Strain Raisers

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Mechanical Engineering

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Dec 6, 2023

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SKYLER COOK, 30163872 10/16/23 ASSESSMENT OF STRAIN RAISERS USING PHOTOELASTICITY Introduction: Geometric discontinuities, or stress raisers, disturb stress fields in ways that create a higher stress near the stress raiser. It is important to understand the effects of stress raisers in a material, because if a material is brittle or subject to numerous loading cycles these stress raisers can cause premature component failure due to cracks forming at the stress raiser sites. Photoelastic materials are often attached to the material or workpiece to show what the stress field of the material will look like under a load. This is a result of taking in polarized light and doubly refracting it creating two rays when it is stressed. The two rays that emerge create an interference pattern due to their difference in phase, thus creating a pattern of color bands which corresponds to the stress within the part. The objective of this lab is to use photoelacticity to determine stress concentrations around stress raisers. Equipment and Procedure: The equipment used in this lab is the Vishay Micro-Measurements system LF/Z-2 reflection photoelasticity system. The equipment emits a polarized light onto the photoelastic material which is then refracted back to the equipment which reads the interference pattern of the refracted light and produces the color bands corresponding to stress on the material’s face. 1. Calibrate the photoelastic coating on the aluminum by setting up a cantilever beam of aluminum with the coating over top. Start by finding the coating thickness, then using the photoelasticity system find the deflection and compensator reading, which is fringe order, for stress of the color black (both should be 0). Now add deflection to the beam until the next fringe color indicated in table 1 in results and record the deflection and compensator reading. To find the compensator reading turn the dial CCW until the color of the photoelastic material is back to the same black color as the start. Repeat for every fringe color. 2. Plot fringe order versus displacement for the theoretical fringe order found in table 1 in results and experimental fringe order found in step above. Then find the slopes of both lines. 3. Use the calibration coating chart to find the strain optical coefficient K using the slopes found above and the thickness of the coating. 4. Use equation 1 in results to find the fringe value. 5. Take the dimensions of the two tensile samples. 6. Record the fringe orders for the unloaded state at all points indicated on the samples. 7. Record the fringe orders for the loaded state at all points indicated on the samples.

SKYLER COOK, 30163872 10/16/23 ASSESSMENT OF STRAIN RAISERS USING PHOTOELASTICITY Results: Table 1: Isochromatic Fringe Characteristics Fringe Color Fringe Order, N Displacement, D (in) Compensator Reading Black 0.0 0 0 Pale Yellow 0.60 0.1600 0.70 Dull Red 0.90 0.2350 1.14 Red/Blue Transition 1.00 0.2900 1.19 Blue-Green 1.22 0.3160 1.50 Yellow 1.39 0.4200 1.86 Rose Red 1.82 0.4760 2.21 Red/Green Transition 2.00 0.5290 2.42 Green 2.35 0.5950 2.55 Yellow 2.50 0.6000 2.88 Red 2.65 0.7050 3.27 Red/Green Transition 3.00 0.7700 3.52 Green 3.10 0.8040 3.81 Digital Compensator slope = 4.665 inches per fringe order Tabel 1 slope = 3.393 inches per fringe order K (Digital Compensator) = 0.11 K (Table 1) = 0.085 t = 0.112 in or 0.002845 m Equation 1 ɛ 1 − ɛ 2 = ( λ 2 ∗ t ∗ K ) ∗ N = f ∗ N Sample calculation for digital compensator: f = ( 575 ∗ 10 − 9 2 ∗ 0.002845 ∗ 0.11 ) = 0.000918677 f (Digital Compensator) = 0.000918677 m/m per fringe or 918.677 um/m per fringe f (Table 1) = 0.001188876 m/m per fringe or 1188.876 um/m per fringe Table 2: Dimensions of Samples

SKYLER COOK, 30163872 10/16/23 ASSESSMENT OF STRAIN RAISERS USING PHOTOELASTICITY Thickness, t (mm) 2.845 H (mm) 99.90 d (mm) 49.75 r 1 (mm) 0.5 r 2 (mm) 20 2a (mm) 7.00 Table 3: Elastic Properties of 6061-T651 Aluminum Yield Stress (MPa) 276 Elastic Modulus (GPa) 69 Poisson’s Ratio 0.33 Table 4: Data for Sample 1 Measurement Point Fringe Order, N Unloading, P 1 = 0, N1 Loaded, P 2 = 222.7 lb, N2 a 0 2.37 b 0 3.61 Table 5: Data for Sample 2 Measurement Point Horizontal distance from point e (tip of the hole), (mm) Fringe Order, N Unloaded P 1 = 0 N1 Loaded P 2 = 180.1 lb N2 c n/a 0 1.99 d n/a 0 1.70 e 0 0 2.91 f 5 0 2.36 g 11.5 0 2.31 h 16.5 0 2.24 Analysis: Sample calculation of experimental stress for point a on sample 1: σ = ( E 1 + v ) f ( N 2 − N 1 ) σ = ( 69 ∗ 10 9 1 + 0.33 ) ∗ 0.000918677 ∗ ( 2.37 − 0 ) = 112955826.9

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SKYLER COOK, 30163872 10/16/23 ASSESSMENT OF STRAIN RAISERS USING PHOTOELASTICITY Sample calculation of analytical stress for point a on sample 1: σnom = P A = 990.6 2.845 ∗ 49.75 ∗ 10 − 6 = 6998790.08 Sample calculation of analytical stress for point b on sample 1: K t = 4.75 σmax = Kt ∗ σnom = 4.75 ∗ 6998790.08 = 33244252.9 Sample calculation of percent error for point b on sample 1: %error = | σ 2 − σ 1 σ 2 | ∗ 100 = 417.6 Sample calculation of analytical stress for point c on sample 2: K t = 3 σnom = P A = 801.1 2.845 ∗ 49.75 ∗ 10 − 6 = 5659934.11 σmax = Kt ∗ σnom = 3 ∗ 5659934.11 = 16979802.33 Sample calculation of analytical stress for point e on sample 2: Ktg = 0.284 + 2 1 + ( d H ) − 0.6 ∗ ( 1 − ( d H ) ) + 1.32 ( 1 − ( d H ) ) 2 Ktg = 0.284 + 2 1 + ( 49.75 99.90 ) − 0.6 ∗ ( 1 − ( 49.75 99.90 ) ) + 1.32 ( 1 − ( 49.75 99.90 ) ) 2 = 1.65 σnom = P A = 801.1 2.845 ∗ 49.75 ∗ 10 − 6 = 5659934.11 σmax = Kt ∗ σnom = 1.65 ∗ 5659934.11 = 9338891.28

SKYLER COOK, 30163872 10/16/23 ASSESSMENT OF STRAIN RAISERS USING PHOTOELASTICITY Table 6: Sample 1 Results Point P 2 = 222.7 lb or 990.6 N σ 1 Experimental (MPa) σ 2 Analytical (MPa) % Error a 112.96 7.00 1513.71 b 172.06 33.24 417.6 Table 7: Sample 2 Results Point P 2 = 180.1 lb or 801.1 N σ 1 Experimental (MPa) σ 2 Analytical (MPa) % Error c 94.84 16.98 458.5 d 81.02 5.66 1331.4 e 138.69 9.34 1384.9 f 112.48 n/a n/a g 110.10 n/a n/a h 106.76 n/a n/a Discussion: After viewing the analysis, the percentage of error resulting from the experiment is quite large which could be a result of many variables. By looking at these initial results in table 2 and comparing the fringe order to the digital compensator reading, it is seen that the compensator reading is larger than the fringe order. This could be a result of excess light entering into the lab room and refracting off the photoelastic material causing a larger fringe order when calibrating the coating. This same source of error could have caused larger fringe order when evaluating the stress in the samples after loading. This error could have affected the analysis when calculating for σ 1 making the experimental stress larger than the analytical stress. While photoelasticity is an exceptional way to visualize stress concentrations induced by a load on a sample, it allows visualization of stress concentrations in expensive or unique materials where destructive testing is not an option, it does have its limitations. A significant limitation is accurately calculating stress based on fringe order, one reason is because the interpretation of fringe patterns can be different between analysts. Another limitation is that photoelastic materials are extremely sensitive to environmental conditions such as temperature, vibrations and excess light. The magnitudes of stress at various points on the sample can be seen in table 7. By looking purely at the analytical stress, the max stress in the sample occurs at the notch

SKYLER COOK, 30163872 10/16/23 ASSESSMENT OF STRAIN RAISERS USING PHOTOELASTICITY of the sample which is verified by the equation σmax = Kt ∗ σnom . The second highest stress occurs at the point closest to the stress raiser and as the points increase in distance from the stress raiser the stress decreases. So, to mitigate the effects of stress raisers in a sample introducing notches into the sample to redistribute the stress, as seen in the experiment, it causes the max stress to occur at a different point. Conclusion: Materials that include strain raisers cause a higher stress to occur around that point due to the discontinuity of the material. The higher stress around the stress raiser could cause premature component failure if the material being used is subject to many loading cycles or if the material is brittle. The stress concentrations around the stress raiser were analysed using photoelasticity which gave us a visual of the stress concentrations resulting from the loaded sample. The experiment was an overall success due to the fact that the relationship between stress raisers and stress concentrations was seen while using photoelasticity and the effects of notches in the sample causing a max stress.

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