Stress-Strain

Stress-Strain
Part A
Before starting the experiment, I assembled everything I needed, that includes the scale balance, cans, plastic container, polythene/plastic shopping bag and a piece of wood.

Figure 1: Materials

Figure 2: Scale Balance
I then measured the weights of an empty can and one with peas and another with beans and tabulated the mass of the empty can, one with peas and another with beans.

Figure 3: Experiment setup
I set up my structure as shown in figure 3 and used a flimsy bag to hold the plastic can. I added first two cans with peas and then a can with beans in the container one by one while taking measurements of their weights on the scale balance as shown in figure 3 and figure 4.

Figure 4: Experiment Set-up
At each measurement on the scale balance, I tabulated the reading.
Part B
Results
Number of cans Total weight of cans stretch
Two cans of peas 731.2 grams 1.5 cm
Two cans of peas + one can of beans 1261.4 grams 2.5 cm
Using Flimsy bags
The cross-sectional area of thicker bags = 7×10-5mConverting grams to newtons
1 gram=0.00980665 N1162.3 grams= ?1162.3 g ×0.00980665N1g=11.40NConverting centimeters to meters
1 meter = 100 centimeter? = 2.5 centimeter=0.025 metersFracture stress is given by
ForceCross-Sectional Area x Stretch=11.40 N8×10-6m×0.025 m=57.0 MPaFrom the results obtained in the experiment the fracture stress if 57.0 MPa slightly higher than maximum limit for high-density polyethylene. The slight error in the result might have been obtain from erroneous readings.

Therefore, by approximating the fracture stress of the material lies within the 20MPa and 30MPa for the high-density polythene. Hence, the material used to make the plastic bag used in the experiment is low-density polythene (LDPE).
Part C
The masses of the cans should be evenly distributed in the plastic container used to hold them as this will ensure there is an equal distribution of force at both sides of the plastic bag hence giving it the same amount of stretch. Moreover, it took two cans of peas and one can of bean to fracture the plastic thus, the mass of a single can of beans was heavier than that of a single can of peas. The range of values that fracture stress falls in between is approximately between 7N and 13N.
Part D
The Yield Stress (Yield Strength)
To obtain the Yield Strength on the curve, a straight line is usually drawn from the strain axis a distance D (0.2% offset point at the strain axis for most metals) upwards parallel to the straight-line section of the curve to intersect with the stress-strain curve. Then the point of interaction of the curve and the line drawn is extended of the stress axis to give the Yield Strength (Arrayago et al., 2015).
The strain at the elastic limit (the yield point)
This is the point on the curve where there starts to be an unproportioned change in the stress and strain properties of the curve.
The extension at the elastic limit (the yield point)
This is the point where the change in the graph is no longer linear, that is, between the proportional limit and the yield point
The ultimate tensile stress
This is the maximum possible stress, that is, the highest point of the curve in the stress axis,
The Young’s modulus
This is obtained by computing the gradient of the section of the curve that is a straight line. In this case, it is the change in stress divided by the change in strain along the straight-line part of the curve (Arrayago et al., 2015).
The fracture stresses
Getting fracture stresses will require one to obtain the actual force and the area of the necking section from the graph.
Yield strength = 250MPa
The strain at the elastic limit (the yield point) = 0.005The extension at the elastic limit (the yield point) = 0.01-0.005 = 0.005The ultimate tensile stress = 275 MPaThe Young’s modulus =250-0×1060.005= 5 GPa
Reference
Arrayago, I., Real, E., & Gardner, L. (2015). Description of stress–strain curves for stainless steel alloys. Materials & Design, 87, 540-552.