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Properties of Ceramic Materials
1-3.6 VISCOUS FLOW
Viscous flow is an important mechanism for permanent deformation in glasses.
Viscous flow is also a mechanism by which ceramics containing IGFs undergo creep.
So it is a characteristic that is both beneficial and deleterious, but unavoidable at high
temperature. Under most conditions oxide glasses behave as Newtonian fluids, i.e.,
the strain rate, dγ/dt, is a linear function of the applied shear stress, τ. An important
consequence of this behavior is that when we draw glasses, such as during the
formation of optical fibers, the cross section reduces at a constant rate. In other
words, we do not get necking of narrow sections of the fiber. At high stress levels
non-Newtonian behavior, which is common in polymers, may be observed in oxide
glasses. Models of viscous flow include the following:
Absolute-rate theory: Viscous flow is a thermally activated process involving a highenergy activated state. Viscosity follows an Arrhenius expression with activation
energy for viscous flow, Ev. The preexponential term has a weaker dependence on
temperature than the exponential term. This theory is applicable only over a narrow
range of temperatures.
Free-volume theory: Molecular motion involves the availability of vacancies. The
vacancy volume is the free volume, VF, of the liquid, approximately the difference in
volume of the liquid, VL, and crystalline, Vc, forms. VF is a function of temperature. D
is a constant close to unity. The Williams–Landel–Ferry (WLF) equation uses a
similar approach in which fg is the fraction of free volume at Tg, about 0.025, and βL
and βC are the volumetric thermal expansion coefficients of the liquid and solid,
respectively.
Excess-entropy theory: There is a decrease in the configurationally entropy, Sc, of a
liquid when it is cooled down—fewer molecular arrangements are possible. This
makes deformation more difficult. Es is proportional to the potential energy barrier
for molecular rearrangement.
The Vogel–Fulcher– Tammann (VFT) equation is an empirical expression relating
η to T and can be interpreted in terms of the different models. The VLT expression is
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Properties of Ceramic Materials
accurate over a wide range of temperatures and is widely used in many practical
applications.
The viscosity of a specific glass depends on temperature as shown in Figure 1.22
Glass blowing is often performed at viscosities of ~10 MPa・s. This is at the top end
of the working range, which extends from 1 kPa・s to 10 MPa・s. If the viscosity
was at the fining temperature (~5 Pa・s) the gas would have been able to escape
easily. If the viscosity were too high the glass would not have been able to deform in
this way. There is also time dependence to the viscosity, particularly near Tg and
above. At these temperatures structural relaxation occurs.
FIGURE 1.22 Temperature dependence of
Viscosity for a soda lime- silica glass.
*EQUATIONS FOR VISCOUS FLOW:
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Properties of Ceramic Materials
1-4. Friction, wear and abrasion
The relative displacement, or sliding, of two parts maintained in contact does
not take place without resistance. The tangential force T needed for ensuring the
movement depends on the normal force N at contact: this is the phenomenon of
friction. This phenomenon is well defined by Coulomb formula T = µN, where µ is
the coefficient of friction. The friction causes wear of the two parts at the level of the
contact surfaces. For a couple of given materials, the wear, as well as the value of µ,
depends on the temperature, the atmosphere or even on the sliding speed. This wear
is generally harmful to the in-service behavior of the part and we will look for
operating conditions and surface treatments which will minimize it. It is, however,
desirable in machining by abrasion. Ceramics are excellent materials for applications
where friction is present by virtue of their high hardness, their chemical inertia and
their temperature stability. Their applications include friction parts and seal
components for the automobile industry (sealing items for water pump), gears, valve
heads, precision ball bearings, cutting tools, conduits for casting of refractory metals,
abrasives, etc.
1-4.1 Wear
Wear resistance is the ability of a material to resist mechanical (or chemicalmechanical) abrasion. There are two main mechanisms that lead to removal of
material from the surface of a ceramic:
- Grain pullout: In polycrystalline ceramics with weak grain boundaries
- Cracking: Fracture due to abrasion, gouging, or erosion
Wear resistance is usually closely associated with hardness and corrosion
resistance. Erosion usually specifies wear of a material by an abrasive in a fluid, the
type of situation encountered when ceramics are polished.
Although ceramics are generally characterized as being wear resistant their
commercial use as wear parts is less than 10% of the overall market. Alumina is the
most commonly used wear-resistant ceramic. One of the early applications was in
seal faces for rotary water pumps for automobiles. Alumina is particularly suitable
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Properties of Ceramic Materials
because it is resistant to engine cooling fluids. Another application for alumina,
which we mentioned, is in total hip prosthesis. In terms of wear rates at the contact
surfaces between the ball and socket, alumina is far superior to alternative metal and
polymer systems.
Alumina and toughened zirconia ceramics are used in the wire drawing industry as
capstans, pulleys, and guides. Improved product quality, longer component service
life, and lower manufacturing costs have been attributed to the use of ceramics. For
example, ceramic capstans last up to 10 times longer than carbide-coated capstans.
As with other mechanical properties there are standard tests to measure wear
resistance. The main method is described in ASTM G99, which uses a pin-on-disk
apparatus. This test is used to measure sliding wear of ceramics and ceramic coatings.
1-4-2 Friction and wear
Wear can be measured at the depth of the friction track by the volume of
material removed per unit length of friction or by volume of unit length and normal
force (specific wear rate). Ceramic wear is more of the abrasive type and is
characterized by the generation of debris giving rise to propagation of cracks in type I
and II mixed (opening and straight sliding). It increases drastically above the critical
load.
The volume of wear V is proportional to the contact load N and to the friction
distance x. We may therefore account for the wear by using the specific wear rate
defined by:
Vs = V/ (xN)
(1.22)
It is difficult to measure the quantity of wear. It can be done indirectly by
measuring the decrease in the mass of the specimen, which would also include all
mass changes due to physico-chemical processes or the adherence of debris, or by
measuring the volume of material removed along the friction path by optical or
electronic microscope. The first method gives an overall result with accuracy
increasing as the specimen size gets smaller.
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Properties of Ceramic Materials
Friction and wear are complex phenomena, whose mechanisms are not well
known. Following the classic model of friction and wear in the presence of adhesion,
it is possible to relate Vs to the hardness and to the geometry of areas of contact. Let
us suppose, for example, that the contact zones are disks of radius (a) and that their
number is n. The force distribution on the entire surface is given by the relationship:
n = N/ (Hπa2)
(1.23)
Where H is the hardness of the softer material.
We suppose that each adhesion zone disappears after a displacement over a distance
of 2a, while new zones of contact get formed. The total number nT of “points” of
adhesion for a friction distance x will be:
nT = nx/(2a) = Nx/(2πHa3)
(1.24)
Therefore, if k is the probability of forming a volume of wear debris at a point
corresponding to a hemisphere of radius a, the total quantity of wear is given by
equation:
V = knT2πa3/3 = kNx/ (3H)
(1.25)
which gives a specific wear:
Vs = k/ (3H)
(1.26)
The factor k is known as the coefficient of wear. For a conical indenter with halfangle at apex θ, k will be 3cotanθ/π and Vs = cotanθ/ (πH). This relationship confirms
the observation that harder materials are more wear resistant. The wear resistance
also increases with toughness and, in fact, it appears that the ratio KIc/H governs it. A
brittleness index B has in fact been defined as the inverse of the ratio: B = H/KIc
It also varies very appreciably with the sliding speed: in most cases, the wear rate
goes through a maximum for speeds between 0.1 and 10 ms-1.
The atmosphere also plays an important role on friction and wear. In particular,
friction is higher under vacuum and humidity leads to physico-chemical
modifications of the contact surfaces, which is clearly reflected in the tribological
behavior (in general µ and Vs increase with humidity).
Under friction at high speed and under small load, and in ambient air, silicon
nitride is presently the ceramic which offers best wear resistance.
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Properties of Ceramic Materials
1-4.3. Abrasion
With the increase in load or contact speed between a hard object (diamond
indenter, for example) and a ceramic material, we see the transition from a relatively
soft regime of scratching without removal of material to a plowing regime with
removal of material (mechanical polishing) and finally to a rapid wear regime with
peeling corresponding to mechanical abrasion. Materials with the highest abrasion
resistance are used as abrasives and are meant for application in polishing surface
finishing, or in machining (grinding). We then find that diamond, boron nitride (cBN)
silicon and aluminum carbide are high on the list.
Diamond tools are widely used for shaping grinding wheels. Single tip diamond
tools are used to cut Al mirror (high precision). Polycrystalline diamond may be used
to cut aluminum alloys (small business though). Major technical drawbacks of
diamond are its reaction with many metals and its oxidation above 600°C. Problems
occur in particular with cast-iron, titanium, nickel, etc. The grinding of light metals
such as aluminum and Ni-based alloys is difficult. Local burning may occur. As a
matter of fact, although cBN is less hard than diamond, it is more suitable as far as
ferrous alloys are concerned. The market for cBN is growing rapidly (10%/year).
Three families of abrasive are defined, namely:
– Coated abrasives (suitable for plastics and metals);
– Bonded abrasives (suitable for hard metals and ceramics);
– Super abrasives (suitable for hard ceramics and crystals).
In order to understand the mechanisms which govern machining by abrasion, we
should analyze the different interactions between the tool and the material being
machined. For a grinding operation, we refer to the following four interactions:
abrasive/material, binder (grinding wheel)/material, abrasive/debris and binder/
debris. This difficult problem is further complicated by physico-chemical processes
linked particularly to the use of “cutting” fluids, which not only acts as a lubricant,
but also condition thermodynamic machining parameters (contact temperature) and
the kinetics of removal of debris. The understanding of abrasion is still at a very
superficial level. All the same, technical solutions, which are satisfactory in most
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Properties of Ceramic Materials
cases, have been found due to the ingenuity and know-how of industries confronted
with this problem. For a given material and a particular surface condition to be
obtained, the fabrication scheme consists of a set machine/grinding wheel/ lubricant /
machining parameters. Super abrasives with diamond, cubic boron nitride or other
hard ceramics base, as well as new binders for grinding wheels, are in the process of
development.
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