RusMet2004009GrigorevKOR1-1

ISSN 0036-0295, Russian Metallurgy (Metally), Vol. 2020, No. 4, pp. 493–499. © Pleiades Publishing, Ltd., 2020.
Russian Text © The Author(s), 2019, published in Deformatsiya i Razrushenie Materialov, 2019, No. 12, pp. 29–36.
DIAGNOSTICS
AND MECHANICAL TEST TECHNIQUES
Determination of the Mechanical Properties of the Materials
Produced by Electric Pulse Powder Consolidation
E. G. Grigor’eva, V. Yu. Gol’tsevb, *, N. A. Gribovb, A. V. Osintsevb,
A. S. Plotnikova, and K. L. Smirnova
a
Institute of Structural Macrokinetics and the Problems of Materials Science, Russian Academy of Sciences,
Chernogolovka, Moscow oblast, 142432 Russia
b
National Research Nuclear University MEPhI, Moscow, 115409 Russia
*e-mail: gvy587@gmail.com
Received July 19, 2019; revised August 29, 2019; accepted September 3, 2019
Abstract—The field of applicability of bending of thin disks test on an annular support and the “Brazilian test”
for short cylinders is discussed. These methods are used to determine the tensile strengths of the materials
formed by electric pulse powder consolidation. These techniques of testing small samples make it possible to
study the influence of technological factors on the strengths of the consolidated materials.
Keywords: electric pulse powder consolidation, bending of a thin disk on an annular support, Brazilian test,
tensile strength, small samples
DOI: 10.1134/S0036029520040096
1. INTRODUCTION
The methods of electric pulse powder consolidation (spark plasma sintering [1–4], flash sintering
[5‒7], microwave sintering [8–10], high-voltage consolidation [11–13]) are characterized by a high heating
rate, comparatively low integral temperatures, and
short consolidation processes and make it possible to
form compositions from hard-to-sinter powder materials. The ability to manufacture bulk nanomaterials
makes these methods very important.
A number of products of modern engineering are
disks with a diameter of at most 10–15 mm and a
thickness of 1–10 mm [13]. The standard methods of
mechanical testing are not applicable to such smallsized samples; in this case, indirect methods, in particular, bending of thin disks on an annular support
and compression of short cylindrical samples in the
diametrical plane according to the “Brazilian test”
scheme, are used to estimate the strength properties of
materials. These methods are designed to test brittle
materials. Several methods are known for testing thin
disks by bending on an annular support. They differ in
both the indenter that transfers the load and the support device [14–17]. The breaking stresses are determined using the formulas of the theory of bending of
thin plates [18] on the assumption of fracture under
the maximum tensile stresses. The Brazilian test
[19, 20] is used to determine the tensile strength of
rocks: samples with a diameter of at least 50 mm with
a thickness-to-diameter ratio of 0.2–0.75 are tested.
The purpose of this work is to estimate the possibility of using the results of bending of thin disks on an
annular support and testing of short cylinders according to the Brazilian test scheme to determine the tensile strength of brittle materials formed by electric
pulse powder consolidation.
2. EXPERIMENTAL
2.1. Model Materials
We used model materials, namely, SCCH-10 gray
cast iron according to GOST 1412 and MPG-6 and
ARV-1 graphite to adjust the techniques of testing thin
disks on an annular support and the Brazilian test
compression of short cylinders. Their mechanical
properties are given in the Table 1. The strength of cast
iron was refined in tensile test of 12 fivefold proportional specimens 10 mm in diameter according to
GOST 1497 and in compression of 12 specimens 8 mm
in diameter and 12 mm in height according to GOST
25.503. The strength of MPG-6 graphite was refined
when testing 4 samples by compression in accordance
with GOST 25.503 and by static three-point bending
of flat specimens 4 mm thick and 8 mm high, and the
distance between the supports was 40 mm. The test
results were close to the tabulated values except for the
results of bending of graphite specimens: their strength
turned out to be close to the tensile strength.
493
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GRIGOR’EV et al.
Table 1. Strengths of the model materials under various
loading conditions
Material
bend
σcomp
, σtens
, τsh
u
u , σu
f ,
Source
MPa MPa MPa MPa
SSch-10-40 cast iron 530 100
MPG-6 graphite
73.6 25
ARV-1 graphite
45
12
280
34.3
15
110
—
—
[21]
[22]
[23]
The letters in subscript indicate the type of loading: comp. stands
for compression; tens, for tension; bend., bending; and sh., shear.
2.2. Aluminum Dioxide
We used the following two powder fractions formed
by oxidation of dispersed aluminum in the air plasma
of an electric arc discharge: nanosized and ultradispersed (UD) fractions with an average particle size of
45 and 150 nm, respectively. The particles had a spherical shape. The specific surface area of the nanopowder was 35.8 m2/g and that of the UD powder was
10.1 m2/g. The powders were consolidated by sparkplasma sintering in a SPS Labox 625 (Sinter Land
Inc., Japan) setup in graphite equipment in vacuum at
a pressure of 50 MPa, a heating rate of 100°C/min, the
maximum temperature of 1400°C, and a holding time
of 10 min at the maximum temperature.
2.3. Composite Ceramic β-Si5AlON7
(SiC, TiN, BN, Y2O3)
The powders of the initial refractory compounds
were formed by self-propagating high-temperature
synthesis. The sintering of β-Si5AlON7 and h-BN
powders was based on filtration combustion in nitro-
gen of reaction mixtures containing silicon, aluminum, and boron. The initial nitrogen pressure in the
reactor was 8–10 MPa. To ensure the necessary degree
of conversion of the combustible components, a diluent (namely, β-Si5AlON7 and h-BN powders) was
additionally introduced into the composition of the
reaction mixtures. According to X-ray diffraction
(XRD) results, the initial β-Si5AlON7, h-BN, and TiN
powders did not contain impurity phases, and insignificant traces of residual β-Si3N4 powder were noted
in the composition of the β-SiC powder.
The preparation of sintering mixtures was combined with grinding of the synthesized powders and
was carried out in a high-speed planetary mill. The
specific surface area of the mixtures after this treatment increased by a factor of 4–6. The following conditions of sintering of β-Si5AlON7-based powder compositions were used: heating from room temperature
to 600°C without loading followed by heating to 1550–
1800°C at a pressure of 50 MPa. The heating rate was
50°C/min and the holding time at the maximum temperature was 5 min. Sintering was carried out in an
SPS Labox 625 setup.
2.4. VNZh-90 Alloy
The samples of a heavy tungsten alloy were prepared by high-voltage consolidation from an industrial
powder of the following composition (wt %): 6.93 Ni,
3.12 Fe, W for balance. The powder was formed by
mechanical mixing of the components. The theoretical density of the powder was 17.13 g/cm3 at an average
particle size of 6.03 μm. The shape of the particles was
close to spherical and partial agglomeration took place
(Fig. 1). XRD analysis revealed the presence of FeNi3.
We studied various consolidation conditions and varied the applied voltage from 4.5 to 5.8 kV and the pressure from 100 to 250 MPa.
2.5. Tests of Thin Disks on an Annular Support
We used the technique of loading a disk on an
annular support described in [14]. The loading scheme
is shown in Fig. 2. The tests were carried out using an
Instron machine. The calculation of the breaking
stress was carried out according to the formula
()
50 µm
Fig. 1. VNZh alloy powder (scanning electron microscopy).
2
⎡
⎤
(1)
σ = 3P 2 ⎢4 − (1 − μ ) d + 4 (1 + μ ) ln D ⎥ ,
D
d⎦
8πh ⎣
where P is the maximum load during the fracture of
the sample, D is the inside diameter of the support
ring, d is the diameter of the flat indenter; h is the sample thickness, and μ is Poisson’s ratio.
The formula was obtained under the assumption
that the contact pressure is uniformly distributed over
the contact spot of the indenter with the disk and the
disk is hinged against the inner edge of the ring support. In addition, the diameter of the disk was assumed
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495
Y
P
Z
X
1
2
h
3
d
4
Fig. 3. Calculation model for testing short cylinders
according to the Brazilian test scheme.
D
Fig. 2. Scheme of testing a disk on an annular support in
loading by a flat-tip indenter: (1) indenter, (2) holder,
(3) sample, and (4) support ring.
to be slightly larger than the inner diameter of the
annular support.
An analysis of the state of stress of the model sample, which was performed using the verified ANSYS
Mechanical calculation complex of version 16.2
[24, 25], showed the presence of a triaxial state of
stress in the indenter–disk contact interaction region.
On the reverse side of the disk (as would be expected),
a plane stress state arises with the maximum circumferential tensile stresses, which are the cause of brittle
fracture of the sample [26]. Fracture nucleation is possible under the maximum tangential stresses in the
near-contact zone of loading.
2.6. Brazilian Test
The ultimate tensile strengths of the materials
under study were determined during compressive tests
according to the Brazilian test technique.
Short cylindrical samples were loaded by uniformly
distributed forces along diametrical generatrices with
(Fig. 3). The strength of the material was determined
by the formula [20]
σt = 2P ,
πtD
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where P is the maximal load to be withstood by the
sample and t and D are the sample thickness and
diameter, respectively.
The possibility of applying this method to materials
of a nongeological origin was substantiated in [27]. A
calculation analysis with the study of the effect of the
thickness-to-diameter ratio of the cylinder on the
maximum tensile stresses showed that parameter σt is
a good estimate of the first principal stress averaged in
the YZ plane of the cylinder (see Fig. 3). As a result of
simulation, we found that the local maximum principal stresses can exceed the average σt stresses by a factor of 2.5. This finding can affect the applicability of
Eq. (2) to brittle materials sensitive to stress concentration.
3. RESULTS AND DISCUSSION
3.1. Analysis of the Field of Application of the Technique
of Bending Thin Disks on an Annular Support
We tested disks 10–15 mm in diameter and 1–
1.5 mm in thickness made of SCh-10 cast iron and
disks 15 mm in diameter and 1.7–1.8 mm in thickness
made of MPG-6 graphite. The test results indicate no
brittle fracture of the cast iron samples and brittle fracture of the graphite samples (Figs. 4, 5).
The presence of a smooth decrease in the load after
the maximum in the bending diagram of the cast iron
disks (see Fig. 4a) is associated with slow controlled
growth and opening of cracks under tensile stresses. In
the process of deformation, a cast-iron disk bends,
which is unacceptable in determining the strength of a
brittle material, and the disk material is indented in
the indenter contact area. In this case, circumferential
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GRIGOR’EV et al.
2.0
0.10
(a)
0.08
Load, kN
1.5
Load, kN
(b)
1.0
0.06
0.04
0.5
0.02
0
0.1
0.2
0.3
Displacement, mm
0.4
0
0.05
0.10
0.15
Displacement, mm
0.20
Fig. 4. Characteristic load–displacement diagrams obtained upon bending disks 10 mm in diameter and 1.5 mm in thickness
made of (a) SCh-10 cast iron and (b) MPG-6 graphite.
(a)
cracks form on the back of the disk and cause radial
cracks to develop under the action of tensile stresses
(see Fig. 5a).
The test results showed that the breaking stress of
cast iron determined by Eq. (1) does not coincide with
its tensile strength and is numerically closer to its compressive strength. Therefore, Eq. (1) cannot be used to
determine the ultimate tensile strength of the material
that manifests itself as a plastic material in bending.
When testing the MPG-6 graphite disks, a completely different picture was observed. For example,
brittle dynamic fracture of graphite into several parts
occurs (see Fig. 5b) in an almost linear machine bending diagram up to fracture (see Fig. 4b). The level of
breaking stresses calculated by Eq. (1) is approximately 20% higher than the level of tensile strength of
the material.
3.2. Analysis of the Field of Application
of the Brazilian Test
(b)
Fig. 5. Character of fracture of disks 10 mm in diameter
made of (a) SCh-10 cast iron and (b) MPG-6 graphite.
According to the Brazilian test scheme, short cylindrical samples made of SCh-10 cast iron and ARV-1
graphite were studied [27]. The cast iron cylinders had
D × t sizes of 10 × 4 and 15 × 4 mm. Figure 6a shows
the compression diagram of a 10 × 4 cast iron cylinder,
which was recorded according to the Brazilian test
scheme.
Initial cracks in the cast iron sample formed in the
contact area, where the maximum tangential stresses
are operative. The smooth decrease in the load after
the maximum is due to slow crack propagation and the
separation of one half of the sample from the other. No
explosive failure, which is characteristic of brittle fracture induced by normal stresses, was observed. The
breaking stress and the ultimate tensile strength of cast
iron are comparable, σt ≈ σfu . Therefore, the test
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7
0.8
(a)
497
(b)
6
0.6
Load, kN
Load, kN
5
4
3
2
0.4
0.2
1
0
0.2
0.4
0.6
Displacement, mm
0.8
0
0.1
0.2
Displacement, mm
0.3
Fig. 6. Machine Brazilian test compressive diagrams of cylinders made of cast iron 10 × 4 mm in size and (b) ARV-1 graphite
8 × 8 mm in size.
results of the small cast iron cylinders according to the
Brazilian test scheme confirmed the possibility of
application of Eq. (2) to determine the tensile strength
of the material.
Graphite cylinders were of the following three D × t
sizes: 8 × 4, 8 × 8, and 8 × 12 mm. The characteristic
compression diagram of a 8 × 8 mm graphite cylinder
in the diametral plane is shown in Fig. 6b. Graphite
turned out to be a more brittle material. The graphite
cylinder failed dynamically in the linear section of the
diagram at the maximum load with the separation of
the sample into fragments. Initial cracks in the contact
region, which caused the fracture of the sample, were
revealed. The ratio of the tensile strength to the breaking stress of graphite determined by Eq. (2) was σt ≈
For β-Si5AlON7, we studied the effect of various
additives and the disk thickness on the bending
strength. Disks with a diameter of 10 mm (D = 7.5 mm,
d = 3.75 mm; see Fig. 2) and 15 mm (D = 11.5 mm, d =
3.75 mm) were tested. The samples failed dynamically
at the maximum load in the linear section of the diagram without crack jumps (Fig. 7). The fracture of all
β-Si5AlON7 samples was brittle, with separation into
many small fragments. A decrease in the strength of
the material with an increase in the sample thickness
from 1 to 2 mm was revealed (Fig. 8). A weak depen0.6
0.7σfu ; that is, the fracture strength estimated by
Eq. (2) is 1.5 times lower than the true rupture
strength of the material.
0.4
Load, kN
Therefore, Eq. (2), which is used to determine the
tensile strength of brittle materials having a linear
compression diagram up to failure, should be corrected by increasing the calculation result by 1.5 times.
0.5
0.3
0.2
3.3. Deformation and Fracture
of Thin Ceramic Disks
0.1
A comparative study of the compacts of aluminum
dioxide made of nano- and UD powders showed a
higher strength of the UD powder compacts. For
example, the fracture resistance in bending the disks
10 mm in diameter and 1–1.3 mm in thickness made
of UD and nanopowders was 174 and 141 MPa,
respectively.
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0
0.02
0.04
Displacement, mm
0.06
Fig. 7. Machine bending diagram of a β-Si5AlON7 disk
15 mm in diameter and 1.5 mm in thickness.
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GRIGOR’EV et al.
800
300
700
250
Stress, MPa
Stress, MPa
600
200
150
100
0
1.0
300
1.5
Thickness, mm
2.0
200
200
Stress, MPa
250
150
2
4
6
Y2 O 3 , %
8
4.5
5.0
5.5
Sintering voltage, kV
6.0
Fig. 10. Fracture strength of VNZh-90 alloy vs. the capacitor bank voltage during high-voltage electric pulse sintering at a pressure of (individual point) 150, (1) 200, and
(2) 250 MPa.
250
0
2
100
0
4.0
Fig. 8. Breaking stress vs. the sample thickness (disk
10 mm in diameter) for β-Si5AlON7 + 30% BN + 8% Y2O3
ceramic.
100
1
400
200
50
Stress, MPa
500
10
150
100
50
Fig. 9. Breaking stress vs. the Y2O3 content in
β-Si5AlON7-based ceramic.
0
1
dence of the strength of β-Si5AlON7 on the Y2O3 content in the range under study was noted (Fig. 9).
These results indicate that the technique of testing
thin disks on an annular support can be used to estimate the influence of technological factors on the
strength of the compacts formed by electric pulse
powder consolidation.
3.4. Deformation and Fracture of Short Cylinders
Made of VNZh Alloy and Al2O3
The tests of short cylindrical samples made it possible to determine the consolidation parameters that
provide the optimal strength properties of the VNZh90 alloy. Figure 10 shows the dependence of the
strength of the alloy on the sintering stress; samples
were formed at various pressures. In all cases, the fracture strength of the material was calculated by Eq. (2).
The strength of the samples sintered at a pressure of
200 MPa increased when the stress increased to 5.4 kV,
then decreased, and stabilized at a high level. The
increase and decrease in the strength occurred against
the development of plastic deformation, which pre-
3
5
7
9
11
Thickness, mm
Fig. 11. Fracture strength of aluminum oxide made of a
nanopowder measured according to the Brazilian test
scheme. The left point is the result of testing a disk 10 mm
in diameter and 1.3 mm in thickness.
ceded the brittle fracture of the samples. The samples
sintered at 250 MPa failed in a brittle manner without
noticeable traces of plastic deformation. The sample
sintered at 150 MPa (point in Fig. 10) has the highest
strength (at the same voltage of 5.5 kV). Significant
plasticity preceded the fracture of the samples.
The tensile strength of the cylindrical samples
10 mm in diameter made of aluminum dioxide nanopowder decreased almost linearly with increasing
thickness (Fig. 11), demonstrating the effect of the
scale factor during brittle fracture. Note that the
results of testing short cylinders according to the Brazilian test scheme are in good agreement with the
results of bending of thin aluminum oxide disks with
10 mm in diameter and of 1.5 mm in thickness on an
annular support.
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4. CONCLUSIONS
The bending of small disks on an annular support
and the compression of short cylinders according to
the Brazilian test scheme make it possible to determine the ultimate tensile strength of the brittle materials formed by spark plasma sintering and high-voltage powder consolidation. These techniques were
used to study the influence of a number of technological factors on the strength of the consolidated materials, namely, the effect of various additives to a
β-Si5AlON7 alloy, the pressure in sintering of VNZh
alloy samples, and the effect of the particle size and
the aluminum dioxide sample thickness.
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Translated by K. Shakhlevich