MAE244 OPTICAL Methods of Stress Analysis - Photoelasticity Lab 3
Photoelastic Stress Analysis – Experimental Procedures
Introduction
Strain gages allow very accurate measurements of strain. A major limitation of strain gages is, however, the fact that they measure only local strain, at specific locations where the strain gages are bonded. In many applications, the strain/stress field has to be determined over the entire structure, or over a designated region of the structure. Such information is often essential for preliminary design studies, since it permits the engineer to identify problem areas, and specific regions of high ocalized stress concentrations. Optical techniques, such as photoelasticity, provide a means to obtain full-field stress distributions.
Objective
The primary goal of this experiment is to learn and implement the basic principles and procedures of photoelasticity. It will demonstrate the ability of photoelasticity to depict visually stress distributions over significantly large areas of a test specimen. The technique is applied also to illustrate the experimental analysis of stress concentrations in a notched tensile specimen.
Equipment
- Circular polariscopes equipped with white light source and monochromator.
- Two different types of photoelasticity specimens, for different types of loading: semi-circular notch specimen under tension for stress concentration determination and beam specimen under four-point bending for flexural bending stress evaluation.
Procedures
1.Stress concentration factor of a semi-circular notched specimen in tension
a.Study and comprehend the setup of a circular polariscope and the functions of each element.
b.Measure and record the dimensions of the semi-circular notch specimen. Place the test specimen in the loading fixture of the polariscope.
c.Set the analyzer at an orientation of 90 and set the polarizer at an angle of 0, to generate "Dark field", integer-order fringes.
d.Load the specimen first to 80 lbs and carefully observe the formation of fringes in white light. Follow carefully the pattern of each fringe and observe its movement.
e.Measure the distance from the edge of the notch to the center of the black fringe. Based on the recorded digital images, determine both the half and whole (integer) order fringes, at the notched section of the specimen (section of minimum area). Extrapolate the fringe distributions to the outer boundary of the specimen, in order to estimate the maximum fringe order (and thus the maximum shear stress) in that region.
- Determine the stress concentration factor
- Increased the applied load to 160 lbs and repeat steps e, f, and g.
2.Beam bending test
a.Measure and record all the relevant dimensions of the beam. Calculate the Moment of Inertia of its cross-section.
b.Record the positions of the load application points in the four-point-bend fixture and draw the shear and moment diagrams.
c.The polariscope is set-up to observe whole order fringes (dark field) when the polarizer and the analyzer are set at orientations 90 apart from each other. Check the setting to verify that the polarizer is set, indeed, at 0 while the analyzer is set at 90.
d.Mount the beam in the center of the loading fixture and load it in small steps, up to the maximum load. Note the positions, characteristics, and formation of the fringes during the loading process: the first fringe will appear on the top and the bottom of the beam. Subsequently, it will move towards the beam center as the load is increased.
e.At maximum load, measure the positions of all the fringes from the center of the beam. This includes fringes in both the positive and the negative directions from the neutral axis (fringes in the top and bottom of the beam, respectively).
Report
- Semi-circular notched specimen
(apply two loads)
- For each applied load, calculate the maximum stress that is present at the notch of the grooved specimen.
b.For each applied load, calculate the stress concentration factor by using the average net stress and the maximum stress calculated in question "a."
c.For each applied load, compare the theoretical stress concentration factor (from the given chart) with the experimental stress concentration factor calculated in question "b". Comment on the accuracy of predicting stress concentration using the photoelastic technique.
2.Beam bending specimen
a.Calculate the experimental stress value corresponding to each fringe, by using the fringe constant given in class having units of lb/(in-fringe).
b.For each fringe location, as measured by its distance from the center of the beam, calculate the theoretical bending stress, by using the beam bending equation and the section moment (resultant moment) from the bending moment diagram.
c.Tabulate the fringe constant, the distance from the beam center, the theoretical bending stress and the experimental stress values calculated from Eq.(2) for the corresponding fringe orders. Compare, in terms of % difference, the theoretical bending stress and the corresponding stress value calculated from the fringe order. Comment of the accuracy of the photoelastic technique.
d.Give some examples of possible applications of photoelasticity or other optical techniques that would be particularly useful.