material properties 2

8/2/2019 Material Properties 2

1/21

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.


5/21

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


10/21

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




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


11/21

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 =


12/21

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


13/21

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


14/21

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


15/21

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:


16/21

= 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.


17/21

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)


19/21

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)

material properties 2

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