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INFLUENCE OF THE STRAIN RATE ON THE TENSILE STRENGTH

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INFLUENCE OF THE STRAIN RATE ON THE TENSILE STRENGTH Powered By Docstoc
					       INFLUENCE OF THE STRAIN RATE ON THE TENSILE STRENGTH IN ALUMINAS OF
                              DIFFERENT PURITY



                                        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



                                                     e-mail: fgalvez@mater.upm.es




         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.




1.   INTRODUCTION

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 [1],
[2], 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 [3] and ceramics [4] at low strain rates, and has been recently
introduced to high strain rates [5], [6], [7].
       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 [7], Najar [8] or Gálvez [9], 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 [10], and is presented in a separated paper
2.    MATERIALS

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
                                                                                                          8                4
                                                                               A94 & A995
     A98       3877         366       9717            2.4
                                                                                Splitting
  A995         3905         391      10004            10.4                                               12                6
                                                                               A98 & AZR
     AZR       4027         348       9292            2.0                       Spalling                  8               100




3.    EXPERIMENTAL

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 [9]. The tensile stress in the loading plane is obtained from
the following expression:

                                                                        2P
                                                                σt =                                                                (1)
                                                                       πLD

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
                                                     Spliting
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 [9] 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
following expression:

                                              •
                                                                 1  ∂σ t 
                                              ε              =                                                         (3)
                                                                 E  ∂t  FracturePlane
                                                  Spalling




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
strain rate.
       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.
           Material
                                   A1        A2                  C            D
                                                                                                                  Mean tensile strength (MPa)
           94% Al2O3               5              4              9            8
                                                                                                                                     Testing device
           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.


           500                                                                                     500

                      Material: A94                                                                           Material: A98

           400                                                                                     400
                                                                              C
                                                                                                                                                                      C
           300                                                                                     300
                                                                                         σ (MPa)
 σ (MPa)




                                                                     B                                                                                       B
                                                                                             t
     t




           200                                                                                     200
                                                  A                                                                    A
                               A

           100                                                                                     100



            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 )
                                              eq                                                                                           eq

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.

           500                                                                                     500

                      Material: A99                                                                           Material: AZR

           400                                                                                     400


                                                                                                                                                                      C
                                                                                                   300
                                                                                         σ (MPa)




           300
 σ (MPa)




                                                                                                                                                             B
                                                                              C
                                                                     B
                                                                                             t
     t




           200                                                                                     200
                                                                                                                                           A
                               A                  A                                                                    A

           100                                                                                     100



            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 )
                                              eq                                                                                           eq

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.




References


[1]    Nemat-Nasser S., Deng H. “Strain rate effect on brittle failure in compression”. Acta metall. mater. Vol
       42, No 3, pp 1013-1024, 1994
[2]    Lankford J. “Temperature-strain rate dependance of compressive strength and damage mechanisms in
       aluminium oxide”. J.of Mat. Sci. 16 pp. 1567-1578, 1981.
[3]    Neville A.M. “Properties of concrete”. Pitman publishing. 1973.
[4]    Ovri J.E.O., Davies T. J. “Diametral compression of silicon nitride”. Materials science and engineering. 96,
       pp 109-116, 1987.
[5]    Rodríguez J., Navarro C., Sánchez-Gálvez, V. “Numerical assessment of the dynamic tension test using
       the Split Hopkinson Bar” J. of Testing and Evaluation Vol.22 No.4 pp 335-342, 1994.
[6]   Rodríguez J., Navarro C., Sánchez-Gálvez, V. “Splitting tests: an alternative to determine the dynamic
      tensile strenth of ceramic materials”. Journal de Physique IV, Colloque C8 Supplément au Journal de
      Physique III, nº4, pp.101-106 septembre 1994.
[7]   Johnstone C., Ruiz C., “Dynamic Testing of Ceramics under Tensile Stress”, Int. J. Solids Structures, Vol.
      32, No. 17/18, pp. 2647-2656, 1995.
[8]   Najar J. “Dynamic tensile fracture phenomena at wave propagation in ceramic bars”. Journal de Physique
      IV, Colloque C8 Supplément au Journal de Physique III, nº4, pp.647-652 septembre 1994.
[9]   Gálvez Díaz-Rubio F., Rodríguez J., Sánchez-Gálvez, V. “Tensile Strength Measurements of Ceramic
      Materials at High Rates of Strain”. Journal de Physique IV, Colloque C3 Supplément au Journal de
      Physique III, nº7, pp.151-156 d’Août 1997.
[10] Gálvez F. “Caracterización mecánica de materiales cerámicos avanzados a altas velocidades de
     deformación”. Ph. D. Thesis. 1999.

				
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