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Study of static and dynamic behavior of TiB2–B4C composite
Study of static and dynamic behavior of TiB 2 –B4 C composite Yubo Gao, Tiegang Tang, Chenhong Yi, Wei Zhang, Dacheng Li, Wenbo Xie, Wei Huang, Nan Ye PII: DOI: Reference:
S0264-1275(15)30982-5 doi: 10.1016/j.matdes.2015.12.123 JMADE 1147
To appear in: Received date: Revised date: Accepted date:
21 September 2015 20 December 2015 21 December 2015
Please cite this article as: Yubo Gao, Tiegang Tang, Chenhong Yi, Wei Zhang, Dacheng Li, Wenbo Xie, Wei Huang, Nan Ye, Study of static and dynamic behavior of TiB2 –B4 C composite, (2015), doi: 10.1016/j.matdes.2015.12.123
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ACCEPTED MANUSCRIPT Study of static and dynamic behavior of TiB2-B4C composite Yubo Gao a b
a,
b
b
a,**
, Tiegang Tang , Chenhong Yi , Wei Zhang
a
a
a
, Dacheng Li , Wenbo Xie , Wei Huang , Nan Ye
a
Hypervelocity Impact Research Center, Harbin Institute of Technology, Heilongjiang, Harbin, P.R. China
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Laboratory for Shock Wave and Detonation Physics Research Institute of Fluid Physics, CAEP, Mianyang, Sichuan, P.R.
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China
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Abstract: The microstructure and phase analysis of TiB2-B4C composite were investigated by the X-ray diffraction (XRD) and scanning electron microscope (SEM) techniques, and the mechanical properties were studied by improved experimental facilities under quasi-static and dynamic loading conditions.
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Results show that regular grain of TiB2 is distributed uniformly in the grown grain of B4C, and the fracture mechanism of TiB2-B4C composite includes intergranular fracture and transcrystalline fracture.
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In tensile tests, the Flattened Brazilian Disc (FBD) method was introduced to reduce stress concentration between the platens of the test machine and circular boundaries of the specimen. The results of 2D-DIC
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method show a good agreement with the data obtained by strain gauges, thus proved the validity of the
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improved experiment facilities. Meanwhile, both the tensile and compressive strength increase with the increasing of strain rates. The reason is mainly attributed to the presence of TiB2 addition which serves as
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a strengthening and toughening agent. The comparison of strength and microstructure among the TiB2-B4C composite, the pure B4C and the pure TiB2 show that the mechanical properties were dominated by the microstructure and fracture mode of the composite.
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Keywords: TiB2-B4C composite, mechanical properties, microstructure, strain-rate sensitivity
1. Introduction
Boron carbide (B4C) has many excellent physical properties, such as extremely high hardness, high wear resistance, low specific gravity and high chemical stability. Up to now, it has been widely used in wear-resistant components, lightweight armor products and neutron radiation shields, etc [1]. However, it also has some weaknesses of mechanical property restricting its applications. For example, the fracture toughness of boron carbide is low due to its characteristic of crystal structure. Various kinds of papers have been performed to study the mechanical properties of boron carbide (B4C), especially with the
First author. Tel.: +86 451 86417978 18；Fax: +86 451 86402055.
**
Corresponding author. Tel.: +86 451 86417978 18；Fax: +86 451 86402055.
E-mail addresses: [email protected] (Yubo Gao), [email protected] (Wei Zhang). 1
ACCEPTED MANUSCRIPT addition of titanium diboride (TiB2) [2-5]. Generally, the increasing research efforts on the TiB2-B4C composite have been focused on the microstructure, hardness, fracture toughness, flexural strength, elastic modulus, etc [2, 6-8]. T. S. Srivatsan et al. analyzed the influence of TiB2 content on microstructure and
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hardness of TiB2-B4C composite [6]. Microhardness measurements showed a gradual increase in hardness
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with an increasing of TiB2 content in the starting powder mixture. Y. J. Wang et al. proposed that the
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elastic modulus and fracture toughness of the composite increased remarkably after raising the TiB2 content [2]. However, relatively little is known about the static and dynamic mechanical properties of TiB2-B4C composite, while it is of importance to numerous applications in mechanical engineering and
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structural engineering.
The TiB2-B4C composite has got typical mechanical properties of ceramic, such as high strength, high
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elasticity modulus, brittle, low failure strain etc. Based on a series of experiments, the compressive mechanical properties of ceramic have been performed by using different shapes of specimens [9-11] and improved experimental schemes [9-14]. For the experiments of tensile properties, it is hard to obtain
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tensile strength directly due to the low failure strain of ceramic. So the Brazilian test (also called the split
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tensile test), an indirect tensile method, has been applied to be a popular choice [15-18]. However, the
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traditional Brazilian test cannot eliminate the stress concentration completely between the platens of the test machine and circular boundaries of the disc specimen. The crack is not initiated from the center of the disc as a premature breakage of the specimen occurs at the contact point [19]. In order to avoid the
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unreasonable failure mode of the disc, Wang et al. proposed the Flattened Brazilian Disc (FBD) method which machine two parallel flat ends on the disc circumference for the appliance of the distributed load [20-22]. For the microscopic level, the main drawback of ceramic lies in their extreme brittleness and the limited ability to withstand the plastic deformation, given their low fracture toughness and the marked difference between their tensile and compressive strengths. The failure mode of ceramic is attributed to the microcrack propagation and coalescence. J. D. Clayton et al. proposed a new continuum constitutive theory to study polycrystalline brittle solids subjected to possible large stress and strain rates, including finite deformation kinematics, balance laws, thermodynamics and defect kinetics etc. [23-24]. But so far few detail reports showed the difference between tensile and compressive properties about the ceramic, especially the strain-rate sensitivity of tensile strength. In the present study, the phase and microstructure analysis of TiB2-B4C composite were observed by the X-ray diffraction (XRD) and the scanning electron microscope (SEM) techniques. Then the tensile 2
ACCEPTED MANUSCRIPT and compressive properties of TiB2-B4C composite were performed by the geometries design of specimens and the improved experimental facilities under quasi-static and dynamic loading conditions. In dynamic FBD experiments, the 2D digital image correlation method (DIC), a kind of non-contact and
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full-field optical measurement method, was employed to analyze the entire crack propagation and the
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failure strain of specimen. Finally, the dynamic tensile and compressive strength of TiB2-B4C composite
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was calculated based on the one dimension stress wave theory. It is found that not only the compressive strength but also the tensile strength is increased with the increasing of strain rates, and the compressive
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strength has a marked difference (an order of magnitude) compared with tensile strength.
2. The phase analysis and microstructure of TiB2-B4C composite
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In the present study, the TiB2-B4C composite was sintered by a fine powders mixture using of titanium diboride (TiB2) and boron carbide (B4C). Fig.1 was the XRD patterns of the TiB2-B4C composite. Results of the energy spectrum analysis (EDS) also provided powerful evidence to determine material
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composition of the composite, as shown in Fig.2. The result indicates that the sintering body is composed
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12000
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by B4C and TiB2 phases. There are not new phases or substance in the detection process.
B4C B4C TiB2 TiB2
8000 6000
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Intensity/a.u.
10000
4000 2000 0 20
30
40
50
60
70
80
90
2θ/degree Fig.1. XRD patterns of TiB2-B4C composite
Fig.2 shows the SEM micrograph and the elements distribution of the composite surface by the EDS analysis. The boron (B) is distributed throughout the scan area, which is denser in dark grey phrase compared with the light grey phrase, as shown in Fig. 2(a) and (b). The titanium (Ti) and carbon (C) is found in light grey phrase and dark grey phrase respectively, as shown in Fig. 2(c) and (d). The result shows that the light grey area is the TiB2 phase, and the dark grey area is the B4C phrase. 3
ACCEPTED MANUSCRIPT (b)
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(a)
(d)
10μm
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10μm
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(c)
10μm
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10μm
Fig.2. SEM micrograph (a), and elemental distribution on the surface of TiB2-B4C composite: (b) boron (B); (c) titanium (Ti); (d) carbon (C).
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The scanning electron microscope (SEM) was adopted to observe the microstructure and fracture
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morphology of TiB2-B4C composite. Little grain of TiB2 (light grey phase) is distributed uniformly in the
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grown grain of B4C (dark grey phrase), as shown in Fig.3. The particle shape of TiB2 phase is a regular rod whose dimension is less than 5μm. A few TiB2 particles have a larger size, but not beyond 15μm. In addition, a certain amount of fine microscopic pores distributed uniformly thoughout the composite
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microstructure. The entire fine pores were located on the junction of grain boundary between the TiB2 phase and B4C phase, and have a size under 2μm.
Fig.3. SEM images of the TiB2-B4C composite
The fracture mechanism of TiB2-B4C composite includes intergranular fracture and transcrystalline fracture, as shown in Fig.3 and 4. The binding force of grain boundary was strengthened by a mass of 4
ACCEPTED MANUSCRIPT transcrystalline fracture because the crack propagation through grains consumes more energy than that of the intergranular fracture mode. Fig.3 and 4 show that the intergranular fracture occurred mainly along the grain boundary of TiB2 phase, while transcrystalline fracture mainly happened within the B4C
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particles.
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Fig.4. Fracture microtopography of TiB2-B4C composite
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3 Experimental procedure
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3.1 Static and dynamic tensile tests
The TiB2-B4C composite has a density of 3.2g/cm3. The Flattened Brazilian Disc specimens (Φ16×6.6
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mm) were used both in the quasi-static and the dynamic tensile tests. The parallelism and flatness of the disc was 0.001mm and 0.01mm respectively. Two parallel flat ends were used in the disc to reduce the stress concentration and change the loading manner into distributed forces, as shown in Fig.5. The
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loading angle 2α= 20° of FBD was chosen to ensure the crack initiating in the center of the disc, which was calculated and verified by Wang et al. (2004) [22].
Fig.5. Loading mode on the FBD specimen
The quasi-static tensile tests were conducted on the INSTRON5500R universal material testing machine. An improved split Hopkinson pressure bar was employed in the dynamic tensile tests to realize one dimensional stress wave loading on FBD specimens, as shown in Fig.6. High strength steel inserts were added between the flat ends of disc and the compressive bar to avoid the irreversible damage on the 5
ACCEPTED MANUSCRIPT ends of the bar. As ceramic usually fails promptly at a small strain and have a short time to be destroyed under the condition of high strain rates, a Φ3.5×0.5mm aluminum pulse shaper was glued concentrically at the impacted end of the incident bar to ensure that the rising front of the pulse is not so steep and
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produce a uniform stress distribution in the specimen during the experiments. Meanwhile, the 2D-DIC
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technique was employed to validate the improved experimental facilities. Black and white matted paints
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were sprayed on the discs successively, providing digital images with high contact speckle patterns. Finally, due to the low failure strain of the composite, strain gauges were glued centrally on both the plane sides of disc to measure the strain directly. The size of the strain gauges was 4.7×2.6 mm, smaller
Incident Bar
Steel Inserts
Damper
Strain Gauge
Transmitted Bar
Absorption Bar
High-speed Camera
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Striker Bar
Specimen
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Strain Gauge
Pulse Shaper
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compared with the FBD specimen.
Fig.6. Schematic of modified split Hopkinson pressure bar
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In split Hopkinson bar tests, the effects of friction between the specimen and the bar have a great influence on the measurement of experimental data. It was found that larger stresses were required to obtain a given strain without lubricant, which indicated that there was a considerable amount of friction
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between the specimen and the bars [25]. To reduce the friction of the contact area among bars, inserts and specimen, each surface of them were lubricated appropriately by the addition of molybdenum disulfide (MoS2) before placed in the apparatus. The material parameters of the steel compressive bar were: elasticity modulus E=210Gpa, density ρ0=7850kg/m3, velocity of sound C0=5200m/s. The incident and transmit bar were both 1000mm in length, and the striker bar was 200mm. All bars have a diameter of 12.7mm. The strain gauges were glued symmetrically in the middle of incident and transmit bar to record the incident, reflected and transmission waves and ensure the uniformity of axial stress signal over the entire cross section of the bars, as shown in Fig.6.
3.2 Static and dynamic compressive tests In the quasi-static and dynamic compressive tests, the effect of stress concentration was considered due to the high strength and low failure strain of ceramic. According to the Saint-Venant principle, the effect 6
ACCEPTED MANUSCRIPT of stress concentration would get weak after increasing the the L/D ratio of specimen properly. But an excessive increasing of the ratio would lead to buckling of specimen. According to the ASTM standard, the specimen dimensions of static and dynamic compressive tests were set as Φ6.35×9.5mm and
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Φ5.5×11mm [13] respectively.
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The quasi-static compressive tests were conducted on a material testing machine (MTS809). As shown
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in Fig.7, high strength and stiffness inserts of steel alloy (W18Cr4V2) were employed in the tests to avoid the damage of the loading equipment. As the size of specimen was much smaller than that of the loading device, a hoop constraint was used to realize the uniaxial loading on the specimen. For the dynamic
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compressive tests, the modified split Hopkinson pressure bar was also employed to measure mechanical properties of the composite, as shown in Fig.6. But material of the pulse sharper in the apparatus was
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replaced by the copper with a dimension of Φ4×0.5 mm in order to increase the rise time of the incident wave and reduce the likelihood of premature failures of the specimen. Lastly, a strain gauge was glued on
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the axial direction of the specimen to measure the strain directly.
Fig.7. Schematic of quasi-static loading apparatus
4. Results The theoretical strength of ceramic is much larger than that of laboratory measurements. But the ceramic usually fails in a brittle manner of axial splitting as a result of microcrack propagation and coalescence. The existence of microscopic defects lower the strength of the ceramic, such as the microscopic cracks on both surfaces and dispersed internal, small cavities (fine microscopic pores and voids), et al. However, the size of specimen is much larger than the microscopic defects in the present study, and the particle of TiB2 phase and B4C phase, and microscopic defects were distributed uniformly throughout the composite microstructure, as shown in Fig.3. Therefore, the stress and strain of the composite can be assumed as homogeneous material, and not producing an unacceptable error [26]. 7
ACCEPTED MANUSCRIPT 4.1 Tensile properties 4.1.1 Quasi-static tensile results
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The elastic mechanics provides a theoretical method in calculating the tangential stress σθ and the radial
2P 4D2 1 Dt D 2 4r 2
(1)
(2)
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r
2P Dt
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stress σr from the data obtained in traditional Brazilian disc experiments [27-28]:
where P is the concentrated force; D, t are the diameter and thickness of the disc respectively; r is the
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distance between the reference point and center of circle. Wang et al. (2009) [22] proposed the Flattened Brazilian Disc (FBD) method, and formulated the tensile strength of FBD using the Griffith strength criterion.
2 Pc Dt
(3)
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D
t k
where Pc is the critical loading in the tests; k is a dimension coefficient of the flattened disc. If 2α= 0°,
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k=1, which corresponds to the solution of traditional Brazil disc tests. If 2α= 20°, k is approximated to 0.95 according to finite element analysis. In quasi-static tensile tests, two loading strain rates, 1×10-3s-1 and 5×10-3s-1, were achieved in a
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universal material testing machine. As shown in Fig.8, the load-displacement curve is close to a straight line, illustrating that the TiB2-B4C composite is a kind of typical elastic brittle material. The critical loading Pc is 57kN, and the tensile strength σt is 330MPa calculated by Eq. (3).
Fig.8. Load-displacement curves at strain rates of 1×10-3s-1 and 5×10-3 s-1. 8
ACCEPTED MANUSCRIPT 4.1.2 Dynamic tensile results In dynamic tensile tests, the strain rate was controlled by changing the pressure of nitrogen in a gas gun. Fig.9 shows a typical set of the strain recordings of the incident, reflected and transmitted signals in a
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SHPB experiment. As shown, the loading waveform has a rising time of about 33.4μs optimized after
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adding the wave pulse shaper. In Fig.9 (a), an apparent turning point following a steep rising exists in the
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reflected wave, which corresponds to the crush of the disc. Then the residual wave totally turned back into the incident bar. As shown in Fig.9 (b), the response time from initiated loading to crush of the specimen is approximately equal to that of the transmitted wave. Fig.9 (c) is the recording of tensile strain
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history at the center of disc. An obvious shock signal actually proves the failure of the specimen in this section. However, only the intermediate curve is useful as the shock line shows a cut-off for the
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measurement range of strain and hence of no use.
(a) Incident and reflected wave
(b) Transmitted wave
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(c) Tensile wave at the center of disc
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Fig.9. Typical recording in dynamic tensile tests
The critical loading was measured at the turning point where the tensile stress at the disc center got peak value. The dynamic tensile strength σt can be calculated by Eq. (3). Based on the one dimension
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stress wave theory [26], the loading P can be calculated by: EA0 i t r t t t 2
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P
(4)
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where A0 is the cross-section area of compressive bar; i t , r t and t t are the strain of incident wave, reflected wave and transmitted wave respectively. The strain rate at the center of the FBD specimen can be calculated by the derivation of the tensile
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strain history s t with respect to time:
t
d s t dt
(5)
Table 1 is the dynamic tensile strength of the FBD specimen under different impact velocities (V0). As shown, the corresponding parameters such as dynamic tensile strength, strain rates and failure strain increase with the increasing of impact velocities. The failure strain is about 10-2 providing the extreme brittle properties of the TiB2-B4C composite.
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ACCEPTED MANUSCRIPT Table 1. Dynamic tensile strength of TiB2-B4C composite under different impact velocities. (Aver: average value; Std: standard deviation)
σt
Aver ( )
Std ( )
Aver (σt)
Std (σt)
-1
s
MPa
-1
-1
MPa
MPa
kN
10
T01
34.4
59
0.84
33
340
T02
34.4
61
1.10
34
348
T03
30.4
59
1.12
36
340
T04
32.8
60
1.11
47
341
T05
---
65
1.11
82
374
T06
35.2
64
1.14
88
368
T07
34.2
65
1.55
97
371
T08
36.8
71
1.44
183
408
T09
37.4
71
1.52
196
411
T10
36.8
73
1.45
200
418
T11
39.0
76
1.99
244
437
T12
38.4
73
1.96
250
421
T13
---
75
2.05
264
434
T14
41.6
77
2.13
265
443
s
s
38
5.59
89
193
256
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m/s
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-2
342
3.35
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Pc
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V0
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No.
6.16
371
2.45
7.26
412
4.19
9.25
434
8.04
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The strain rate always plays an important role in establishing the constitutive relation of materials.
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Solid materials can be classified into rate sensitivity materials (positive or negative) and rate-independent materials based on the relation between the flow stress and the strain rate. Fig.10 shows that the strength
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of the material increases with the increasing of strain rates. It can be seen that the strain-rate sensitivity of TiB2-B4C composite is positive under dynamic tensile loading conditions.
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450
Tensile strength (Gpa)
420
390
360
330
300 0
50
100
150
200
250
300
-1
Strain rate (s )
Fig.10. Tensile strength at different strain rates.
In tests of T08 and T12, one surface of the disc was attached by a strain gauge, while the opposite side was specked and captured providing digital images for 2D-DIC calculations. Fig.11 shows the strain 11
ACCEPTED MANUSCRIPT distribution in the Y direction (Fig.5) obtained by the 2D-DIC technique, and the crack propagation of the FBD obtained by a high speed camera. The crack is first initiated at the center of the disc, satisfying the underlying principle of the Brazilian disc test. In order to evaluate the effect of measurements between
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2D-DIC method and strain gauge, quantitative analysis was carried out by adding coordinate system on
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the disc. The X-axis was paralleled with the loading direction, and the original point (O) was the location
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of the strain gauge. As shown in Fig.11 (a) and (b), failure strains obtained by 2D-DIC method were 0.0141 and 0.0218 in the test of T08 and T12 respectively, which has a difference of -0.0003 and 0.0022 compared with the data acquired by strain gauge. The cracking initiation in the test T12 is not as close to
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the specimen center as that in test T08, causing the difference of T12 tests higher than T08 tests. However, the results of 2D-DIC method still showed a good agreement with the experiment data of strain gauges,
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thus proved the validity of the improved experimental facilities. Meanwhile, the stress concentration on the flat ends of the disc before crack generation is controlled in an acceptable range, as shown in strain
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distribution of the disc.
(a) T08 (183s-1)
(b) T12 (250s-1)
(c) The crack propagation Fig.11. Strain distribution obtained by 2D-DIC technique 12
ACCEPTED MANUSCRIPT 4.2 Compressive properties In quasi-static tests, the strain rate of loading by the MTS was 1×10-3s-1, and the critical loading was 125.5kN corresponding to the compressive strength of 3.97GPa, as shown in Fig.12. The
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load-displacement curve is approximately linear, which is the same as in the tensile tests.
Fig.12. Load-displacement curve in quasi-static compressive test
Fig.13 shows a typical set of strain recordings of incident, reflected, and transmitted signals in the
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dynamic compressive tests. A plateau stage in the reflected signal indicates that the specimen experienced
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a loading of constant strain rate before failure. Then, a steep amplitude signal appears and increases
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drastically because the shattered specimen provides little resistance to the advance of the incident bar end. The response time of reflected wave before its turning point approximately equals that of the shock
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loading obtained by the strain gauge on the specimen.
Fig.13. Typical incident, reflected and transmitted signals obtained by dynamic compressive experiment.
The strain was measured directly by the gauge glued on the axis direction of specimen. The strain rate can be calculated by Eq. (5). Based on the one dimension stress wave theory [26], the stress history can be gained by: 13
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A0 E t t As
(6)
where As is the cross sectional area of specimen.
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The table 2 shows that the dynamic compressive strength and the failure strain of specimen are increased with the increasing of strain rates, providing that the positivity of strain rate sensitivity once
magnitude.
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again. The compressive strength has a marked difference with the tensile strength, reaching an order of
Table 2. Summary of dynamic compressive tests(Aver: average value; Std: standard deviation) Aver ( ) Std ( ) Aver (σi) Std (σi) V0 Failure strain σi m/s
--
s-1
C01
21
0.0104
387
C02
21
---
377
C03
22
---
C04
25
0.0094
C05
25
0.0106
C06
23
---
C07
28
0.0112
510
5.55
C08
27
0.0111
522
5.43
C09
28
0.0120
532
5.79
C10
30
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Specimens
0.0131
614
6.12
C11
30
0.0130
610
6.12
C12
31
---
592
5.56
C13
32
0.0142
697
6.76
C14
34
0.0147
680
6.78
0.0135
723
6.46
32
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s-1
s-1
GPa
GPa
382
4.0825
4.65
0.1694
420
4.6428
5.13
0.1702
521
8.9938
5.59
0.1497
605
9.5685
5.93
0.2640
700
17.6823
6.67
0.1464
4.55
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4.51
382
4.89
418
5.17
426
5.31
415
4.90
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CE P
AC
C15
GPa
For comparing and analyzing the mechanical properties among the TiB2-B4C composite, the pure B4C and the pure TiB2, compressive strengths via strain rates of those ceramic were showed in Fig.14. In case of B. Paliwal and K. T. Ramesh, dynamic compressive strength of hot-pressed boron carbide was gained by a MTS machine and split-Hopkinson pressure bar technique under loading rates of 10-5s-1 and 103s-1 [29]. Hoke et al. studied the mechanical properties of titanium diboride in the quasi-static (10-5s-1) tests and dynamic compressive (102s-1) tests [30]. Fig.14 shows that compressive strength of the TiB2-B4C composite is higher than that of both the pure B4C and the pure TiB2. On the other hand, the strain-rate sensitivity of the composite is similar to that of the pure TiB2 material. Researches stated that almost all the mechanical properties measured on hot-pressed (or sintered) boron carbide samples differ and depend on specific impurity contents and distribution, porosity, clusters of diffusion pores, grain size, etc [31]. The addition of TiB2 decreases and inhibits the grown size of particles and internal fine pores throughout 14
ACCEPTED MANUSCRIPT the composite microstructure (as shown in Fig.3), thus clearly promotes the densification of B4C [31]. In view of the fracture mechanism of the TiB2-B4C composite, it can be concluded that the presence of uniformly distributed TiB2 particles and a well sintered fine-grained B4C matrix enhanced the
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compressive strength of the composite. Meanwhile, the strain-rate sensitivity of the composite is mainly
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attributed to the presence of TiB2 addition which serves as a strengthening and toughening agent.
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7
5
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Compressive strength (Gpa)
6
2
The TiB2-B4C composite (Present study) The pure B4C (Paliwal and Ramesh)
1
0
200
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0
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The pure TiB2 (Hoke et al.)
400
600
800
1000
-1
The strain rate (s )
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Fig.14. Dynamic compressive strength via strain rates
Fig.15 shows a linear relationship of the stress-strain behavior of the composite in the dynamic compressive tests, indicating that the deformation of the composite is stayed at elastic stage before failure.
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The elasticity modulus varies from 490Gpa to 525Gpa with the increasing of strain rates, although its increment is limited. In previous studies, the elastic modulus of the pure B4C is about 462 Gpa [32], and the quasi-static (10-5s-1) and dynamic (102s-1) elastic modulus of the pure TiB2 is 410Gpa and 440Gpa respectively [30]. Obviously, the strain rates have greater influence on elastic modulus of the pure TiB2 than that of the pure B4C. This phenomenon provides further evidence that the addition of TiB2 leads to the improvement of strain-rate sensitivity of the composite. In addition, it is known that the elastic modulus is decreased with the porosity increasing [31]. As shown in Fig.3, the grain size and porosity of the composite was inhibited apparently by the addition of TiB2, which is another reason why the elastic modulus of the composite is higher than their matrix of the pure B4C.
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Fig.15. Stress-strain curves of TiB2-B4C composite at different strain rates
5. Conclusions
Based on the examination of TiB2-B4C composite, the following are the conclusions:
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1) Regular grain of TiB2 (light grey phase) is distributed uniformly in the grown grain of B4C (dark
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grey phrase). A certain amount of fine microscopic pores distributed uniformly throughout the composite
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microstructure, and were located on the junction of grain boundary between the TiB2 phase and B4C phase. The intergranular fracture occurs along the grain boundary of TiB2 phase, while the transcrystalline fracture occurs within the B4C particles.
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2) In the tensile tests, the addition of parallel flat ends on FBD was introduced to reduce the stress concentration of specimen. The crack is initiated from the center of the disc obviously, satisfying the underlying principle of the Brazilian disc test. Meanwhile, the results of 2D-DIC method show a good agreement with the data obtained by strain gauges, thus proved the validity of the improved experimental facilities. 3) Both the tensile and compressive strength were acquired, and increase with the increasing of strain rates. The compressive strength has a marked difference with the tensile strength, reaching an order of magnitude. The strain-rate sensitivity of the composite is mainly attributed to the presence of TiB2 addition. The comparison of compressive strength and elastic modulus among the TiB2-B4C composite, the pure B4C and the pure TiB2 was achieved. Results show that the mechanical properties were dominated by the microstructure and fracture mode of the composite.
Acknowledgements 16
ACCEPTED MANUSCRIPT The author gratefully acknowledges the support on financial and technical support of China Academy of Engineering Physics, and the support of material by Wuhan University of Technology.
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References
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[1] D. W. Wang, S. L. Ran, L. Shen, H. F. Sun, Q. Huang, Fast synthesis of B4C–TiB2 composite
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powders by pulsed electric current heating TiC–B mixture, J. Eur. Ceram. Soc. 35 (2015) 1107–1112. [2] Y. J. Wang, H. X. Peng, F. Ye, Y. Zhou, Effect of TiB2 content on microstructure and mechanical properties of in-situ fabricated TiB2/B4C composite, T. Nonferr. Metal. Soc. 21 (2011) 369–373.
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[3] Mehri Mashhadi, Ehsan Taheri-Nassaj, Maryam Mashhadi, Vincenzo M. Sglavo, Pressureless sintering of B4C–TiB2 composite with Al additions, Ceram. Int. 37 (2011) 3229–3235.
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[4] C. M. Xu, Y. B. Cai, K. Flodström, Z. S. Li, S. Esmaeilzadeh, G. J. Zhang, Spark plasma sintering of B4C ceramic: The effects of milling medium and TiB2 addition, Int. J. Refract. Met. Hard Mater. 30 (2012) 139–144.
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[5] L. Nikzad, R. Licheri, T. Ebadzadeh, R. Orrù, G. Cao, Effect of ball milling on reactive spark plasma
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sintering of B4C–TiB2 composite, Ceram. Int. 38 (2012) 6469–6480. [6] T. S. Srivatsan, G. Guruprasad, D. Black, R. Radhakrishnan, T. S. Sudarshan, Influence of TiB2
161–167.
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content on microstructure and hardness of TiB2–B4C composite, Powder Technol. 159 (2005)
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[7] D. Chicot, P. de Baets, M. H. Staia, E. S. Puchi-Cabrera, G. Louis, Y. Perez Delgado, J. Vleugels, Influence of tip defect and indenter shape on the mechanical properties determination by indentation of a TiB2–60%B4C ceramic composite, Int. J. Refract. Met. Hard Mater. 38 (2013)102–110. [8] S. G. Huang, K. Vanmeensel, O. J. A. Malek, O. Van der Biest, J. Vleugels, Microstructure and mechanical properties of pulsed electric current sintered B4C–TiB2 composite, Mater. Sci. Eng. A, 528 (2011)1302–1309. [9] C. A. Tracy, A compressive test for high strength ceramic, J. Test. Eval. 15 (1987)14–19. [10] H. Awaji, T. Watanabe, Y. Nagano, Compressive testing of ceramic, Ceram. Int. 20 (1994)159–167. [11] P. Forquin, C. Denoual, C. E. Cottenot, F. Hild, Experiments and modelling of the compressive behavior of two SiC ceramic, Mech. Mater. 35 (2003) 987–1002. [12] W. Chen, G. Subhash, G. Ravichandran, Evaluation of ceramic specimen geometries used in Split-Hopkinson pressure bar, Dymat J. 1 (1994) 193–210. 17
ACCEPTED MANUSCRIPT [13] G. Subhash, G. Ravichandran, Split-Hopkinson pressure bar testing of ceramic, American Society for Materials Handbook, 8th edn. American Society for Metals International, Materials Park, OH, (2000) 497–504.
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[14] G. Sunny, F. Yuan, V. Prakash, J. Lewandowski, Design of inserts for Split-Hopkinson pressure bar
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testing of low strain-to-failure materials, Mech. Mater. 49 (2009) 479–490.
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[15] M. R. M. Aliha, M. R. Ayatollahi, Analysis of fracture initiation angle in some cracked ceramic using the generalized maximum tangential stress criterion, Int. J. Solids Struct. 49 (2012) 1877–1883. [16] A. Brückner-Foit, T. Fett, D. Munz, K. Schirmer, Discrimination of multiaxiality criteria with the
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Brazilian disc test, J. Eur. Ceram. Soc. 17 (1997) 689–696.
[17] L. Banks-Sills, N. Travitzky, D. Ashkenazi, Interface fracture properties of a bimaterial ceramic
MA
composite, Mech. Mater. 32 (2000) 711–722.
[18] Pathikumar Sellappan, Erheng Wang, Christian J. Espinoza Santos, Tommy On, John Lambros, Waltraud M. Kriven, Wave propagation through alumina-porous alumina laminates, J. Eur. Ceram.
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Soc. 35 (2015) 197–210.
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[19] Q. Z. Wang, W. Li, H. P. Xie, Dynamic split tensile test of Flattened Brazilian Disc of rock with
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SHPB setup, Mech. Mater. 41 (2009) 252–260. [20] Q. Z. Wang, L. Xing, Determination of fracture toughness K IC by using the Flattened Brazilian Disk specimen for rocks, Eng. Fract. Mech. 64 (1999) 193–201.
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[21] Q. Z. Wang, W. Li, X. L. Song, A method for testing dynamic tensile strength and elastic modulus of rock materials using SHPB, Pure Appl. Geophys. 163 (2006) 1091–1100. [22] Q. Z. Wang, X. M. Jia, S. Q. Kou, Z. X. Zhang, P. –A. Lindqvist, The Flattened Brazilian Disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results, Int. J. Rock Mech Min. 41 (2004) 245–253. [23] J. D. Clayton, A. L. Tonge, A nonlinear anisotropic elastic-inelastic constitutive model for polycrystalline ceramic and minerals with application to boron carbide, Int. J. Solids. Struct. 64–65 (2015) 191–207. [24] J. D. Clayton, Finite strain analysis of shock compression of brittle solids applied to titanium diboride, Int. J. Impact Eng. 73 (2014) 56–65. [25] H. Kolsky, An investigation of the mechanical properties of materials at very high rates of loading, Proc. Phys. Soc. B. 62 (1949) 676–700. 18
ACCEPTED MANUSCRIPT [26] W. N. Chen, B. Song, Split Hopkinson (Kolsky) Bar Design, Testing and Applications, Springer Press, New York, 2011. [27] ISRM Suggested methods for determining tensile strength of rock materials. Int. J. Rock. Mech. Min.
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Sci. Geomech. Abstr. 15 (1978) 99–103.
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[28] S. P. Timoshenko, J. N. Goodier, Theory of elasticity. McGraw-Hill Press, New York, 1970.
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[29] B. Paliwal, K. T. Ramesh, Effect of crack growth dynamics on the rate-sensitive behavior of hot-pressed boron carbide. Scripta. Mater. 57 (2007) 481–484.
[30] D. A. Hoke, M. A. Meyers, L. W. Meyer, G. T. Gary, Reaction synthesis/dynamic compaction of
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titanium diboride. Metall. Trans. A, 23 (1992) 77–86.
[31] F. Thevenot, Boron carbide-a comprehensive review. J. Eur. Ceram. Soc. 6 (1990) 205–225.
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[32] G. R. Johnson, T. J. Holmquist, Response of boron carbide subjected to large strains, high strain rates,
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and high pressures. J. Appl. Phys. 85 (1999) 8060–8073.
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ACCEPTED MANUSCRIPT Steel Inserts
Strain Gauge
Incident Bar Striker Bar
Damper
Strain Gauge
Transmitted Bar
Specimen of TiB2-B4C composite
Absorption Bar
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Pulse Shaper
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Comparison
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High Speed Camera
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Graphical abstract
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Cylindrical Specimen
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FBD
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ACCEPTED MANUSCRIPT Highlights 1) The improved experimental facility was verified by the 2D digital image correlation technique. 2) The strength and elastic modulus of TiB2-B4C composite at different strain rates was acquired.
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3) Higher compressive strength of TiB2-B4C composite than pure B4C and pure TiB2 is affected by
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microstructure and fracture mode.
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CE P
TE
D
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4) Strain rate sensitivity of TiB2-B4C composite is attributed to the presence of TiB2 phase.
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S0264-1275(15)30982-5 doi: 10.1016/j.matdes.2015.12.123 JMADE 1147
To appear in: Received date: Revised date: Accepted date:
21 September 2015 20 December 2015 21 December 2015
Please cite this article as: Yubo Gao, Tiegang Tang, Chenhong Yi, Wei Zhang, Dacheng Li, Wenbo Xie, Wei Huang, Nan Ye, Study of static and dynamic behavior of TiB2 –B4 C composite, (2015), doi: 10.1016/j.matdes.2015.12.123
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ACCEPTED MANUSCRIPT Study of static and dynamic behavior of TiB2-B4C composite Yubo Gao a b
a,
b
b
a,**
, Tiegang Tang , Chenhong Yi , Wei Zhang
a
a
a
, Dacheng Li , Wenbo Xie , Wei Huang , Nan Ye
a
Hypervelocity Impact Research Center, Harbin Institute of Technology, Heilongjiang, Harbin, P.R. China
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Laboratory for Shock Wave and Detonation Physics Research Institute of Fluid Physics, CAEP, Mianyang, Sichuan, P.R.
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China
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Abstract: The microstructure and phase analysis of TiB2-B4C composite were investigated by the X-ray diffraction (XRD) and scanning electron microscope (SEM) techniques, and the mechanical properties were studied by improved experimental facilities under quasi-static and dynamic loading conditions.
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Results show that regular grain of TiB2 is distributed uniformly in the grown grain of B4C, and the fracture mechanism of TiB2-B4C composite includes intergranular fracture and transcrystalline fracture.
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In tensile tests, the Flattened Brazilian Disc (FBD) method was introduced to reduce stress concentration between the platens of the test machine and circular boundaries of the specimen. The results of 2D-DIC
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method show a good agreement with the data obtained by strain gauges, thus proved the validity of the
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improved experiment facilities. Meanwhile, both the tensile and compressive strength increase with the increasing of strain rates. The reason is mainly attributed to the presence of TiB2 addition which serves as
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a strengthening and toughening agent. The comparison of strength and microstructure among the TiB2-B4C composite, the pure B4C and the pure TiB2 show that the mechanical properties were dominated by the microstructure and fracture mode of the composite.
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Keywords: TiB2-B4C composite, mechanical properties, microstructure, strain-rate sensitivity
1. Introduction
Boron carbide (B4C) has many excellent physical properties, such as extremely high hardness, high wear resistance, low specific gravity and high chemical stability. Up to now, it has been widely used in wear-resistant components, lightweight armor products and neutron radiation shields, etc [1]. However, it also has some weaknesses of mechanical property restricting its applications. For example, the fracture toughness of boron carbide is low due to its characteristic of crystal structure. Various kinds of papers have been performed to study the mechanical properties of boron carbide (B4C), especially with the
First author. Tel.: +86 451 86417978 18；Fax: +86 451 86402055.
**
Corresponding author. Tel.: +86 451 86417978 18；Fax: +86 451 86402055.
E-mail addresses: [email protected] (Yubo Gao), [email protected] (Wei Zhang). 1
ACCEPTED MANUSCRIPT addition of titanium diboride (TiB2) [2-5]. Generally, the increasing research efforts on the TiB2-B4C composite have been focused on the microstructure, hardness, fracture toughness, flexural strength, elastic modulus, etc [2, 6-8]. T. S. Srivatsan et al. analyzed the influence of TiB2 content on microstructure and
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hardness of TiB2-B4C composite [6]. Microhardness measurements showed a gradual increase in hardness
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with an increasing of TiB2 content in the starting powder mixture. Y. J. Wang et al. proposed that the
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elastic modulus and fracture toughness of the composite increased remarkably after raising the TiB2 content [2]. However, relatively little is known about the static and dynamic mechanical properties of TiB2-B4C composite, while it is of importance to numerous applications in mechanical engineering and
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structural engineering.
The TiB2-B4C composite has got typical mechanical properties of ceramic, such as high strength, high
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elasticity modulus, brittle, low failure strain etc. Based on a series of experiments, the compressive mechanical properties of ceramic have been performed by using different shapes of specimens [9-11] and improved experimental schemes [9-14]. For the experiments of tensile properties, it is hard to obtain
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tensile strength directly due to the low failure strain of ceramic. So the Brazilian test (also called the split
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tensile test), an indirect tensile method, has been applied to be a popular choice [15-18]. However, the
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traditional Brazilian test cannot eliminate the stress concentration completely between the platens of the test machine and circular boundaries of the disc specimen. The crack is not initiated from the center of the disc as a premature breakage of the specimen occurs at the contact point [19]. In order to avoid the
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unreasonable failure mode of the disc, Wang et al. proposed the Flattened Brazilian Disc (FBD) method which machine two parallel flat ends on the disc circumference for the appliance of the distributed load [20-22]. For the microscopic level, the main drawback of ceramic lies in their extreme brittleness and the limited ability to withstand the plastic deformation, given their low fracture toughness and the marked difference between their tensile and compressive strengths. The failure mode of ceramic is attributed to the microcrack propagation and coalescence. J. D. Clayton et al. proposed a new continuum constitutive theory to study polycrystalline brittle solids subjected to possible large stress and strain rates, including finite deformation kinematics, balance laws, thermodynamics and defect kinetics etc. [23-24]. But so far few detail reports showed the difference between tensile and compressive properties about the ceramic, especially the strain-rate sensitivity of tensile strength. In the present study, the phase and microstructure analysis of TiB2-B4C composite were observed by the X-ray diffraction (XRD) and the scanning electron microscope (SEM) techniques. Then the tensile 2
ACCEPTED MANUSCRIPT and compressive properties of TiB2-B4C composite were performed by the geometries design of specimens and the improved experimental facilities under quasi-static and dynamic loading conditions. In dynamic FBD experiments, the 2D digital image correlation method (DIC), a kind of non-contact and
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full-field optical measurement method, was employed to analyze the entire crack propagation and the
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failure strain of specimen. Finally, the dynamic tensile and compressive strength of TiB2-B4C composite
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was calculated based on the one dimension stress wave theory. It is found that not only the compressive strength but also the tensile strength is increased with the increasing of strain rates, and the compressive
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strength has a marked difference (an order of magnitude) compared with tensile strength.
2. The phase analysis and microstructure of TiB2-B4C composite
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In the present study, the TiB2-B4C composite was sintered by a fine powders mixture using of titanium diboride (TiB2) and boron carbide (B4C). Fig.1 was the XRD patterns of the TiB2-B4C composite. Results of the energy spectrum analysis (EDS) also provided powerful evidence to determine material
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composition of the composite, as shown in Fig.2. The result indicates that the sintering body is composed
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12000
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by B4C and TiB2 phases. There are not new phases or substance in the detection process.
B4C B4C TiB2 TiB2
8000 6000
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Intensity/a.u.
10000
4000 2000 0 20
30
40
50
60
70
80
90
2θ/degree Fig.1. XRD patterns of TiB2-B4C composite
Fig.2 shows the SEM micrograph and the elements distribution of the composite surface by the EDS analysis. The boron (B) is distributed throughout the scan area, which is denser in dark grey phrase compared with the light grey phrase, as shown in Fig. 2(a) and (b). The titanium (Ti) and carbon (C) is found in light grey phrase and dark grey phrase respectively, as shown in Fig. 2(c) and (d). The result shows that the light grey area is the TiB2 phase, and the dark grey area is the B4C phrase. 3
ACCEPTED MANUSCRIPT (b)
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(a)
(d)
10μm
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10μm
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(c)
10μm
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10μm
Fig.2. SEM micrograph (a), and elemental distribution on the surface of TiB2-B4C composite: (b) boron (B); (c) titanium (Ti); (d) carbon (C).
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The scanning electron microscope (SEM) was adopted to observe the microstructure and fracture
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morphology of TiB2-B4C composite. Little grain of TiB2 (light grey phase) is distributed uniformly in the
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grown grain of B4C (dark grey phrase), as shown in Fig.3. The particle shape of TiB2 phase is a regular rod whose dimension is less than 5μm. A few TiB2 particles have a larger size, but not beyond 15μm. In addition, a certain amount of fine microscopic pores distributed uniformly thoughout the composite
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microstructure. The entire fine pores were located on the junction of grain boundary between the TiB2 phase and B4C phase, and have a size under 2μm.
Fig.3. SEM images of the TiB2-B4C composite
The fracture mechanism of TiB2-B4C composite includes intergranular fracture and transcrystalline fracture, as shown in Fig.3 and 4. The binding force of grain boundary was strengthened by a mass of 4
ACCEPTED MANUSCRIPT transcrystalline fracture because the crack propagation through grains consumes more energy than that of the intergranular fracture mode. Fig.3 and 4 show that the intergranular fracture occurred mainly along the grain boundary of TiB2 phase, while transcrystalline fracture mainly happened within the B4C
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particles.
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Fig.4. Fracture microtopography of TiB2-B4C composite
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3 Experimental procedure
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3.1 Static and dynamic tensile tests
The TiB2-B4C composite has a density of 3.2g/cm3. The Flattened Brazilian Disc specimens (Φ16×6.6
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mm) were used both in the quasi-static and the dynamic tensile tests. The parallelism and flatness of the disc was 0.001mm and 0.01mm respectively. Two parallel flat ends were used in the disc to reduce the stress concentration and change the loading manner into distributed forces, as shown in Fig.5. The
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loading angle 2α= 20° of FBD was chosen to ensure the crack initiating in the center of the disc, which was calculated and verified by Wang et al. (2004) [22].
Fig.5. Loading mode on the FBD specimen
The quasi-static tensile tests were conducted on the INSTRON5500R universal material testing machine. An improved split Hopkinson pressure bar was employed in the dynamic tensile tests to realize one dimensional stress wave loading on FBD specimens, as shown in Fig.6. High strength steel inserts were added between the flat ends of disc and the compressive bar to avoid the irreversible damage on the 5
ACCEPTED MANUSCRIPT ends of the bar. As ceramic usually fails promptly at a small strain and have a short time to be destroyed under the condition of high strain rates, a Φ3.5×0.5mm aluminum pulse shaper was glued concentrically at the impacted end of the incident bar to ensure that the rising front of the pulse is not so steep and
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produce a uniform stress distribution in the specimen during the experiments. Meanwhile, the 2D-DIC
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technique was employed to validate the improved experimental facilities. Black and white matted paints
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were sprayed on the discs successively, providing digital images with high contact speckle patterns. Finally, due to the low failure strain of the composite, strain gauges were glued centrally on both the plane sides of disc to measure the strain directly. The size of the strain gauges was 4.7×2.6 mm, smaller
Incident Bar
Steel Inserts
Damper
Strain Gauge
Transmitted Bar
Absorption Bar
High-speed Camera
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Striker Bar
Specimen
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Strain Gauge
Pulse Shaper
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compared with the FBD specimen.
Fig.6. Schematic of modified split Hopkinson pressure bar
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In split Hopkinson bar tests, the effects of friction between the specimen and the bar have a great influence on the measurement of experimental data. It was found that larger stresses were required to obtain a given strain without lubricant, which indicated that there was a considerable amount of friction
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between the specimen and the bars [25]. To reduce the friction of the contact area among bars, inserts and specimen, each surface of them were lubricated appropriately by the addition of molybdenum disulfide (MoS2) before placed in the apparatus. The material parameters of the steel compressive bar were: elasticity modulus E=210Gpa, density ρ0=7850kg/m3, velocity of sound C0=5200m/s. The incident and transmit bar were both 1000mm in length, and the striker bar was 200mm. All bars have a diameter of 12.7mm. The strain gauges were glued symmetrically in the middle of incident and transmit bar to record the incident, reflected and transmission waves and ensure the uniformity of axial stress signal over the entire cross section of the bars, as shown in Fig.6.
3.2 Static and dynamic compressive tests In the quasi-static and dynamic compressive tests, the effect of stress concentration was considered due to the high strength and low failure strain of ceramic. According to the Saint-Venant principle, the effect 6
ACCEPTED MANUSCRIPT of stress concentration would get weak after increasing the the L/D ratio of specimen properly. But an excessive increasing of the ratio would lead to buckling of specimen. According to the ASTM standard, the specimen dimensions of static and dynamic compressive tests were set as Φ6.35×9.5mm and
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Φ5.5×11mm [13] respectively.
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The quasi-static compressive tests were conducted on a material testing machine (MTS809). As shown
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in Fig.7, high strength and stiffness inserts of steel alloy (W18Cr4V2) were employed in the tests to avoid the damage of the loading equipment. As the size of specimen was much smaller than that of the loading device, a hoop constraint was used to realize the uniaxial loading on the specimen. For the dynamic
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compressive tests, the modified split Hopkinson pressure bar was also employed to measure mechanical properties of the composite, as shown in Fig.6. But material of the pulse sharper in the apparatus was
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replaced by the copper with a dimension of Φ4×0.5 mm in order to increase the rise time of the incident wave and reduce the likelihood of premature failures of the specimen. Lastly, a strain gauge was glued on
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the axial direction of the specimen to measure the strain directly.
Fig.7. Schematic of quasi-static loading apparatus
4. Results The theoretical strength of ceramic is much larger than that of laboratory measurements. But the ceramic usually fails in a brittle manner of axial splitting as a result of microcrack propagation and coalescence. The existence of microscopic defects lower the strength of the ceramic, such as the microscopic cracks on both surfaces and dispersed internal, small cavities (fine microscopic pores and voids), et al. However, the size of specimen is much larger than the microscopic defects in the present study, and the particle of TiB2 phase and B4C phase, and microscopic defects were distributed uniformly throughout the composite microstructure, as shown in Fig.3. Therefore, the stress and strain of the composite can be assumed as homogeneous material, and not producing an unacceptable error [26]. 7
ACCEPTED MANUSCRIPT 4.1 Tensile properties 4.1.1 Quasi-static tensile results
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The elastic mechanics provides a theoretical method in calculating the tangential stress σθ and the radial
2P 4D2 1 Dt D 2 4r 2
(1)
(2)
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r
2P Dt
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stress σr from the data obtained in traditional Brazilian disc experiments [27-28]:
where P is the concentrated force; D, t are the diameter and thickness of the disc respectively; r is the
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distance between the reference point and center of circle. Wang et al. (2009) [22] proposed the Flattened Brazilian Disc (FBD) method, and formulated the tensile strength of FBD using the Griffith strength criterion.
2 Pc Dt
(3)
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D
t k
where Pc is the critical loading in the tests; k is a dimension coefficient of the flattened disc. If 2α= 0°,
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k=1, which corresponds to the solution of traditional Brazil disc tests. If 2α= 20°, k is approximated to 0.95 according to finite element analysis. In quasi-static tensile tests, two loading strain rates, 1×10-3s-1 and 5×10-3s-1, were achieved in a
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universal material testing machine. As shown in Fig.8, the load-displacement curve is close to a straight line, illustrating that the TiB2-B4C composite is a kind of typical elastic brittle material. The critical loading Pc is 57kN, and the tensile strength σt is 330MPa calculated by Eq. (3).
Fig.8. Load-displacement curves at strain rates of 1×10-3s-1 and 5×10-3 s-1. 8
ACCEPTED MANUSCRIPT 4.1.2 Dynamic tensile results In dynamic tensile tests, the strain rate was controlled by changing the pressure of nitrogen in a gas gun. Fig.9 shows a typical set of the strain recordings of the incident, reflected and transmitted signals in a
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SHPB experiment. As shown, the loading waveform has a rising time of about 33.4μs optimized after
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adding the wave pulse shaper. In Fig.9 (a), an apparent turning point following a steep rising exists in the
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reflected wave, which corresponds to the crush of the disc. Then the residual wave totally turned back into the incident bar. As shown in Fig.9 (b), the response time from initiated loading to crush of the specimen is approximately equal to that of the transmitted wave. Fig.9 (c) is the recording of tensile strain
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history at the center of disc. An obvious shock signal actually proves the failure of the specimen in this section. However, only the intermediate curve is useful as the shock line shows a cut-off for the
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D
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measurement range of strain and hence of no use.
(a) Incident and reflected wave
(b) Transmitted wave
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(c) Tensile wave at the center of disc
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Fig.9. Typical recording in dynamic tensile tests
The critical loading was measured at the turning point where the tensile stress at the disc center got peak value. The dynamic tensile strength σt can be calculated by Eq. (3). Based on the one dimension
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stress wave theory [26], the loading P can be calculated by: EA0 i t r t t t 2
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P
(4)
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where A0 is the cross-section area of compressive bar; i t , r t and t t are the strain of incident wave, reflected wave and transmitted wave respectively. The strain rate at the center of the FBD specimen can be calculated by the derivation of the tensile
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strain history s t with respect to time:
t
d s t dt
(5)
Table 1 is the dynamic tensile strength of the FBD specimen under different impact velocities (V0). As shown, the corresponding parameters such as dynamic tensile strength, strain rates and failure strain increase with the increasing of impact velocities. The failure strain is about 10-2 providing the extreme brittle properties of the TiB2-B4C composite.
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ACCEPTED MANUSCRIPT Table 1. Dynamic tensile strength of TiB2-B4C composite under different impact velocities. (Aver: average value; Std: standard deviation)
σt
Aver ( )
Std ( )
Aver (σt)
Std (σt)
-1
s
MPa
-1
-1
MPa
MPa
kN
10
T01
34.4
59
0.84
33
340
T02
34.4
61
1.10
34
348
T03
30.4
59
1.12
36
340
T04
32.8
60
1.11
47
341
T05
---
65
1.11
82
374
T06
35.2
64
1.14
88
368
T07
34.2
65
1.55
97
371
T08
36.8
71
1.44
183
408
T09
37.4
71
1.52
196
411
T10
36.8
73
1.45
200
418
T11
39.0
76
1.99
244
437
T12
38.4
73
1.96
250
421
T13
---
75
2.05
264
434
T14
41.6
77
2.13
265
443
s
s
38
5.59
89
193
256
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m/s
T
-2
342
3.35
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Pc
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V0
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No.
6.16
371
2.45
7.26
412
4.19
9.25
434
8.04
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The strain rate always plays an important role in establishing the constitutive relation of materials.
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Solid materials can be classified into rate sensitivity materials (positive or negative) and rate-independent materials based on the relation between the flow stress and the strain rate. Fig.10 shows that the strength
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of the material increases with the increasing of strain rates. It can be seen that the strain-rate sensitivity of TiB2-B4C composite is positive under dynamic tensile loading conditions.
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450
Tensile strength (Gpa)
420
390
360
330
300 0
50
100
150
200
250
300
-1
Strain rate (s )
Fig.10. Tensile strength at different strain rates.
In tests of T08 and T12, one surface of the disc was attached by a strain gauge, while the opposite side was specked and captured providing digital images for 2D-DIC calculations. Fig.11 shows the strain 11
ACCEPTED MANUSCRIPT distribution in the Y direction (Fig.5) obtained by the 2D-DIC technique, and the crack propagation of the FBD obtained by a high speed camera. The crack is first initiated at the center of the disc, satisfying the underlying principle of the Brazilian disc test. In order to evaluate the effect of measurements between
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2D-DIC method and strain gauge, quantitative analysis was carried out by adding coordinate system on
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the disc. The X-axis was paralleled with the loading direction, and the original point (O) was the location
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of the strain gauge. As shown in Fig.11 (a) and (b), failure strains obtained by 2D-DIC method were 0.0141 and 0.0218 in the test of T08 and T12 respectively, which has a difference of -0.0003 and 0.0022 compared with the data acquired by strain gauge. The cracking initiation in the test T12 is not as close to
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the specimen center as that in test T08, causing the difference of T12 tests higher than T08 tests. However, the results of 2D-DIC method still showed a good agreement with the experiment data of strain gauges,
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thus proved the validity of the improved experimental facilities. Meanwhile, the stress concentration on the flat ends of the disc before crack generation is controlled in an acceptable range, as shown in strain
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distribution of the disc.
(a) T08 (183s-1)
(b) T12 (250s-1)
(c) The crack propagation Fig.11. Strain distribution obtained by 2D-DIC technique 12
ACCEPTED MANUSCRIPT 4.2 Compressive properties In quasi-static tests, the strain rate of loading by the MTS was 1×10-3s-1, and the critical loading was 125.5kN corresponding to the compressive strength of 3.97GPa, as shown in Fig.12. The
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load-displacement curve is approximately linear, which is the same as in the tensile tests.
Fig.12. Load-displacement curve in quasi-static compressive test
Fig.13 shows a typical set of strain recordings of incident, reflected, and transmitted signals in the
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dynamic compressive tests. A plateau stage in the reflected signal indicates that the specimen experienced
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a loading of constant strain rate before failure. Then, a steep amplitude signal appears and increases
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drastically because the shattered specimen provides little resistance to the advance of the incident bar end. The response time of reflected wave before its turning point approximately equals that of the shock
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loading obtained by the strain gauge on the specimen.
Fig.13. Typical incident, reflected and transmitted signals obtained by dynamic compressive experiment.
The strain was measured directly by the gauge glued on the axis direction of specimen. The strain rate can be calculated by Eq. (5). Based on the one dimension stress wave theory [26], the stress history can be gained by: 13
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A0 E t t As
(6)
where As is the cross sectional area of specimen.
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The table 2 shows that the dynamic compressive strength and the failure strain of specimen are increased with the increasing of strain rates, providing that the positivity of strain rate sensitivity once
magnitude.
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again. The compressive strength has a marked difference with the tensile strength, reaching an order of
Table 2. Summary of dynamic compressive tests(Aver: average value; Std: standard deviation) Aver ( ) Std ( ) Aver (σi) Std (σi) V0 Failure strain σi m/s
--
s-1
C01
21
0.0104
387
C02
21
---
377
C03
22
---
C04
25
0.0094
C05
25
0.0106
C06
23
---
C07
28
0.0112
510
5.55
C08
27
0.0111
522
5.43
C09
28
0.0120
532
5.79
C10
30
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Specimens
0.0131
614
6.12
C11
30
0.0130
610
6.12
C12
31
---
592
5.56
C13
32
0.0142
697
6.76
C14
34
0.0147
680
6.78
0.0135
723
6.46
32
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s-1
s-1
GPa
GPa
382
4.0825
4.65
0.1694
420
4.6428
5.13
0.1702
521
8.9938
5.59
0.1497
605
9.5685
5.93
0.2640
700
17.6823
6.67
0.1464
4.55
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4.51
382
4.89
418
5.17
426
5.31
415
4.90
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C15
GPa
For comparing and analyzing the mechanical properties among the TiB2-B4C composite, the pure B4C and the pure TiB2, compressive strengths via strain rates of those ceramic were showed in Fig.14. In case of B. Paliwal and K. T. Ramesh, dynamic compressive strength of hot-pressed boron carbide was gained by a MTS machine and split-Hopkinson pressure bar technique under loading rates of 10-5s-1 and 103s-1 [29]. Hoke et al. studied the mechanical properties of titanium diboride in the quasi-static (10-5s-1) tests and dynamic compressive (102s-1) tests [30]. Fig.14 shows that compressive strength of the TiB2-B4C composite is higher than that of both the pure B4C and the pure TiB2. On the other hand, the strain-rate sensitivity of the composite is similar to that of the pure TiB2 material. Researches stated that almost all the mechanical properties measured on hot-pressed (or sintered) boron carbide samples differ and depend on specific impurity contents and distribution, porosity, clusters of diffusion pores, grain size, etc [31]. The addition of TiB2 decreases and inhibits the grown size of particles and internal fine pores throughout 14
ACCEPTED MANUSCRIPT the composite microstructure (as shown in Fig.3), thus clearly promotes the densification of B4C [31]. In view of the fracture mechanism of the TiB2-B4C composite, it can be concluded that the presence of uniformly distributed TiB2 particles and a well sintered fine-grained B4C matrix enhanced the
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compressive strength of the composite. Meanwhile, the strain-rate sensitivity of the composite is mainly
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attributed to the presence of TiB2 addition which serves as a strengthening and toughening agent.
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5
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4 3
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Compressive strength (Gpa)
6
2
The TiB2-B4C composite (Present study) The pure B4C (Paliwal and Ramesh)
1
0
200
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0
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The pure TiB2 (Hoke et al.)
400
600
800
1000
-1
The strain rate (s )
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Fig.14. Dynamic compressive strength via strain rates
Fig.15 shows a linear relationship of the stress-strain behavior of the composite in the dynamic compressive tests, indicating that the deformation of the composite is stayed at elastic stage before failure.
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The elasticity modulus varies from 490Gpa to 525Gpa with the increasing of strain rates, although its increment is limited. In previous studies, the elastic modulus of the pure B4C is about 462 Gpa [32], and the quasi-static (10-5s-1) and dynamic (102s-1) elastic modulus of the pure TiB2 is 410Gpa and 440Gpa respectively [30]. Obviously, the strain rates have greater influence on elastic modulus of the pure TiB2 than that of the pure B4C. This phenomenon provides further evidence that the addition of TiB2 leads to the improvement of strain-rate sensitivity of the composite. In addition, it is known that the elastic modulus is decreased with the porosity increasing [31]. As shown in Fig.3, the grain size and porosity of the composite was inhibited apparently by the addition of TiB2, which is another reason why the elastic modulus of the composite is higher than their matrix of the pure B4C.
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Fig.15. Stress-strain curves of TiB2-B4C composite at different strain rates
5. Conclusions
Based on the examination of TiB2-B4C composite, the following are the conclusions:
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1) Regular grain of TiB2 (light grey phase) is distributed uniformly in the grown grain of B4C (dark
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grey phrase). A certain amount of fine microscopic pores distributed uniformly throughout the composite
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microstructure, and were located on the junction of grain boundary between the TiB2 phase and B4C phase. The intergranular fracture occurs along the grain boundary of TiB2 phase, while the transcrystalline fracture occurs within the B4C particles.
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2) In the tensile tests, the addition of parallel flat ends on FBD was introduced to reduce the stress concentration of specimen. The crack is initiated from the center of the disc obviously, satisfying the underlying principle of the Brazilian disc test. Meanwhile, the results of 2D-DIC method show a good agreement with the data obtained by strain gauges, thus proved the validity of the improved experimental facilities. 3) Both the tensile and compressive strength were acquired, and increase with the increasing of strain rates. The compressive strength has a marked difference with the tensile strength, reaching an order of magnitude. The strain-rate sensitivity of the composite is mainly attributed to the presence of TiB2 addition. The comparison of compressive strength and elastic modulus among the TiB2-B4C composite, the pure B4C and the pure TiB2 was achieved. Results show that the mechanical properties were dominated by the microstructure and fracture mode of the composite.
Acknowledgements 16
ACCEPTED MANUSCRIPT The author gratefully acknowledges the support on financial and technical support of China Academy of Engineering Physics, and the support of material by Wuhan University of Technology.
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References
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[1] D. W. Wang, S. L. Ran, L. Shen, H. F. Sun, Q. Huang, Fast synthesis of B4C–TiB2 composite
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powders by pulsed electric current heating TiC–B mixture, J. Eur. Ceram. Soc. 35 (2015) 1107–1112. [2] Y. J. Wang, H. X. Peng, F. Ye, Y. Zhou, Effect of TiB2 content on microstructure and mechanical properties of in-situ fabricated TiB2/B4C composite, T. Nonferr. Metal. Soc. 21 (2011) 369–373.
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[3] Mehri Mashhadi, Ehsan Taheri-Nassaj, Maryam Mashhadi, Vincenzo M. Sglavo, Pressureless sintering of B4C–TiB2 composite with Al additions, Ceram. Int. 37 (2011) 3229–3235.
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[4] C. M. Xu, Y. B. Cai, K. Flodström, Z. S. Li, S. Esmaeilzadeh, G. J. Zhang, Spark plasma sintering of B4C ceramic: The effects of milling medium and TiB2 addition, Int. J. Refract. Met. Hard Mater. 30 (2012) 139–144.
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[5] L. Nikzad, R. Licheri, T. Ebadzadeh, R. Orrù, G. Cao, Effect of ball milling on reactive spark plasma
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sintering of B4C–TiB2 composite, Ceram. Int. 38 (2012) 6469–6480. [6] T. S. Srivatsan, G. Guruprasad, D. Black, R. Radhakrishnan, T. S. Sudarshan, Influence of TiB2
161–167.
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content on microstructure and hardness of TiB2–B4C composite, Powder Technol. 159 (2005)
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[7] D. Chicot, P. de Baets, M. H. Staia, E. S. Puchi-Cabrera, G. Louis, Y. Perez Delgado, J. Vleugels, Influence of tip defect and indenter shape on the mechanical properties determination by indentation of a TiB2–60%B4C ceramic composite, Int. J. Refract. Met. Hard Mater. 38 (2013)102–110. [8] S. G. Huang, K. Vanmeensel, O. J. A. Malek, O. Van der Biest, J. Vleugels, Microstructure and mechanical properties of pulsed electric current sintered B4C–TiB2 composite, Mater. Sci. Eng. A, 528 (2011)1302–1309. [9] C. A. Tracy, A compressive test for high strength ceramic, J. Test. Eval. 15 (1987)14–19. [10] H. Awaji, T. Watanabe, Y. Nagano, Compressive testing of ceramic, Ceram. Int. 20 (1994)159–167. [11] P. Forquin, C. Denoual, C. E. Cottenot, F. Hild, Experiments and modelling of the compressive behavior of two SiC ceramic, Mech. Mater. 35 (2003) 987–1002. [12] W. Chen, G. Subhash, G. Ravichandran, Evaluation of ceramic specimen geometries used in Split-Hopkinson pressure bar, Dymat J. 1 (1994) 193–210. 17
ACCEPTED MANUSCRIPT [13] G. Subhash, G. Ravichandran, Split-Hopkinson pressure bar testing of ceramic, American Society for Materials Handbook, 8th edn. American Society for Metals International, Materials Park, OH, (2000) 497–504.
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[14] G. Sunny, F. Yuan, V. Prakash, J. Lewandowski, Design of inserts for Split-Hopkinson pressure bar
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testing of low strain-to-failure materials, Mech. Mater. 49 (2009) 479–490.
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[15] M. R. M. Aliha, M. R. Ayatollahi, Analysis of fracture initiation angle in some cracked ceramic using the generalized maximum tangential stress criterion, Int. J. Solids Struct. 49 (2012) 1877–1883. [16] A. Brückner-Foit, T. Fett, D. Munz, K. Schirmer, Discrimination of multiaxiality criteria with the
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Brazilian disc test, J. Eur. Ceram. Soc. 17 (1997) 689–696.
[17] L. Banks-Sills, N. Travitzky, D. Ashkenazi, Interface fracture properties of a bimaterial ceramic
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composite, Mech. Mater. 32 (2000) 711–722.
[18] Pathikumar Sellappan, Erheng Wang, Christian J. Espinoza Santos, Tommy On, John Lambros, Waltraud M. Kriven, Wave propagation through alumina-porous alumina laminates, J. Eur. Ceram.
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Soc. 35 (2015) 197–210.
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[19] Q. Z. Wang, W. Li, H. P. Xie, Dynamic split tensile test of Flattened Brazilian Disc of rock with
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SHPB setup, Mech. Mater. 41 (2009) 252–260. [20] Q. Z. Wang, L. Xing, Determination of fracture toughness K IC by using the Flattened Brazilian Disk specimen for rocks, Eng. Fract. Mech. 64 (1999) 193–201.
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[21] Q. Z. Wang, W. Li, X. L. Song, A method for testing dynamic tensile strength and elastic modulus of rock materials using SHPB, Pure Appl. Geophys. 163 (2006) 1091–1100. [22] Q. Z. Wang, X. M. Jia, S. Q. Kou, Z. X. Zhang, P. –A. Lindqvist, The Flattened Brazilian Disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results, Int. J. Rock Mech Min. 41 (2004) 245–253. [23] J. D. Clayton, A. L. Tonge, A nonlinear anisotropic elastic-inelastic constitutive model for polycrystalline ceramic and minerals with application to boron carbide, Int. J. Solids. Struct. 64–65 (2015) 191–207. [24] J. D. Clayton, Finite strain analysis of shock compression of brittle solids applied to titanium diboride, Int. J. Impact Eng. 73 (2014) 56–65. [25] H. Kolsky, An investigation of the mechanical properties of materials at very high rates of loading, Proc. Phys. Soc. B. 62 (1949) 676–700. 18
ACCEPTED MANUSCRIPT [26] W. N. Chen, B. Song, Split Hopkinson (Kolsky) Bar Design, Testing and Applications, Springer Press, New York, 2011. [27] ISRM Suggested methods for determining tensile strength of rock materials. Int. J. Rock. Mech. Min.
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Sci. Geomech. Abstr. 15 (1978) 99–103.
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[28] S. P. Timoshenko, J. N. Goodier, Theory of elasticity. McGraw-Hill Press, New York, 1970.
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[29] B. Paliwal, K. T. Ramesh, Effect of crack growth dynamics on the rate-sensitive behavior of hot-pressed boron carbide. Scripta. Mater. 57 (2007) 481–484.
[30] D. A. Hoke, M. A. Meyers, L. W. Meyer, G. T. Gary, Reaction synthesis/dynamic compaction of
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titanium diboride. Metall. Trans. A, 23 (1992) 77–86.
[31] F. Thevenot, Boron carbide-a comprehensive review. J. Eur. Ceram. Soc. 6 (1990) 205–225.
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[32] G. R. Johnson, T. J. Holmquist, Response of boron carbide subjected to large strains, high strain rates,
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and high pressures. J. Appl. Phys. 85 (1999) 8060–8073.
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ACCEPTED MANUSCRIPT Steel Inserts
Strain Gauge
Incident Bar Striker Bar
Damper
Strain Gauge
Transmitted Bar
Specimen of TiB2-B4C composite
Absorption Bar
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Pulse Shaper
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Comparison
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High Speed Camera
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Graphical abstract
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Cylindrical Specimen
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FBD
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ACCEPTED MANUSCRIPT Highlights 1) The improved experimental facility was verified by the 2D digital image correlation technique. 2) The strength and elastic modulus of TiB2-B4C composite at different strain rates was acquired.
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3) Higher compressive strength of TiB2-B4C composite than pure B4C and pure TiB2 is affected by
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microstructure and fracture mode.
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4) Strain rate sensitivity of TiB2-B4C composite is attributed to the presence of TiB2 phase.
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