INFLUENCE OF THE STRAIN RATE ON THE TENSILE STRENGTH IN ALUMINAS OF
F. Gálvez, J.Rodríguez and V. Sánchez Gálvez
Department of Materials Science. ETSI Caminos Canales y Puertos
Polytechnic University of Madrid. Ciudad Universitaria s/n. 28040 Madrid, Spain
Abstract. It is well known that the properties of the materials may be different as the strain rate increases. Advanced
ceramic materials such as aluminas, could present an increase in their strength as the strain rate becomes higher. In
this paper the investigation is focused on the influence of the strain rate on the tensile strength of alumina. The
influence of this variable on this property is experimentally analysed by means of two different kind of tests carried
out from low to high strain rates. The splitting test of brittle materials is a testing technique widely used at low strain
rates. It has been recently extended to dynamic conditions using the Hopkinson split pressure bar. In this work this
method is used both in static and dynamic conditions with servohydraulic machines and a Hopkinson bar. The
tensile strength of alumina has been measured at three different strain rates. The spalling test of long bars is an
additional technique that provides the dynamic tensile strength of brittle materials in uniaxial conditions. The test
procedure and the experimental details are also presented and discussed in a separate paper. This technique has also
been used to measure dynamic tensile strength of alumina at higher strain rates. The influence of the strain rate on
the tensile strength is presented and a comparison between the two kind of tests is also discussed. To identify the
physical mechanisms causing the failure, a microscope analysis of fracture surfaces using SEM has also been
performed. The study has been applied to the different specimens tested at low and high strain rates with the two
different kind of tests. The results of the fractographic analysis are presented and discussed.
The effect of the strain rate on the mechanical properties of materials is well known. Mechanical properties of
ceramic materials are affected by the strain rate, and its effect on the compressive strength has been studied ,
, showing an increase in strength with strain rate. But the effect of strain rate under tensile loads has not been
widely studied. In this paper, an experimental programme of tensile tests of alumina based ceramics with different
testing devices covering strain rates from 10-6 s-1 to 103 s-1 is presented.
The splitting tests of short discs and the spalling tests of long bars are the basis of the programme. The
splitting tests are performed both in static machines as well as in a Hopkinson bar. This technique is widely used
since years in brittle materials as concrete  and ceramics  at low strain rates, and has been recently
introduced to high strain rates , , .
The spalling test of long bars is a novel technique that provides the tensile strength of brittle materials at
high strain rates under uniaxial stress conditions. This technique is based on the wave propagation in long bars
and has been used by some authors like Johnstone , Najar  or Gálvez , but the procedure to obtain the
tensile strength has not been still verified. The correct method to obtain the test results with this method has also
been studied in detail by Gálvez , and is presented in a separated paper
To analyse the effect of the strain rate on the tensile strength of ceramic materials, four different ceramic materials
were selected, three aluminas with different purity, 94% (A94), 98% (A98) and 99.5% (A995) and an alumina
reinforced with zirconia (AZR). The density and the elastic modulus were measured in order to obtain the elastic
wave velocity and the results are summarised in Table 1. To measure the elastic modulus an impulse excitation
technique has been used. To determine the average grain size, a polish of the specimen followed by a chemical
etching was done and the data obtained is included in the same table. The materials, manufactured by Morgan
Matroc, were directly supplied with the actual specimen geometry except in the case of 98% alumina and AZR,
where the specimens were mechanised from 100-mm square tiles. The specimen geometry is discs for the
splitting tests and rods for the spalling tests as indicated in Table 2.
Table 1. Properties of materials measured before testing. Table 2. Geometry of specimens for the different tests.
Material ρ (Kg/m3) E (GPa) c (m/s) Grain size (µm) Specimen Geometry Diameter (mm) Length (mm)
A94 3658 303 9108 8.3 Splitting
A94 & A995
A98 3877 366 9717 2.4
A995 3905 391 10004 10.4 12 6
A98 & AZR
AZR 4027 348 9292 2.0 Spalling 8 100
To cover a wide range of strain rate, two kinds of tests have been employed. The diametral compression of short
cylinders, called splitting tests, and the spalling test of long bars. The splitting tests were performed in two
different loading devices. Tests at low and medium strain rates were performed in a servohydraulic testing
machine with low and fast displacement control respectively, and tests at high strain rates were performed in a
Hopkinson bar. The spalling tests were used to achieve higher strain rates and to ensure a uniaxial stress state in
the specimen during the tests.
The machine used for the splitting tests at low and medium strain rates was an Instron 8501 with a 25 kN
and a 100 kN load cells. The test was performed with displacement control at velocities of 0.2 µm/s and 2000
µm/s, and the load history was recorded. To ensure that the load is applied in a loading point, the specimen is
positioned between two ceramic supports and the load plates were protected with two steel discs. The testing
method has been previously described by the authors . The tensile stress in the loading plane is obtained from
the following expression:
σt = (1)
where P is the load applied, D the specimen diameter and L the specimen length. The strain rate in each test is
obtained from the history of stresses in the loading plane with the following expression:
1 ∂σ t
ε = (2)
E ∂t LoadPlane
The mean strain rates achieved were 10-6 s-1 in the slower tests, and 10-2 s-1 in the faster ones.
The splitting tests at high strain rates were performed in a Hopkinson bar. The specimen was positioned
between two small ceramic blocks to ensure loading in a point, and two steel discs of the same material of the
bars were employed to protect the bars. The force transmitted to the specimen was recorded by means of strain
gauges attached to the output bar. The tensile stresses and the strain rate in the specimen were derived with the
same expression than that used in the static tests. The strain rate achieved using the Hopkinson bar has been 102
s-1 for the splitting tests.
The spalling tests were used to achieve higher strain rates and to ensure a uniaxial stress state in the
specimen during the tests. The principles of this testing method have been previously presented  and the
procedure to obtain the tensile strength is fully described in a separate paper. The mean strain rate reached in the
spalling tests has been up to 103 s-1 and has been obtained from the stresses derived in the fracture plane with the
1 ∂σ t
ε = (3)
E ∂t FracturePlane
4. RESULTS AND DISCUSSION
The number of tests performed in each condition is shown in Table 3 and the results of tensile strength and its
standard deviation are presented in Table 4. The data obtained for the different materials exhibit a wide scatter,
which can be inherent of ceramics. A Weibull approach could be recommended, but not enough specimens have
been tested. Nevertheless the results obtained are enough to show the tendency of the tensile strength with the
The results for 94% alumina are shown in Figure 1, for 98% alumina in Figure 2, for 99.5% alumina in
Figure 3 and for alumina reinforced with zirconia in Figure 4. In all cases no changes in the tensile strength in the
range 10-6 to 10-2 s-1 have been observed. When testing with the Hopkinson bar a strain rate of 102 s-1 has been
obtained and the tensile strength presents now an increment compared to static tests. The strength is increased in
40% for the A94, 37% for the A98, 50% for the A995 and 84% for the AZR. When the spalling technique is
employed, the results are greater compared to splitting Hopkinson tests. The increase of strain rate is about an
order of magnitude from 102 to 103 s-1 and the increase in the strength is 23% for the A94, 20% for the A98,
12% for the A995 and 13% for the AZR. These results show a clear dependence of the tensile strength with the
strain rate, but the changes in the testing technique cannot be neglected.
To analyse the possible changes in the fracture mode, a fractographic analysis with a scanning electron
microscope was done. The specimens were metalised in the fracture surface and examined in detail. The results
have been the same in all materials and the micrographs for A94 are shown in next figures. The fracture surface
of a splitting specimen tested at a strain rate of 10-6 s-1 is shown in Figure 5, a splitting test in Hopkinson bar at
102 s-1 in Figure 6, a spalling test in Figure 7 and a detail of a spalling test in Figure 8. In all cases a brittle fracture
is shown and an absence of plasticity is clearly observed. All specimens show a predominant transgranular
cracking, but with some intergranular borders. Cleavage marks can be easily identified in all cases. Nevertheless,
at different tests and different conditions no changes in fracture mode can be assumed, and no change on the
fracture mode with the strain rate has been identified.
Table 3. Number of tests done with each technique. Number of tests
Testing device Table 4. Results of tests with each loading method.
A1 A2 C D
Mean tensile strength (MPa)
94% Al2O3 5 4 9 8
98% Al2O3 6 0 6 5 Material
A1 A2 B C
99.5% Al2O3 10 5 8 7
94% Al2O3 161 (23) 181 (8) 278 (28) 358 (51)
AZR 7 1 6 5
98% Al2O3 179 (21) - 285 (31) 329 (78)
99.5% Al2O3 161 (26) 163 (29) 243 (43) 271 (38)
AZR 155 (12) 172 288 (30) 322 (35)
Note to Table 3 and Table 4: A1 represents splitting tests at very low strain rate, A2 splitting tests at intermediate strain rate, B
splitting tests in Hopkinson bar and C spalling tests of long bars.
Material: A94 Material: A98
0 0 -8 -6 -4 -2 0 2 4
-8 -6 -4 -2 0 2 4 10 10 10 10 10 10 10
10 10 10 10 10 10 10
. . -1
ε (s -1) ε (s )
Figure 1: Tensile strength and its standard deviation versus Figure 3: Tensile strength and its standard deviation
strain rate in 94% alumina. versus strain rate in 98% alumina.
Material: A99 Material: AZR
A A A
-8 -6 -4 -2 0 2 4 -8 -6 -4 -2 0 2 4
10 10 10 10 10 10 10 10 10 10 10 10 10 10
. . -1
ε (s ) -1
ε (s )
Figure 2: Tensile strength and its standard deviation versus Figure 4: Ttensile strength and its standard deviation
strain rate in 99.5% alumina. versus strain rate in alumina reinforced with zirconia.
Note to Figure 1, Figure 2, Figure 3 and Figure 4: Results of splitting tests in servohydraulic machines (A), the same type of
tests in Hopkinson bar (B) and spalling tests of long bars (C).
Figure 5. 1000x fracture surface of a splitting test of 94% Figure 7. 1000x fracture surface of a spalling test of 94%
alumina carried out in static machine. Strain rate ≈10-6 s -1. alumina. Strain rate ≈103 s -1.
Figure 6. 1000x fracture surface of a splitting test of 94% Figure 8. 2000x fracture surface of a spalling test of 94%
alumina carried out in Hopkinson bar. Strain rate ≈102 s -1. alumina. Strain rate ≈103 s -1.
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