Spark Plasma Sintered B4C-Structural, Thermal, Electrical and Mechanical Properties.

The structural, thermal, electrical and mechanical properties of fully dense B4C ceramics, sintered using Spark Plasma Sintering (SPS), were studied and compared to the properties of B4C ceramics previously published in the literature. New results on B4C’s mechanical responses were obtained by nanoindentation and ring-on-ring biaxial strength testing. The findings contribute to a more complete knowledge of the properties of B4C ceramics, an important material in many industrial applications.


Introduction
Boron carbide (B 4 C) is an important ceramic material and plays a significant role in many industrial applications, such as abrasives, materials for nuclear plants or protective materials for ballistic impact. The choice of B 4 C in numerous applications is determined by its unique properties, such as low density, high hardness and elastic modulus, high neutron capture cross section and others [1]. Its density is in the range of 2.46 g/cm 3 for B 10.4 C to 2.52 g/cm 3 for B 4 C and is determined by the light elements that form B 4 C's crystal structure increasing linearly with increasing carbon content where slightly different stoichiometry is defined by either excess B or C [2][3][4]. The crystal structure of B 4 C consists of 12-atom icosahedra units located at the vertices of a rhombohedra lattice, with 3-atom linear chains that link the icosahedra along the rhombohedral axis [5][6][7][8][9]. The reported rhombohedral lattice parameters of B 4 C are a = 5.16 Å and α = 65.7 Å, or, if represented as a hexagonal lattice, its lattice parameters become a 0 = 5.60 Å, c 0 = 12.07 Å with an axial ratio of c 0 / a 0 = 2.155 [10][11][12][13][14]. The R3m B 4 C structure implies the existence of four types of the atomic bonding-the interchain bonds, the chain icosahedral electronic properties dominated by hopping type transport [65,66]. The direct current (DC) electrical conductivity of boron carbide varies from 3 Ωcm to 23 Ωcm and is a function of carbon content, with a maximum in conductivity at~13 at% C, corresponding to the B 6.5 C stoichiometry [5,67]. Here, in this research paper we present a systematic study of the properties of boron carbide sintered by Spark Plasma Sintering and also present, for the first time, biaxial strength data and compare it to 4-point bending strength data.

Materials and Methods
A commercially available B 4 C Grade HD07 powder from H.C. Starck (selb, Germany) was used to sinter dense B 4 C samples for flexural and biaxial testing. The 3 mm × 4 mm × 45 mm and 2 mm × 2.5 mm × 25 mm bars for bending experiments were cut from a large 100mm diameter and 10 mm thickness disk sintered in a graphite die at 2150 • C, 40 MPa with a 10 min dwell time. For the biaxial strength tests a 20 mm diameter graphite die was lined with graphite foil and charged with 2 g of B 4 C. The die was then placed into the Spark Plasma Sintering (SPS) furnace (FCTHPD25; FCTSystemeGmbH, Rauenstein, Germany) and heated at a rate of 100 • C/min under a minimum pressure of 16 MPa to 1800 • C, held for 10 min while the pressure was increased to 40 MPa and then heated at 25 • C/min to 2150 • C for a 10 min hold before cooling to room temperature over 20-25 min. The sintering regime for the B 4 C disks is shown in Figure 1. The final density of the B 4 C bars and disks after sintering was measured using Archimedes technique.
Materials 2020, 13, x FOR PEER REVIEW 3 of 22 conductivity of boron carbide varies from 3 Ωcm to 23 Ωcm and is a function of carbon content, with a maximum in conductivity at ~13 at% C, corresponding to the B6.5C stoichiometry [5,67]. Here, in this research paper we present a systematic study of the properties of boron carbide sintered by Spark Plasma Sintering and also present, for the first time, biaxial strength data and compare it to 4-point bending strength data.

Materials and Methods
A commercially available B4C Grade HD07 powder from H.C. Starck (selb, Germany) was used to sinter dense B4C samples for flexural and biaxial testing. The 3 mm × 4 mm × 45 mm and 2 mm × 2.5 mm × 25 mm bars for bending experiments were cut from a large 100mm diameter and 10 mm thickness disk sintered in a graphite die at 2150 °C , 40 MPa with a 10 min dwell time. For the biaxial strength tests a 20 mm diameter graphite die was lined with graphite foil and charged with 2 g of B4C. The die was then placed into the Spark Plasma Sintering (SPS) furnace (FCTHPD25; FCTSystemeGmbH, Rauenstein, Germany) and heated at a rate of 100 °C/min under a minimum pressure of 16 MPa to 1800 °C, held for 10 min while the pressure was increased to 40 MPa and then heated at 25 °C/min to 2150 °C for a 10 min hold before cooling to room temperature over 20-25mins. The sintering regime for the B4C disks is shown in Figure 1. The final density of the B4C bars and disks after sintering was measured using Archimedes technique. The crystal structure of B4C ceramics was studied using an X-ray diffractometer (XRD, Bruker-AXS D8 Advanced Bragg-Brentano X-ray Powder Diffractometer, Bruker, WI, USA). The vibrational properties of B4C ceramics were studied using a Renishaw InVia Raman microscope (Renishaw Inc., Gloucestershire, UK). The Raman microscope system comprises a laser (532 nm line of solid Si) to excite the sample and a single spectrograph fitted with holographic notch filters. Before collecting spectra, the spectrometer was calibrated with a standard silicon wafer using the Si band position at 520.3 cm −1 . The average collection time for a single spectrum was 30 s and the spectrum was collected from the polished surface of a sintered B4C sample. Thermal expansion measurements were carried using a thermal mechanical analyzer (NETZSCH TMA 402F3, NETZSCH-Gerätebau GmbH, Selb, in Germany) in the temperature range of 30 to 1000 °C with a heating rate of 5 °C/min. One bar of B4C with dimensions of 3 mm × 4 mm × 25 mm was used for the measurement of thermal expansion. The The crystal structure of B 4 C ceramics was studied using an X-ray diffractometer (XRD, Bruker-AXS D8 Advanced Bragg-Brentano X-ray Powder Diffractometer, Bruker, WI, USA). The vibrational properties of B 4 C ceramics were studied using a Renishaw InVia Raman microscope (Renishaw Inc., Gloucestershire, UK). The Raman microscope system comprises a laser (532 nm line of solid Si) to excite the sample and a single spectrograph fitted with holographic notch filters. Before collecting spectra, the spectrometer was calibrated with a standard silicon wafer using the Si band position at 520.3 cm −1 . The average collection time for a single spectrum was 30 s and the spectrum was collected from the polished surface of a sintered B 4 C sample. Thermal expansion measurements were carried using a thermal mechanical analyzer (NETZSCH TMA 402F3, NETZSCH-Gerätebau GmbH, Selb, in Germany) in the temperature range of 30 to 1000 • C with a heating rate of 5 • C/min. One bar of B 4 C with dimensions of 3 mm × 4 mm × 25 mm was used for the measurement of thermal expansion. The load was set to 0.1 N and the average linear coefficient of thermal expansion was determined from the obtained thermal expansion data. Room temperature DC electrical conductivity of the 4 mm × 3 mm × 45 mm bars was measured using a 4-probe experimental set up connected to a Keithley 2450 source meter (Textronix UK, Ltd., Berkshire, UK). Four B 4 C samples were used for the measurements of electrical conductivity. A potential difference of 1 V was applied through the outer probes and the corresponding current between the inner probes was measured for calculation of the resistance values.
The Impulse Excitation Technique (IE, Grindo-SonicMk5"Industrial" J.W. Lemmens, Leuven, Belgium) was used to determine the elastic modulus of the B 4 C bars at room temperature and the measurements were carried out in accordance with the EN843-2 standard [68]. Samples, in the form of 3 mm × 4 mm × 45 mm bars of known density, were lined up with a supporting cylinder and placed over a microphone.
To determine the elastic modulus at room temperature using the natural frequency of vibration of the bars, they were struck lightly using a small hammer and the acoustic vibrations were recorded using the microphone. Then, using the dimensions of the sample, its density and natural frequency of vibration, the Young's modulus was calculated. A total of four samples were used for the IE measurements.
In addition to the IE measurement, the Young's and shear moduli of B 4 C were also measured using a Resonant Ultrasound Spectroscopy technique using a custom made high-temperature resonant ultrasound spectroscope (HT-RUS) that utilizes a commercially available room temperature (RT) RUS (Magnaflux Quasar, Albuquerque, NM, USA) system. RUS is a high-precision dynamic technique, which is used to determine the elastic moduli and energy dissipation (mechanical damping) of materials by measuring the vibrational spectrum of samples with well-defined geometry, usually in the shape of parallelepipeds or cylinders [69][70][71][72][73]. A B 4 C sample in the form of disc with 20 mm diameter and 1.5 mm thickness was supported by three piezoelectric transducers. One transducer, which is a transmitting transducer, generates an elastic wave of constant amplitude but of varying frequency covering a large number of vibrational eigenmodes of the sample. The resonance response of the excited sample is detected by the other two transducers, which are receiving transducers. To study the elastic moduli as a function of temperature, SiC extension rods were added to transmit the ultrasound waves to the RT RUS equipment. This arrangement allowed the B 4 C disk to be held on the tip of the extension rods, at the desired temperature in the furnace, while the transducers were unaffected by high temperature. The measurements were performed under vacuum. The B 4 C sample was heated at a rate of 10 • C/min and resonance spectra were collected at an interval of 25 • C up to 1000 • C after an isothermal hold of 20 min. Depending on the density and stiffness of the material, measurements were done in the 20-500 kHz frequency range to cover the first 40 frequencies. The RUS spectra cannot be de-convoluted directly to deduce the elastic constants. Starting from the known sample dimensions, density and a set of "guessed" elastic constants-namely C 11 and C 44 for an isotropic solid, where C 11 = 542.8 GPa and C 44 = 164.8 GPa as reported in Reference [21], the elastic moduli were determined from collected RUS spectra using a multidimensional algorithm (MagnafluxQuasar, Albuquerque, NM, USA) that minimizes the root-mean-square (RMS) error between the measured and calculated resonant peaks. Two B 4 C samples were used for the measurements of elastic properties by RUS.
Nanoindentation of B 4 C was performed using a Hysitron TI Premier machine equipped with a Berkovich tip. A total of 25 indents were produced on the polished surface of B 4 C samples using a maximum load of 9500 µN, which was held for 3s at the maximum load between loading and unloading. Load vs. displacement curves were analyzed to calculate the hardness, H and reduced modulus, E r , using a method described by Oliver and Pharr [74,75]. The mean contact pressure was calculated as where P i is the instantaneous indentation load taken from the corresponding load-displacement diagram (P i may be taken directly from indentation data points); A i is the contact area, which is determined using the area function: where C 0 , C 1 , C 2 , C 3 , C 4 and C 5 are the coefficients determined for a given indenter from a series of indents at various contact depths in a sample of known elastic modulus (typically fused quartz). Note that C 0 = 24.5 for an ideal Berkovich probe; (h c ) i is the contact depth corresponding to P i , which can be calculated as where h i is the total measured indenter displacement corresponding to P i (h i may be taken directly from indentation data points); (h e ) i is the corresponding elastic deflection [74][75][76][77][78]: where (h e ) max is the elastic deflection at maximum load P max of the indentation diagram; the unloading stiffness S is the slope at the beginning of the unloading portion of the indentation diagram; is a constant that depends on the indenter's geometry (ε = 0.75 for Berkovich indenter). After calculation, the mean contact pressure can be plotted against the contact depth.
The B 4 C sample surface was first ground and further polished down to a 1 mm diamond grit size to determine the Vickers hardness of the ceramics. A Vickers hardness tester Durimet (Ernst-Leitz, Germany) was used for hardness tests in accordance with EN843-4 standard. The hardness of the samples was measured using a 9.8 N load applied for a period of 15 s. Twenty impressions were produced for the measurements of the sizes of the impression diagonals. The hardness H (GPa) was calculated according to the equation [79].
where P is the indentation load in N and d is the impression diagonal length in µm.
Four-point bending tests were performed to measure flexure strength using B 4 C samples with dimensions of 2 mm × 2.5 mm × 25 mm. Seven B 4 C samples were used to measure the flexural strength.
To obtain load-displacement bending diagrams, the B 4 C samples were loaded using a four-point bending jig with 3 mm diameter rollers with a 10 mm loading span and 20 mm supporting span using a 2 kN load cell on an universal testing machine (Zwick, Ulm, Germany) in accordance with the EN 843-1 standard [80].
The biaxial strength of B 4 C samples were tested using a ring-on-ring testing jig [81]. A total of 27 B 4 C samples were used for the biaxial strength testing. Disks with 20 mm diameter and 1.5 mm thickness were placed on the support ring and loaded with a loading ring in load control mode with a loading rate of 80 N/s or 22 MPa/s until failure of the disk occurred. The disks were polished on one side and the polished surface was on the tensile side of the ring-on-ring fixture. The recorded load was recalculated into stress using the ASTM Standard C1499 equation [82]. As the deflection of the disk was not recorded during loading, the deformation of the B 4 C samples was calculated using the measured Young's modulus in the elastic beam equation, as it is well known that B 4 C behave elastically and does not show any plasticity during static deformation at room temperature [83,84]. A standard Weibull analysis of strength data was carried out [85][86][87][88]. Finite Elements Analysis (FEA) modeling of the biaxial strength testing of B 4 C was performed using the functions of the Simulia Abaqus ® 6.11-1 software (Dassault Systems, Vélizy-Villacoublay, Paris, France). The B 4 C specimen was treated as a deformable body and the loading/supporting rings as discrete rigid bodies. Load and support rings were defined as a 2D axisymmetric and homogenous model, with properties of 4140 alloy steel. The sample was defined using properties t obtained experimentally from the B 4 C biaxial strength tests. The elastic modulus and the Poisson's ratio for a B 4 C sample were taken as 429 GPa and 0.185 and for 4140 alloy steel were taken as 200 GPa and 0.29, respectively. The contact between the specimen and ring-on-ring surfaces were defined as surface-to-surface contacts with a master surface on the rings. The simulation was performed with a friction of 0.1. In order to conduct a simulation, a support-ring was fully fixed in its position in any direction, however the loading ring was fully fixed besides the direction of the force in the Y-axis. The experimental data showed that the sample broken at a load of 1530 N, therefore the force for the simulation for the loading ring was chosen to be 1530 N in order to simulate a uniform pressure along the load-ring surface area. The mesh element type was defined as Discrete Rigid Element (RAX2) and for the sample as an Axisymmetric Stress (CAX4) with a reduced integration. The size of the mesh for a sample was chosen to be 0.2 mm and 0.1 mm for the loading and supporting rings.
Fracture toughness was measured using the Single Edge V Notch Beam (SEVNB) technique in accordance with the CEN/TS 14425-5 standard [89]. Three B 4 C samples were used for the K 1C testing. A single notch was made on the 3 mm side of the 3 × 4 × 45 mm 3 bar as near to the center as possible with a depth between 20% and 40% of the total thickness of the bar, since it was shown that within this range the depth of the notch has no influence on the measured K 1c values [90]. A diamond saw was used to make the initial 0.5 mm depth notch; after that the final 1-1.5 mm depth notch with ∼1.8-2.2 µm tip radius was produced by machine cutting using a razor blade with 6 µm and then 1 µm diamond paste deposited. Three samples were tested at room temperature with a crosshead speed of 0.5 mm/min.

Results and Discussions
3.1. Shrinkage Behavior, Structure, Thermal Expansion and Electrical Conductivity of Sintered B 4 C Ceramics Figure 1 shows the shrinkage of B 4 C ceramic during Spark Plasma Sintering together with the pressure and temperature profiles, as a function of sintering time. The sample was heated from 400 • C to 1800 • C in 20 min under a minimal pressure of 16 MPa, then dwelled for 10 min during which a pressure of 40 MPa was fully applied, then the temperature was increased to 2150 • C and dwelled at this sintering temperature for 10 min before cooling down to room temperature. To protect the sample from fracture, the 40 MPa pressure was decreased at the beginning of the dwell time at 2150 • C in a such way that it reduced back to 16 MPa in 10 min by the end of dwell. As can be seen in Figure 1, expansion of the equipment was observed upon heating all of the way up to 1800 • C (region A, Figure 1) until the moment when the applied pressure was increased, causing shrinkage of the sample (region B, Figure 1). Under the constant pressure but with temperature increasing, most of the shrinkage of the B 4 C sample occurred (section C, Figure 1). When the sample dwelled at 2150 • C but with decreasing pressure, the shrinkage remained constant (section D, Figure 1), possibly because the majority of the densification process had already occurred. During cooling from the sintering temperature, shrinkage of the sample occurred (section E, Figure 1). After sintering, the samples were machined, surfaces polished and the density was measured to be equal to 2.50 ± 0.07 g/cm 3 showing less than 1% of porosity.
An X-ray diffraction pattern taken from polished surface of B 4 C is shown in Figure 2A. All of the diffraction peaks in the pattern belong to the rhombohedral Bravais lattice of space group of B 4 C and the peak at~26.16 • 2θ belonging to carbon indicates that a small quantity of carbon was present as a secondary phase [8,91]. Raman spectrum obtained using a 532 nm laser measured from a polished surface of B 4 C is shown in Figure 2B. The spectrum resembles the surface spectrum of B 4 C published in Reference [91,92]. The grain size of B 4 C was equal to 3.4 ± 0.05 micron as estimated from the fracture surface of broken samples (Figure 3).  The thermal expansion of B4C was almost linear and the average coefficient of thermal expansion was calculated to be equal to 6 × 10 −6 / K in the 25-1000 °C temperature range (Figure 4). The measured  The thermal expansion of B 4 C was almost linear and the average coefficient of thermal expansion was calculated to be equal to 6 × 10 −6 / K in the 25-1000 • C temperature range (Figure 4). The measured values of CTE corresponded very well to previously published results, where the CTE of hot pressed B 4 C was reported to be equal to 6 × 10 −6 /K [93]. The room temperature DC electrical conductivity was measured to be equal to 0.00284 ± 0.0009 Ω m ( values of CTE corresponded very well to previously published results, where the CTE of hot pressed B4C was reported to be equal to 6 × 10 −6 /K [93]. The room temperature DC electrical conductivity was measured to be equal to 0.00284 ± 0.0009 Ω m (Table 1), which is typical of the values reported for B4C [63].

Elastic Properties of B4C by Impulse Excitation (IE) Technique and Resonant Ultrasound Spectroscopy
The Young's modulus of B4C measured using the IE technique at room temperature was equal to 442 ± 3 GPa (Table 1), which corresponds very well with the values of 440 to 560 GPa reported in other papers [94,95]. Table 1. Thermal, electrical and mechanical properties of B4C at room temperature.

Elastic Properties of B 4 C by Impulse Excitation (IE) Technique and Resonant Ultrasound Spectroscopy
The Young's modulus of B 4 C measured using the IE technique at room temperature was equal to 442 ± 3 GPa (Table 1), which corresponds very well with the values of 440 to 560 GPa reported in other papers [94,95]. The results of the measurements of Young's and the shear moduli along with bulk modulus and Poisson's ratio by RUS as a function of temperature are shown in the Figure 5. The Young's modulus of B 4 C measured by RUS was slightly higher compared to that measured using IE and was equal to 458.7 GPa at room temperature. The Young's modulus decreased linearly upon heating in in vacuum and was 436.7 at 1000 • C. The shear modulus, also measured by RUS, was equal to 195.7 GPa at room temperature but slightly decreased linearly on heating to 186.5 GPa at 1000 • C. The bulk modulus and Poisson's ratio were calculated from Young's and shear moduli data and were equal to 220.9 GPa and 0.172 at 1000 • C. Note that Poisson's ratio of B 4 C remains the same for the whole RT -1000 • C temperature interval ( Figure 5B). All of the values of elastic properties of B 4 C presented in Figure 5 correspond very well with previously published data, where Young modulus was reported in the range of 440-560 GPa, shear modulus was reported in the range of 188-194 GPa, bulk modulus was reported in the range of 220-248 GPa and Poisson's ratio was reported in the range 0.19-0.21 [94][95][96][97].

Young's Modulus and Hardness by Nanoindentation and Vickers Hardness
The Young's modulus along with hardness of B 4 C was also measured using the nanoindentation technique. A total 50 impressions were made into a polished B 4 C surface using a Berkovich indenter and the average values of Young's modulus and hardness were measured to be equal to 419.2 ± 47.3 GPa and 41.1 ± 5.7 GPa, respectively ( Table 1). The Young's modulus values measured by nanoindentation are very similar to the ones measured by IE and RUS but were slightly lower than the 506 GPa values, also measured by nanoindentation, reported in Reference [98]. However, in Reference [98] the reported high value of 506 GPa for the Young's modulus was measured on a single crystal in one specific crystallographic directions of (0001) and (10−11) respectively, thus the anisotropy of the bond strength in a certain crystallographic direction of B 4 C may explain this discrepancy. The average hardness value measured during nanoindentation was calculated to be equal to 41.1 ± 5.7 GPa, while the Vickers hardness measured using a microhardness tester was equal to 28.5 ± 1.2 GPa ( Table 1). The Vickers hardness impression after indention with a 1 kg load is shown in Figure 6. Materials 2020, 13, x FOR PEER REVIEW 10 of 22  The three different load-displacement plots in Figure 7 illustrate the different types of nanoindentation behavior observed. While many of the measured load-displacement plots were smooth and showed no deviation from a continuous increase in load and displacement ( Figure 7A), many of the load-displacement plots showed multiple or at least one pop-in events upon loading ( Figure 7C). While only three load-displacement plots in the data set of 50 indentation plots that showed a well pronounced "elbow" effect upon unloading ( Figure 7E). The absence or presence of "pop-ins" or "elbows" in the load-displacement plots during loading and unloading of B4C are indicative of the absence or presence of structural changes such as crystal phase transitions or amorphization. It is generally accepted that the absence of sudden volumetric changes associated with a structural transformation in the material produce a monotonic loading/unloading response during nanoindentation ( Figure 7A) [5].
The maximum mean contact pressure under such conditions is about 43 GPa ( Figure 7B), which corresponds very well to the average hardness values of 41.1 ± 5.7 GPa ( Table 1). Some of the loaddisplacement plots obtained during nanoindentation of B4C exhibited one to three discontinuities during loading ( Figure 7C). The presence of such pop-in events during nanoindentation is explained by transition from the elastic to elastoplastic deformation upon nanocontact in the imprint [55]. A second order phase transition in B4C was reported to occur at 32 GPa to 35 GPa due to reordering of polar atoms [99]. It was found that this second order transition, which is characterized by atomic site exchange with hysteresis, is a relaxation process that is reversible [100]. It was also predicted that both the chain bending of the three-atom carbon chain and disordering of the structure were detected above 70 GPa, where non-hydrostatic stresses are present. It was explained that the non-ideal structure of B4C can activate chain bending guided by polar carbon atom location in the icosahedron even at lower stresses above 38 GPa as observed in shock-wave experiments [101]. The discontinuities during nanoindentation of B4C occurred first at 43 GPa with a mean contact pressure decreasing to below 40 GPa during this first pop-in event occurring at a contact depth of 20 nm ( Figure 7D). The three different load-displacement plots in Figure 7 illustrate the different types of nanoindentation behavior observed. While many of the measured load-displacement plots were smooth and showed no deviation from a continuous increase in load and displacement ( Figure 7A), many of the load-displacement plots showed multiple or at least one pop-in events upon loading ( Figure 7C). While only three load-displacement plots in the data set of 50 indentation plots that showed a well pronounced "elbow" effect upon unloading ( Figure 7E). The absence or presence of "pop-ins" or "elbows" in the load-displacement plots during loading and unloading of B 4 C are indicative of the absence or presence of structural changes such as crystal phase transitions or amorphization. It is generally accepted that the absence of sudden volumetric changes associated with a structural transformation in the material produce a monotonic loading/unloading response during nanoindentation ( Figure 7A) [5].
The maximum mean contact pressure under such conditions is about 43 GPa ( Figure 7B), which corresponds very well to the average hardness values of 41.1 ± 5.7 GPa ( Table 1). Some of the load-displacement plots obtained during nanoindentation of B 4 C exhibited one to three discontinuities during loading ( Figure 7C). The presence of such pop-in events during nanoindentation is explained by transition from the elastic to elastoplastic deformation upon nanocontact in the imprint [55]. A second order phase transition in B 4 C was reported to occur at 32 GPa to 35 GPa due to reordering of polar atoms [99]. It was found that this second order transition, which is characterized by atomic site exchange with hysteresis, is a relaxation process that is reversible [100]. It was also predicted that both the chain bending of the three-atom carbon chain and disordering of the structure were detected above 70 GPa, where non-hydrostatic stresses are present. It was explained that the non-ideal structure of B 4 C can activate chain bending guided by polar carbon atom location in the icosahedron even at lower stresses above 38 GPa as observed in shock-wave experiments [101]. The discontinuities during nanoindentation of B 4 C occurred first at 43 GPa with a mean contact pressure decreasing to below 40 GPa during this first pop-in event occurring at a contact depth of 20 nm ( Figure 7D). Upon further loading, the mean contact pressure recovered back to above 40 GPa, where a second pop-in event was detected at a contact penetration depth of about 50 nm. The appearance of such pop-in events during loading of B4C can possibly be explained either by plastic deformation by nucleation of dislocations [55] or a high pressure structural phase transition, with an associated decrease in the volume of the high-pressure phase [99,101]. The simulated estimate of ~4% sudden volume reduction were reported in [102], however, the pressure where such a significant volume change would occur was estimated to be ~22.8 GPa. Structural recovery and formation of disordered phases were reported to occur in a number of materials upon unloading [103]. The discontinuities and changes in the slopes upon unloading of B4C were reported in [56]. In our nanoindentation Upon further loading, the mean contact pressure recovered back to above 40 GPa, where a second pop-in event was detected at a contact penetration depth of about 50 nm. The appearance of such pop-in events during loading of B 4 C can possibly be explained either by plastic deformation by nucleation of dislocations [55] or a high pressure structural phase transition, with an associated decrease in the volume of the high-pressure phase [99,101]. The simulated estimate of~4% sudden volume reduction were reported in [102], however, the pressure where such a significant volume change would occur was estimated to be~22.8 GPa. Structural recovery and formation of disordered phases were reported to occur in a number of materials upon unloading [103]. The discontinuities and changes in the slopes upon unloading of B 4 C were reported in [56]. In our nanoindentation experiments, three load-displacement nanoindentation plots exhibited the formation of an "elbow" (Figure 7E), which can be explained by the amorphization of the deformed B 4 C structure upon unloading and the formation of a phase with larger volume, causing a change in the slope of the mean contact pressure vs. contact depth deformation plot ( Figure 7F).

Strength and Fracture Toughness of B 4 C
While B 4 C exhibits a very high Young's modulus and hardness compared to other ceramics, its average flexural strength is not so highs and it averages between 250-450 MPa [10,36,41,45,[57][58][59][104][105][106]. The flexural strength of B 4 C measured in the current research had an average value of 585 ± 70 MPa. The relatively high flexural strength in the current study suggests that the strength determining defects must have been relatively small. A typical stress vs. time plot of loading of B 4 C in 4-point bending is shown in Figure 8, with inserts showing the fracture surface of B 4 C samples after failure. experiments, three load-displacement nanoindentation plots exhibited the formation of an "elbow" (Figure 7E), which can be explained by the amorphization of the deformed B4C structure upon unloading and the formation of a phase with larger volume, causing a change in the slope of the mean contact pressure vs contact depth deformation plot ( Figure 7F).

Strength and Fracture Toughness of B4C
While B4C exhibits a very high Young's modulus and hardness compared to other ceramics, its average flexural strength is not so highs and it averages between 250-450 MPa [10,36,41,45,[57][58][59][104][105][106]. The flexural strength of B4C measured in the current research had an average value of 585 ± 70 MPa. The relatively high flexural strength in the current study suggests that the strength determining defects must have been relatively small. A typical stress vs time plot of loading of B4C in 4-point bending is shown in Figure 8, with inserts showing the fracture surface of B4C samples after failure. The average biaxial strength b of B4C was measured to be 239 ± 122 MPa using a ring-on-ring configuration [81]. The typical stress-strain deformation behavior of B4C during ring-on-ring loading is shown in Figure 9. The two inserts show micrographs of B4C samples after failure. As expected, the samples that failed at relatively high loads were broken into multiple pieces after failure, while the samples that failed at low loads were broken into two pieces, as can be seen in the inserts Figure  9. It is not clear why the strength of B4C measured in 4-point bending and ring-on-ring tests were so different but the quality of the surface after machining likely to contributed to such low biaxial strength values. The average biaxial strength σ b of B 4 C was measured to be 239 ± 122 MPa using a ring-on-ring configuration [81]. The typical stress-strain deformation behavior of B 4 C during ring-on-ring loading is shown in Figure 9. The two inserts show micrographs of B 4 C samples after failure. As expected, the samples that failed at relatively high loads were broken into multiple pieces after failure, while the samples that failed at low loads were broken into two pieces, as can be seen in the inserts Figure 9. It is not clear why the strength of B 4 C measured in 4-point bending and ring-on-ring tests were so different but the quality of the surface after machining likely to contributed to such low biaxial strength values. Weibull modulus mf is equal to 9.9 for 4-point bending strength values but the Weibull modulus mb is only 2.2 for the ring-on-ring strength values (Table 1). The Weibull distribution for biaxial as well as 4-point bending is presented in the Figure 10. The characteristic strength σ0f was equal to 611 MPa in 4-point bending experiments and the scale parameter σ0b was equal to 271 MPa in ring-onring tests (Table 1). Weibull modulus m f is equal to 9.9 for 4-point bending strength values but the Weibull modulus m b is only 2.2 for the ring-on-ring strength values (Table 1). The Weibull distribution for biaxial as well as 4-point bending is presented in the Figure 10. The characteristic strength σ 0 f was equal to 611 MPa in 4-point bending experiments and the scale parameter σ 0b was equal to 271 MPa in ring-on-ring tests ( Table 1). The maximum biaxial strength during the mechanical testing of B4C specimens came out to be 440 MPa with a maximum applied load of 1530 N, which was used for a numerical simulation. The stress distribution during biaxial ring-on-ring loading of B4C was modeled using Abaqus [81], which showed that the highest tensile biaxial strength occurred along the bottom surface of B4C specimen ( Figure 11) and was equal to 436.1 MPa. The region A in Figure 11 represents the highest uniform tensile stresses at the polished bottom surface of B4C between the surface contact of the specimen and support-ring, as well as a high compressive strength which developed at the line of the contact of the B4C samples with the load-ring. The maximum biaxial strength during the mechanical testing of B 4 C specimens came out to be 440 MPa with a maximum applied load of 1530 N, which was used for a numerical simulation. The stress distribution during biaxial ring-on-ring loading of B 4 C was modeled using Abaqus [81], which showed that the highest tensile biaxial strength occurred along the bottom surface of B 4 C specimen ( Figure 11) and was equal to 436.1 MPa. The region A in Figure 11 represents the highest uniform tensile stresses at the polished bottom surface of B 4 C between the surface contact of the specimen and support-ring, as well as a high compressive strength which developed at the line of the contact of the B 4 C samples with the load-ring.
Materials 2020, 13, x FOR PEER REVIEW 16 of 22 Figure 11. The stress distribution in a B4C disk upon biaxial loading. σr is the stress distribution in the radial direction and σt is the stress distribution in the tangential direction.
The region B in the Figure 11 depicts the stresses that are no longer uniform and by the end of region B, at the point when the sample has a contact with the support ring, the compressive stresses rise rapidly. However, it does not represent the critical condition and the values show that it is not a critical point of failure during testing. The stress distribution depicted by a numerical model are similar to those reported in a previous study of the biaxial strength of ZrB2-SiB6 ceramic composite [81]. The fracture toughness of B4C measured by SEVNB was equal to the 3 ± 0.19 MPa m 1/2 . The load vs time plot used for the calculation of KlC is shown in Figure 12, while the insert shows an optical micrograph of the V-notch with the measured tip diameter equal to 2.1 µ m. Figure 11. The stress distribution in a B 4 C disk upon biaxial loading. σr is the stress distribution in the radial direction and σt is the stress distribution in the tangential direction.
The region B in the Figure 11 depicts the stresses that are no longer uniform and by the end of region B, at the point when the sample has a contact with the support ring, the compressive stresses rise rapidly. However, it does not represent the critical condition and the values show that it is not a critical point of failure during testing. The stress distribution depicted by a numerical model are similar to those reported in a previous study of the biaxial strength of ZrB 2 -SiB 6 ceramic composite [81]. The fracture toughness of B 4 C measured by SEVNB was equal to the 3 ± 0.19 MPa m 1/2 . The load vs. time plot used for the calculation of K lC is shown in Figure 12, while the insert shows an optical micrograph of the V-notch with the measured tip diameter equal to 2.1 µm.

Conclusions
The thermal, electrical and mechanical properties of dense B4C ceramics (99%) sintered using Spark Plasma Sintering were investigated. It was determined by XRD and Raman spectroscopy that the major phase was indeed B4C. A minor presence of a C phase was also detected by X-ray diffraction. The grain size of B4C after sintering was in the range of 2.5-3.5 micron as estimated by SEM. Both the measured thermal expansion and electrical conductivity of the B4C ceramics is similar to data published in the literature. The Young's modulus of B4C measured by three different techniques -IE, RUS and nanoindentation showed a very good overlap in values, which ranges from 419.2 ± 47.3 GPa for nanoindentation to 458.7 GPa for RUS measurements at room temperature. Both the Young's, shear and bulk moduli decreased by about ~5% at 1000 ˚C compared to their room temperature values, however, the Poisson's ratio remained constant at 0.172 in the whole RT to 1000 °C temperature range measured by RUS. The difference in hardness values measured by nanoindentation as 41.1 ± 5.7GPa and Vickers microhardness at 1kg as 28.5 ± 1.2 GPa was expected and it could be explained by indentation size effect and/or formation of radial cracks from the corner of impressions, which relieved the indentation stress and decreased the hardness value above a certain critical load during indentation. The mean contact pressure-contact depth plots obtained from load-displacement nanoindentation data indicated pop-in events during loading and an "elbow" event during unloading, both of which are indicative of possible structural changes in B4C structure during nanoindentation. The 4-point bending strength of the B4C ceramics was σo 585 ± 70 MPa with a shape parameter mf equal to 9.9 and scale parameter σof equal to 611 MPa. The biaxial strength pf B4C was measured to be much lower and equal to 238.6 ± 122 MPa with a shape parameter of 2.2 and scale parameter σob equal to 271 MPa. It was determined that failure occurred by fully transgranular

Conclusions
The thermal, electrical and mechanical properties of dense B 4 C ceramics (99%) sintered using Spark Plasma Sintering were investigated. It was determined by XRD and Raman spectroscopy that the major phase was indeed B 4 C. A minor presence of a C phase was also detected by X-ray diffraction. The grain size of B 4 C after sintering was in the range of 2.5-3.5 micron as estimated by SEM. Both the measured thermal expansion and electrical conductivity of the B 4 C ceramics is similar to data published in the literature. The Young's modulus of B 4 C measured by three different techniques-IE, RUS and nanoindentation showed a very good overlap in values, which ranges from 419.2 ± 47.3 GPa for nanoindentation to 458.7 GPa for RUS measurements at room temperature. Both the Young's, shear and bulk moduli decreased by about~5% at 1000 • C compared to their room temperature values, however, the Poisson's ratio remained constant at 0.172 in the whole RT to 1000 • C temperature range measured by RUS. The difference in hardness values measured by nanoindentation as 41.1 ± 5.7 GPa and Vickers microhardness at 1kg as 28.5 ± 1.2 GPa was expected and it could be explained by indentation size effect and/or formation of radial cracks from the corner of impressions, which relieved the indentation stress and decreased the hardness value above a certain critical load during indentation. The mean contact pressure-contact depth plots obtained from load-displacement nanoindentation data indicated pop-in events during loading and an "elbow" event during unloading, both of which are indicative of possible structural changes in B 4 C structure during nanoindentation. The 4-point bending strength of the B 4 C ceramics was σ o 585 ± 70 MPa with a shape parameter mf equal to 9.9 and scale parameter σ of equal to 611 MPa. The biaxial strength pf B 4 C was measured to be much lower and equal to 238.6 ± 122 MPa with a shape parameter of 2.2 and scale parameter σ ob equal to 271 MPa. It was determined that failure occurred by fully transgranular fracture, with no intergranular failure. Using the SEVNB technique, a K lc = 3 ± 0.19 was measured for B 4 C, which is similar to previously reported values.