pressure in an inclusion for the geometry and boundary conditions presently considered has also been derived in an explicit form when applied to cell (β), and this gives ð8Þ
where p∞ is the remote pressure. Thus bpc> and p∞ are generally unequal c ∞ (and so are the stresses b σ11 > and σ11 ) according to the cell model, unless λc =1 for all grains. This contrasts with the two-phase self-consistent approach, where λc =λ is generally assumed to be the same for all grains. In that special case, the average pressure can be written as: ð9Þ
where kSC is the predicted overall viscosity. In another special case, since the neighborhood of any grain consists of the whole material in the self-consistent scheme, k =kSC, which leads to bpc>=p∞. _ c associated with cell (β) Finally, the plastic work rate density w and the average work rate density is D E D E _ c i ¼ 2 kc δ2c = δ2c · ε ∞11 2 hw
ð10Þ
which is less than (or equal to) _ ∞ i ¼ 2k ε∞11 2 ¼ 2ðhkc δc i=hδc iÞ· ε∞11 2 : hw
ð11Þ
_ c i≤w _ ∞ whatever the aspect ratios of the Since 〈kcδc2〉 ≤ 〈kcδc〉〈δc〉, hw grains. In order to analyze the uniform distribution for microstructural grains, it is assumed that the grains are equiaxed, i.e. λc = 1 for any cell of the array. Furthermore, the size of the aggregate is infinite and the two kinds of constituents, A and B, are randomly and uniformly distributed. The following analytical derivations are given for plane strain deformation; however, their extension to the three-dimensional case is straightforward. The probability for any cell (of the A or B type) to have exactly p cells of type A within its neighborhood is n! n p n−p p n−p f ð1−f Þ f ð1−f Þ ¼ p P!ðn−P Þ!
ZW0 ZW10 ZW20 ZW30 ZW40
possible reaction
ΔGθT
Result
1 2 3 4 5 6
ZrB2 + TiC = ZrC + TiB2 ZrO2 + TiC = ZrC + TiO2 ZrO2 + WC = ZrC + WO2 2ZrB2 + 3 N2 = 2ZrN + 4BN ZrO2 + N2 = ZrN + NO2 2ZrO2 + N2 = 2ZrN + 2O2
+25,688 +123,230 — — +702,595 +1,075,799
No occurrence
where f is the volume fraction of phase A. The average values of the localization factors associated with the A and B grains are then hδA i ¼
n X
V ðpÞδA ðpÞ and hδB i ¼
n X
V ðpÞδB ðpÞ
ð13Þ
p¼0
where δA(p) and δB(p) are the localization factors pertaining to a cell A or cell B surrounded by exactly p cells of type A. 3. Experimental procedure The raw material used for the matrix is ZrB2, which has a ZrB2 content of 92.2% ± 0.1% by volume and a ZrO2 content of 7.8% ± 0.1% by volume, according to the manufacturer's information. The average particle size is approximately 1.7 μm. (Ti,W)C (99% purity 99%) is a solid-solution powder with an average grain size of approximately 0.8 μm. Four different volume fractions of (Ti,W)C (10, 20, 30, and 40 vol.%) were used in designing ZrB2/(Ti,W)C materials. The compositions of the ZrB2 matrix ceramics are shown in Table 1. The suffixes in ZW0, ZW10, ZW20, ZW30, and ZW40 represent the (Ti,W)C volume content. For example, in AZ0, the (Ti,W)C volume content is zero. The original ZrB2 powders were refined via wet ball milling with cemented carbide balls in alcohol for 150 h to reduce the particle size. The combined (Ti,W)C and refined ZrB2 powders were then dispersed in an ultrasonic oscillator (HS10260D, Shanghai Troody Analytical Instrument Co., Ltd., China) to prevent material agglomeration in the subsequent step. The (Ti,W)C and refined ZrB2 powders were then mixed with cemented carbide balls in alcohol via wet ball milling for 300 h to obtain a homogeneous mixture. The slurry was dried at 150 °C in a vacuum oven (ZK-82A, Shanghai Silong Scientific Instrument Co., Ltd., China) and then screened using a 0.1 mm aperture sieve. Following the forming stage, the compacted powders were filled into a graphite die via uniaxial hot pressing in an N2 atmosphere at 1800 °C (30 °C·min−1) and at a pressure of 35 MPa for 40 min to produce a disk. X-ray diffraction (XRD) analysis (BRUKER AXS D8 ADVANCE, Bruker Axis Corporation, Germany) was performed to
ZrB2 TiC WC ZrO2
1200 1000
ð12Þ
Table 1 Starting compositions of hot pressed composites. Specimen
Code
CPS/(S-1)
2 ∞ 1−λ2 kSC − k hpc i ¼ p∞ − ε_ 11 2 3 1þλ
V ðpÞ ¼
Table 2 The possible reaction in sintering ZW series ceramic materials at 1800 °C.
p¼0
2 2 ∞ 1−λc kc δc pc ¼ p∞ − ε_ 11 −k 2 3 1 þ λc hδc i
169
800 600 400
Composition (vol.%) (Ti,W)C
ZrB2
ZrO2
0 10 20 30 40
92.2 82.98 73.76 64.54 55.32
7.8 7.02. 6.24 5.46 4.68
200 0 20
30
40
50
60
70
2θ/(o) Fig. 2. X-ray diffraction phase analysis of ZW30 specimen.
80
170
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identify the crystal phases after sintering. The microstructure of the polished and fracture surfaces were examined via scanning electron microscopy (SEM, HITACHI S-570, Hitachi Corporation, Japan). 4. Results and discussion Based on the Gibbs free energy function, the standard reaction Gibbs free energy can be calculated using θ
ΔG
T
¼ ΔH
θ
′ 298 −TΔΦ T
ð14Þ
θ
where ΔH 298 is the thermal effect of the standard reaction at room temperature (J); T is the sintering temperature (absolute tempera′ ture, K); and ΔΦ T is the Gibbs free energy function (J·K −1) of the reaction. The reaction cannot proceed when ΔGθ T > 0, whereas the θ reaction occurs when ΔG T b0. Table 2 shows the possible reactions during the sintering of the ZW series of ceramic materials at 1800 °C. “—” indicates that the reaction product cannot be formed at this temperature. Based on Table 2, the reaction or product is not formed in Reactions (3) and (4) at 1800 °C, with exception for them, other reactions cannot occur. The X-ray diffraction results for the ZW30 specimen (Fig. 2) show the presence of ZrB2, WC, TiC, and ZrO2 phases. Thus, the standard reaction Gibbs energy can be used for analyzing chemical compatibility.
×2,000
10 µm
Fig. 4. SEM micrograph of the fracture surface of monolithic ZrB2.
Fig. 2 shows that the composite contains a large amount of ZrO2 despite its moderate content in the starting powder. This increase in ZrO2 content may be due to oxidation during long-term milling (150 and 300 h).
(a)
(b)
(c)
(d)
Fig. 3. Simulated microstructure of ZW series ceramic composite at 1800 °C. The series ceramics are: (a) ZW0; (b) ZW10; (c) ZW20; (d) ZW30, respectively.
B. Li, H. Wang / Int. Journal of Refractory Metals and Hard Materials 36 (2013) 167–173
×2,000
171
in Fig. 4; the fracture surfaces of ZW10, ZW20, ZW30, and ZW40 are shown in Figs. 5–8, respectively. In Fig. 6, the black areas in No. 1 are ZrB2 and ZrO2, as identified via energy-dispersive X-ray spectroscopy; the white areas in No. 3 are (Ti,W)C compounds; and the junction in No. 2 contains ZrB2 and (Ti,W)C. The results above show significant microstructural differences among the composites. The fracture mode of monolithic ZrB2 is primarily intergranular, and the mean grain size is approximately 15 μm. The addition of (Ti,W)C compounds results in the formation of finer and more homogeneous composite microstructures. The fracture mode remains intergranular with the incorporation of 10 and 20 vol.% (Ti,W)C compounds (Figs. 5 and 6, respectively). However, the fracture mode becomes a combination of transgranular and intergranular failures as the concentration of (Ti,W)C compounds reaches 30 vol.% (Fig. 7). Further addition of (Ti,W)C compounds results in a primarily intergranular fracture mode, accompanied by a small percentage of transgranular failure (Fig. 8). The WC and TiC particles are uniformly distributed throughout the microstructure (Fig. 7). The size of the ZrB2 grains range from 4 μm to 5 μm and is considerably smaller than that of the monolithic ZrB2 grains. In Fig. 6, the bond strength of the grains increases when the fracture mode is a combination of transgranular and intergranular failures. In other words, the fracture mode changes from intergranular to a combination of transgranular and intergranular failures. The change is mainly due to the strengthening of the grain boundaries of the composites as a result of the addition of moderate amounts of (Ti,W)C compounds. This transformation causes a significant increase in the bending strength and fracture toughness. As previously mentioned, the mean grain size of monolithic ZrB2 is approximately 15 μm, whereas those of ZW10, ZW20, ZW30, and ZW40 are approximately 10, 8, 5, and 7 μm, respectively. The grain size of monolithic ZrB2 is larger than those of the composites strengthened by (Ti,W)C compounds under identical conditions. This result indicates that the addition of (Ti,W)C compounds prevents the abnormal growth
10 µm
Fig. 5. SEM micrograph of the fracture surface of ZW10 ceramic composite.
The initial microstructure was formed via a normal grain growth algorithm. The primary grains and the newly formed grains have an orientation which was randomly set in the program. Fig. 3 shows the simulated microstructure of the ZW series of ceramic composites at 1800 °C. For comparison, all simulated microstructures were based on the same initial microstructure. To simulate the experimental observations accurately, the mean diameter of the starting grains in the calculation was set to around 15 μm. Figs. 4–8 show significant microstructural differences among the composites. The relative density increased with increasing percentage of (Ti,W)C compounds, whereas the mean grain size decreased from 15 μm to 7 μm. The SEM photomicrograph of the fracture surface of monolithic ZrB2 sintered for 40 min at 1800 °C under a 35 MPa pressure is shown
a 3
2 1
×2,000
b
c
10 µm
d
Fig. 6. (a) SEM micrograph of the fracture surface of ZW20 ceramic composite; (b) EDX energy spectrum diagram of area 1 ; (c) EDX energy spectrum diagram of area 2; (d) EDX energy spectrum diagram of area 3.
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transgranular
This change increases the bending strength and fracture toughness. One reason is that the grain boundaries of the composites are strengthened. The other is that the addition of (Ti,W)C compounds prevents the abnormal growth of ZrB2 grains in the composites. When the amount of (Ti,W)C exceeds 30 vol.%, the densification becomes more difficult, and the mechanical properties of the composites decrease.
intergranular Acknowledgements
×2,000
10 µm
Fig. 7. SEM micrograph of the fracture surface of ZW30 ceramic composite.
of ZrB2 grains in the composites [25]. When the amount of (Ti,W)C was increased to 40 vol.% (Fig. 8), the bonds between grains become weaker than those in ZW30, which resulted in lower densification and weaker mechanical properties compared with those of ZW30. Thus, the addition of a moderate amount of (Ti,W)C compounds results in the formation of finer and more homogeneous composite microstructures as well as stronger bonds between grains. Based on the simulations and on the experimental analyses, the addition of 30 vol.% (Ti,W)C compounds results in higher performance compared with those of other amounts. 5. Conclusions ZrB2/(Ti,W)C composites were fabricated via hot-pressing technology. Cellular automata models were then used to predict the microstructural effects on ceramic materials. Particular attention was given to the effect of the addition of (Ti,W)C compounds on the microstructure. The following conclusions were drawn from the results: 1. Simulations using CA models show significant microstructural differences among the composites. The relative density increased with the increasing percentage of (Ti,W)C compounds, whereas the mean grain size decreased from 15 μm to 7 μm; 2. The addition of (Ti,W)C compounds results in the formation of finer and more homogeneous composite microstructures. 3. The fracture mode becomes a combination of transgranular and intergranular failures when the amount of (Ti,W)C reaches 30 vol.%.
×2,000
10 µm
Fig. 8. SEM micrograph of the fracture surface of ZW40 ceramic composite.
The work described in this paper is supported by the National Natural Science Foundation of China (No. 51105188), the Natural Science Foundation of Education Department of Henan Province (No. 12B460016), and the Development Program for Science and Technology of Luoyang. References [1] Fahrenholtz WG, Hilmas GE, Zhang SC, Zhu S. Pressureless sintering of zirconium diboride: particle size and additive effects. J Am Ceram Soc 2008;91(5):1398-404. [2] Mishra SK, Das SK, Pathak LC. Sintering behaviour of self-propagating high temperature synthesised ZrB2–Al2O3 composite powder. Mater Sci Eng, A 2006;426(1–2): 229-34. [3] Li B, Deng JX, Li YS. Oxidation behavior and mechanical properties degradation of hot-pressed Al2O3/ZrB2/ZrO2 ceramic composites. Int J Refract Met Hard Mater 2009;27(4):747-53. [4] Monteverde F. The addition of SiC particles into a MoSi2-doped ZrB2 matrix: effects on densification, microstructure and thermo-physical properties. Mater Chem Phys 2009;113(2–3):626-33. [5] Kim KH, Shim KB. The effect of lanthanum on the fabrication of ZrB2–ZrC composites by spark plasma sintering. Mater Charact 2003;50(1):31-7. [6] Millet P, Hwang T. Preparation of TiB2 and ZrB2. Influence of a mechano-chemical treatment on the borothermic reduction of titania and zirconia. J Mater Sci 1996;31(2):351-5. [7] Shew B-Y, Huang J-L. Investigation of chemical reactions in TiB2/Si3N4 composites. Mater Sci Eng, A 1992;159(1):127-33. [8] Parthasarathy TA, Rapp RA, Opeka M, Kerans RJ. A model for the oxidation of ZrB2, HfB2 and TiB2. Acta Mater 2007;55(17):5999-6010. [9] Opeka MM, Talmy IG, Wuchina EJ, Zaykoski JA, Causey SJ. Mechanical, thermal, and oxidation properties of refractory hafnium and zirconium compounds. J Eur Ceram Soc 1999;19(13–14):2405-14. [10] Zhang SC, Hilmas GE, Fahrenholtz WG. Pressureless sintering of ZrB2–SiC ceramics. J Am Ceram Soc 2008;91(1):26-32. [11] Hu P, Guolin W, Wang Z. Oxidation mechanism and resistance of ZrB2–SiC composites. Corros Sci 2009;51(11):2724-32. [12] Raabe D, Becker RC. Coupling of a crystal plasticity finite-element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminium. Modell Simul Mater Sci 2000;8:445. [13] Chen W, Brouwers HJH, Shui Z. Three-dimensional computer modeling of slag cement hydration. J Mater Sci 2007;42(23):9595-610. [14] Brown S, Bruce N. Three-dimensional cellular automaton models of microstructural evolution during solidification. J Mater Sci 1995;30(5):1144-50. [15] Mitchell M, Crutchfield JP, Das R. Evolving cellular automata with genetic algorithms: a review of recent work; 1996. [16] Psakhie SG, Horie Y, Ostermeyer GP, Korostelev SY, Smolin AY, Shilko EV, et al. Movable cellular automata method for simulating materials with mesostructure. Theor Appl Fract Mech 2001;37(1–3):311-34. [17] Österle W, Dörfel I, Prietzel C, Rooch H, Cristol-Bulthé AL, Degallaix G, et al. A comprehensive microscopic study of third body formation at the interface between a brake pad and brake disc during the final stage of a pin-on-disc test. Wear 2009;267(5): 781-8. [18] Österle W, Dmitriev AI, Kloß H. Possible impacts of third body nanostructure on friction performance during dry sliding determined by computer simulation based on the method of movable cellular automata. Tribol Int 2012;48:128-36. [19] Mishra SK, Pathak L. Effect of carbon and titanium carbide on sintering behaviour of zirconium diboride. J Alloys Compd 2008;465(1–2):547-55. [20] Monteverde F, Guicciardi S, Bellosi A. Advances in microstructure and mechanical properties of zirconium diboride based ceramics. Mater Sci Eng, A 2003;346(1–2): 310-9. [21] Rangaraj L, Suresha SJ, Divakar C, Jayaram V. Low-temperature processing of ZrB2–ZrC composites by reactive hot pressing. Metall Mater Trans A 2008;39(7):1496-505. [22] Chamberlain AL, Fahrenholtz WG, Hilmas GE. Reactive hot pressing of zirconium diboride. J Eur Ceram Soc 2009;29(16):3401-8. [23] Chamberlain AL, Fahrenholtz WG, Hilmas GE. Pressureless sintering of zirconium diboride. J Am Ceram Soc 2006;89(2):450-6. [24] Mishra SK, Das SK. Sintering and microstructural behaviour of SHS produced zirconium diboride powder with the addition of C and TiC. Mater Lett 2005;59(27): 3467-70. [25] Saidi A, Barati M. Production of (W, Ti)C reinforced Ni–Ti matrix composites. J Mater Process Technol 2002;124(1–2):166-70.
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