material properties 2
TRANSCRIPT
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Lab Assignment
Part A Analysis of Literature Data1.
Figure 1 Proof Stress vs Cold Work of 70/30 Brass
As can be seen from Figure 1, the 0% cold worked points (Sample 5) for each grain size is in line with the
curve of the other four points. The amount of proof stress increases with increased cold work, but
approaches an asymptote at a point of maximum increase in proof stress.
Cold working uses processes such as drawings to deform the grains in a material, thereby increasing the
proof stress of the material.
2.
(i) Grain size strengthening is a process that reduces the sizes of the grains in a material, typically by
annealing. This works to increase the strength of the material through the fact that grain boundaries act
as a barrier to dislocations. As can be seen in Figure 1, decrease in grain size causes an increase in proof
stress.
Cold working involves plastically deforming a material such that dislocations become concentrated.
These dislocations then become entangled, hindering further dislocation movement, thereby increasing
0
100
200
300
400
500
600
0 10 20 30 40 50 60 70
Proofstress(M
Pa)
Cold work (%)
Proof Stress vs Cold Work
15m
70m
Sample 5 - 15m
Sample 5 - 70m
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the strength of the material. As can be seen in Figure 1, proof stress can be increased dramatically by
cold work hardening, but only to a point.
(ii)
Grain size strengthening and cold work hardening can be used together to form a much stronger
material. Grain size strengthening reduces the size of grains whilst cold work hardening increases the
grain size and decreases ductility. The combination of these two processes cancels the negative effects
of eachother.
B1.
Using the Hall-Petch equation:
= + Calculations:
193.06 = + 15
= 193.06 15
1
110.32 = + 70
= 110.32 70
2
Equating (1) and (2):
193.06 15
= 110.32 70
70 193.06 = 15 110.32
= 39.012Subbing back into (2):
= 110.32 39.01270
= 0.597MPa.m
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Part B Analysis of Experimental Data
B1 Laboratory 1
Method:
For this experiment, a length of 70/30 as received brass was drawn through three consecutively
smaller sized die (draw rate of 300mm/min). The diameter and length of the sample after each draw
was recorded. Two marks were made on the wire to maintain consistency of measurements taken.
As Received:
Length 70.14mm
Diametre 2.89mm
Draw 1:
Die Size 0.1065 inch
Length 81.82mm
Diametre 2.67mm
Draw 2:
Die Size 0.094 inch
Length 104.26mm
Diametre 2.38mm
Draw 3:
Die Size 0.085 inch
Length 127.14mm
Diametre 2.13mm
Equations:
= =
% increase = Q
Q 100
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3.
Draw
Initial
Diametre
(mm)
Initi
Lengt
(mm
1 2.89 70.1
2 2.67 81.8
3 2.38 104.2
Sample
Annealed
Draw 1
Draw 2
Draw 3
Comments:
Each % reduction in areat the start of the draw.
Volume of the sample sgeometry. I.e. As diame
inaccuracies in measure
From work hardening ththe yield stress increasi
From the graphs, a poinpoint at which the grap
4.
Dr
1
2
3
l
h
)
Final
Diametre
(mm)
Final
Length
(mm)
%
Reduction
of Area
% In
of L
2.67 81.82 14.65% 16.
2.38 104.26 20.54% 27.
6 2.13 127.14 19.91% 21.
Table 1
Non-Lubricated
Draw Force (N)
Lubricated
Draw Force (N)
Ben
Forc
2
700 - 5
- 1100 5
1000 - 6
Table 2
and % increase of length has been calculated b
This provides a good indication of how each dra
ouldnt change as same amount of material still
er decreases, length increases. Small errors fro
ments account for the small changes.
eory, force required to initiate bending is expec
ng
of initial bending isnt overly discernable. For th
begins to flatten out was taken as the initial po
= Force Distance
w Force (N)Distance
(mm)(J)
700 81.82 57.274
1100 104.26 114.686
1000 127.14 127.14
Table 3
rease
ngth
% Volume
Change
65% -0.43%
43% 1.25%
95% -2.33%
ing
(N)
sed on the dimensions
w effects the sample.
exists, with different
calculations as well as
ed to increase due to
e values selected, the
int of bending.
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Comments:
As can be seen from Table 3, increased cold work increases for required to initiate bending inthe sample, as expected. The lubricant used in draw two resulted in a high force but a lower
distance. As expected, due to the theory of cold work, the material is stronger when drawn but
is also more brittle, accounting for the change in distance required to bend the sample.
B1 - Graphs
Figure 2
-5
0
5
10
15
20
25
30
35
40
-1 0 1 2 3 4 5 6 7
BendingForce(N)
Displacement (mm)
Bending - Annealed
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Figure 3
Figure 4
-200
0
200
400
600
800
1000
0 50 100 150 200 250 300
DrawingForce(N)
Displacement (mm)
Wire Draw 1
-10
0
10
20
30
40
50
60
70
80
90
0 1 2 3 4 5 6 7 8 9
BendingForce(N)
Displacement (mm)
Bending - Draw 1
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Figure 5
Figure 6
-200
0
200
400
600
800
1000
1200
1400
0 50 100 150 200 250
DrawingForce(N)
Displacement (mm)
Wire Draw 2
-10
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12
BendingForce(N)
Displacement (mm)
Bending - Draw 2
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Figure 7
Figure 8
-200
0
200
400
600
800
1000
1200
0 50 100 150 200 250 300
DrawingForce(N)
Displacement (mm)
Wire Draw 3
-10
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12
BendingForce(N)
Displacement (mm)
Bending - Draw 3
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B2 Laboratory 2
Method:
For this experiment, lengths of 70/30 Brass were subject to tensile testing. This was to enable the
development of the engineering stress-strain curve and thus some of the mechanical properties of the
materials. Two samples, one annealed and one cold worked, were tested. Vickers hardness (VHN)
testing was also performed on several samples of 70/30 brass. The samples were embedded in an epoxy
resin base then polished.
Equations:
: = : =
: = : =
: =
5(i)
Figure 9
Comments:
As can be seen in Figure 9, the true engineering stress/strain curve accounts for the change inlength and cross sectional area of the sample as it is put into tension. As necking occurs, the
cross sectional area of the sample changes dramatically. Engineering stress/strain relies purely
on the original gemotry of the sample and is hence only an approximation.
0
100
200
300
400
500
600
700
0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00%
Stress(MPa)
Strain (%)
Stress vs Strain (Annealed)
Engineering Stress/Strain True Stress/Strain
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Figure 10
Comments:
As can seen in Figure 10, the yield stress on the material has increased dramtically after onestage of cold working, supporting cold work theory. In this case, the engineering stress/strain
and true stress/strain are slightly closer due to the increase in yield stress. Beyond this, thegeometry of the sample again causes the engineering stress/strain to again be an
approximation.
(ii)
SampleVickers Hardness
(VHN)
Annealed 65
Drawn Once 132.7
Drawn Twice 182.1
Drawn Thrice 232.7
Fully Cold Worked 147
Annealed 1 min 135
Annealed 5 min 126
Annealed 80 min 106.6
Annealed 120 min 79.7
Annealed 240 min 74.3
Annealed 420 min 70.7
Table 4 Vickers Hardness
0
100
200
300
400
500
600
0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00%
Stress(MPa)
Strain (%)
Stress vs Strain (Drawn Once)
Engineering Stress/Strain True Stress/Strain
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Comments:
As can be seen in Table 4, the hardness of a material is dramatically increased by cold workhardening, as is expected by work hardening theory. The effects of hardening processes such as
cold work hardening is further evident in the reduction in hardness as the samples are annealed.
As the samples are annealed for long, dislocations are more free to move within the material,
increasing the ductility of the material.
6.
AnnealedCold Worked
(Drawn)
Yield Stress (MPa) 132 310
Ultimate Tensile Strength (MPa) 351 412
Strain at Fracture (%) 75 35.7
Youngs Modulus (GPa) 3.09 15.90
Table 5
Comments:
The figures in Table 5 have been taken directly off the engineering stress/strain curves of Figure9 and Figure 10. (Youngs Modulus calculated from these values). As expected, the yield stress
was increased by cold working but the ultimate tensile strength remains unchanged. As
expected with cold work theory, the strain to fracture decreases with increased cold work.
B2
Equations:
= + For annealed sample:
582 = 95.5 + 0.577For cold worked sample:
553 = 309.5 + .2903A =
X =
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B3 Laboratory 3
Method:
For this experiment, several samples of 70/30 Brass were examined under a microscope. The purpose of
this was to form a correlation between grain sizes, cold work hardening and annealing. The samples
included one as received, three cold worked and five annealed for various lengths of time. Images were
taken at various magnifications to grain dimensions and slip lines.
Equations:
=
7.
Sample Direction
Average
Grain
Width
(mm)
Mean
Grain
Size
(mm)
Grain
Shape
Factor
As Received
Parallel 0.115
0.11115 1.0717614Transverse 0.1073
Drawn Once
Parallel 0.143
0.11805 1.7360285Transverse 0.0931
Drawn Twice
Parallel 0.1665
0.1232 2.1875Transverse 0.0799
Drawn Thrice
Parallel 0.199
0.12455 3.5728543Transverse 0.0501
Annealed (1 min)
Parallel 0.1951
0.124 3.4990548Transverse 0.0529
Annealed (3 min)
Parallel 0.1148
0.10995 0.1556257Transverse 0.1051
Annealed (5 min)
Parallel 0.0577
0.080025 2.4553191Transverse 0.10235
Annealed (60 min)
Parallel 0.050022
0.075116 1.1635459Transverse 0.10021
Annealed (24 Hrs)
Parallel 0.050019
0.075015 1.0619745Transverse 0.10001
Table 6
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8
Figure 11
Comments:
As expected, as percentage of cold work increases, the grains align and elongate in the directionof the applied force. Figure 11 shows how grain dimensions that are parallel to the force are
increasing in length whilst grain dimensions that are perpendicular(transverse) to the applied
force are shortening, as expected by conservation of volume.
Figure 12
0
0.05
0.1
0.15
0.2
0 10 20 30 40 50 60
GrainSize(mm)
% Cold Worked
Grain Size vs % Cold Work
Parallel Transverse
0
0.5
1
1.52
2.5
3
3.5
4
0 10 20 30 40 50 60
Grainshape(mm)
Cold work (%)
Grain shape vs Cold work
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Comments:
As defined by the grain shape factor, as more cold work is applied, the ratio of the parallel totransverse dimension of the grain increases. This agrees with results from Lab 1 and Figure 11.
Figure 13
Comments:
Figure 13 shows how annealing of a sample dramatically decreases the grain sizes back to theiroriginal state. This change occurs within the first few minutes of annealing. After approx 5 mins,
there is little change in grain size between 5 mins and 24 hrs of annealing.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 10 20 30 40 50 60 70
Meangrainsize(mm)
Annealing time (minutes)
Mean grain size vs Annealing time
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C Overview
9.
% Cold Work Grain SizeExpected Yield
Strength (MPa)
Yield
Strength
(Lab 2)
0 0.11115 150 132
15 0.11805 300 310
35 0.1232 380 -
55 0.12455 420 -
Table 7
Comments:
As expected, yield strength of the material is increasing with cold work. Differences in values can be attributed to inaccuracies in measurement, as well as the fact that
grain size used is a mean value. Grain growth is not linear and highly irregular. Slip planes visible
in the samples also diminishes the deformation of grains (the advantage of cold work hardening)
10.
Equations:
=
The stress/strain curves from Lab 2 were used to calculate the internal work for the annealed and first
drawn samples. This is achieved by taking the area under the plastic region of the true stress/strain
curve.
For the annealed sample - triangle:
= 12 0.5148588MPa = 151.351MJ/m3
For the cold worked sample (drawn once) triangle + rectangle:
= 12 0.3150)+0.3400 = 142.5MJ/m3
Convert cold drawn external work:
= 571.365 104.26 = 93.39MJ/m3
B3.
Using:
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= 39.012MPa k = 0.597 MPa.m Data from Laboratory 3 The Hall-Petch equation
= +
The yield strength of each sample can be calculated, using the mean grain size calculated in Lab 3:
SampleMean Grain
size (mm)
Yield strength
(MPa)
Annealed 0.11115 96.54
Drawn Once 0.11805 94.86
Drawn Twice 0.1232 93.70
Drawn 3 times 0.12455 93.41
Annealed 1 min 0.124 93.52
Annealed 3 mins 0.10995 96.85
Annealed 5 mins 0.080025 106.65
Annealed 60 mins 0.075116 108.79
Annealed 24 hrs 0.0750145 108.84
Table 8
Notes:
- The above yield strength values are not in accordance with cold working and annealing theory.As cold work percentage is increased, the yield stress should increase. As the samples are
annealed, the yield stress should decrease.
- The grain measurements may be inaccurate due to form of measurement.- Due to the dependence of the equation on measurement of grain size, errors result in a large
difference in the calculated yield strength.
- Calculations in Lab 1 for constant values may also be different to those of the sample material.
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B4.
As can be seen from the hardness results in Lab 2, Hardness decreases the longer a sample isannealed from a fully cold worked state. In relation to the images from Lab 3, this can be
correlated with the decrease in grain size associated with the annealing process.
As a sample is annealed, grain size decreases. Although smaller grain sizes reduce the ability ofdislocations to move, it in turn increase the ductility of a material and the bond between the
grain is weaker. When a hardness test is conducted, the more ductile that material, the lower
the Vickers Hardness.
Overall, annealing results in a material with lower grain sizes and a lower hardness.Lab 3 Images
Figure 14 As Received (50x Mag)
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Figure 15 Cold Drawn Once (20x Mag)
Figure 16 Cold Drawn Twice (50x Mag)
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Figure 17 Cold Drawn Thrice (50x Mag)
Figure 18 Annealed 1min (50x Mag)
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Figure 19 Annealed 3 min (50x Mag)
Figure 20 Annealed 5 min (50x Mag)
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Figure 21 Annealed 60 mins (50x Mag)
Figure 22 Annealed 24Hrs (100x Mag)