‫فرع السيراميك ومواد البناء‬/‫المرحلة الثالثة‬
Characteristic of Ceramic Materials/mechanical properties
1-7 MECHANICAL TESTING
With the increasing role of ceramics in technology, further understanding of
mechanical properties has become increasingly more important. This has resulted in
the use and standardization of various test methods to better understand and quantify
mechanical properties.
1-7.1 Strength
One of the most important properties for characterizing a material is strength.
The characterization of the fracture strength (approximately equal to ultimate strength
for brittle materials) distribution is needed when ceramic design for structural
applications involves failure probability as criteria. Various test methods are
employed to determine the fracture strength of a given ceramic material. Usually, the
fracture strength is equated to the maximum stress at the point of fracture, which
requires that the stress distribution in the test specimen be known. A common source
of error in tests measuring fracture strength is that the strength of ceramic materials is
strongly influenced by the test specimen’s size, geometry, and surface finish.
Tension
The tensile test equipment consists of two main parts, the test specimen grip
holding the actual test specimen and the interface attachment that connects the test
specimen grip to the test machine. The grip should be designed to reduce any
eccentricity in order to maintain a uniaxial stress state. The attachment interfacing
between the test specimen grip and the test machine is usually one of two designs:
flexible, self-aligning and fixed, alignable. Ideally, the stress state will be
characterized by the simple equation:
Where σ is the normal stress, P is the applied force, and A is the cross sectional area.
However, the actual stress state in the gauge section, σgs, will include error from
eccentricity in the testing equipment and/or the test specimen and can be
characterized as:
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‫فرع السيراميك ومواد البناء‬/‫المرحلة الثالثة‬
Characteristic of Ceramic Materials/mechanical properties
where
Fig. 1 Schematic of tensile, flexure, and compressive setups.
with e being the eccentricity distance, r being the distance from the point in the gauge
section at which the stress is being measured to the centroid, and I being the moment
of inertia in the gauge section cross section.
*American Society for Testing and Materials (ASTM),† ‘‘Standard Test Method for
Tensile Strenth of Monolithic Advanced Ceramics at Ambient Temperatures,’’
C1273-95
*ASTM, ‘‘Standard Test Method for Tensile Strength of Monolithic Advanced
Ceramics at Elevated Temperatures,’’ C1366-97
Compression
The compression strength of ceramic materials is usually much greater than
that in tension. Consequently, tensile strength is usually the critical factor in terms
design. The compression test usually consists of two load blocks exerting a
compressive force on a cylindrical test specimen. The test specimen should be
uniform to avoid buckling of individual layers aligned with the applied load.
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‫فرع السيراميك ومواد البناء‬/‫المرحلة الثالثة‬
Characteristic of Ceramic Materials/mechanical properties
Common sources of error are size mismatches between the load block and
specimen, surface irregularities, and eccentric loading as explained in the tensile
testing section. The first three errors bring about excessive stresses in the ends of the
test specimen, which can cause failures in the non-gauge section of the test specimen.
Eccentricity, as in tensile testing, reduces uniformity in the gauge section stress state.
*JISC, ‘‘Testing Method for Compressive Strength of High Performance Ceramics,’’
R1608-1990
*ASTM, ‘‘Standard Test Method for Compressive (Crushing) Strength of Fired
White ware Materials,’’ C773-88
Flexure
Testing in flexure typically involves a three- or four-point loading of a test
specimen as shown in Fig. 2. Compared to tension and compression tests, flexure
tests are less expensive, simpler in setup, and easier to adapt to elevated temperature
testing. The applied moment, M, yields the equation for uniaxial normal stress, σ:
where the moment of inertia I is (bh3)/12 (b = width and h= height) and C is the
distance from the neutral axis to the outer surface of the test specimen. Given that the
moment M= P (Lo- Li)/4 (Lo = outer span, Li = inner span) and y= h/2 we can
substitute into the equation to find the fracture strength, Sƒ, which is the maximum
tensile stress obtained at the fracture force, Pƒ:
Various sources of internal and external errors in the testing process can affect the
measured results of flexure tests. Errors classified as ‘‘internal’’ involve deviations
from simple beam theory and involve test specimen geometry and properties. A test
specimen with an initial curvature resulting from residual stresses generated during
machining would cause an internal error. Another example of an internal error would
be excessive specimen deflection during testing. Support point frictional forces at
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‫فرع السيراميك ومواد البناء‬/‫المرحلة الثالثة‬
Characteristic of Ceramic Materials/mechanical properties
large deflections will have a component aligned with the applied force that will
increase the applied moment. ‘‘External’’ errors are those classified as being caused
by incorrect test fixture geometry. Improper location of the inner load points is an
example that causes external error. Another example is the generation of torque on
the test specimen. This can be caused by an initially twisted test specimen, unparallel
line loads, or nonuniform line loads at the contact points. External error can also
occur from compressive contact stresses at the support pins, which can result in
localized crushing. This error can be reduced by using support pins above a critical
radius rc.
To minimize the errors associated with flexure testing, the test specimen and test
fixtures must adhere to certain restraints and standards. Test specimen geometry has
been standardized based on error considerations. A common geometry in the United
States is 3 by 4 by 50 mm for the test specimen and inner and outer spans of 20 and
40 mm, respectively, for the fixtures. The test specimen must be isotropic and
homogeneous to apply the maximum tensile stress equation previously given. In
addition, the specimen should be as free as possible of surface defects as the
maximum tensile stress occurs on the surface.
In comparing the three- and four-point flexure test methods, it is found that the
four-point method is more appropriate for determining fracture strength because no
shear stresses are generated as in the three-point test method. The three point test
method with its simpler geometry, however, may be more attractive for tests in which
stable crack growth must be induced into the test specimen.
*JISC, ‘‘Testing Method for Flexural Strength of Fin Ceramics at Elevated
Temperature,’’ R1604-1995
*ASTM, ‘‘Standard Test Method for Flexural Strength of Advanced Ceramics at
Ambient Temperatures,’’ C1161-94
*ASTM, ‘‘Standard Test Method for Flexural Strength of Advanced Ceramics at
Elevated Temperatures,’’ C1211-92
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‫فرع السيراميك ومواد البناء‬/‫المرحلة الثالثة‬
Characteristic of Ceramic Materials/mechanical properties
Fig. 2 Three- and four-point flexure testing and resulting stress state
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