Aim: To find exeprimentally the tensile stress strain curve for Aluminium, Steel, Nylon and PMMA. To derive and compare the (tensile) mechanical properties of those materials tested.
Background: Stress $\sigma$ and strain $\epsilon$ (engineering) are defined as $$\sigma = \cfrac{\color{#C1272D}F}{A}$$ Where $F$ is the applied load on the speciman (in this case tensile load), and $A$ is the cross sectional area perpendicular to the load ($A = {\color{#F15A24}t} \times \color{#006837}w$ see figure 1). $$\epsilon = \cfrac{d l}{\color{#0071BC}l_0}$$ Where $dl$ is the change in length and $l_0$ is the initial gauge length. The gauge length is the initial length taken to find the strain (illustrated in figure 1)
Method:
Figure 1
  1. Measure the width $w$ and thickness $t$ in the gauge length section of the speciman using vernier callipers.
  2. Load speciman into universal testing machine (Instron 5567, Capacity 30kN) by fixing the speciman in the lower grips, then into the top grips.
  3. Align the speciman in the axial direction and tighten the grips.
  4. Set testing speed in the program.
  5. Zero load and displacement readings, then perform test.
Table 1.1
Sample dimensions
Sample Width $w$ $(mm)$ Thickness $t$ $(mm)$ Area $A$ $(m^{2})$
Al-1 12.91 2.95 $3.8085 \times 10^{-5}$
Al-2 12.9 2.97 $3.8313 \times 10^{-5}$
Al-3 12.94 2.98 $3.8561 \times 10^{-5}$
Nylon-1 12.7 2.18 $2.7686 \times 10^{-5}$
Nylon-2 12.72 2.19 $2.7857 \times 10^{-5}$
Nylon-3 12.72 2.18 $2.773 \times 10^{-5}$
PMMA-1 12.73 2.95 $3.7554 \times 10^{-5}$
PMMA-2 12.71 2.94 $3.7367 \times 10^{-5}$
PMMA-3 12.7 2.94 $3.7338 \times 10^{-5}$
Steel-1 12.88 2.95 $3.7996 \times 10^{-5}$
Steel-2 12.92 2.97 $3.8372 \times 10^{-5}$
Steel-3 12.86 2.96 $3.8066 \times 10^{-5}$
Gauge length $l_0 = 50mm$ for all samples
Strain (mm/mm) Stress (MPa) Aluminium stress-strain 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 Graph 1
sample E (GPa) UTS (MPa) YS (MPa) FS (mm/mm)
Al-1 9.19 161.42 126.24 0.1595
Al-2 9.76 161.34 122.81 0.1567
Al-3 8.54 162.36 125.42 0.1461
mean 9.16 161.71 124.82 0.1541
Table 2.1
Strain (mm/mm) Stress (MPa) Nylon stress-strain 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 Graph 2
sample E (GPa) UTS (MPa) YS (MPa) FS (mm/mm)
Nylon-1 0.23 46.49 27.12 3.6855
Nylon-2 0.24 40.69 24.72 2.9699
Nylon-3 0.25 39.84 24.09 2.4225
mean 0.24 42.34 25.31 3.026
Table 2.2
Strain (mm/mm) Stress (MPa) PMMA stress-strain 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Graph 3
sample E (GPa) UTS (MPa) YS (MPa) FS (mm/mm)
PMMA-1 1.22 74.51 39.15 0.1785
PMMA-2 1.3 73.22 35.77 0.1771
PMMA-3 1.18 68.22 40.02 0.0792
mean 1.23 71.99 38.31 0.1449
Table 2.3
Strain (mm/mm) Stress (MPa) Steel stress-strain 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0 50 100 150 200 250 300 350 400 450 500 550 Graph 4
sample E (GPa) UTS (MPa) YS (MPa) FS (mm/mm)
Steel-1 13 533.29 402.89 0.4297
Steel-2 12.71 527.5 375.5 0.4371
Steel-3 13.13 535.17 400.56 0.4497
mean 12.95 531.99 392.98 0.4388
Table 2.4
source E (GPa) UTS (MPa) YS (MPa) FS (mm/mm)
Aluminium Average 9.16 161.71 124.82 0.1541
Aluminium Literature 68.9 124-290 83 - 110 0.12 - 0.25 [1]
Nylon Average 0.24 42.34 25.31 3.026
Nylon Literature 1.3 - 4.2 50-90 40 - 100 0.05 - 1.2 [2]
PMMA Average 1.23 71.99 38.31 0.1449
PMMA Literature 2.7 - 3.3 62-83 65-83 0.03 - 0.064 [3]
Steel Average 12.95 531.99 392.98 0.4388
Steel Literature 200 420 350 0.15 [4]
Table 3.1
Discussion:
Possible errors could be from load cell reading reliability, speciman preperation and defects. The scale of the graph may also affect the derived youngs modulus and yield strength. As necking displays non uniform deformation, the most variance between samples (especially metalic) can be seen in this region, this will affect elongation at failure.

It can be seen that the metals had a very defined elastic region, in the polymer materials it was hard to tell what was the elastic region, or if there even was one. The polymer materials failed catastrophically without warning where as the metals exhibited non uniform deformation (necking) before failure.

Steel exhibited upper an lower yielding, where as aluminium did not. Steel was stronger and more ductile than aluminium. Both metals began necking before failure.

Nylon and PMMA did not have very defined elastic regions, to find youngs modula's was hevily dependant on the scale of the graph. Nylon was extreamly ductile as opposed to PMMA which was brittle. Both polymers fractured before necking.
[1] https://en.wikipedia.org/wiki/6061_aluminium_alloy
[2] http://matweb.com/search/DataSheet.aspx?MatGUID=8d78f3cfcb6f49d595896ce6ce6a2ef1&ckck=1
[3] http://www.matweb.com/search/datasheet.aspx?bassnum=O1303&ckck=1
[4] http://www.matweb.com/search/datasheet.aspx?matguid=10e1c14130cd4ed6ae64b85723be53af