Kuliah v. Metalografi Kuantitatif

QUANTITATIVE QUANTITATIVE METALLOGRAPHYMETALLOGRAPHY

Perhitungan Metalografi KuantitatifPerhitungan Metalografi Kuantitatif

• Ukuran besar butir

• Persentase fasa dan endapan

• Distribusi fasa dan endapan

• Teknik Pengukuran Khusus– Microhardness– Ketebalan lapisan– Kekasaran permukaan

IntroductionIntroduction

• Many materials investigations are concern with the relationship between the bulk properties of materials and their microstructures.

• In the past qualitative relationship have often been reported but as metallurgy become transformed from an art to science quantitative relationship become necessary.

IntroductionIntroduction

• For this reason it is desirable to be able to describe quantitatively the microstructure of material as observed by metallographic technique.

• The two most common cases to which quantitative metallography can be applied are:– The determination of grain size and shape and the

grain size distribution in a single phase polycrystalline structure

– The size, shape, volume fraction of component phase in multi-phase structure

Grain Size in a Single Phase StructureGrain Size in a Single Phase Structure

• The most common method of performing quantitative grain size measurements consists of taking random sections through bulk specimens and preparing the surfaces of the sections for optical microscopy by standard metallographic techniques.

• The methods of revealing grain structure on a polished section include: – Chemical etching – Polarized light microscopy – Several miscellaneous techniques

Chemical EtchingChemical Etching

• this results in either the preferential attack of grain boundaries by the etching solution (grain boundary grooving) or orientation-sensitive surface roughening.

• In the former case light impinging on grain boundaries is reflected outside the objective aperture of the microscope while in the latter case the amount of light reflected outside the aperture varies from grain to grain.

Polarized Light MicroscopyPolarized Light Microscopy

• if an anisotropic material is examined in the as-polished condition between crossed polars the intensity of transmitted light is a function of the crystallographic orientation of the surface.

• Thus contrast is obtained between regions of different orientation, i.e. grains.

Several miscellaneous techniquesSeveral miscellaneous techniques

• Several miscellaneous techniques can be used which rely on the deposition of a surface layer, the thickness or roughness of which is a function of orientation.

• These techniques include heat-tinting, stain-etching in chemical solution and anodizing.

• Grain size can be reported in one of several ways: – Mean distance between grain boundaries

intersected by random lines across the section.

– Number of grains per unit area of section. – Average area per grain on the section.

Direct Measurement TechniquesDirect Measurement Techniques

• Linier intercept methods – in this approach random line are drawn across photomicrograph of the grain structure and the number of grain boundaries intersect for a given random line is counted.

• This parameter is denoted nL and represents the inverse of the mean intersected grain width.


• The average number of grain per unit area is conveniently measuredsimply by counting the number of grains on a given area of micrograph

• This parameter, nA, is the inverse of the mean intersected grain area. • In both the above techniques it is obviously important to know the magnification of the micrograph accurately.


• The mean intersected grain area can be measured directly by means of a planimeter.• If it is assumed that all the grains are the same size and take the shape of truncated octahedra

(tetrakaidecahedra) the following relationships are valid:

nV = 0.422nL3 = 0.677nA

3/2

• Where nv = number of grain per unit volume


• The grain diameter d is defined as the diameter of a circle having the same area as the maximum area obtaining by sectioning tetrakaidecahedron and is given by:

AL nnd

53.178.1

The ratio of grain interfacial area S to grain volume V is given by :

LnV

S2

The parameters d and S/V are used frequently in investigations of mechanical properties; for example it has been found that the yield strength of steel is a function of the inverse square root of d.

Grain Size in Multi-Phase StructureGrain Size in Multi-Phase Structure

• The simplest technique for determining the relative phase fractions in a microstructure consisting a several phases is tu cut up a photomicrograph along phase boundaries and weigh the amounts of photographic paper corresponding to each phase.

• This gives the area fraction of each phase.• Alternatively a planimeter can be

employed to give the same parameter.


• A random line technique can also be used on two phase structure. In this case the fractions of a length of random line passing across each phase are measured

• A point counting method can also be employed. A square grid of lines is superimposed on a micrograph of the structure and the interactions of grid lines are taken as points. The number of points falling in each phase is then counted.


• The volume fraction of a phase in multiphase structure can be easily determined from th above techniques since :

V

V

A

A

L

L

N

N

Where :

N = number of point falling in a phase

N = total number of point counted

L = length of random line across a phase

L = total length of random line

= volume fraction

ContohContohObtain a representative area and produce a micrograph showing the overall structure. A second, higher resolution picture might be required to show detail.

The grain size and volume fraction of ferrite/pearlite in the annealed/normalised steels must be measured. Grain size is measured using a linear intercept technique, the volume fraction of each of the microconstituents is measured using point counting.

Point Counting Point Counting

• In the point counting method a square grid is superimposed over the sample microstructure.

• The grid spacing should be similar in size, or smaller than the features being measured.

• The number of points to be counted depends on both the volume fraction of the phase and the desired level of precision in the result.

• On a rectangular grid consisting of 10x10 or 100 points (the total number of points is PT), the number of grid intersections, points, intersecting the phase of interest is counted, Pa.

Point CountingPoint CountingThe volume fraction of the phase is then

if this is repeated for n fields of view then

Point CountingPoint Counting

clearly for each field of view the value of fa will vary so there will be an error in fa

enables the standard error to be calculated. However, this appraoch does not allow the calculation of the number of points required to get a given error, for that we use

where s is the error, fa, the volume fraction of phase a and N, the total number of points. You should aim for an error of ±1%

Grain Size - Linear InterceptGrain Size - Linear InterceptA straight line is drawn across the sample and its length is noted - to do this you will need to use the stage micrometer to determine the real length of the line, l.

Linear InterceptLinear InterceptAlternatively, a circle may be drawn with a known diameter and hence circumference (l). Again the interecpts of all the grain boundaries with the circle are counted (n) and the grain size determined as above.

Linear InterceptLinear Intercept

The number of grain boundary intercepts is then counted, n, and the grain size, d, determined

The error in the measurement is

where sd is the standard deviation of all of the measurements of d that were made and N is the number of grains measured. It follows from the above equation that for a given error, s, the number of grains to be measured can be estimated. Obviously the process is iterative since sd changes as the number of measurments is increased

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Kuliah v. Metalografi Kuantitatif