Lab Assignment
Part A – Analysis of Literature Data 1.

Proof Stress vs Cold Work
600 500 Proof stress (MPa) 400 15µm 300 200 100 0 0 10 20 30 40 50 60 70 Cold work (%) 70µm Sample 5 - 15µm Sample 5 - 70µm

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

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 each other. B1. Using the Hall-Petch equation: = Calculations: 193.06 ∴ = = 15 + − 15 − 1 +

193.06

110.32 ∴ Equating (1) and (2): 193.06 15 70 × 193.06 − − =

= 70

+ −

70 − 2

110.32

=

110.32 70

−

= 15

× 110.32

−

∴ Subbing back into (2): = 110.32

= 39.012 − 39.012

70

= 0.597MPa. m

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 = ℎ −Q × 100 Q

3. Initial Diametre (mm) 2.89 2.67 2.38 Initial Length (mm) 70.14 81.82 104.26 Final Diametre (mm) 2.67 2.38 2.13 Final Length (mm) 81.82 104.26 127.14
Table 1

Draw 1 2 3

% Reduction of Area 14.65% 20.54% 19.91%

% Increase of Length 16.65% 27.43% 21.95%

% Volume Change -0.43% 1.25% -2.33%

Sample Annealed Draw 1 Draw 2 Draw 3 Comments: • •

Non-Lubricated Draw Force (N)

Lubricated Draw Force (N)

Bending Force (N) 25 50 55 60

700 1000
Table 2

1100 -

• •

Each % reduction in area and % increase of length has been calculated based on the dimensions at the start of the draw. This provides a good indication of how each draw effects the sample. Volume of the sample shouldn’t change as same amount of material still exists, with different still geometry. I.e. As diameter decreases, length increases. Small errors from calculations as well as inaccuracies in measurements account for the small changes. From work hardening theory, force required to initiate bending is expected to increase due to ected the yield stress increasing From the graphs, a point of initial bending isnt overly discernable. For the values selected, the point at which the graph begins to flatten out was taken as the initial point of bending.

4. = Force × Distance Draw 1 2 3 Force (N) 700 1100 1000
Table 3

Distance (mm) 81.82 104.26 127.14

(J) 57.274 114.686 127.14

Comments:
•

As can be seen from Table 3, increased cold work increases for required to initiate bending in the 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

Bending - Annealed
40 35 30 Bending Force (N) 25 20 15 10 5 0 -1 -5 0 1 2 3 4 Displacement (mm) 5 6 7

Figure 2

Wire Draw 1
1000 800 Drawing Force (N) 600 400 200 0 0 -200 50 100 150 Displacement (mm) 200 250 300

Figure 3

Bending - Draw 1
90 80 70 Bending Force (N) 60 50 40 30 20 10 0 -10 0 1 2 3 4 5 Displacement (mm) 6 7 8 9

Figure 4

Wire Draw 2
1400 1200 Drawing Force (N) 1000 800 600 400 200 0 -200 0 50 100 150 Displacement (mm) 200 250

Figure 5

Bending - Draw 2
80 70 60 Bending Force (N) 50 40 30 20 10 0 -10 0 2 4 6 Displacement (mm) 8 10 12

Figure 6

Wire Draw 3
1200 1000 Drawing Force (N) 800 600 400 200 0 0 -200 50 100 150 Displacement (mm) 200 250 300

Figure 7

Bending - Draw 3
70 60 50 Bending Force (N) 40 30 20 10 0 0 -10 2 4 6 Displacement (mm) 8 10 12

Figure 8

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: :σ= :σ= : 5(i) = :ε= :ε =

σ ε

Stress vs Strain (Annealed)
700 600 Stress (MPa) 500 400 300 200 100 0 0.00% 10.00% 20.00% 30.00% 40.00% Strain (%) Engineering Stress/Strain
Figure 9

50.00%

60.00%

70.00%

80.00%

True Stress/Strain

Comments:
•

As can be seen in Figure 9, the true engineering stress/strain curve accounts for the change in length 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.

Stress vs Strain (Drawn Once)
600 500 Stress (MPa) 400 300 200 100 0 0.00%

5.00%

10.00%

15.00%

20.00% Strain (%)

25.00%

30.00%

35.00%

40.00%

Engineering Stress/Strain

True Stress/Strain

Figure 10

Comments:
•

As can seen in Figure 10, the yield stress on the material has increased dramtically after one stage 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, the geometry of the sample again causes the engineering stress/strain to again be an approximation.

(ii) Sample Annealed Drawn Once Drawn Twice Drawn Thrice Fully Cold Worked Annealed 1 min Annealed 5 min Annealed 80 min Annealed 120 min Annealed 240 min Annealed 420 min Vickers Hardness (VHN) 65 132.7 182.1 232.7 147 135 126 106.6 79.7 74.3 70.7

Table 4 – Vickers Hardness

Comments:
•

As can be seen in Table 4, the hardness of a material is dramatically increased by cold work hardening, 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. Annealed Yield Stress (MPa) Ultimate Tensile Strength (MPa) Strain at Fracture (%) Youngs Modulus (GPa)
Table 5

132 351 75 3.09

Cold Worked (Drawn) 310 412 35.7 15.90

Comments:
•

The figures in Table 5 have been taken directly off the engineering stress/strain curves of Figure 9 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 + For cold worked sample: 553 = 309.5 + A= X= × .2903 × 0.577 +

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: ℎ 7. Average Grain Width (mm) 0.115 0.1073 0.143 0.0931 0.1665 0.0799 0.199 0.0501 0.1951 0.0529 0.1148 0.1051 0.0577 0.10235 0.050022 0.10021 0.050019 0.10001 0.075015 1.0619745 0.075116 1.1635459 0.080025 2.4553191 0.10995 0.1556257 0.124 3.4990548 0.12455 3.5728543 0.1232 2.1875 0.11805 1.7360285 0.11115 1.0717614 Mean Grain Size (mm) =

Sample As Received Drawn Once Drawn Twice Drawn Thrice Annealed (1 min) Annealed (3 min) Annealed (5 min) Annealed (60 min) Annealed (24 Hrs)

Direction Parallel Transverse Parallel Transverse Parallel Transverse Parallel Transverse Parallel Transverse Parallel Transverse Parallel Transverse Parallel Transverse Parallel Transverse

Grain Shape Factor

Table 6

8

Grain Size vs % Cold Work
0.2 Grain Size (mm) 0.15 0.1 0.05 0 0 10 20 30 % Cold Worked Parallel
Figure 11

40

50

60

Transverse

Comments:
•

As expected, as percentage of cold work increases, the grains align and elongate in the direction of 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.

Grain shape vs Cold work
4 3.5 Grain shape (mm) 3 2.5 2 1.5 1 0.5 0 0 10 20 30 Cold work (%) 40 50 60

Figure 12

Comments:
•

As defined by the grain shape factor, as more cold work is applied, the ratio of the parallel to transverse dimension of the grain increases. This agrees with results from Lab 1 and Figure 11.

Mean grain size vs Annealing time
0.14 0.12 Mean grain size (mm) 0.1 0.08 0.06 0.04 0.02 0 0 10 20 30 40 50 60 70 Annealing time (minutes)

Figure 13

Comments:
•

Figure 13 shows how annealing of a sample dramatically decreases the grain sizes back to their original 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.

C – Overview 9.

% Cold Work 0 15 35 55 Comments:
• •

Grain Size 0.11115 0.11805 0.1232 0.12455
Table 7

Expected Yield Strength (MPa) 150 300 380 420

Yield Strength (Lab 2) 132 310 -

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: = 1 × 0.5148 × 588MPa = 151.351MJ/m3 2

For the cold worked sample (drawn once) – triangle + rectangle: = 1 × 0.3 × 150)+ 0.3 × 400 = 142.5MJ/m3 2 57 = 93.39MJ/m3 1.365 × 104.26

Convert cold drawn external work: = B3. Using:

• • • •

= 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: Sample Annealed Drawn Once Drawn Twice Drawn 3 times Annealed 1 min Annealed 3 mins Annealed 5 mins Annealed 60 mins Mean Grain size (mm) 0.11115 0.11805 0.1232 0.12455 0.124 0.10995 0.080025 0.075116 Yield strength (MPa) 96.54 94.86 93.70 93.41 93.52 96.85 106.65 108.79

Annealed 24 hrs

0.0750145
Table 8

108.84

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.

-

B4.
•

•

•

As can be seen from the hardness results in Lab 2, Hardness decreases the longer a sample is annealed 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 of dislocations 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)

Figure 15 – Cold Drawn Once (20x Mag)

Figure 16 – Cold Drawn Twice (50x Mag)

Figure 17 – Cold Drawn Thrice (50x Mag)

Figure 18 – Annealed 1min (50x Mag)

Figure 19 – Annealed 3 min (50x Mag)

Figure 20 – Annealed 5 min (50x Mag)

Figure 21 – Annealed 60 mins (50x Mag)

Figure 22 – Annealed 24Hrs (100x Mag)