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TRANSCRIPT
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IMAGE ANALYSIS & QUANTITATIVE METALLOGRAPHY
A. N. Sinha
Scientist
National Metallurgical Laboratory
Jamshedpur - 831 007
INTRODUCTION
The metallographic examination constitutes simply a planar
section view of a three dimensional structure. It is not enough to
recognize this fact; one must also understand how shape in a three
dimensional construction can degenerate into traces in random planar
section. In fact, one must be able by mental visual skill to recreate from
slices of hard boiled egg, the oblate ellipsoid when they came. For
example, an inclusion, or porosity can appear to be different when
observed in different planer section and the assessment of volume will
be qualitative and only quantitative to the extent of visual judgement.
Actual quantitative evaluation of inclusion and porosity, their shape and
size distribution are very important for predicting the mechanical
properties of the metals and alloys. Similarly, the grain size is another
important factor in the hardenability of steels, ductility of brass and in
the ductile-brittle transition of alloys. The amount of ferrite in stainless
steels is a factor in their foregeability. The average flake size of graphite
is a control parameter in the strength of gray cast iron. These are only a
few instances where numerical limits to metallographic parameters are
practical factors in quality or production control. Since we can not
obtain large number of specimens to get correct three dimensional
picture, quantitative analysis is an appropriate alternative. Two factors
must be assumed in all such quantitative studies. The planar section or
sections be representative of the whole. In the matter of arriving at
average values for dimensions of distributed particles one must have a
knowledge of the actual or approximate shape of the particles. Few
particles are actually perfectly spherical. but this is a mathematical
convenience.
Kinds of Measurement
The quantities one may wish to determine can be derived from
one or more of several kinds of measurements based upon real analysis,
point counting, and lineal analysis.
Areal analysis involves the measurement with a planimeter (or by
other means) of the area of a microconstituent intercepted by a planar
cross section. Point counting involves the superposition of an
appropriate line grid such as transparent graph paper into a
microstructural feature, counting the number per unit area of grid
intersections which fall on that type of feature. Lineal analysis involves
the estimate of the proportion per unit length of a random line
superimposed on a micrograph occupied by the specific type of
microstructural feature. Lineal analysis involves the estimate of the
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proportion per unit length of a random line superimposed on a
micrograph occupied by the specific type of microstructural feature. In
another version of this, a count is made of the number of intersections
per unit length which a random line makes with a specific type of
distributed particle.
A basic rule in quantitative observations made on planar section is
that all three ratios are equal and that in turn they are equal to the
volume fraction.
Va a Na La
V
= A
=
N =
L
Earlier it used to be made manually and quantitative
measurements were very time consuming and difficult. Thanks to
computer technology, a large variety of Automatic Image Analysers are
available and now we can measure grain size, particle size, distribution,
aspect ration of odd shaped flakes of cast iron, retained austenite in
ferrite, and ferrite in stainless steel with ease. However, the basic
principle remains the same.
Measurement of Grain size
Most of the basic difficulties in quantitative metallographv are
contained in the problem of assignment of numerical magnitudes to the
grains of a polycrystalline aggregate. All the grains may not be of same
size and so on. Therefore, an average statistical concept is taken into
consideration assuming all grains to be spherical.
One of the basic measurements in grain size determination is the
number of grains counted per unit area of planar field of observation.
From analysis of the distributions of sections which will be encountered
in space occupied by truncated octahedra, the ASTM system gives the
following relationship :
n 2N-1
where n = number of grains per square inch.
at 100 x magnification
& N= ASTM grain size number
Standard charts are available and by comparing the
microstructures at 100 x magnification one can determine the ASTM
grain size of the microstructures. Image Analysers are now available for
this with suitable programming.
Measurement of Particle Sizes
The volume fraction of a dispersed phase can be determined by
simple lineal, areal, or point count analysis and this determination is
independent of the shape, ideal or otherwise, which the particles
posses. This is not true, however. for the problem of estimating the
number of particles per unit volume and the dimensions of particles. In
both the cases, the shape of the particle must be known. In practice
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one must be able to decide whether the distributed phase approximates
a sphere, a disc, a rod, an ellipsoid, or some such ideal geometric
shape. Relationships have been derived for particle density and
dimensions using parameters measurable on a polished section. Each
relationship pertains to a specific geometric shape and assumes a
uniform size distribution. The problem of nonuniform size distribution
must be considered separately. However, all these rigorous
mathematical derivations are beyond the scope of present course.
Quantitative metallography equipments can do these without any human
factor, except to use them with skill. A histogram of particle size and
volume can obtained easily which gives the idea of distribution.
Normally inclusions are determined by this method. However, for day to
day work, ASTM charts are available which are designated A, B, C & D
for Sulphides, Alumina, Silicates and Oxides types of inclusions. They
are thick and thin. All these charts are at 100 x magnifications. By
comparison with these charts, inclusions of the microstructures can be
identified and quantified. The volume % of these inclusions can be
measured with the help of Image Analyser.
Automatic Image Analyser
Now-a-days a large number of versatile programmed Automatic
Image Analysers are available for quantitative metallography. These can
be operated manually also. The image analyser is interfaced with an
optical microscope which produces microstructures and is transmitted
to TV screen with the help of TV camera. It works on the basic
principle of differentiating between the greyness of phases or particles,
which can be initiated electronically as per choice. Once initiated.
these phases or particles can be measured both manually as well as by
automatic computer programming. The image analysers have got three
options, namely area, count and intercept functions. Sometimes we may
like to edit the picture on TV screen. Therefore, image editors are also
available with image analyser. Besides optical microscope. the TV
camera can be shifted for analysing the photographs also. No
metallography laboratory can be complete without image analyser.
However. for routine type of industrial work ASTM charts for
ASTM grain size. inclusions charts for Alumina. Sulphides, Silicates and
Oxides are sufficient, as the image analysers are very costly and are
needed for advanced quantitative metallography only. Here, one thing
must be mentioned that special etching is needed to produce different
greyness to the required phases. without which image analyzer is
useless. Probably, colour metallography laboratory is a must.
REFERENCES
1.
R.T. Howard and M.Cohen. Trans. AIME 172, 413-426 (1947).
2.
C.S,Smith and L.Guttman, Trans. AIME, 197, 81-87 (1953).
3.
J.E.Hillard and J.W.Cahn. Trans, AIME, 221, 344-352. 1961.
4.
R.L.Fullman, Trans, AIME, 197, 447-452 (1953).
5.
William Rostoker and James R.Dvovak, Interprtation of
Metallographic Structures, Academic Press, New York, 1965.
6. Metals Handbook - ASM
J-3
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