The use of safety goggles is to ensure no excess specimens enter the eye.
Results Table:
The table above shows the experimental value of Young’s Modulus for thin and thick polyethylene and polystyrene. ‘Young’s Modulus is the coefficient of elasticity of a substance, expressing the ratio between a that acts to change the length of a body and the fractional change in length caused by this ’.
Young’s modulus is calculated my using the graph i.e. find the gradient of the stress-strain cure of the linear elastic region. The data produced by the computer is used to calculate stress and strain and plot the graph using spreadsheet. Stress is the force acting per unit area. It is measured in Pascal. Strain is the ratio of extension and original length. It is dimensionless. Therefore,
Analysis: The analysis of stress-strain curve of a deforming polymer can be done in three different stages. At low strains, polymers show elastic behaviour. Elastic means reversible i.e. when the stress is removed, the polymer returns to its original shape. At moderate strains, polymers show yielding behaviour followed by plastic behaviour at high strains. Plastic means irreversible. When the stress is removed, the polymer retains its new shape.
The graph on the right hand side shows the Stress-Strain curve of two thin samples of polyethylene. When the samples are stretched, distance between molecules of polymer increases. The intermolecular forces are still strong enough to bring the molecules back to their original place if the stress is removed. This is known as elastic deformation. The polymer is stretched further and it reaches to its yield point (yield point is the maximum point on both the curves). It is the amount of energy required to deform the polymer plastically. Form this point, the polymer is stretched further. Now, the intermolecular forces are not strong enough to hold the molecules and therefore, the polymer starts do deform plastically. Necking is also observed when plastic deformation takes place. As the polymer is stretched further, the stress decreases gradually, as expected. Till now, graphs for sample 1 and sample 2 looked similar. From this point, graphs start to differ slightly. There are lot of variations in the graph of sample 2 when compared to sample 1. For sample 1, after the stress decreases gradually, it stays almost constant for a while. This is known as strain softening. After strain softening reaches minimum, strain hardening comes in. This causes the stress to increase again. The strain hardening then reaches maximum, causing the polymer fracture. This point is called Ultimate Tensile Strength [UTS]. Ultimate tensile strength is the maximum stress for which the material can withstand without breaking. For different polymers, Ultimate Tensile Strength can be greater or less than the yield stress. Sample 1 and sample 2 have similar yield stresses but different UTS. This is because of the difference in the degree of crystallininty or because of some impurities in the polymer. Also, the graph for sample 2 shows a straight line coming down at the point of fracture, this is because of computer error. Now, from the graph, Young’s Modulus can be easily calculated from the elastic region of the graph. Note that the curve does not pass through the centre of the axis; this is because the polymer needs certain amount of stress to extend. The experimental value obtained for Young’s Modulus of sample 1 and sample 2 is 0.621GPa and 0.733GPa respectively. Also, UTS of sample 1 is greater than sample 2, this shows that sample 1 is tough.
Now, the graph on the left shows the stress-strain curve for two thick samples of polyethylene. The curve passes through origin and obeys Hooke’s law for very less strains. As the strain increases, stress increases and the polymer reaches to its yield point. In real, yield strength for both samples of thick polyethylene is really hard to determine because the graph is in the form of curve from the beginning. After this point, it starts to deform plastically. You can also see that the stress remains almost constant most of the time. This feature of the graph shows that this material is ductile. When the material breaks, the strain remains constant. The stress goes down to zero and the computer also records some negative values. It is impossible for the force to take negative values but it is observed that when the machine fractures a sample of polymer, the computer keeps on recording data. Also, the grip of the machine shows a very small oscillation, this might have caused the computer to record negative values. Now, the Young’s Modulus calculated from the linear elastic region of this graph has values 1.12GPa and 1GPa for sample 1 and sample 2 respectively. The Ultimate Tensile Strength of thick polyethylene samples is around 63MPa and 61MPa for sample 1 and sample 2 respectively. When the graphs of thick and thin samples of polyethylene are compared, it is observed that thin sample of polyethylene has more area under its stress-strain graph than that of thick sample. This shows that thin sample of polyethylene is more ductile. This also shows that thin sample of polyethylene is harder to fracture that the thick polyethylene samples.
The stress-strain graph of polystyrene is on shown on the left. The graph shows that when the stress is applied, the graph does not obey Hooke’s law straight away i.e. the stress is not directly proportional to strain. This is because polystyrene is said to be ‘crystallising’ (crystallization is explained in detail in discussions). After the crystallization process, the graph starts to obey Hooke’s law. The gradient of the graph is easy to measure and is steep, but it is shallower than the others in comparison, which means that the polystyrene is not as stiffest of all. When the yield stress is applied, polystyrene samples break before undergoing plastic deformation. This means that polystyrene is brittle and is very weak compared to polyethylene [callister]. The Young’s Modulus for thick and thin sample of polystyrene is 1.15GPa and 1.18GPa. And the yield strength for both the samples is same as their Ultimate Tensile Strength. For sample 1, UTS is at 38.898 MPa and for sample 2, it is at 31.586 MPa.
Discussion:
The table below shows the experimental and actual values of Young’s Modulus for all the samples.
After comparing my experimental values of Young’s modulus of polyethylene(thick and thin) and polystyrene with their actual values, I found that the values for Polyethylene (thin and thick) fall within the range that is given by existing records, which shows that the experiment has been conducted with a good degree of accuracy. However, the values of Young’s Modulus for both the samples of polystyrene fall below the actual range. This is because the experiment is affected by several factors.
First one amongst them is the crystallization of polymers. When a polymer is melt, it’s long molecular chains turn into irregular and entangled coil. When this molten polymer is solidified, the chain goes back to its original shape but some parts of this chain retain this distorted structure. When the polymer is stretched with this distorted structure, the sample breaks well before it is expected to break. For example, this is the reason why the yield strength of sample 1 of polystyrene greater than that of sample 2. Furthermore, the hardness of the polymer is also affected by the degree of crystallinity. Higher crystallinity results into harder polymers. But the drawback of this is that the polymer becomes more brittle. This means that sample 2 of polystyrene has is less crystallized compared to sample 1 [Callister].
Second amongst them are the temperatures at which the polymers have been stretched. The mechanical characteristics of polymers are much more sensitive to temperature changes. The elasticity modulus of polymer decreases with an increase in temperature. Also, the tensile strength decreases and the ductility of the polymer increases with an increase in temperature [Callister]. For example, when this experiment was done, the temperature at each test could have been different. This is another why the sample 1 of thin polyethylene is stretched more than sample 2.
Conclusions:
After comparing the graphs of polyethylene (thick and thin) and polystyrene, it is observed that thin polyethylene is the most ductile polymer amongst the 3 polymer samples. Thick polyethylene is semi ductile and polystyrene is brittle. The area under the graph of thin polyethylene samples is the highest compared to the other two polymers. It also has the highest Ultimate Tensile Strength. This shows that thin polyethylene is the hardest, stiffest, and most ductile polymer amongst the 3 samples and hence most useful for daily purposes.
References:
[PPE]: NG McCrum, CP Buckley and CB Bucknall. Principles of Polymer Engineering, second edition. Oxford University Press (2001)
[Callister]: William C. Callister, Jr. Materials science and engineering an introduction, seventh edition. John Wiley and sons, Inc 2007
[matbase]: