Stoichiometry of a precipitation reaction lab

Lab 2, photoelasticity

Introduction

Photoelasticity is used for observation of stress concentrations within a part. The light is projected onto the part and the reflection is viewed through a polariscope to view the fringe count on the surface. Under a constant tensile load, we neglect stress concentrations at the pinned ends and use a plastic plate of sufficient length to distribute the tensile load evenly before approaching the region that we were interested in finding the stress concentrations. Using the characteristic 8dimensions away from the applied tensile force ensures that our measurements can be as accurate as possible. Three points on the U-shaped specimen were studied where critical points of stress were expected to be (See Figure 1).

The purpose is this lab is to become more familiar with FEA and to find KT values using three different methods. The value is sought to be found by using good engineering judgement, results from FEA, and through hand calculations.

Governing equations include:

Methods

The material of the U-shaped specimen was polycarbonate. Our model was first measured, then dimensioned, and finally sketched in AutoCad. Placing our specimen in the tensioner within the polariscope, we applied load until we could see change within our specimen and took stress concentrations at the most critical point, which was around the radius of a fillet at point 3. We had to do this because our compensator dial for the fringe order was limited to a certain number and if load was excessively applied our model would not work. When the experiment proved to give usable results for point 3, point 1 and point 2 were tested (See Figure 1).

A polariscope consists of a plane light (Figure 2(a)), a linear polarization filter denoted “polarizer” (b), an optional λ/4-wave plate (c), the object to analyze (d), another optional λ/4-plate (e), another linear polarization filter denoted “analyzer” (f), and the observer or optical acquisition device (g). In a circular polariscope, both λ/4-plates are present, whereas they are missing in a plane polariscope. A wave plate causes a retardation, i.e., a lower speed of light, on the

light components oriented along its “slow” direction (blue arrows in Figure 2), whereas components along its “fast” direction are less retarded. This results in a phase shift of the slow component relative to the fast component. A λ/4-

plate causes a phase shift of p/2, producing circularly polarized light from linearly polarized light. Hence, the linear polarization filter (b) together with the wave plate (c) can be subsumed as a circular polarization filter (circular polarizer),

and the wave plate (e) together with the analyzer (f) as a second circular polarization filter. In a circular polariscope, the two wave plates are oriented perpendicular, i.e., with opposite fast and slow directions (Bußler 143).

Results

Type of Calculation

FEA

Hand

Experimental

Max Stress-σ (psi)

12,101

11,239

7906.8

Percent Error to FEA

0%

7.123%

34.660%

From FEA analysis, σMAX=12,101 psi. From the hand calculations σMAX=11,239 psi. From experimental method, σMAX=7906.8 psi. A high percentage error occurs for the experimental calculation. Reasons include inaccuracies in recording data, human error, and imperfections in the specimen tested.

*Refer to the last section in the Appendices for Results using MathCad*

Discussion

Computer software such as Simulation Mechanical makes engineering more practical in design and testing. Relying solely on computers to run calculations is not enough though. One must understand how equations are being applied to different stress situations. FEA is much more time saving and accurate if you set up your model correctly. The percent error for the hand calculations was fairly small at 7.1% whereas the percent error for the experimental method proved to be very high at 34.6%. Such a large error doesn’t correspond to the other two methods and proves that human error was to blame.

References

Bußler, M., T. Ertl, and F. Sadlo. "Photoelasticity Raycasting." Computer Graphics Forum 34.3 (2015): 141-150. Business Source Complete. Web. 13 Oct. 2016.

(for Methods section)

http://www.efunda.com/designstandards/plastic_design/radius.cfm

(for Figure 5)

Appendices

Figure 1. 2D Specimen with Test Points

C:\Users\Dominic\AppData\Local\Microsoft\Windows\INetCacheContent.Word\Specimen 2D with Points.png

Figure 2. Polariscope Illustration

Figure 3. Fringe Order Data

Compensator Dial Reading

Reading

Point 1

Point 2

Point 3

1

60

50

132

2

53

49

138

3

67

48

138

4

56

44

135

5

69

46

140

AVG

61

47.4

136.6

Calibration Constant for Compensator = 44

N-Values

N1=1.386

N2=1.077

N3=3.105

Figure 4. FEA of Prototype

E:\Stress & Strain Lab\Stress Strain Lab #2\FEM(1).jpg

Figure 5. Chart for chosen KT value

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