The Brazilian test: a tool for measuring the toughness of a material

Int J Fract (2006) 139:455–460
DOI 10.1007/s10704-006-0067-6
O R I G I NA L A RT I C L E
The Brazilian test: a tool for measuring the toughness
of a material and its brittle to ductile transition
José Rafael Capua Proveti · Gérard Michot
Received: 17 November 2005/Accepted: 14 March 2006
© Springer Science+Business Media B.V. 2006
Abstract Due to their brittleness, assembling of
ceramics pieces is generally achieved through brazing but thermal stresses during cooling frequently
induce cracking of the material used for brazing.
In order to check if such damage is avoidable, it is
necessary to characterize the brittle to ductile transition (BDT) of the material. Simple compression
is not suited for crack studies, because of mixed
loading (mode II + compressive mode I cracking).
Another type of test, the cylinder splitting test,
known as the Brazilian test, can be carried out
by applying compressive forces on two opposite
generatrix of a cylinder: this causes a uniform tensile stress on the plane containing the axis of the
cylinder and the generatrix, leading to mode I cracking. The advantage of this test is to avoid expensive and random machining of brittle samples. This
study shows that the Brazilian test is well adapted
for the measurement of toughness and the characterization of the BDT of materials whose room
temperature behaviour is brittle (silicides, intermetallics etc.).
J. R. C. Proveti
UFES, CCE Departamento de Fisica, Av. Fernando
Ferrari S/N, Campus Goiabeiras. 29060 900, Vitoria ES,
Brasil
G. Michot (B)
Ecole des Mines de Nancy, UMR INPL-CNRS 7556,
Parc de Saurupt, F-54042 Nancy Cedex, France
e-mail: [email protected]
Keywords Mechanical test · Brazilian test ·
Toughness · Brittle to ductile transition · Silicide ·
Chalk · Complex potentials
1 Introduction
Brittleness is a handicap for the development of
ceramics. Their low ability to deform and low reliability in service restrict their applications. One
possible route for shaping of pieces is assemblage
by brazing. For example, silicon carbide supports
can be directly brazed on large silicon carbide mirrors designed for astronautical applications. However, cracking of the brazing materials is frequent
(Lamy 2000), probably due to thermal stressing
during processing. The determination of optimum
cooling conditions requires knowledge of the brittle to ductile behaviour of the brazing material.
Compression tests on cylinders are unsuitable
because of friction effects at the surfaces of the
cracks, loaded in mode II. This study shows that
the splitting test, also known as the Brazilian test,
is well suited to measure toughness and to characterize brittle to ductile transition.
2 The Brazilian test
A cylindrical disk is placed between two alumina
anvils attached to the jaws of the testing machine.
Ideally, two symmetric line loadings F/B (N/m, per
unit thickness) are applied along the X-axis (Fig. 1).
456
J. R. C. Proveti and G. Michot
Fig. 1 Principle of the
Brazilian test
y
sy
y
F
F
R
2M
R
x
z
F
txy
F
F
Fig. 2 Modified Brazilian test with machined flat contact
surfaces
The stress field in the disk can be calculated by
different techniques (Frocht 1947; Muskhelishvili
1954, 1977; Timoshenko and Goodier 1970).
In the plane y = 0, σyy is constant and equal to
F/π RB, except at X = ±R where it tends
towards infinity, explaining the easy development
of cracks at the contact points with the anvils. In
order to decrease these stress localizations, two flat
surfaces were introduced (Fig. 2), either by polishing or directly by controlled plastic deformation at
high temperature.
Hondros solved the elastic problem for this modified geometry years ago (1959). An other resolution technique, based on the complex potentials
method of Muskhelishvili (1977) and described by
Dugdale and Ruiz (1972), was used for this study,
coupled with the Bueckner method, well adapted
to the determination of stress intensity factors.
sx
F
x
of the material, sintered chalk, which is isotropic,
was chosen. Disks were sawed in 9.5 mm cylinders
after machining flat surfaces by polishing. A hole
of 1.5 mm diameter was drilled in the middle of the
disk in order to (i) introduce micro defects capable
of initiating cracking; (ii) enhance the local opening stress (roughly by a factor 3, since around the
y = 0 plane the normal stress is nearly constant
around the y = 0 plane). During compression the
onset of cracking is detected by a load drop. Then
the sample is unloaded, the lengths of the cracks
optically measured (a pair of cracks is generally
observed). The sample is loaded again, up to the
load drop: this critical load for crack propagation
is related to the crack length and the toughness of
the material through the calibration relation given
below:
2
2KMB
√ =
√
(1
−
υ) π
F R
a2
α
α
a R2 sin 2 + sin 2θ − 2
× cos θ
3/4 ,
4
2
R
1 + Ra 4 − 2 Ra 2 cos 2θ
where a is the crack length, sin θ = M/R and
tgα = sin 2θ/(cos 2θ − a2 /R2 ).
Among ten experiments, the two giving very
low toughness values, probably due to pre existing defects, were ignored. The eight others give the
toughness of the chalk as (1.15 ± 0.15) MPa m1/2 ,
a value close to silicon’s or most brittle materials.
3 Experiments
3.2 The brittle to ductile transition
3.1 Toughness measurements
Preliminary tests were performed at room temperature on various natural materials. Since the
results can be strongly distorted by the anisotropy
Ideally, the brazing alloy designed to assemble silicon carbide pieces should contain silicon and second, an element avid for carbon. To satisfy the
latter condition, silicides of transition metals were
The Brazilian test: a tool for measuring the toughness of a material
457
Fig. 3 Compression
curves of polycrystalline
Ni31 Si12 obtained at
different temperatures
under a strain rate of rate
2.8×10−3 s−1
developed (Gasse 1996; Rado et al. 1999).
Different cobalt and nickel silicides, exhibiting
various interface reactivity, were studied, but this
paper will focus on the behaviour of Ni31 Si12 in
order to underline the advantages of the Brazilian
test. This hexagonal compound melts at 1282◦ C.
Alloying is first achieved by induction melting of
powders of the pure constitutive elements in a cold
crucible. Then the homogenized material is cast
into cylindrical ingots of 7 mm diameter, in a graphite block to rapidly cool down the material. The
samples are finally obtained by sawing off 3.5 mm
thick slices. The flat surfaces were obtained by controlled plastic deformation at high temperature.
Mechanical tests were performed under inert gas
(500 hPa) within a temperature range 400–1150◦ C,
at deformation rates 5 × 10−6 –3 × 10−3 s−1 .
3.2.1 Classical compression tests
In order to assess the improvement provided by
the Brazilian test, classical compression tests were
first performed. Cylindrical samples, 15 mm long
and 7 mm in diameter, of polycrystalline Ni31 Si12
were compressed parallel to their revolution axis.
The results obtained at strain rate of 2.8.10−3 are
shown in Fig. 3. First the material deforms elastically, then yields plastically—the lower the test
temperature, the higher the yielding stress.
Usually, cracking cannot be directly detected since
load drops on the compression curve are very rare.
A post mortem observation by optical microscopy
indicates cracking at 800 and 850◦ C. Under such
dynamic loading, the transition from a low energyabsorbing fracture mode to a high energyabsorbing ductile mode results from the
competition between the increasing stored elastic
energy on the one hand, and the plastic relaxation
induced by nucleation and motion of dislocations
on the other hand. For this loading rate, the brittle to ductile transition temperature probably lies
between 850 and 900◦ C.
If the strain rate is decreased to 5 × 6 10−6 s−1 ,
the transition shifts towards lower temperature:
more time is allotted to deformation and this counterbalances the decrease in dislocation mobility.
The general aspect of the compression curves is
modified (Fig. 4). A yield drop, characteristic of
materials with a low density of mobile dislocations,
is noticed. But again smooth curves are observed
(excepted for the complete failure at 650◦ C of the
sample), and no load drops are detected.
In fact, cracks rarely develop under mode I opening on compressed samples. It is assumed that friction force between opposite surfaces of the crack
submitted to mode II (or III) loading lowers the
elastic energy release rate. To monitor crack generation, a mode I opening must be involved: this is
characteristic for the Brazilian test.
458
J. R. C. Proveti and G. Michot
Fig. 4 Compression
curves of polycrystalline
Ni31 Si12 obtained at
different temperatures
under a strain rate of rate
5.7 10−6 s−1
Fig. 5 Brazilian test :
stress versus the relative
anvils displacements
(l̇/l0 = 2.8 10−4 s−1 at
different temperatures)
80
70
60
50
40
30
20
10
0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.0
3.2.2 Results for the Brazilian tests
Cracking is clearly detected by load drops (Fig. 5)
allowing a precise determination of the brittle range.
Since the stress field is inhomogeneous in the disk,
the σ stress values plotted in Fig. 5 correspond to
the normal stress σyy acting on the y = 0 plane at
the centre of the disk, linked to the external applied
load F by the following relation:
σyy = 2F π DB
In the high temperature compression device, the
maximum load is limited by the brittleness of the
graphite jaws supporting the alumina anvils. Hence
Fig. 6 Observed central cracks developed at 825◦ C (left)
and 950◦ C (right) under l̇/l0 = 2.8 × 10−4 s−1
the compression test at 750◦ C was interrupted and
the material considered as brittle. At 800◦ C the
sample breaks into many pieces. For the remaining
The Brazilian test: a tool for measuring the toughness of a material
459
Fig. 7 Transition
(straight continuous line)
from ductile (full
symbols) to brittle (open
symbols) behaviours, as
determined by the
Brazilian test applied to
polycrystalline Ni31 Si12 at
different temperatures
and loading rates. As a
matter of interest, the
dotted line corresponds to
the same transition as
determined by classical
compression tests
experiments, the sample exhibited central cracking analysis (Fig. 6), as expected from the stress
analysis.
In the elastic deformation range, a nearly constant loading rate σ̇ can be associated to the
imposed l̇/l0 value. Thus the parameter σ̇ will
be used to describe the time dependant part of the
brittle to ductile transition.
All the results obtained for different stress rates
σ̇ are collected in the Arrhenius plot type of Fig. 7.
A straight line can be drawn between two domains,
one with full symbols characterizing a ductile
behaviour, one with open symbols characterizing
a brittle behaviour. The slope of this line gives the
activation energy Q for the process at the transition
temperature:
4.1 ≤ Q ≤ 4.9 eV
Both plastic deformation and brittle to ductile
transition (BDT) are thermally activated. Since the
two activation energies are very close in silicon
crystals submitted to various experimental conditions, it is assumed that the BDT is controlled by
the dislocation mobility (see for instance Hirsch
and Roberts (1996). The Brazilian test can easily
(but indirectly) evaluate an important plastic property like the activation energy for glide; in that case,
the measured value, 4.5 eV is high but not surprising, considering the size and the complexity of the
cell. Of course, classical compression tests can be
used, but it should be noticed that the transition
line as determined by this technique is shifted by
about 200◦ C (Fig. 7), in other words, the material
appears more ductile that it is. This fact conveys
the inability of this technique to detect the early
cracking.
4 Conclusions
The Brazilian test is well adapted to measure the
fracture resistance of materials, which are brittle
at room temperature. Their toughness and their
BDT can be measured. Concerning the latter property, more accurate experiments can be designed
by testing pre-cracked poly or single crystals. These
experiments are close to those performed on silicon single crystals (Michot et al. 1999), in which
the loading rate σ̇ was replaced by a variable more
representative of fracture problems, K̇.
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