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Microstructural optimization of solid-state sintered silicon carbide

Dissertation
Author: Lionel R. Vargas-Gonzalez
Abstract:
Silicon carbide armor, manufactured through solid-state sintering, liquid-phase sintering, and hot-pressing, is being used by the United States Armed Forces for personal and vehicle protection. There is a lack of consensus, however, on which process results in the best-performing ballistic armor. Previous studies have shown that hot-pressed ceramics processed with secondary oxide and/or rare earth oxides, which exhibit high fracture toughness, perform well in handling and under ballistic impact. This high toughness is due to the intergranular nature of the fracture, creating a tortuous path for cracks and facilitating crack deflection and bridging. However, it has also been shown that higher-hardness sintered SiC materials might perform similarly or better to hot-pressed armor, in spite of the large fracture toughness deficit, if the microstructure (density, grain size, purity) of these materials are improved. In this work, the development of theoretically-dense, clean grain boundary, high hardness solid-state sintered silicon carbide (SiC) armor was pursued. Boron carbide and graphite (added as phenolic resin to ensure the carbon is finely dispersed throughout the microstructure) were used as the sintering aids. SiC batches between 0.25-4.00 wt.% carbon were mixed and spray dried. Cylindrical pellets were pressed at 13.7 MPa, cold-isostatically pressed (CIP) at 344 MPa, sintered under varying sintering soaking temperatures and heating rates, and varying post hot-isostatic pressing (HIP) parameters. Carbon additive amounts between 2.0-2.5 wt.% (based on the resin source), a 0.36 wt.% B 4 C addition, and a 2050°C sintering soak yielded parts with high sintering densities (∼95.5-96.5%) and a fine, equiaxed microstructure (d50 = 2.525 μm). A slow ramp rate (10°C/min) prevented any occurrence of abnormal grain growth. Post-HIPing at 1900°C removed the remaining closed porosity to yield a theoretically-dense part (3.175 g/cm3 , according to rule of mixtures). These parts exhibited higher density and finer microstructure than a commercially-available sintered SiC from Saint-Gobain (Hexoloy Enhanced, 3.153 g/cm3 and d50 = 4.837 μm). Due to the optimized microstructure, Verco SiC parts exhibited the highest Vickers (2628.30 ± 44.13 kg/mm 2 ) and Knoop (2098.50 ± 24.8 kg/mm2 ) hardness values of any SiC ceramic, and values equal to those of the "gold standard" hot-pressed boron carbide (PAD-B4 C). While the fracture toughness of hot-pressed SiC materials (∼4.5 MPa[Special characters omitted.] m ) are almost double that of Verco SiC (2.4 MPa[Special characters omitted.] m ), Verco SiC is a better performing ballistic product, implying that the higher hardness of the theoretically-dense, clean-grain boundary, fine-grained SiC is the defining mechanical property for optimization of ballistic behavior.

TABLE OF CONTENTS ACKNOWLEDGEMENTS..........................iii LIST OF TABLES...............................vi LIST OF FIGURES..............................vii SUMMARY....................................xi I INTRODUCTION.............................1 II LITERATURE REVIEW.........................5 2.1 Silicon Carbide..............................5 2.2 Sintering.................................7 2.2.1 Solid-State Sintering.......................8 2.2.2 Liquid Phase Sintering.....................16 2.2.3 Hot Pressing...........................28 2.3 Silicon Carbide Sintering........................29 2.4 Silicon Carbide Armor Developments.................36 III EXPERIMENTAL PROCEDURE...................38 3.1 Additive Optimization Study......................38 3.2 Sintering Optimization Studies.....................41 3.2.1 Mechanical Testing.......................41 3.2.2 Characterization.........................45 3.3 Ballistic Evaluation of SiC Armor...................46 IV RESULTS..................................48 4.1 Additive Optimization Study......................48 4.2 Sintering Optimization Study......................57 4.3 Mechanical Characterization......................65 4.4 Ballistic Evaluation of SiC Armor...................85 V DISCUSSION................................94 iv

VI CONCLUSION...............................98 v

LIST OF TABLES Table 1 Merit Factor for B 4 C Armor Samples As Tested By Foster-Miller.2 Table 2 Listed Material Properties for Silicon Carbide............7 Table 3 Mass Transport Mechanisms During Solid-State Sintering [22]....8 Table 4 SiC Compositions for Sintering Study................39 Table 5 Steps in Grinding/Polishing for the Preparation of Specimens for Hardness Evaluation..........................40 Table 6 Armor Compositions Chosen for Mechanical Testing........42 Table 7 Listing of Mechanical Properties Evaluated.............42 Table 8 Calculated Theoretical Density of SS1–SS25 Compositions.....48 Table 9 Post Sintering Density of SS1–SS25 Compositions..........49 Table 10 Vickers Hardness Values For SS23–SS25 Samples and Hexoloy En- hanced..................................51 Table 11 Average Grain Size for SS and Hexoloy Samples...........54 Table 12 Sintering and Post-HIPing Data for 44.45 mm Samples.......61 Table 13 Mean Values for Carbon Inclusions in Sintered SiC Materials...72 Table 14 Mean Values for Grain Size of All Armor Ceramics.........74 Table 15 Mechanical Characterization of Armor Ceramics...........75 Table 16 Merit Factor for SiC Armor Samples.................92 vi

LIST OF FIGURES Figure 1 The silicon-carbon binary phase diagram [17].............6 Figure 2 Two-sphere solid state sintering model for neck formation between two particles in contact [23].......................10 Figure 3 The effect of interfacial curvature on the vacancy concentration and vapor pressure of a solid-vapor interface.A concave surface exhibits a higher concentration of vacancies in the solid and a lower vapor pressure of the solid in the vapor [21].................12 Figure 4 Pore and grain structure in the intermediate stage of sintering [23].13 Figure 5 Pore and grain structure in the final stages of sintering [23].....14 Figure 6 The effect of boundary curvature on grain growth.Grains with con- cave boundaries grow and those with convex surfaces shrink.Un- usually large grains in a matrix of fine grains grow quickly,causing pore entrapment and a reduction in densification [24]........15 Figure 7 Effect of the liquid-solid contact angle on the wetting of the solid. The top diagram illustrates an attractive force between particles due to a low contact angle and high wetting.The lower diagram illustrates particle separation due to a high contact angle and low wetting [23]................................18 Figure 8 Two-sphere LPS model used for the calculation of the capillary force exerted by the liquid.[28]........................20 Figure 9 Pictoral representation of the pore-filling model:(a) grains and liq- uid before pore filling,(b) the critical criteria for instability,where the liquid meniscus fully wets the pore surface,and (c) liquid filling of the pore after the critical instability.ρ is the radius of curvature for the liquid meniscus,where ρ 1 < ρ 2 < ρ

2 [21]............26 Figure 10 The elongated α-SiC platelet microstructure formed fromthe sinter- ing of a mixture of α and β SiC powders [43].............33 Figure 11 The effect of annealing time on fracture toughness of 100% α-SiC and 90% β/10% α-SiC powders [44].The solution and precipitation of β-SiC into α-SiC increased the fracture toughness with increasing α-SiC grain growth...........................34 Figure 12 Fine equiaxed microstructure formed from sintering α-SiC powder at 1950 ◦ C and heat treating for 16 hours [43].............35 Figure 13 Dilatometry traces for samples SS1-SS21.Sinterability increases as carbon content is increased,however,the extent is far less than desired.49 vii

Figure 14 Dilatometry traces for samples SS22–SS25,of which SS23 and SS24 show the highest relative densities of the sintering group.The SS25 sintering extent is greater than that of SS23;however,the sintered density is lower..............................50 Figure 15 Vickers hardness values of SS23–SS25 and Hexoloy Enhanced.Unop- timized,as-sintered specimens demonstrated higher hardnesses than Hexoloy Enhanced.Note that Saint Gobain does not publish an exact relative density for Hexoloy Enhanced,but reports a value greater than 98% in their literature..................52 Figure 16 X-ray diffraction traces of specimens with 2,3,and 4 wt.% carbon additions.ICDD data:A:01-073-1664 Moissanite 4H;B:01-073- 1663 Moissanite 6H;C:01-073-1662 Moissanite 15R;G:01-075-2078 Graphite.................................53 Figure 17 X-ray diffraction traces concentrated in the region of the most intense graphite peak..............................54 Figure 18 Optical micrographs (20×) of polished and thermally-etched speci- mens with the indicated carbon weight percentages and the Hexoloy specimen.Hexoloy exhibits a much coarser and high aspect grain microstructure,indicating abnormal grain growth...........55 Figure 19 Grain size distributions of the specimens with varying carbon con- tent along with the Hexoloy specimen,as determined by the linear intercept method.Samples SS23–SS25 exhibit similar distributions.56 Figure 20 Dilatometry traces for powder compacts exposed to differing heating rates...................................57 Figure 21 SS23 samples sintered at various heating rates.The sample sintered with the 10 ◦ C/min heating rate exhibits the finest grain structure.58 Figure 22 SS23 samples sintered at 10 and 50 ◦ C/min,imaged at 50×.....59 Figure 23 Spray-dried granules attained through use of a ultrasonic atomizing nozzle from Sono-Tek Corporation...................61 Figure 24 Dilatometry traces for the initial Anhydro spray-drying trials.Num- bers in the figure correspond to weight percentages of added phenolic resin.The sample with the 2.5 wt.% carbon content sintered the best.62 Figure 25 Hardness and relative density values for specimens which were sin- tered and post-HIPed as a function of sintering soak temperature. Hexoloy Enhanced hardness value is added as a reference......63 viii

Figure 26 Etched microstructures of sintered and post-HIPed specimens which were sintered at the indicated soak temperatures.Abnormal grain growth is evident in samples soaked above 2100 ◦ C,which leads to the decrease in Vickers hardness for those samples..........64 Figure 27 A Vickers indentation in the post-HIPed specimen which was sin- tered at 2100 ◦ C.Transgranular fracture behavior is exhibited....65 Figure 28 EDS scans of the 2050 ◦ C sample after post-HIPing.Blemishes in the triple points are revealed to be pockets of carbon.No excess carbon could be found along the grain boundaries...............66 Figure 29 XRD patterns for Verco B 4 C and PAD-B 4 C.Trace amounts of alu- mina are present in the PAD-B 4 C...................67 Figure 30 XRD patters for SiC-N FH and LA3.................68 Figure 31 XRD patterns for Hexoloy Enhanced and Verco SiC........69 Figure 32 EDS scan of PAD-B 4 C showing aluminum existing in inclusions at the grain corners.............................70 Figure 33 EDS scan of SiC-N fracture surface.The grain facets on the fracture surface are coated with the interfacial phase containing aluminum and oxygen................................71 Figure 34 Fracture surfaces of all ceramics as imaged by the LEO SEM.The scale bar is 10 μm.SiC-N is the only material to show an intergran- ular fracture mode...........................73 Figure 35 Crack propagating intergranularly on the fracture surface of SiC-N.74 Figure 36 Optical micrographs of the B 4 C and SiC samples.The scale bar on all images is 10 μm...........................75 Figure 37 Grain size distributions for all samples.Verco B 4 C,Verco SiC and SiC-N varieties share similar size distributions.Hexoloy Enhanced and PAD-B 4 C have a coarser and broader distribution........76 Figure 38 Flexural strength for all ceramic materials tested using the ASTM C1161-02c standard.SiC-Nbars exhibit the highest flexural strength values for all compositions.The Verco SiC specimen showed a com- paratively wide distribution in strengths................77 Figure 39 Chevron-notch fracture toughness values for all the ceramic sam- ples using the ASTMC1421-01b standard.SiC-N samples exhibited higher fracture toughness values,due to the intergranular nature of the fracture mode............................79 ix

Figure 40 Vickers hardness indentation values for all samples according to the recommendations of the ASTM C1327–99 standard (1 kgf load). Verco B 4 C and SiC are the hardest materials in both their respective materials.Verco SiC has a mean value approximately equal to that of PAD-B 4 C...............................80 Figure 41 Optical micrography of Vickers indentations in a) SiC-N and b) Verco B 4 C.Both SiC-N samples were unmeasurable at varying in- dentation loading levels as the intergranular nature of the cracking caused erratic indentation patterns...................81 Figure 42 Knoop indentations taken in SiC-N FH exhibiting erratic central cracking but clear,defined diagonal edges...............82 Figure 43 Knoop hardness indentation values for all samples taken in accor- dance with the ASTMC1326–03 standard (2 kgf).The general trend is similar as those shown in the Vickers hardness results,however, Verco SiC indentation values overtake those of PAD-B 4 C......83 Figure 44 Knoop hardness (2 kgf) as a function of chevron-notched beam frac- ture toughness.The trend suggests an inverse relationship between the two mechanical properties.....................84 Figure 45 Vickers indentation results for all ceramic armor samples at 0.5,1, and 2 kgf loadings............................86 Figure 46 Knoop indentation results for all ceramic armor samples at 0.5,1, and 2 kgf loadings............................87 Figure 47 Vickers and Knoop indentations ranging from 0.5–2 kgf for each ceramic.A general downward trend is evident for all samples in accordance with the indentation size effect.Verco SiC exhibits a higher hardness compared to PAD-B 4 C at increasing indentation load for both Vickers and Knoop....................88 Figure 48 Typical sintering run for SiC in the Centorr System VII furnace..90 Figure 49 Zoomed in view of the area of severe outgassing between 995–1160 ◦ C.91 Figure 50 Merit factors calculated through ballistic testing of SiC tiles using a 7.62 × 54R mild steel ball round.Verco SiC exhibits the highest ballistic behavior.............................93 Figure 51 Microstructure of Verco SiC taken at 100×.Curved grain boundaries are evident,suggesting that there might be a liquid-phase sintering mechanism present............................95 x

SUMMARY Silicon carbide armor,manufactured through solid-state sintering,liquid-phase sintering,and hot-pressing,is being used by the United States Armed Forces for personal and vehicle protection.There is a lack of consensus,however,on which process results in the best-performing ballistic armor.Previous studies have shown that hot-pressed ceramics processed with secondary oxide and/or rare earth oxides, which exhibit high fracture toughness,perform well in handling and under ballistic impact.This high toughness is due to the intergranular nature of the fracture,creating a tortuous path for cracks and facilitating crack deflection and bridging.However, it has also been shown that higher-hardness sintered SiC materials might perform similarly or better to hot-pressed armor,in spite of the large fracture toughness deficit, if the microstructure (density,grain size,purity) of these materials are improved. In this work,the development of theoretically-dense,clean grain boundary,high hardness solid-state sintered silicon carbide (SiC) armor was pursued.Boron car- bide and graphite (added as phenolic resin to ensure the carbon is finely dispersed throughout the microstructure) were used as the sintering aids.SiC batches between 0.25–4.00 wt.%carbon were mixed and spray dried.Cylindrical pellets were pressed at 13.7 MPa,cold-isostatically pressed (CIP) at 344 MPa,sintered under varying sinter- ing soaking temperatures and heating rates,and varying post hot-isostatic pressing (HIP) parameters.Carbon additive amounts between 2.0–2.5 wt.% (based on the resin source),a 0.36 wt.% B 4 C addition,and a 2050 ◦ C sintering soak yielded parts with high sintering densities (∼95.5–96.5%) and a fine,equiaxed microstructure (d 50 = 2.525 μm).A slow ramp rate (10 ◦ C/min) prevented any occurrence of abnormal grain growth.Post-HIPing at 1900 ◦ C removed the remaining closed porosity to yield xi

a theoretically-dense part (3.175 g/cm 3 ,according to rule of mixtures).These parts exhibited higher density and finer microstructure than a commercially-available sin- tered SiC from Saint-Gobain (Hexoloy Enhanced,3.153 g/cm 3 and d 50 = 4.837 μm). Due to the optimized microstructure,Verco SiC parts exhibited the highest Vickers (2628.30 ± 44.13 kg/mm 2 ) and Knoop (2098.50 ± 24.8 kg/mm 2 ) hardness values of any SiC ceramic,and values equal to those of the “gold standard” hot-pressed boron carbide (PAD-B 4 C).While the fracture toughness of hot-pressed SiC materials (∼4.5 MPa √ m) are almost double that of Verco SiC (2.4 MPa √ m),Verco SiC is a better performing ballistic product,implying that the higher hardness of the theoretically- dense,clean-grain boundary,fine-grained SiC is the defining mechanical property for optimization of ballistic behavior. xii

CHAPTER I INTRODUCTION Ceramic armor (e.g.Al 2 O 3 ,AlN,B 4 C,SiC,and TiB 2 ) has been deployed by the United States Armed Forces since the 1960’s and has undergone continuous evolution since then [1].The dominant materials for this market are boron and silicon carbides, and aluminum oxide. Until recently,boron carbide (B 4 C) has been considered the best ceramic ar- mor for personal protection because of its low theoretical density and high hardness. Commercially-available B 4 C armor is manufactured via uniaxial hot pressing;sinter- ing pure boron carbide to acceptable density has historically been difficult.Hot press- ing has the additional advantage of densifying less-costly coarser-grained powder into acceptably-dense compacts (∼98% relative density).However,complex-shaped parts cannot be fabricated through hot-pressing,and hot-pressing can introduce a fine-scale non-spherical porosity [2].Boron carbide has been successfully pressureless-sintered to acceptable relative densities through use of second phase additives (e.g.Al 2 O 3 ,SiC, TiB 2 ,AlF 3 ,and W 2 B 5 ),which may promote activated sintering,liquid phase sinter- ing,and/or inhibit grain growth [3,4,5,6].Carbon additives are effective sintering aids,and can react-away B 2 O 3 coatings invariably formed on B 4 C particle surfaces, yielding sintered bodies with ∼98% relative density [7].However,all of these addi- tives are detrimental to the hardness of the ceramic [8,9].Lee et al.used hydrogen gas to eliminate B 2 O 3 particle coatings at a temperature below the onset of sintering, and rapid heating to a soak temperature to mitigate evaporation/condensation-based particle coarsening which was rapid relative to sintering in the lower portions of the sintering temperature range [10,11].In follow-up work,Cho et al.optimized soak 1

Table 1:Merit Factor for B 4 C Armor Samples As Tested By Foster-Miller Sample Merit Factor Supplier 1 “Gold Standard” 1.000 Supplier 2 0.993 Supplier 3 (Type 1) 0.818 Supplier 3 (Type 2) 0.871 Supplier 4 0.776 Verco B 4 C 1.013 temperatures and times and used of a post hot-isostatic pressing (HIP) step on the closed-porosity sintered samples,bringing them to a fully pore-free state [2].These optimizations led to the creation of a sintered boron carbide that has been shown to be superior to hot-pressed boron carbide armor currently on the market in a recent ballistic performance test by Foster-Miller (Table 1).B 4 C,developed by Verco,was backed by composite coupons and shot with a 7.62mm × 51 NATO armor piercing (AP) round.The merit factor is an aggregate number based on the V 50 value and the areal density of the part. However,boron carbide armor has fallen out of favor in some circles for several reasons.Boron carbide has the highest Hugoniot elastic limit (HEL) of all ceramic materials.However,a large decrease in the ballistic performance of boron carbide under lower than expected impact rates and pressures is observed.Chen et al.found evidence of localized bands of amorphous boron carbide in the shards of material impacted at velocities above 850 m/s [12].These localized bands were shown by TEM studies to be aligned in specific crystallographic directions,dissimilar from the direction of twins and stacking faults.Fanchini et al.followed with the discovery that the B 12 (CCC) boron carbide polytype amorphized into B 12 and amorphous carbon bands 2-3 nm wide,leading to the breakdown of the boron carbide structure and ultimately to failure at high impact velocities [13].Also,boron carbide is produced in small quantities,and difficult to mill to sub-micron particle sizes,making sinter-grade powder cost-inhibitive. 2

In this work,the development of theoretically-dense,clean grain boundary,high hardness solid-state sintered silicon carbide (SiC) armor was pursued.There are var- ious methods to create dense armor using solid-state sintering,liquid-phase sintering, and hot-pressing techniques;however,there is a lack of consensus into what process- ing,or what microstructural features,creates the best performing ballistic armor. Hazell et al.performed a test on the effectiveness of mosaic armor made from sin- tered SiC and hot-pressed (using liquid-phase sintering additives) SiC [14].In his findings he found that not only did the sintered SiC exhibit a significantly lower depth of penetration (DOP) than the hot pressed SiC samples,but the DOP de- creased the further the target was hit from its border and into the center.In the hot pressed sample,the DOP was comparable over all areas of the sample tile.Flinders et al.performed a study on the ballistic behavior of solid-state sintered SiC versus hot-pressed SiC to determine whether there was any advantage between any of the materials and to determine whether the mechanical behavior of the material would correlate with the ballistic behavior [15].While the hot pressed SiC samples had almost a threefold increase in fracture toughness versus the sintered SiC samples, the DOP was greater,proving that increasing hardness resulted in a lower DOP and higher mass efficiency.The V 50 testing also showed little variability between sintered versus hot-pressed samples.SiC-B performed slightly better over all other samples, and the argument for this was its high density (3.21 g/cm 3 ) and intergranular frac- ture,causing it to have a higher fracture toughness and therefore creating a more tortuous path for cracks during fracture.Adding to the argument between hardness and fracture toughness,ballistic properties were found to vary greatly depending on the type of backing/encapsulation used [16].The right type of encapsulation could provide improved handling strength to the system as a whole,reducing the need for higher toughness armor. It was then concluded that the best course of action for this work was to optimize 3

the solid-state sintering of SiC to create theoretically dense,clean grain boundary silicon carbide for ceramic armor use.It was hoped that the optimization of mi- crostructure and hardness,as was done with the previous sintering optimizations of boron carbide,would yield a sintered SiC armor with superior ballistic properties to that of any other silicon carbide material currently on the market. 4

CHAPTER II LITERATURE REVIEW 2.1 Silicon Carbide Silicon carbide is used in a variety of high-wear,high-strength applications such as sandpaper grit,friction material in high-end brake applications,and for cutting tools. Applications also exist for SiC in electronic materials,where doped SiC materials are used in blue LED’s,substrates,and diodes. SiC is also used for ballistic armor.The SiC crystal structure is strong due to its high degree of covalent bonding.SiC is moderately light due to the low theoretical density of SiC,which is 3.211 g/cm 3 for α-SiC (6H) and 3.214 g/cm 3 for β-SiC [17]. The combined properties of high strength and low weight make SiC a desirable ma- terial for ground personnel and vehicle armor. SiC is produced by the carbothermal reduction of silica (SiO 2 ),which is more formally called the Acheson process: SiO 2(s) +3C (s) →SiC (s) +2CO (g) SiC exists as a line compound along 50 mol % line in the silicon-carbon binary phase diagram,and exhibits a peritectic reaction at 2545 ◦ C.Under certain cases (depending on processing conditions) decomposition of SiC can occur far under the peritectic point,as low as 1700 ◦ C [17].The silicon-carbon binary phase diagram is shown in Figure 1. SiC can exist as two different crystal symmetries:α-SiC,formed at reaction tem- peratures above 2000 ◦ C,and β-SiC,formed at lower synthesis temperatures (1500- 1600 ◦ C).α-SiC exists as a hexagonal (or rhombohedral) cell and can form various 5

3000 2600 2200 1800 1400 1000 Temperature (°C) Mol % C 2830 ± 40 2540 ± 40 SiC + C L + SiC SiC + C L + C L L 1402 ± 5 Si C20 40 50 60 80 SiC Figure 1:The silicon-carbon binary phase diagram [17]. 6

Table 2:Listed Material Properties for Silicon Carbide Density Sintering Young’s Flexural Hardness Fracture Temperature Modulus Strength Toughness (g/cm 3 ) ( ◦ C) (GPa) (MPa) (GPa) (MPa √ m) 3.211-3.214 2100 [20] 475 [17] 350-600 [17] 24.5-28.2 [17] 4.6 [20] structural polytypes (as many as 250 [18,19]) based on the stacking of silicon and carbon layers in the close-packed (<0001>) direction.The most commonly available polytypes of α-SiC are 4H (ABACABAC stacking sequence) and 6H (ABCACBABC stacking sequence).β-SiC exists as a zinc blende structure (similar to the diamond structure).The close-packed (<111>) direction stacking sequence is always AB- CABC. Commonly listed material properties of SiC are listed in Table 2.1. 2.2 Sintering Silicon carbide can be densified through sintering.Sintering is the process of heat treating a powder to produce atomic mass transport that densifies a powder compact through the creation of solid bonding between particles and through pore removal. Sintering processes can be classified into two sintering mechanisms:solid-state and liquid-phase sintering.For both cases,densification and grain growth occur during sintering,which can be modeled by Δ(γA) = γΔA+ΔγA (1) where γ is the interfacial energy (solid-vapor and solid-solid interfaces for solid-state sintering or solid-liquid and liquid-vapor for liquid-phase sintering) and A is the sur- face area of the particles [21].Δ(γA) describes the total change in the surface energy in a system with the combined effects of densification and grain growth.A change in surface area without a change in interfacial energy γΔA is coarsening which does not 7

Table 3:Mass Transport Mechanisms During Solid-State Sintering [22]. Mechanism Path of Atoms Result Evaporation-Condensation Surface to vapor to neck Coarsening Surface diffusion Surface to neck Coarsening Adhesion Surface to lattice to neck Coarsening Volume diffusion Boundary or lattice to neck Densification Dislocation climb Dislocation to neck Densification Grain boundary diffusion Boundary to neck Densification lead to densification.Densification ΔγA occurs when solid bonds are formed which removes pores from the interstices between grains,bringing grain centers closer to each other and changing the shape of the grain to accommodate into an arrangement that reduces the surface energy.The surface energy is a consequence of atoms on a free surface (such as a solid-vapor interface) having more free energy than atoms within the interior bulk of a material,due to the surface atoms having broken interatomic bonds.The equilibrium state of any natural process is the one with the minimum free energy,therefore it is the reduction of the surface energy which provides the driving force for particle sintering. 2.2.1 Solid-State Sintering In solid-state sintering,densification occurs through lattice and grain boundary dif- fusion.A complete list of mass transport processes that can occur in solid-state sintering are listed in Table 2.2.1. Solid-state sintering occurs in the absence of a wetting liquid.Many systems are sintered through this method to reduce any adverse material properties,such as loss of refractoriness,that could arise due to wetting liquids.The process by which a material changes through solid-state sintering can be classified into three stages. These are: • First stage:Neck formation between adjacent particles through surface diffu- sion or evaporation/condensation processes.The atoms at the surface need less 8

driving force than interior atoms to undergo diffusion due to the excess free energy at the surface arising from the lower number of interatomic bonds that have to be broken,therefore surface diffusion is prevalent at the lower temper- atures of sintering.Pore volume is decreased ∼10–12%.Particle surfaces are smoothed and surface area is reduced,however densification does not occur. • Second stage:The necks between the particles grow.Grain boundary and lattice diffusion works to move atoms from grain interiors to fill vacancies and pores, reducing porosity and bringing the centers of grains closer together.Solid-vapor interfaces are replaced with solid-solid interfaces,which have less surface energy. Remaining porosity is pushed to the grain edges and forms an interconnected channel throughout the microstructure.Most of the shrinkage during sintering occurs in this step,as much as ∼20%. • Third stage:Grain growth occurs during the last stage of sintering.Grains grow through bulk and grain boundary diffusion,thereby reducing the grain boundary area.Densification in this step is around 3–5%.Pores coalesce into the junction between three grain corners (triple point).Exaggerated grain growth during this step could lead to pore entrapment in grain interiors where removal becomes impossible,leading to lower densification. At the beginning stage of sintering,necks between particles are formed.Asintering stress σ arises as a consequence of curvature at an interface,given by the Laplace equation σ = γ

1 R 1 + 1 R 2

(2) where R 1 and R 2 are the radii of curvature [23].A two-sphere model for neck forma- tion is shown in Figure 2. 9

Figure 2:Two-sphere solid state sintering model for neck formation between two particles in contact [23]. The sign convention for the sintering stress is positive (tensile) for a radius beneath a convex surface,and negative (compressive) for a concave surface.The necks formed between particles are concave and therefore compressive in stress.The atoms in the neck region have more satisfied bonds than the atoms on the particle surfaces,which decreases the surface energy in the neck region and lowers the chemical potential. Also,the vapor pressure of the area around the neck is lower than the equilibrium vapor pressure.The neck region has a high stress gradient,where the sign of the stress changes fromnegative to positive in a small distance.The gradient,the reduced chemical potential,and the lower vapor pressure of the atoms in the neck provide a driving force for mass transport from the surface to the neck region.Surface diffusion and evaporation/condensation are the dominant mass transport mechanisms during the initial stages of sintering due to the free energy of the surface atoms.At the lower range of sintering temperatures,the temperature is not high enough to promote diffusion of atoms in the bulk interior. The shrinkage rate ΔL L 0 with respect to grain size and temperature during the initial stages of sintering has been modeled as 10

ΔL L 0 =

KD V γ S V V t k B Td n

m (3) where d is the grain size,K is a geometric constant,D V is the diffusivity of the vacancies in the volume V V ,and mand n are constants relating to the mass transport mechanisms being used.Later stages of sintering have many variables to consider because several mass transport mechanisms occur simultaneously,therefore this model is adequately rigorous to describe the sintering behavior beyond the first stage of sintering [24]. In the intermediate stage of sintering,after solid bridges between particles have formed through surface diffusion processes,densification of the part occurs through lattice (volume) diffusion of atoms from the particle interior to the neck and from diffusion of atoms through the grain boundaries.The driving force is the elimination of solid-vapor interfacial energy.The rate of lattice diffusion is dependent on the concentration of vacancies in the material,as vacancies are required to facilitate the diffusion of interior atoms to the neck regions.The vacancy concentration can be increased by raising the sintering temperature,since the vacancy concentration is exponentially proportional to temperature.The vacancy concentration can also be increased through adding sintering aids. Vacancy concentration in the material is also a function of the curvature of par- ticles during sintering.The effect of curvature on vacancy concentration C can be modeled using the following function C = C 0

1 − γΩ kT

1 R 1 − 1 R 2

(4) where C 0 is the equilibriumconcentration (a function of temperature),γ is the surface energy,Ω is the atomic volume,T is the absolute temperature,and k is Boltzmann’s constant [23].For a concave surface,such as the neck between particles,the vacancy concentration is higher than the equilibrium concentration.Conversely,the vacancy 11

Figure 3:The effect of interfacial curvature on the vacancy concentration and vapor pressure of a solid-vapor interface.A concave surface exhibits a higher concentration of vacancies in the solid and a lower vapor pressure of the solid in the vapor [21]. concentration is lower than the equilibrium concentration for a convex surface,which describes the curvature of a particle surface.This provides a vacancy gradient for mass flow from the areas of low vacancy concentration to the areas of high vacancy concentration.The effect of curvature on vacancy concentration is illustrated in Figure 3. Particles that have sintered together form grain boundaries between each other due to the mismatch in the lattice orientation between the particles.This mismatch lowers the activation energy needed for mass flow to occur,thus the rate of grain boundary diffusion is higher than lattice diffusion at lower sintering temperatures. The rate will depend on the type of boundary formed,which is a function of the angle of misorientation between the crystal lattices.Lattice diffusion will become 12

Figure 4:Pore and grain structure in the intermediate stage of sintering [23]. more dominant as the sintering temperature is increased. Figure 4 shows the ideal case of the microstructure in the intermediate stage of sintering.The particle shape has changed from spherical to that of a tetrakaidecahe- dron,a shape with 14 sides.Vacancies are moved onto the tetrakaidecahedron edges and create an interconnected pore structure throughout the microstructure. The final stage of solid-state sintering involves grain growth through movement of grain boundaries.As the interconnected pore structure begins to collapse,the pinning effect of pores on grain boundary migration diminishes and grain growth increases rapidly.The pore structure changes from the cylindrical interconnected pore shape to isolated pores on the grain edges and corners.The idealized model of the microstructure is shown in Figure 5.The ability of a pore to shrink depends on pore size,coordination number,and the dihedral angle (the internal angle formed 13

Full document contains 118 pages
Abstract: Silicon carbide armor, manufactured through solid-state sintering, liquid-phase sintering, and hot-pressing, is being used by the United States Armed Forces for personal and vehicle protection. There is a lack of consensus, however, on which process results in the best-performing ballistic armor. Previous studies have shown that hot-pressed ceramics processed with secondary oxide and/or rare earth oxides, which exhibit high fracture toughness, perform well in handling and under ballistic impact. This high toughness is due to the intergranular nature of the fracture, creating a tortuous path for cracks and facilitating crack deflection and bridging. However, it has also been shown that higher-hardness sintered SiC materials might perform similarly or better to hot-pressed armor, in spite of the large fracture toughness deficit, if the microstructure (density, grain size, purity) of these materials are improved. In this work, the development of theoretically-dense, clean grain boundary, high hardness solid-state sintered silicon carbide (SiC) armor was pursued. Boron carbide and graphite (added as phenolic resin to ensure the carbon is finely dispersed throughout the microstructure) were used as the sintering aids. SiC batches between 0.25-4.00 wt.% carbon were mixed and spray dried. Cylindrical pellets were pressed at 13.7 MPa, cold-isostatically pressed (CIP) at 344 MPa, sintered under varying sintering soaking temperatures and heating rates, and varying post hot-isostatic pressing (HIP) parameters. Carbon additive amounts between 2.0-2.5 wt.% (based on the resin source), a 0.36 wt.% B 4 C addition, and a 2050°C sintering soak yielded parts with high sintering densities (∼95.5-96.5%) and a fine, equiaxed microstructure (d50 = 2.525 μm). A slow ramp rate (10°C/min) prevented any occurrence of abnormal grain growth. Post-HIPing at 1900°C removed the remaining closed porosity to yield a theoretically-dense part (3.175 g/cm3 , according to rule of mixtures). These parts exhibited higher density and finer microstructure than a commercially-available sintered SiC from Saint-Gobain (Hexoloy Enhanced, 3.153 g/cm3 and d50 = 4.837 μm). Due to the optimized microstructure, Verco SiC parts exhibited the highest Vickers (2628.30 ± 44.13 kg/mm 2 ) and Knoop (2098.50 ± 24.8 kg/mm2 ) hardness values of any SiC ceramic, and values equal to those of the "gold standard" hot-pressed boron carbide (PAD-B4 C). While the fracture toughness of hot-pressed SiC materials (∼4.5 MPa[Special characters omitted.] m ) are almost double that of Verco SiC (2.4 MPa[Special characters omitted.] m ), Verco SiC is a better performing ballistic product, implying that the higher hardness of the theoretically-dense, clean-grain boundary, fine-grained SiC is the defining mechanical property for optimization of ballistic behavior.