In this essay, the chemical structure of two polymers, polyethylene (PE) and polystyrene (PS) will be discussed. With this information and a previously conducted experiment, a range of stress strain curves will be created
STRESS-STRAIN ANALYSIS
Abstract:
In this essay, the chemical structure of two polymers, polyethylene (PE) and polystyrene (PS) will be discussed. With this information and a previously conducted experiment, a range of stress strain curves will be created; from which analysis of the different aspects of each polymer shall be discussed.
Aim:
The aim of this experiment is to compare the effects of tensile load testing of polyethylene and polystyrene; with the usage of stress-strain analysis.
Background Theory:
In order to test these polymers it is first essential to have an understanding about the materials that will be used, including their chemical structures.
Polyethylene (PE):
This is the simplest hydrocarbon polymer [PPE]. This is commonly shown as:
Where represents a monomer, and are the repeat units used to make the chain for polyethylene. The subscript shows the number of repeats from the repeat units. Polyethylene is a thermoplastic polymer. Some of the major characteristics of polyethylene are its electrically insulating, tough, low strength and poor resistance to effects of weathering [Callister]. As one of these properties is tough, this means that polyethylene can undergo a lot of plastic deformation before reaching the breaking stress.
Polystyrene (PS):
This polymer is made from chains of styrene monomers (left). The heptagonal element bonded to the carbon is called benzene, the addition of this to the repeat unit changes the physical characteristics from polyethylene. The subscript shows the number of repeats from the repeat units. Polystyrene is a thermoplastic polymer. Some of its properties are that its hard, brittle, good electrical properties and resistant to UV light [Callister]. The fact that one of the properties of this material is hard, shows that it is hard to scratch and dent; moreover another property is that it is brittle, this means that it will not undergo any plastic deformation. Hence the polystyrene should undergo brittle fracture, where the material cracks due to a notch being formed and resulting in crack propagation.
Both these polymers come under the thermoplastic category; these types of polymers can be reheated and remolded due to their molecular bonding. Due to this when these polymers are heated or heat is generated; their weak Van der Waals forces between the molecules start to diminish, causing them to change state (only at high temperatures) [Callister].
Young's Modulus:
Young's Modulus measures the stiffness of an elastic material. It is defined as:
Tensile stress is defined as the force per unit area, and tensile strain is a ratio between the extension and the original length. From this another equation for Young's Modulus can be created:
Creation of Graphs:
The graphs have been created on excel, in order to do this the values of stress and strain were calculated. We were given the values of the cross-sectional area and the length; and the force and extension were measured from the experiment. Once ...
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Young's Modulus:
Young's Modulus measures the stiffness of an elastic material. It is defined as:
Tensile stress is defined as the force per unit area, and tensile strain is a ratio between the extension and the original length. From this another equation for Young's Modulus can be created:
Creation of Graphs:
The graphs have been created on excel, in order to do this the values of stress and strain were calculated. We were given the values of the cross-sectional area and the length; and the force and extension were measured from the experiment. Once these were calculated, the graph of stress against stain could be created. Below is a table of the information obtained from the graphs:
Properties
Polyethylene (thin)
Polyethylene (thick)
Polystyrene
Sample 1
Sample 2
Sample 1
Sample 2
Sample 1
Sample 2
Young's Modulus (GPa)
0.70
0.83
.12
.00
.15
.18
Elastic Limit (MPa)
67.806
66.845
2.000
4.000
38.898
31.586
Ultimate Tensile strength (MPa)
67.806
66.845
63.506
61.906
38.898
31.586
Breaking Stress (MPa)
52.524
60.181
63.506
61.906
38.898
31.586
Graph analysis:
This graph shows the thin specimen of polyethylene. When the Young's Modulus is worked out, sample 1 is 0.70 GPa and sample 2 is 0.83 GPa. These values are fairly similar which shows that the atomic structure of these materials is roughly the same. The elastic limit is defined as the point after which the material undergoes plastic deformation, before this is generally a linear increase which shows the elastic deformation; the gradient of which represents the Young's Modulus. As the gradients are steep this shows that polyethylene is also stiff. The elastic limit for sample 1 is 67.806 MPa and for sample 2 it is 66.845 MPa; as these are the largest values of stress on the graph, this is also the ultimate tensile strength of the polymer. This is a high value which suggests that polyethylene is also strong; this is shown again by the high breaking stress value, sample 1 is 52.524 MPa and sample 2 is 60.181 MPa.
On both graphs this is followed by a stain softening, this is what shows the plastic deformation commencing. This section is also known as necking, where the chains of hydrocarbons are forced to stretch and this aligns them, resulting in the polymer becoming crystalline; which in turn makes it more brittle [PPE].
Following this part is a fairly level plastic region, where polyethylene is deformed plastically. For sample two; this plastic deformation continues and the necking increases until the stain value of approximately 2.05 where the polymer cracks, resulting in a sudden decrease in the stress values. However, in sample 1, the atomic structure is less densely packed. This means that the polyethylene can undergo more necking than sample 2. It is clear from the graph that sample 1 doesn't crack; this is due to the process of drawing. Through this process the polymer fibers are 'strengthened by elongation' [Callister], which is why the stress continues to increase after the drawing process and sample 1, does not crack.
This graph shows the thick sample of polyethylene. The Young's modulus of sample 1 is 1.12 GPa and for sample 2 it is 1.00 GPa; this shows that the thick sample is fairly stiff, which means it can be stretched more than those with a smaller Young's Modulus. The elastic region of both the graphs is very short, and therefore identifying the elastic limit is difficult. However for sample 1 it is approximately 12.000 MPa and for sample 2 it is approximately 14.000 MPa. This is followed by a large section of plastic deformation, which is what causes the curve in the graph.
The shape of this graph shows that the thick polyethylene is a ductile material. They both crack, and have fracture points of 63.506 MPa for sample 1 and 61.906 MPa for sample 2. There is no sign of necking from the graph, this means that as the stress increased the polymer became more brittle. Consequently, this means that the atoms in the polymer crystallized. As the load was increased, the stress on the intermolecular bonds increased, which resulted in an 'entanglement' of the molecular structure of the polymer into a crystalline one; hence resulting in the brittleness. In sample 1, the process of crystallization must have been faster as the breaking stain is smaller than that of sample 2.
This graph shows the samples for polystyrene. The Young's Modulus for the first sample is 1.15 GPa and for sample 2 is 1.18 GPa. This shows that the chemical structure of the two samples is similar. The linear part is defined as the elastic limit, and with the gradient the young's modulus can be found. The gradient is fairly steep, but it is shallower than the others in comparison, which means that the polystyrene is not as stiff. The linear increase shows the elastic deformation of the polymer. The elastic limit, the ultimate tensile strength and facture points are all the same for both samples. Sample 1 is at 38.898 MPa and sample 2 is at 31.586 MPa. The elastic limit shows that the material is fairly strong, which means that it should have a high breaking stress. However in these samples, as they are all the same, this means that the chemical structure of the polystyrene affects the breaking stress.
The fact that there is a drastic drop in the stress values in both samples suggests that the polymer is brittle, which is coherent from the background theory section. From this property it can be stated that there is no plastic deformation and this is also reflected in the graph as there is no necking. This can also suggests that brittle fracture occurs, where a notch is formed due to high stressed on a localized point, and this causes crack propagation resulting in the fracture of the polymer.
Conclusion:
To check the reliability of these results it is vital to check them against existing values for this test [matbase].
Properties
Polyethylene (thin)
Polyethylene (thick)
Polystyrene
Sample 1
Sample 2
Check values
Sample 1
Sample 2
Check values
Sample 1
Sample 2
Check values
Young's Modulus (GPa)
0.70
0.83
0.60 - 1.40
.12
.00
0.60 - 1.40
.15
.18
.80 - 2.50
This shows that the values for Polyethylene (thin and thick) are within the range that is given by existing records, which shows that the experiment has been conducted with a good degree of accuracy. However, both the values that are obtained for the polystyrene sample are below the existing records. This can be due to human error or a calibration error. In both cases there is an issue with the beginning of the graph, where the graph does not show linear proportionality. This can be due to calibration error as the device may not have been calibrated to zero which would affect the starting values for the graph. Nevertheless, if this was the case there would be a systematic error that continued throughout the experiment. This seems very likely as there is an offset of about 3 to 3.5 MPa in both sets of data. However, the inaccuracy in the Young's Modulus can be a result of difference in temperature, when the readings were being taken. As the air around the polymer gets warmer, this increases the kinetic energy of the molecules inside the polystyrene; consequently the stiffness increases which in turn decreases the value of the Young's Modulus [PPE]. This may be a reason for the difference in values. Moreover, this may also be a result due to crystallization. At the beginning of both curves there is a section that is not linear; however this should show the elastic limit of the polymer; this can be a result of crystallinity as this would make the polymer more brittle and hence decrease the Young's Modulus.
When comparing the thick and thin sample of Polyethylene, it is vital to understand why the graph shapes are so different. The main cause of this is due to the difference in packing density. From the Young's Modulus obtained from the graphs it is clear that both the polyethylene are high density polyethylene (HDPE). However, within this bracket, the values for the density vary. If we assume that the thin polymer is a constant; then in order for the breaking stain value to be lower the extension for the same load must be lower, for there to be a lower strain value as the length is assumed to be constant. For this scenario to occur the packing density of the thick polymer must be greater which is why necking and hence crystallization can be seen in the thin samples.
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]: http://www.matbase.com/material/polymers/commodity/ps-hips/properties
