The largest source of uncertainty in making measurements of yield strength from the stress-strain curves is in reading the relevant value off of the graph. We have made the assumption that the points on the graph are discernable to half of the smallest division. The divisions used for the stress-strain curves of the polymer materials are finer than those used for the metals, which accounts for their lower levels of uncertainty. This uncertainty has been tabulated in the table of yield strength data below.
* All measurements in MPa
Table 4: Yield Strengths of the provided materials
3.3 Tensile Strength
As continually higher strains are applied to a material, the material will eventually fracture. Tensile strength is defined in a slightly different manner for metals and for polymers. For metals, tensile strength is defined as the maximum level of stress on the stress-strain curve (Callister, 1997). At this point, the material’s cross-sectional area begins to decrease along a localized region in a process known as necking. All successive deformation occurs at this neck. For polymers, tensile strength corresponds to the level of stress where the material fractures (Callister, 1997). Note that no value of tensile strength could be recorded for the white polymer sample, as it could not be strained adequately to cause it to fracture.
The largest source of uncertainty in making measurements of tensile strength from the stress-strain curves is in reading the relevant value off of the graph. We have again made the assumption that the points on the graph are discernable to half of the smallest division.
* All measurements in MPa
Table 5: Tensile Strengths of the provided materials
3.4 Resistivity
We also attempted to determine the resistivities of each of our materials. Since the samples each possessed a known cross sectional area and length, measuring the resistance of these samples would theoretically have allowed us to determine their resistivities. We used a power supply to pass a voltage through each of the samples, and then attempted to use a DMM to measure the voltage drop over each sample. Unfortunately, were such good conductors that they caused the power supply to enter its current limiting mode of operation. Additionally, none of the three types of DMMs provided in the lab could measure a discernable voltage drop across any of the polymer samples. In both cases, more accurate equipment or techniques are required to obtain a qualitative measure of the resistivities of our samples.
Table 6: Resistivities of the provided materials
3.5 Hardness
Hardness is a measure of a material’s resistance to plastic indentation. Quantitative hardness tests typically force a small indenter into the surface of a substance, using a carefully controlled load and application rate. A hardness number is then determined from the size of the subsequent indentation. Unfortunately, the testing apparatus required to perform this technique was not available to us. However, we were able to obtain an approximate gauge of the relative hardnesses of our materials by measuring the energy that caused these materials to plastically deform. In order to accomplish this, we dropped a known mass of 10.00 g from continuously increasing heights until we discerned deformation in the sample. The mass of 10.00 g was measured by an electronic scale, which was denoted to have an uncertainty of ±0.01g accuracy. The heights from which the mass was dropped was measured by a ruler. We could discern the intervals on the ruler to an accuracy of half the smallest division, or 5x10-4 m. We used a value of 9.8 m/s2 ± 0.1 m/s2 as the constant of acceleration due to gravity. The relative uncertainties in each of these terms have been summed to yield the relative uncertainty in the energy required for deformation.
Table 7: Hardnesses of the provided materials
Hardness and tensile strength are approximately proportional for a given class of materials, since both gauge of a material’s resistance to plastic deformation (Callsiter, 1997). By comparing the energy required for deformation of our three polymers, we can see that the white polymer required the lowest energy of the three. This correlates with the fact that the white polymer has lower yield and tensile strengths than the black or clear polymers. As metals #1 and #2 are fundamentally different materials from the three polymers, the energies which caused them to deform cannot be correlated with the energies of the polymers.
3.6 Toughness
Toughness is defined as the energy required for fracture of a material. It is also equal to the area under the stress-strain curve up to the point at which a material fractures. The toughnesses of our materials were determined by using the Sigmaplot graphical analysis package to integrate the areas under each of the stress-strain curves. It is unknown what algorithm the Sigmaplot software utilized to calculate the area under each stress-strain curve. However, the uncertainties involved in our stress and strain measurements must be accounted for. Therefore, an estimation of the total uncertainty in the area calculation was made by summing the relative uncertainty in measuring the stress to the relative uncertainty in measuring the strain, and multiplying this relative uncertainty by the number of data points involved in each of our stress-strain curves.
Table 8: Toughnesses of the provided materials
The above table of toughness values indicates that the toughness of the black polymer is significantly lower than that of any of the other materials. Even though the black polymer has a moderately high tensile strength, it is brittle, causing it to reach that tensile strength at a relatively low value of strain. Consequently, the black polymer encloses a relatively low volume under its stress-strain curve up until the point of fracture. Metal #1 and Metal #2 also exhibit notably different toughnesses, despite possessing very similar values for tensile strength. Again, this is because Metal #2 reached its tensile strength at a lower value of strain than Metal #1.
3.8 Elongation
After the materials were strained to their tensile strengths, we calculated the final dimensions of the materials. These dimensions have been summarized in the table below
* All measurements are in centimeters
Table 9: Final measurements
We can then calculate the percent elongation (%EL), the percentage of plastic strain at fracture, using the following formula:
The values for %EL have been tabulated in the following table:
* All measurements are in centimeters
Table 10: Percent Elongation
3.7 Analysis of Materials
We noticed that the yield and tensile strengths of our black and white polymer materials were lower than those of our metal materials. This agrees with polymer theory. Inter-molecular bonding within polymers is typically dominated by Van der Waals forces (Flory, P.J, 1953). Polymers therefore tend to have lower yield and tensile strengths than metals because these secondary Van der Waals forces are much weaker than the primary metallic intermolecular forces in metals (Flory, P.J, 1953).
We can obtain additional insight about the structure of our polymers by considering polymer theory. Polymers with a linear atomic configuration tend to be stronger (Kinloch and Young, 1983). Strength is also generally increases with molecular weight until it plateaus at a moderately constant value for some critical molecular weight (Kinloch and Young, 1983). This implies that the black and clear polymers possess more linear structures and have a higher molecular weight than the white polymer, as they possessed higher tensile strengths.
3.71 Black Polymer
If we observe the stress-strain curve of the black polymer, it appears as though there is a region prior to the elastic region in which the material undergoes notable strain without being subjected to significant stress. This may be due to slippage in the clamps. As noted previously, the black polymer was notably stiff, making it susceptible to slippage. This would have accounted for the error in the magnitude of the stress measured over this region.
The black polymer was fractured before experiencing any discernable plastic deformation. It also possessed a higher tensile strength and Young’s Modulus than the white polymer, implying that it possesses a higher degree of crystallinity. Having a more crystalline structure will cause a polymer to have higher tensile and yield strengths, as its intermolecular bonding forces will be stronger (Kinloch and Young, 1983). Additionally, the increasing the amount of cross-linking between chains in a polymer will restrain the movement of those chains, and therefore make the polymer more brittle (Kinloch and Young, 1983). Crystallization is favoured in chemically simple polymers, such as polyethylene and polytetrafluoroethylene (Callister, 1997). Therefore, the black polymer is likely to be chemically simple and possess a crystalline structure.
From the hardness data in table 7, we can observe that the black polymer required significantly more energy for deformation than the clear polymer, in spite of the black and clear polymers having similar yield and tensile strengths. Comparing the stress-strain curves of the black and clear polymers, however, we can see that the black polymer is significantly more brittle. Therefore, the black polymer likely possesses a more crystalline structure than the clear polymer, causing it to be harder.
Upon fracture, the black polymer sample exhibited a clean break. This again supports that the black polymer has a crystalline crystal structure.
In order to determine more specific information about the polymers examined in this experiment, we can attempt to correlate the mechanical characteristics of typical polymers with those measured in this experiment.
Polymerweb (see references) provides a wealth of data on the mechanical properties of polymers. This data can be correlated to our three polymers to better determine what they may be. We began by considering the chemically simple polymers that have been cited as likely to possess a crystal structure, such as polyethylene and polytetrafluoroethylene. Polyethylene was found to have a tensile strength of 45.424 MPa, which agrees well with our measured value of 54.5 MPa (Polymerweb, 2003). However, it was also shown to have an elastic modulus of 0.2-1.7 GPa, and an elongation (in 2 inches) of 70-90%. Polytetrafluoroethylene was found to have a tensile strength of 24.5 MPa, an elastic modulus of 0.38 GPa, and an elongation (in 2 inches) of 200-450%. These results varied drastically from our measured elastic modulus and elongation for the black plastic. Table 16.1 in Callister, which depicts the room-temperature mechanical characteristics of common polymers, was then consulted. Of the listed polymers, polystyrene, polymethyl methacrylate, and phenol-formaldehyde all possess values of elastic modulus, tensile strength and elongation at break that agreed with that of the black plastic. In addition, polystyrene and phenol-formaldehyde both do not possess measurable yield strengths, implying that they undergo fracture before any significant plastic deformation occurs.
Therefore, we began to investigate the properties of polystyrene and phenol-formaldehyde. Polystyrene is Polystyrene is the main component of foam coffee cups is also used to make . These include television and computer cabinets, appliances, toys, compact disc jewel cases and audiocassette cases (Polystyrene. 2003). Such rigid structure is consistent with the brittle behaviour exhibited by the black plastic material. According to the stress-strain curves displayed in Stress Strain Behavior of Polymers (see references), exhibits a brittle stress-strain characteristic.
Phenol-formaldehyde, commonly known as bakelite, is also a naturally brittle material. It was was widely used in early consumer electronic products such as telephones and radios and was the first synthesized polymer resin to be produced in large quantities. Both phenol-formaldehyde and polystyrene therefore appear to be possibilties for our black plastic material based on the combination of their mechanical and physical properties.
Upon initial inspection, the black polymer also appeared to resemble the plastic used in cheap cameras and piping material. Upon doing some cursory research, we discovered that a polymer known as ABS plastic is commonly used in both these applications. Additionally, ABS plastic possesses an elastic modulus of 3.1 GPa, a tensile strength of 43.3 MPa, and an elongation (in 2 inches) of 2.5% (Polymerweb, 2003). All of these values correlate well with our measured values for the black plastic polymer. ABS plastic is made up of a terpolymer of acrylonitrile, and styrene, with approximately half of the composition being styrene. Having investigated the properties of polystyrene above, it not surprising that ABS plastic possesses many of the same mechanical properties. Apart from the camera and piping material application that had inspired me to research it ABS plastic is commonly used in applications ranging from electronics housings to computer bezels, doors, side panels, automotive trim, custom cases, refrigerator liners, musical instrument cases, luggage, and enclosures (Polymerweb, 2003). The stress-strain curve of ABS Plastic (Stress Strain Behavior of Polymers, 2003) also supports ABS Plastic having a brittle stress-strain relationship, further supporting the possibility that the black plastic may be composed of this material. Therefore, at this point, we have established three possibilities compositions for the black plastic material – polystyrene, phenol-formaldehyde, and ABS plastic.
3.72 White Polymer
When the white polymer was deformed in its plastic region, it experienced an enormous amount of necking. At the onset of plastic deformation, it began to form a small neck at it midpoint. As it continued to be plastically deformed, this neck propagated along the length of the white polymer, rather than remaining localized to one region. According to Callister, this spreading of the necked region is typical of semicrystalline polymers. Semicrystalline polymers possess distinct crystalline areas that are distributed throughout an amorphous material. Unlike metals, the neck begins to form prior to the tensile strength, and it gets stronger as the material is deformed. This is because deformation aligns the chains that comprise the polymer. This strengthened neck was observed in our white polymer material, which was strained to the limit of the Comten machine without undergoing fracture. Figure 16.6 in Callister displays a stress-strain curve for semicrystalline polymers that closely resembles the stress-strain curve for our white polymer. This further suggests that the white polymer may be a semicrystalline polymer.
Alternatively, the high tensile strength of the white polymer may be due to a phenomenon known as crazing. Crazing can be described in the following manner. In response to a tensile stress, the polymer forms microvoids, chains of small interlinked holes (Flory, P.J., 1953). The molecular chains between the microvoids then become oriented via structures known as fibrillar bridges, which transmit the stresses between the surfaces of the polymer (Flory, P.J., 1953). This combination of microvoids and fibrillar bridges is known as a craze (Flory, P.J., 1953). This craze can absorb energy and subsequently raise the tensile strength of the material (Flory, P.J., 1953). As crazing is typically found in glassy thermoplasts, this may imply that our white polymer is a glassy thermoplast. On the other hand, glassy polymers tend to have small plastic regions (McCrum, N.G., and Buckley, C.P. 1998), which does not correlate with our stress-strain curve for the white polymer.
Parallel to our treatment of the black plastic material, we began to investigate the mechanical characteristics of common polymers and attempted to find those which correlated with the mechanical characteristics of the white polymer. We started by considering the semicrystalline polymers on Polymerweb. One popular semicrystalline polymer we discovered was Kevlar. We discovered that Kevlar (49) has a yield strength of 28 MPa, an elastic modulus of 0.67 and an elongation (in 2 inches) of 60-130%. Although a value for the tensile strength was also provided, it was not useful, as we were unable to obtain a measured tensile strength for our white polymer. Additionally, the stress-strain curve of Kevlar exhibits a large plastic deformation region (Observations, 2003), which agrees with the behaviour we observed for the white polymer material. Upon further investigation, we discovered that Kevlar is an Aramid, which belongs to the family of nylons. It is indeed a crystalline polymer (. 2003). Kevlar is typically applied in creating bullet proof vests, puncture resistant bicycle tires, and even fire-proof clothing (. 2003). From this description, it appeared as though should possess a high hardness. However, considering table 7, we can see that our white polymer was actually the least hard of the five materials tested. Therefore, in light of this contradiction, we decided to continue our search by considering alternate semicrystalline polymers.
Upon discovering the amarid family of polymers, we decided to investigate Nomex, another member of the amarid family. Nomex was found to have an elastic modulus of 1.3 GPa, a yield strength of 35 MPa, and an elongation of 80-110%. The elastic modulus and yield strength data do not correlate particularly well with our measured mechanical characteristics for the white polymer, but they are not completely divergent. Nomex also appears to exhibit a notable plastic deformation region (Horrigan and Aitken 2003). However, we discovered that Nomex is usually used in a fibrous form, which significantly increases its yield and tensile strengths. This allows it to be used in fireproof clothing, similar to Kevlar (Horrigan and Aitken 2003). The white plastic did not appear to be fibrous on inspection. Additionally, according to Horrigan and Aitken, creating a layer of Nomex fibres makes the stress-strain curve of Nomex much more brittle. This results in the commercially available version of Nomex not having very similar stress-strain or mechanical characteristics to that of our white plastic. As a result, it is unlikely that the white plastic is the fibrous version of Nomex. However, a material composed of loosely bound fibres of Nomex appears as though it would possess similar mechanical properties to our white plastic.
Finally, we chose to investigate the family of nylons. Nylons are called polyamides, and thus are intrinsically related to Kevlar and Nomex. They therefore appeared to be a good place for us to continue our investigations. After investigating the properties of nylons, we discovered that there are many varieties of nylons, some of which agree with the mechanical properties of the white plastic, some of which do not. For example, Nylon 66 has a tensile strength of 75.9-94.5 MPa and a yield strength of 44.48-82.8 MPa, making it correlate poorly with the mechanical properties of the white plastic (Callister, 1997). On the other hand, Nylon 6 has an elastic modulus of 0.76, a yield strength of 36 MPa, and an elongation (in 2 inches) of 70-90%, which appears to match the mechanical properties of our white plastic well (Nylons, 2003).
Additionally, nylons are typically crystalline, which agrees with our assumptions. The moisture absorptive properties of nylons cause their mechanical and physical characteristics to be altered (Nylons, 2003). This explains why nylon 6 (as well as other nylons, like nylon 6 12) have mechanical characteristics matching those of our white plastic, while others do not. Applications of nylons typically include electrical connectors, bearings, fabrics, sportswear, and recreational equipment, to name a few.
3.73 Clear Polymer
The white polymer fractured via a clean even break, and experienced less necking than the white polymer. This suggests that the white polymer is not a semicrystalline polymer, or it would have likely reacted in the same manner as the white polymer. It therefore likely a fully crystalline structure, similar to the black polymer. This would also explain its relatively high yield strength and tensile strength.
Additionally, according to History of Plastics and Polymers, 2003 the polymer chains in objects that are translucent and opaque are in a more crystalline arrangement. This is due to the fact that less light can pass through the polymer if the polymer is more crystalline. This is further support of the clear polymer having a crystal structure.
Once again, we began our investigation of the clear polymer by consulting crystalline structures on Polymerweb. Polyvinyl Chloride has an elastic modulus of 1.3 – 3.2 Gpa, a tensile strength of 40.7 – 51.7 Mpa, and a yield strength of 40.7 – 44.8 Mpa. These values correlate well with the calculated mechanical properties of the clear polymer. It also appears to have a relatively large plastic region on the stress-strain curve, which agrees with our measured results (Stress Strain Behavior of Polymers, 2003). However, I soon discovered upon reading about polyvinyl chloride that it is transparent, not translucent. Therefore, its optical properties do not appear to match those of our clear polymer. However, perhaps the clear polymer is translucent rather than transparent due to its thickness, rather than the crystalline structure. If this is the case, it may be possible for our clear plastic to be composed of polyvinyl chloride (History of Plastics and Polymers. 2003). Additionally, we learned that polyvinyl chloride is a vinyl polymer, many of which share similar mechanical properties. Thus, we continued our investigation by investigating other vinyl polymers.
Upon investigating vinyl polymers on Polymerweb, we discovered that polypropylene is a vinyl polymer with an elastic modulus of 1.8 – 3.3 GPa, a tensile strength of 30 – 49 Mpa, and a elasticity of 40 – 200%. This agrees reasonably well with the mechanical properties of our clear polymer. Upon further investigation, we found that one of the primary applications of polypropylene is as a plastic to make objects such as dish-washer friendly food containers. This can be accomplished because polypropylene has a melting point of 160o –320o F. We found that polypropylene is often translucent, which also appears to support the conclusion that our clear plastic material could be composed of polypropylene. However, it has an amorphous rather than a strongly crystalline structure. In our hardness test, we found that the clear plastic material was relatively hard. This is not supported by it being an amorphous material. Nonetheless, because polypropylene has optical and mechanical characteristics that correlate with those of our clear plastic, it may still be that our clear polymer is composed of polypropylene.
Finally, we decided to revisit one of the most common vinyl polymers, polyethylene. In the black polymer material section, we already demonstrated that polyethylene has a tensile strength of 45.424 MPa, an elastic modulus of 0.2-1.7 GPa, and an elongation (in 2 inches) of 70-90%. These values all correlate with the mechanical properties of the clear polymer. In addition, its stress-strain curve exhibits a moderate plastic region (Stress Strain Behavior of Polymers, 2003). Finally, it is used in a variety of applications that demonstrate its translucency, such as plastic grocery bags and shampoo bottles. Therefore, it appears that our clear polymer could also be composed of polyethylene.
3.74 Metal #1 and Metal #2
The yield strengths, tensile strengths and Young’s moduli of Metal #1 and Metal #2 are very well correlated. This supports our initial assumption that the two metals are made of the same material. The lab handout suggests that either aluminum or brass samples were provided. An initial inspection of the colour and lustre of the samples suggests that the metals are composed of brass, rather than aluminum. Brass is a substitutional solid formed primarily between copper and zinc. Brass has an FCC crystal structure, and is relatively ductile and soft, for concentrations of zinc below 35 wt% (Callister, 1997). In contrast, it has a BCC crystal structure for higher concentrations of zinc, and is subsequently harder and stronger with this structure (Callister, 1997). We found during the hardness test that Metals #1 and #2 required significantly less energy for deformation than either the black or clear polymers. Additionally, the stress-strain curves of both Metals #1 and #2 possess large plastic regions, indicating that both Metals #1 and #2 are ductile (Callister, 1997). This appears to support our brass samples having the FCC crystal structure.
In order to determine the composition of Metals #1 and #2 more exactly, we can attempt to correlate the mechanical characteristics of typical brass alloys with those measured for our metals. Bronze and metals information (see references) states the mechanical characteristics of many common copper alloys, including a number of brasses. The elongation, elastic modulus, and yield strength characteristics of many of these brass alloys appeared to correlate well with our measured results (Bronze and metals information, 2003). For example, soft sheet Gilding brass has a yield strength of 70 MPa, an elongation (in 2 inches) of 15%, and an elastic modulus of 15 GPa, while soft yellow brass has a yield strength of 110 Mpa, an elongation (in 2 inches) of 18%, and an elastic modulus of 20 Gpa (Bronze and metals information, 2003). These values correlate well with our measured values for elongation, yield strength and elastic modulus. However, most of the brass alloys we investigated had tensile strength that were approximately 200 – 300 Mpa. In contrast the tensile strengths of our two metal samples were 131.4 and 133.2 Mpa. The only brass alloys that appeared to have tensile strengths resembling those of our samples were soft sheet red brass, which had a tensile strength of 150 Mpa, and commercial rod brass, with a tensile strength of 175 Mpa (Bronze and metals information, 2003). Soft sheet red brass also had a yield strength of 80 Mpa, an elongation (in 2 inches) of 25%, and an elastic modulus of 23 Gpa, while commercial rod brass had a yield strength of 70 Mpa, an elongation (in 2 inches) of 17%, and an elastic modulus of 18 Gpa. These values did not perfectly correlate with our measured mechanical characteristics for the metals, but they were not completely divergent either. The yield strength, tensile strength, elongation and elastic modulus for the commercial rod brass had the best overall agreement the measured mechanical properties for the two metals. Thus, we can conclude that the brass we were provided with was most likely commercial rod brass.
Commercial rod brass is composed of 90.0% copper and 10.0% zinc. It is possesses a rich and pleasing bronze color. It also has the notable practical properties of good (but not remarkably high) malleability, ductility, strength and hardness. This appears to correlate with our measured mechanical properties for the two metals.
In addition, we noticed that the inclusion of lead in brass alloys tended to lower the ductility of those alloys (Bronze and metals information, 2003). Therefore, it appears likely that our brass alloy does not include significant quantities of lead. Brass alloys also tend to have extremely low resistivities. For example, resistivity varied between 4.660x10-8 ohm-m for Red Annealed Brass to 1.437x10-7 ohm-m for High Strength Yellow Brass (Bronze and metals information, 2003). Such an extremely low range explains why we were unable to obtain any meaningful measure for the resisitivity of the metal samples using DMMs in the lab.
4.0 Conclusion
In this experiment, we determined the mechanical characteristics of five unknown samples. Based on collected data we were able to describe such characteristics as relative hardness, relative conductivity, and stress-strain characteristics. Combining these mechanical properties with the theory of material science, we were able to explain some of the characteristics of our materials and hypothesize about their compositions.
5.0 References
Flory, P.J. 1953. Principles of Polymer Chemistry. Cornell University Press, New York.
Bronze and metals information. 2003. http://www.nbm-houston.com/metals/brass260.html
Callister, W.D. 1997. Material Science and Engineering: An Introduction, 4th Edition. Wiley.
Kinloch, A.J., and Young, R.J.. 1983. Fracture Behaviour of Polymers. Applied Science, London.
McCrum, N.G., and Buckley, C.P. 1998. Bucknall, C.B. Principles of Polymer Engineering. Oxford University Press, Oxford.
Polymers. Characteristics, Applications and Processing. 2003.
Polymerweb, 2003. http://www.polymerweb.com/_datash/
Polystyrene. 2003. http://www.psrc.usm.edu/macrog/styrene.htm
Stress Strain Behavior of Polymers. 2003.
Phenol-formaldehyde Plastic. 2003.
. 2003.
Observations. 2003.
Horrigan, D.P.W. and Aitken, A.A. 2003. Finite element anaylsis of impact damaged honeycomb sandwich.
Nylon. 2003.
History of Plastics and Polymers. 2003.
Polypropylene. 2003. http://www.psrc.usm.edu/macrog/pp.htm.
Properties of Copper based Alloys. 2003. http://ourworld.compuserve.com/homepages/MJVanVoorhis/T005.htm