OCTOBER 26, 2015
QUANTITATIVE METALLOGRAPHY
LAB REPORT
ABEL J JAIME
ABEL J JAIME (DW5835), JOSHUA KIRBY (FW8822), JAKE AMATO (FX4974)
BE 131
1
Introduction
Metallography refers to the study of the microstructure of metallic alloys; this can be secondly
stated as the scientific discipline of making observations and determining the atomic and
chemical structures that occur within an inclusion of the-the study of spatial distribution of the
spatial distribution of the metal constituents.
Grain size has effects that are measurable on most mechanical properties. There is a directly
related to their crystal structures. Metals are mostly crystalline in nature of composition and
contain internal boundaries. These limits are commonly known as "grain boundaries." When
processing a metal or a metal alloy, the atoms occurring within each growing grain are lined up
in a specific pattern, this depending on the crystal structure (Callister, 2005). With growth, each
grain will sooner or later impact others and form an interface where the atomic locations change.
To be able to characterize the microstructure of materials in a quantitative manner, the
quantitative metallographic is applied. There are several techniques for carrying out quantitative
metallographic some of the measurements that can be made in this experiment includes the
determination of the volume fraction of a phase or constituent. Additionally, there is the
measurement of the grain sizes in polycrystalline metals and their alloys, also a measurement of
the size and finally size distribution of particles, assessment of the shape of particles, and spacing
between particles. In the experiment, Nodular and pure cast iron were used. Nodular cast iron has
properties such as bending without breakage. The main explanation being that it contains
graphite that gives it flexibility. Cast iron, however, is brittle and breaks when bent. This is
because it mainly consists of carbon and silica.
Materials
•
Metallurgical microscope with a TV camera
•
Television monitor
•
Stage micrometer
•
Metal specimens
•
Transparent plastic sheets
•
Metric ruler.
Methods
Begin by placing a metal specimen of high purity iron on the microscope and image it onto the
screen. The television monitor shows display grains boundaries of the Iron. The screen shows a
small division of millimeters distance on the screen thus can be proved by the use of a metric
ruler going horizontal and vertical. The values obtained from the ruler measurements from the
screen, and the original dimensions of the specimen are used to calculate the magnification of the
microscope.
Once the magnification of the microscope is confirmed, place a transparent plastic sheet onto the
television screen. The plastic sheet should have a square of one hundred fifty by one hundred
fifty millimeters drawn on it. This is used to record the grain boundaries placed onto the box in
the plastic sheet. Count each grain boundary inside the box and count the corners as a fourth and
2
edges as a half. Repeat this procedure five times at different locations of the sample and record
newly selected areas.
After recording the samples for box plastic sheet, place a new transparent plastic sheet with a
circle drawn in between the sheet. The circle should be drawn with a diameter of one hundred
and fifty millimeters in the sheet. Now count and record the number of intersections that grain
boundaries had made contact with the circle. Once the data’s has been written down use the
microscope and move the sample around to a new selected area and record the area for five more
times.
Now switch the sample of the high purity iron with new nodular cast iron sample and replace the
plastic sheet paper with a new plastic sheet paper with five by five test grid on the television
screen. Once the sheet has been put in place, particles that lay in between each grid are counted
and recorded. Each particle counts as one and boundary of the nodule count as a half. Repeat this
counting and recording procedure on fourteen times on the other grids shown on the screen.
Table 1
D1
Horizontal
Vertical
D2
28
29
D3
29
29
Dave
d
29
28.667
30
29.333
magnification (M) Mave
2.8667
286.6667 290
2.9333
293.333 290
Table 2
Trial
# of 1
1
2
3
4
5
N1
N
n
Table 3
# of 1/2
5
6
7
7
7
# of 1/4
4
2
2
4
4
Total
3
3
5
3
3
Average
7.75
7.75
9.25
9.75
9.75
8.85
32.89244
2.121563
0.085127
3
Trial
1
2
3
4
5
# of intercepts Average
13
12
12
12
11
12
0.0255
7.3848
0.1354
2.398336
Plm
Pl
L3
n
Table 4
Trial
# of 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Pp
Vv
% of 1/2 Total
Average
8
7
11.5
13
7
16.5
7
3
8.5
4.0
4
0
8
5
10.5
8
7
11.5
16
9
20.5
7.0
5
4
2
2
3.0
11
5
13.5
6
3
7.5
12
5
14.5
10
7
13.5
10.46
3
2
4.5
0.263888
0.263888
Average = 11.5+16.5+8.5+4.0+10.5+11.5+20.5+7+3+13.5+7.5+14.5+13.5+4.5
=146.5/14
= 10.46
Results and Discussion
4
Quantitative Metallography can be tested within a lab, but it can also be found through
the use of the equations given in the lab manual. Table 1 was used to find magnification given by
d
Average Number
the equation M 
and M: N M 
.
0.01 mm
150  150
Where M is the magnification,
These numbers make sense since they are so close to each other making the percentage error in
the calculation slight. The Magnification is used later to find the grain size of single phase alloy
of high purity iron. High purity iron contains a grain size of 0.085mm.
Table Two discusses the measurement of mean grain intercept at a distance of 150 mm from a
diameter of a circle by finding the average number of intersections on the circle test at three
positions. Then taking the value obtained from the average and divide it by 150 * pies.
Plm= average number of intersections / (150*3.142)
12
(150∗3.142)
= 0.025
This value helps find the actual numbers of intercepts by multiplying that value to the
magnification results found earlier. Finally by taking the inverse of the value obtained we
calculate the mean grain intercept length.
Two phase alloy of iron and carbon contains an average of 9.5 boundaries of graphite nodules.
From the average values from the boundary calculations, we can obtain the volume fraction of
graphite can be found by taking the average and divide it by 36 that give a result of 0.26mm3. All
this values are under the results obtained in Table 4.
𝑉𝑜𝑙𝑢𝑚𝑒 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =
𝑎𝑣𝑒𝑟𝑎𝑔𝑒
36
= 0.2639𝑚𝑚3
Conclusion
This lab experiment successfully enabled us to measure the grain size of a single phase alloy and
the nodular cast iron. From the results achieved in the experiment, we made a comparison with
the actual values and realized that the values that they come close to the real values. However,
the values showed slight variations due to factors such as improper specimen preparation since
the process of polishing the specimen cannot be done to microscopic fineness. Additionally,
metallic structures are affected by physical changes such as temperature variation hence making
the results to have a slight variation with the actual values.
CITATIONS
Callister, W. (2005). Fundamentals of materials science and engineering: An integrated approach (2nd
ed.). Hoboken, NJ: John Wiley & Sons.
5
APPENDIX
Matlab Code
D1h=28;
D2h=29;
D3h=29;
Daveh= (D1h+D2h+D3h)/3;
D1v=29;
D2v=29;
D3v=30;
Davev=(D1v+D2v+D3v)/3;
dh=Daveh/10;
dv=Davev/10;
Mh=dh/.01;
Mv=dv/.01;
Mave=(Mv+Mh)/2;
Plm=12/(pi*150);
PL=Plm*Mave;
L3=1/PL;
n2=-3.36-2.88*log(L3);
FEcave=(11.5+16.5+8.5+4+10.5+11.5+20.5+7+3+13.5+7.5+14.5+4.5)/14;
Pp=FEcave/36;
D1h =
28
D2h =
29
D3h =
29
Daveh =
28.6667
D1v =
29
D2v =
29
D3v =
30
Davev =
29.3333
dh =
6
2.8667
dv =
2.9333
Mh =
286.6667
Mv =
293.3333
Mave =
290
Plm =
0.0255
PL =
7.3848
L3 =
0.1354
n2 =
2.3983
FEcave =
9.5000
Pp =
0.2639
Equations Used:
N1 = NM x M2
N = 2n-1.
PL = PLM x M
Sv = 2 PL mm2 / mm3
n = - 3.36 - 2.88 ln L3
PLM 
Average Number
D
PL  PLM  M
L3  1
PL
7
d
Dave
10
M 
d
0.01 mm
𝑉𝑜𝑙𝑢𝑚𝑒 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =
NM 
𝑎𝑣𝑒𝑟𝑎𝑔𝑒
36
Average Number
150  150