Pulling things appart - The following experiment was designed to determine some of the mechanical characteristics of various materials. These included the stress strain characteristics, such as Young's Modulus, yield strength and tensile strength.

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ENSC 330

LAB #1

PULLING THINGS APART

Andy Somody        97300-6222                                        


1.        Introduction

The following experiment was designed to determine some of the mechanical characteristics of various materials. These included the stress strain characteristics, such as Young’s Modulus, yield strength and tensile strength.  We also performed experiments to determine the resistively, relative hardness, and toughness of the given samples. We then used the theory of material science to help explain the properties of our samples.

Please refer to the lab hand out,  “Pulling Things Apart” for the objectives, materials and procedures.

2.        Observations

The lab handout has specified that two of the provided samples are composed of the same material. In our case, it appeared on initial inspection that metal #1 and metal #2 were composed of the same metal. This initial observation will be supported by comparing the stress-strain characteristics of metals #1 and #2.

The following observations were made before the samples were tested for their various physical properties. The measurements of length were made with a ruler, which have an uncertainty of ±0.01 cm. The measurements of width and thickness were both made using calipers, which have an uncertainty of ±0.002 cm.

* All measurements are in centimeters

Table 1: Initial measurements and observations

 

There were several properties of the materials that may have contributed to errors in this experiment. Metals #1 and #2 were both very soft. Therefore, tightening the clamps with too much force could cause the deformation at the ends of the sample. Since the volume of the sample must be consistent, this would cause a parallel deformation in the remainder of the sample, potentially affecting the results of the experiments. Additionally, the deformation in the ends of the metal sample could allow it to slip in the clamps. The measurements at the point of slippage would be affected, cause spikes in the subsequent stress-strain curve. The black polymer is also extremely stiff, which causes it to have a tendency to slip in the clamps.

Unfortunately we broke our original black polymer sample due to over tightening of the bottom clamp on the Comten machine. While the broken sample possessed a different length from our original sample, it was still suitable for subsequent testing, since it’s material composition was identical to that of the original sample.

2.1.        Stress-Strain Curves

The following results were derived using the Comten machine. Based on the definitions of stress and strain, we were able to use the following relations to create our stress strain data.  

Where ε is the strain,  lf is the final length to which the sample was strained, and li was the initial length of the sample.

Where σ is the stress applied to the sample, F is the instantaneous load applied perpendicular to the cross-section of the sample, w is the sample width, and t is the sample thickness. The generated stress-strain curves are shown in the subsequent figures.

Figure 1: Stress-Strain curve for Black Polymer

Figure 2: Stress-Strain curve for White Polymer

Figure 3: Stress-Strain curve for Clear Polymer

Figure 4: Stress-Strain curve for Metal #1

Figure 5: Stress-Strain curve for Metal #2

* Note: We also calculated true stress and strain. The stress-strain curves were slightly more skewed but the general shapes were the same. As a result we have chosen to show only the calculations and graphs for standard stress and strain.

                

Table 2: Observations of the provided materials on fracture

3.        Discussion and Results

3.1        Young’s Modulus

Young’s Modulus (modulus of elasticity), is the ratio of stress-strain only valid during the elastic deformation region.

                                                (3)

In order to achieve the best approximation of the Young’s Modulus we calculated the slope of a line composed only of data points from the linear (elastic) region of the stress-strain curve. Note that for the white polymer sample, the initial portion of the stress-strain curve was highly non-linear. A secant modulus and a tangent modulus (Callister, 1997) were therefore used in this case. The tangent modulus has been taken at the most elastic portion of the curve. The secant modulus has been taken as the line connecting the origin to the maximum point on the curve. These two modulii have been used as the maximum and minimum modulii of elasticity for the white polymer.

The cross-sectional areas of each of the samples were calculated from their widths and thicknesses, which each possess an uncertainty of ±0.002 cm. The load cell used to measure stress produced sudden variations on the order of 5 newtons when a strain was applied, implying that it has an uncertainty of ±5 newtons. Strain was measured with the calipers which, as previously discussed, possess an uncertainty of ±0.002 cm. However, the largest source of uncertainty in measuring Young’s Modulus is simply in overlaying a slope onto the elastic region of the graph. We have made the assumption that the points on the graph are discernable to half of the smallest discernable division. Since the above formula for Young’s Modulus results in a compounded error, the relative uncertainties for stress and strain have been summed to yield the relative uncertainty for Young’s Modulus. This uncertainty has been tabulated in the table of Young Modulus data below.

* All measurements are in GPa

Table 3: Young’s Moduli of the provided materials

3.2        Yield Strength

 

Yield strength is the stress at which polymer deformation begins. For metals, a convention has been established in order to evaluate the yield strength. A tangent is drawn parallel to the elastic portion of the stress-strain curve with a strain offset of .002 units (Callister, 1997). The yield strength of the material is the stress at which this line intersects with the stress-strain curve.

For plastic polymers, the yield strength is taken at the maximum point on the stress-strain curve (Callister, 1997). This convention has been used to determine the yield strengths of the white polymer and clear polymer.

For the black polymer, there was no discernable peak in the stress-strain curve. Therefore, the plastic polymer convention could not be applied. We attempted to apply the offset tangent method used for metals to this stress-strain curve. However, the black polymer sample fractured just as its stress-strain curve was sufficiently non-linearized to intersect with the offset tangent line. Therefore, no meaningful value for the yield strength of the black polymer material could be obtained. Nonetheless, we have taken the tensile strength, the point at which the black polymer material fractured, to be equal to its yield strength.

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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

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