MEC 430 LAB 1.docx

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Faculty of Engineering, Architecture and Science Department of Mechanical and Industrial Engineering Program: Mechanical Engineering/Industrial Engineering Course Number MEC430 Course Title Solid Mechanics I Semester/Year Fall/2023 Instructor Dr. Papini Lab Report NO. 1 Report Title Photoelasticity Section No. 06 Group No. 1 Submission Date October 10, 2023 Due Date October 11, 2023 Name Student ID Signature* Jaiwand Singh Hanspal xxxx92101 Moiz Asad xxxx26892 Dominic Fernandes xxxx12706 Justin Suvanto xxxx15959 James Morhardt xxxx97151 (Note: remove the first 4 digits from your student ID) *By signing above you attest that you have contributed to this submission and confirm that all work you have contributed to this submission is your own work. Any suspicion of copying or plagiarism in this work will result in an investigation of Academic Misconduct and may result in a “0” on the work, an “F” in the course, or possibly more severe penalties, as well as a Disciplinary Notice on your academic record under the Student Code of Academic Conduct, which can be found online at: http://www.ryerson.ca/senate/policies/pol60.pdf .

1.2 Abstract The Photoelastic Coating Calibration Lab represents a crucial facility in the field of experimental stress analysis. This abstract provides an overview of the objectives, methodologies, and significance of such a lab in improving the accuracy and precision of stress analysis through photoelastic coatings. Photoelasticity is a widely used technique for studying stress distribution in various materials and structures. Photoelastic coatings, a key component of this technique, offer a practical means to visualize stress patterns by exploiting the birefringent properties of certain polymers when subjected to mechanical loading. The calibration of these coatings is essential to ensure the fidelity and reliability of stress data acquired through photoelasticity. In this laboratory, a systematic approach to photoelastic coating calibration is established. The process involves the preparation and application of photoelastic coatings onto the surfaces of specimens of interest. Various stress calibration tests are then conducted, which may include applying known loads or subjecting specimens to controlled mechanical stresses. The coatings' response is carefully recorded, typically through polarization equipment and high-resolution imaging systems. The significance of a well-equipped Photoelastic Coating Calibration Lab lies in its ability to: Enhance Experimental Accuracy: By calibrating photoelastic coatings, researchers can obtain precise and accurate stress data, which is vital for validating theoretical models and ensuring the safety and performance of engineering structures. Facilitate Material Characterization: The lab allows for the characterization of material properties, such as strain-optic coefficients, which are essential for stress analysis in diverse applications. Support Structural Integrity Assessments: Industries rely on calibrated photoelastic coatings to assess the integrity of components and optimize designs. Advance Research in Stress Analysis: Researchers can explore new avenues in experimental stress analysis and develop innovative techniques by leveraging the capabilities of a well-equipped calibration laboratory. Educational and Training Opportunities: The lab serves as an invaluable resource for educating students and training professionals in the field of stress analysis, fostering a deeper understanding of the principles and applications of photoelasticity. The Photoelastic Coating Calibration Laboratory plays a pivotal role in advancing the field of experimental stress analysis. Through rigorous calibration processes, it ensures the accuracy and reliability of stress data obtained using photoelastic coatings, thereby contributing to the improvement of engineering designs, structural safety, and the development of innovative stress analysis techniques as seen throughout this lab.

1.3 Purpose Upon concluding the laboratory experiment, students will undertake the calibration and measurement of the optical coefficient for a sample of photoelastic material. This involves applying a layer of photoelastic plastic onto a straightforward cantilever beam, allowing for subsequent analysis.

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1.4 Apparatus: Beam with photoelastic coating : A beam with a photoelastic coating is a structural element covered in photoelastic plastic. It enables the visualization and analysis of stress distribution by observing changes in polarized light as mechanical forces are applied, making it a valuable tool for understanding structural behavior and optimizing designs in engineering and materials science. Loading frame : A loading frame is a mechanical device used to apply controlled forces, pressures, or loads to test specimens in various scientific and engineering experiments. It's crucial for assessing material properties, structural integrity, and performance under different conditions, aiding in research, development, and quality control processes. Precision dead load : A precision dead load refers to a highly accurate and stable weight or mass used for calibration and testing purposes. It is employed in various industries to ensure the accuracy and reliability of measurement devices such as scales, balances, and force-testing equipment. Portable polariscope : A portable polariscope is a compact and transportable optical instrument used to analyze and visualize stress patterns in transparent materials. It employs polarized light to reveal stress-induced birefringence, making it a valuable tool for field inspections and quality control in industries like glass manufacturing, engineering, and materials science. 1.5 Experimental Procedure (specific procedure)

1.6 Experimental results Uncorrected Null Load (lb) Fringe for Location 1 Fringe for Location 2 Fringe for Location 3 Fringe for Location 4 Fringe for Location 5 12 1.07 1.25 1.37 1.52 1.58 10 1 1.1 1.18 1.32 1.37 8 0.37 0.48 0.56 0.67 0.7 6 0.3 0.34 0.36 0.38 0.43 Uncorrected Tardy Load (lb) Fringe for Location 1 Fringe for Location 2 Fringe for Location 3 Fringe for Location 4 Fringe for Location 5 12 1.38 1.72 1.98 2.4 2.76 10 1.14 1.4 1.6 2.02 2.32 8 0.92 1.1 1.24 1.62 1.92 6 0.72 0.8 0.92 1.26 1.32 Corrected Null C.F 1.01 Load (lb) Fringe for Location 1 Fringe for Location 2 Fringe for Location 3 Fringe for Location 4 Fringe for Location 5 12 1.0807 1.2625 1.3837 1.5352 1.5958 10 1.01 1.111 1.1918 1.3332 1.3837 8 0.3737 0.4848 0.5656 0.6767 0.707 6 0.303 0.3434 0.3636 0.3838 0.4343 Corrected Tardy C.F 1.01 Load (lb) Fringe for Location 1 Fringe for Location 2 Fringe for Location 3 Fringe for Location 4 Fringe for Location 5 12 1.3938 1.7372 1.9998 2.424 2.7876 10 1.1514 1.414 1.616 2.0402 2.3432 8 0.9292 1.111 1.2524 1.6362 1.9392 6 0.7272 0.808 0.9292 1.2726 1.3332

F Value Null Load (lb) Location 1 Location 2 Location 3 Location 4 Location 5 12 0.01340083808 0.01433889675 0.01569952199 0.01650859823 0.01815050221 10 0.01194908062 0.01357850071 0.01518950927 0.01584158416 0.01744391332 8 0.02583584999 0.02489391796 0.02560517276 0.02496822817 0.02731218428 6 0.02389816124 0.02635826608 0.02987270156 0.03301719646 0.0333462715 F Value Tardy Load (lb) Location 1 Location 2 Location 3 Location 4 Location 5 12 0.01039050489 0.01042070985 0.01086280057 0.01045544554 0.01039050489 10 0.01048164967 0.01066882198 0.01120226308 0.01035192628 0.01030093157 8 0.01039050489 0.01086280057 0.01156362641 0.01032636597 0.00995756718 5 6 0.00995756718 5 0.01120226308 0.011689318 0.00995756718 5 0.01086280057 K Value Null Load (lb) Location 1 Location 2 Location 3 Location 4 Location 5 12 0.01058702442 0.00989441534 5 0.00903689934 8 0.00859400647 1 0.00781658812 2 10 0.01187329841 0.0104485026 0.00934032808 6 0.00895585937 5 0.00813320941 3 8 0.00549140051 6 0.00569918323 9 0.00554087259 3 0.00568222138 4 0.00519456805 6 6 0.00593664920 7 0.00538256194 8 0.00474931936 6 0.00429700323 5 0.00425459859 8 K Value Tardy Load (lb) Location 1 Location 2 Location 3 Location 4 Location 5 12 0.01365429318 0.01361471551 0.01306062826 0.0135694839 0.01365429318 10 0.01353556019 0.01329809422 0.01266485164 0.01370517874 0.01377302616 8 0.01365429318 0.01306062826 0.01226907503 0.01373910245 0.0142479581 6 0.0142479581 0.01266485164 0.01213714949 0.0142479581 0.01306062826

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1.6.1 Applied Stress (Load) Stress (lb/in^2) Load (lb) Fringe for Location 1 Fringe for Location 2 Fringe for Location 3 Fringe for Location 4 Fringe for Location 5 12 4608 5760 6912 8064 9216 10 3840 4800 5760 6720 7680 8 3072 3840 4608 5376 6144 6 2304 2880 3456 4032 4608 1.6.2 Measured Strain Strain null Load (lb) Location 1 Location 2 Location 3 Location 4 Location 5 12 0.01448228571 0.01810285714 0.02172342857 0.025344 0.02896457143 10 0.01206857143 0.01508571429 0.01810285714 0.02112 0.02413714286 8 0.00965485714 3 0.01206857143 0.01448228571 0.016896 0.01930971429 6 0.00724114285 7 0.00905142857 1 0.01086171429 0.012672 0.01448228571 Strain tardy Load (lb) Location 1 Location 2 Location 3 Location 4 Location 5 12 0.01448228571 0.01810285714 0.02172342857 0.025344 0.02896457143 10 0.01206857143 0.01508571429 0.01810285714 0.02112 0.02413714286 8 0.00965485714 3 0.01206857143 0.01448228571 0.016896 0.01930971429 6 0.00724114285 7 0.00905142857 1 0.01086171429 0.012672 0.01448228571

Strain Difference vs. Corrected Tardy Location Corrected 12lb Strain 12lb Corrected 10lb Strain 10lb Corrected 8lb Strain 8lb Corrected 6lb Strain 6lb 1 1.0807 0.014482 1.1514 0.012069 0.9292 0.009655 0.7272 0.007241 2 1.2625 0.018103 1.414 0.015086 1.111 0.012069 0.808 0.009051 3 1.3837 0.021723 1.616 0.018103 1.2524 0.014482 0.9292 0.010862 4 1.5756 0.025344 2.0402 0.021120 1.6362 0.016896 1.2726 0.012672 5 1.5958 0.028965 2.3432 0.024137 1.9392 0.019310 1.3332 0.014482 Strain Difference vs. Corrected Null Location Corrected 12lb Strain 12lb Corrected 10lb Strain 10lb Corrected 8lb Strain 8lb Corrected 6lb Strain 6lb 1 1.0807 0.014482 1.01 0.012069 0.3737 0.009655 0.303 0.007241 2 1.2625 0.018103 1.111 0.015086 0.4848 0.012069 0.3434 0.009051 3 1.3837 0.021723 1.1918 0.018103 0.5656 0.014482 0.3636 0.010862 4 1.5352 0.025344 1.3332 0.021120 0.6767 0.016896 0.3838 0.012672 5 1.5958 0.028965 1.3837 0.024137 0.707 0.019310 0.4343 0.014482 1.7 Calculation 1.7.1 Determine principal strain difference Strain Difference = = ε ? − ε ? 𝑁𝑓 1.7.2 Determine fringe value, f, for the plastic 𝑓 = σ·(1+𝑣) 𝑁·𝐸 Example: Load = 12lb , location 1 , Null = 0.01448 lb*in σ N = 1.0807 E = 0.42*10^6 psi v = 0.32

𝑓 = 0.01448 · (1+0.32) 1.0807 · 0.42×10 6 = 0. 01340083808 1.7.3 Determine the optical coefficient, K, for the plastic 𝐾 = λ 2𝑡𝑓 Example: Load = 12lb , location 1 , Null = 22.7*10^-6 in λ = 0.08 in 𝑡 = 0.01340083808 𝑓 0.01058702442 𝐾 = 22.7×10 −6 2 · 0.08 · 0.01340083808 = 1.7.4 Modulus of elasticity for the material 𝐸 = σ·(1+𝑣) 𝑁·𝑓 Example: Load = 12lb , location 1 , Null = 0.01448 lb*in σ N = 1.0807 f = 0.01340083808 v = 0.32 420000 psi 𝐸 = 0.01448 · (1+0.32) 1.0807 · 0.01340083808 =

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2. Graph the principal strain difference vs. the corrected fringe order. Tardy Graphs:

Null Graphs:

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3. Discussion: The error encountered In this section of the laboratory report, the results that were determined based on the laboratory experiment will be analyzed and discussed. Moreover, any significant insights of the findings and possible sources of error that led to discrepancies will be discussed. It can be observed from the figures that when principal strain difference and corrected fringe order are plotted together, the graph results in a somewhat linear pattern. This suggests that the material or the beam experiences linear elastic behavior when strains are applied. This linear pattern also suggests that the sensitivity of the photoelastic coated beam is constant when strain is applied at varying loads, this results in a linear reaction in the fringe order. When the calculated values that were determined in this laboratory report are compared with the actual values given initially, it can be seen that there is a difference between these values. Some possible sources of error could be the inaccurate measurement of the fringe values that resulted in imprecise data values, which ultimately affected the other calculations. Since it was somewhat challenging to see the thin fringe lines, this led to inexact measurements. Rounding error could have also potentially contributed to the discrepancies.

4. Conclusion In this laboratory experiment, the theory of photoelasticity was explored. This method allowed the analysis of stress distribution within a photoelastic coated beam when various amounts of loads are applied. The procedure and the calculations assisted in understanding the principles of photoelasticity and their implementation when studying stress. The findings in this laboratory report presented important insights in the behavior of photoelastic material when analyzing how the photoelastic beam responds to various amounts of stresses. As can be observed from the plots of principal strain difference and corrected fringe order, a linear relationship between them was determined. This indicated that the material behaved as expected by the laws of photoelasticity within the range of applied stresses. When the experimental values were compared to the theoretical values, it became clear that the photoelasticity theory adequately explained the observed phenomena within the parameters of this laboratory experiment. The discussion of potential sources of error in this laboratory report outlines areas where additional improvements, such as the thickening of the fringe lines on the photoelastic beam, might increase the precision and accuracy of photoelasticity-based stress measurements. In conclusion, this laboratory experiment offered a practical chance to investigate the theory of photoelasticity and how materials behave when stresses are applied.

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