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ISE 2204 HW2

by: Claude Zoghzoghi
Claude Zoghzoghi
Virginia Tech
GPA 3.77

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Homework 2 for Manufacturing Processes
Manufacturing Processes
Dr. Sturges
Class Notes
25 ?




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This 3 page Class Notes was uploaded by Claude Zoghzoghi on Tuesday September 6, 2016. The Class Notes belongs to ISE 2204 at Virginia Polytechnic Institute and State University taught by Dr. Sturges in Fall 2016. Since its upload, it has received 20 views. For similar materials see Manufacturing Processes in Industrial Engineering at Virginia Polytechnic Institute and State University.

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Date Created: 09/06/16
Homework 2 Thursday 7 September ISE 2204 Claude Zoghzoghi PROBLEM 3 Problem Statement: Plot the true stress-strain curve for a rubber-band and then comment on the following: Young’s modulus, the Yield strength, the UTS and the K and n values. Assumptions: I used US coins to load a box held by the rubber band (Quarters 5.65 g and Nickels 5.00g) and measured the stretched length of the rubber band [Table 1]. I then recorded everything in Excel and used true strain and stress formulas (ln(L/L ) 0nd F/A respectively). I used Thickness*Width to find the cross-sectional area of the rubber band. Approach: After recording everything, I could plot my true stress-strain curve for a rubber band. True Stress-Strain curve for a Rubber Band 1400000 1200000 1000000 800000 600000 True stress (psi) 200000 0 0 0.2 0.4 0.6 0.8 1 1.2 True Strain Adding more weight was not handy so I stopped at 1.3 kg under the rubber band. It did not fail, so adding more weight is still possible and would make the stress increase in a very high manner. Conclusion: Young’s modulus (E) represents the slope of the stress-strain curve in the elastic region, it is a measure of stiffness of the material. We can see from the graph that the slope is a little bit small, implying a smaller E value for a rubber band. The larger E is, the more resistant is the material to any kind of deformation. The UTS is the maximum force a material can withstand without fracturing when stretched. However, the UTS is very high for rubber bands, since it takes a lot of weight to fracture it and start damaging it. We can also see the value of k from the graph above, which is approximately 120,000 psi or 827 MPa. The n (when the curve stops being linear) value can also be found from the graph; it is approximately 0.4 in this case. The Yield Point is the force at which the rubber band starts to deform permanently. It is difficult to point to the exact Yield Point on this curve because the transition is gradual. th 7 POINT QUESTION We have to use Hooke’s law and find out the stretched length of the rubber band under a certain weight. We know that F = k ∙∆L & F = m∙g. From that, we can conclude that spring constant k = (m∙g)/ ∆L where k is the spring constant, m the mass, g the gravity and ∆L the difference of the distances. After conducting my experiment, I measured the following values: li= 8.8 cm = 0.088 m | l =f9.5 cm = 0.098 m | ∆L = 0.095-0.088 = 0.01 m | m = 0.16 kg k = (0.16 kg). (9.81 m/s ) / (0.01) = 156.96 N/m Appendix Mass (kg) DeltaL (m) Width (m) Weight Thickness (m) Area 0.0615 0.095 0.006 0.603315 0.002 0.000012 0.102 0.097 0.006 1.00062 0.002 0.000012 0.2 0.102 0.006 1.962 0.002 0.000012 0.31 0.11 0.005 3.0411 0.002 0.00001 0.42 0.12 0.005 4.1202 0.002 0.00001 0.535 0.138 0.005 5.24835 0.002 0.00001 0.6 0.144 0.005 5.886 0.002 0.00001 Table 1: Recorded values for the experiment with the rubber band. True Strain True Stress 0.03208831 50276.25 0.0529224 83385 0.10318424 163500 0.17869179 304110 0.26570317 412020 0.40546511 524835 0.44802472 588600 0.55961579 686700 0.69856725 784800 0.87637412 1030050 1.03889305 1275300 Table 2: Values obtained for the respective True Stress and True Strain for the graph.


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