lab 4 - photoelasticity

CET 3135-002Mechanics of Materials with Laboratory

Spring 2014

Laboratory Report Lab 4 – Photoelasticity Demonstration

Submitted by: James Pettus, Marquis Smith, Haroon Rashidi

Laboratory Date: February 26, 2015

Date of Submission: March 5, 2015

Submitted to: Dr. Runing Zhang

Team Members: James Pettus, Marquis Smith, Haroon Rashidi

James Pettus, Marquis Smith, Haroon Rashidi

Lab No. 4 – Photoelasticity Demonstration CET 3135-001

3/5/2015

Table of Contents

Abstract................................................................................................................................3Theoretical Background.......................................................................................................3List of Equipment................................................................................................................4List of Materials...................................................................................................................5Test Procedures....................................................................................................................5Summary of Data.................................................................................................................5Results..................................................................................................................................6Conclusions..........................................................................................................................8Safety...................................................................................................................................9References............................................................................................................................9Signature Page...................................................................................................................10

of 10



3/5/2015

Abstract

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 in two different cases. One Plexiglas (Bayer Makrolon GP Polycarbonate) sample underwent forces applied by the Instron 5569. Contour maps and lines were seen with help from the polarized lenses. These lines showed the stress concentration of the specimen. The second case involved a cantilever beam of the same material with one end clamped to the table while the other end was loaded with the weight of 21.8 Newtons.

Theoretical Background

Photoelasticity is a nondestructive, optical technique for experimental stress analysis that is particularly useful for structural components with complex geometric configurations, or subjected to complex loading conditions. Analytical methods of stress analysis are very cumbersome, and often unavailable for such cases, thus amplifying the importance and the need for a suitable experimental approach. Photoelasticity has been used widely, over an extended period of time, for problems in which stress distributions have to be investigated over large sections, or regions, of the structure. It provides quantitative information on highly stressed areas and the associated peak stresses. Equally important is the capability offered by photoelasticity to discern areas of low stress levels, where structural materials are utilized inefficiently. The method of photoelasticity can be applied in various forms to a wide variety of problems ranging from stress wave propagation to fracture mechanics, to three-dimensional studies. The applications illustrated and practiced in the following experiments are restricted, however, to two-dimensional static problems

The photoelasticity experiment showed how the material reacted under different axial loads. The principle applied to this test is the stress concentration which follows the formulas below (Hibbeler, 2011):

When the geometrical shape of the material is not uniform, stress concentration is not uniform. Thus, maximum stress is important to determine where failure will occur.

of 10



3/5/2015

The principles of this lab include material properties, calculations and laws used, and procedures introduced.Material Properties:

Determine the value of the stress fringe value for the material provided.o N/m2 / m / fringe or N/m o and lb/in2 / in / fringe or lb/in

Experimentally determine the stresses acting in a beam and compare measured and calculated results

o Calculate results using an analytical, continuum, beam modelo Discuss differences in terms of the measured stress fringe value

Experimentally determine the stress state in the model supplied and compare measured and calculated results developed using either numerically or analytical models

Calculations and laws used: N = n + r :where n = lowest fringe order that moves to the test point, r = fraction

read from the COMPENSATOR scale σx= [ E / (1 +ν) ] * f * N⇒σx= [ E / (1 +ν) ] * f *(n + r) : σx and σy= principal

stresses in test part surface, E = elastic modulus of test part, ν= Poisson’s ratio of test part

Kt =σx /σnom: where σnom was calculated to be 93.1 psi.

List of Equipment

Two (2) Scott-Engineering Services Polariscopes Instron © 5569 Load Frame (50 kN – 11,250 lb. force capacity) Microcomputer with BlueHill © Software Two (2) tension grippers for Intron 5569 Load Frame Two (2) 0 to 0.25-inch tension jaws for each tension gripper Two (2), 3-inch deep, 3-foot long steel beams A 6-inch, C-clamp A knife edge weight hanger Two (2) weights with a hook weight hanger totaling 21.8 N (2kg & 217.3g

hanger) Digital calipers 18-inch long measurement ruler High resolution digital camera (optional piece of equipment)

of 10



3/5/2015

List of Materials

The specimens that were used in the photoelasticity lab were made of Bayer Makrolon GP © Polyicarbonate (Plexiglas). One was a solid rectangle shape, the other, had a hole.

Test Procedures

1. Start the computer with the Bluehill software2. Turn on the Instron 5569 Load Frame (this is where specimen will be placed)3. Set up the Polariscope so that its beam of light hits the mid-point marker on

the cantilever beam apparatus.4. Set the compensator ring on the analyzer to zero and move knob B to the magni-

tude position. Make sure also that the dial counter of the angle reads 90 degrees.5. The unloaded beam viewed through the analyzer should appear black except for

the edge of the beam and areas near where the beam is clamped. Load the beam sufficiently to produce at least 3 fringes. The fringe colors in the coating should vary correspondingly and progress as follows: black, yellow, red, purple, blue, yellow, red, purple, blue – green, yellow green, red, green.

6. Photograph and draw the sketch colorbands that appear.7. Set up the Polariscope so that its beam illuminates the top of the center notch. 8. The total weight exerted on the system by the hanger and weights will be 21.8 lbs. 9. Make certain that the angle display reads 0 degrees10. Load Tension specimen into Instron 5569(with and without hole) at a load of 35

lbs. 11. Photograph and hand draw specimen while in place12. Each group of students tests the specimen and record their own drawing of the

data on paper13. Each group should input the group number of their student group prior to testing,

and save their data at the completion of their respective test run.

Summary of Data

The photoelastic demonstration consisted of a cantilever beam apparatus and specific specimen properties that are included in table along with stress and strain values.Cantilever Beam Apparatus- Photo-Elastic DemonstrationDate: February 26, 2015Group No. : 4Material Type: Cantilever BeamHeight towards left: 4.531cmHeight towards center: 4.305cmHeight towards end: 3.983cmThickness: 0.592cm

of 10



3/5/2015

Results

Results from the experiment are shown in the drawings and pictures below.

Drawing 1 – Cantilever Stress

Drawing 2 – Non-uniform stress due to the hole

of 10



3/5/2015

Photo 1- Cantilever specimen

of 10



3/5/2015

Conclusions

The results from the experiment were expected according to our theoretical information. Contour maps of the holed-specimen showed the stress concentration in both ends of the test object as well as the middle section, which experienced the most normal stress. The uniform area of the specimen reflected little or no stress concentration. With heavier axial load, the contour map became clearer at where the normal stress would focus.

The contour maps of the cantilever consisted wave forms which concentrated at the right end of the specimen where the axial load applied. The light wave spread out to the regions with less stress. Overall, the contour maps of the cantilever test object gave more distinct photoelastic fringe patterns.

Since this experiment’s outcomes were graphic demonstration. Possible errors came from set up process and dimension measurements of the specimen. Light interference also contributed to quality of the contour maps.

From the results from the experiments, geometry of products should be considered when designing engineering tool to prevent potential undesired failures.

Using white light the color chosen for observing of dark fringes was red. At low stress the darkest fringes were nor primarily red. Light-material interactions, residual stress in the specimen and specimen twist in the fixture can account for this variation in color. At the three highest loads the uniform color indicates the close to ideal situation of uniform stress. The Polariscope is set up for a light field and so with zero stress in an ideally clear specimen the specimen will appear light. As the stress in the specimen increases a relative retardation between the light waves develops.There are several obvious difficulties and problems with the material calibration proce-dure described above. For example, - A series of measurements is needed and so problems in obtaining load measurements at exactly similar fringe conditions are expected, - The cross section area of the tensile specimen changes with different loads and so prob-lems with specifying the stress at different loads are expected.A way around many material calibration problems is to use a procedure in which several fringes of different order are available from one specimen at one load. The idea is to use a specimen in which stress varies over the specimen and for which the stress state is known.

of 10



3/5/2015

Safety

Safety while performing the test was the highest priority in the experiment. The test was conducted according lab manual procedures. Students performing the test kept a safe dis-tance away from the Instron machine in order to prevent injuries from the moving parts. While the test was running, all group members observed the equipment so that any signs of malfunction would be immediately noticed. We further increased our safety by having the lab coordinator present to observe our experiment.

References

Harris, D.W. and Mattivi, M (2005). Manual for Engineering Materials Laboratory. Uni-versity of Colorado at Denver, Denver, CO.

Hibbeler, R.C. (2011). Mechanics of Materials (9th Edition), Boston, MA: Prentice Hall.

Steinhauser, Edward. "Mechanics of Materials Laboratory Notes." Steel Tensile Test. Civil Engineering Technology, 2014. 1-9. Print.

Steinhauser, Edward. Example Lab Report 01. Denver, CO: Metropolitan State Univer-sity Denver, 2013. Print.

of 10



3/5/2015

Signature Page

Mechanics of Materials Testing Laboratory- CET 3135- Section 001

Laboratory No. 4- Photo-Elastic Demonstration

Group No. 4 – James Pettus, Marquis Smith, and Haroon Rashidi

James Pettus Date

Marquis Smith Date

Haroon Rashidi Date

of 10

lab 4 - photoelasticity

Documents