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Mechanical Engineering

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Apr 3, 2024

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Chapter 5: Performance Test Actuation System: Displacement To test the accuracy of our motorized translation stages for displacement, several tests were performed without a specimen to determine if the stages can move an instructed distance via our LabVIEW program for the x- and y- directions. Using an electronic caliper, we measure the initial distance the translation stages are separate from each other. We will then use the LabVIEW program to instruct the stages to move a specified distance. Afterward, we will measure the total distance repeatable (10 times) with the electronic caliper to ensure the accuracy of the distance traveled by the translational stages. Displacement Test Stage Separation (mm) Average Travel Distance (mm) Average Displacement (mm) Accuracy of Movement First (5 mm) 69.34 74.54 5.2 96% Second (10 mm) 69.64 79.52 9.88 98.8% Third (15 mm) 69.77 84.58 14.78 98.5% Fourth (20 mm) 69.66 89.51 19.85 99.25% Fifth (25 mm) 69.65 94.48 24.83 99.32% Table 14: Validation tests of the translation stages in the x-direction Displacement Test Stage Separation (mm) Average Travel Distance (mm) Average Displacement (mm) Accuracy of Movement First (5 mm) 70.06 75.09 5.03 99.4% Second (10 mm) 70.17 80.21 10.04 99.6% Third (15 mm) 70.13 85.11 14.98 99.87% Fourth (20 mm) 70.19 90.24 20.05 99.75% Fifth (25 mm) 70.16 95.15 24.99 99.96% Table 15: Validation tests of the translation stages in the y-direction In Table 14 and Table 15 , for each of the tests, we see the average total distance traveled and average displacement. Using the average displacement value, we were able to find the accuracy of the translation stages' movement when instructed to move a
specific distance. It can be surmised that the translation stages are capable of causing accurate displacement for our specimens. Actuation System: Strain Rate The strain rate of our system is directed by the Thorlab servo motors, which control the rate of motion of the motorized translation stages. To test the accuracy of our strain rate, we will instruct the translation stages via Labview to move a specific distance with the time to move taken into account. This measurement will be done repeatable (10 times) with the servo motors at different rates of motions, ranging from .01 - 4.8 m/s (0.005 - 2.4 m/s for each translation stage). The average of each measurement will be compared to their respective rate of motion of the servo motor for the accuracy of the strain rate. Horizontal Direction Vertical Direction Target Strain Rate (mm/s) Average Strain Rate (mm/s) Proportion of the Variance Target Strain Rate (mm/s) Average Strain Rate (mm/s) Proportion of the Variance Target Displacement – 50 mm 4.8 mm/s 4.2 mm/s 0.997 4.8 mm/s 4.2 mm/s 0.997 4.0 mm/s 3.6 mm/s 0.998 4.0 mm/s 3.7 mm/s 0.998 3.0 mm/s 2.84 mm/s 0.999 3.0 mm/s 2.85 mm/s 0.999 2.0 mm/s 1.95 mm/s 0.999 2.0 mm/s 1.95 mm/s 1.0 1.0 mm/s 0.99 mm/s 1.0 1.0 mm/s 0.99 mm/s 1.0 Target Displacement – 10 mm 0.2 mm/s 0.2 mm/s 1.0 0.2 mm/s 0.2 mm/s 1.0 0.1 mm/s 0.099 mm/s 0.999 0.1 mm/s 0.099 mm/s 0.999 Target Displacement – 2 mm 0.02 mm/s 0.019 1.0 0.02 mm/s 0.019 mm/s 1.0 Target Displacement – 1mm 0.01 mm/s 0.008 mm/s 0.999 0.01 mm/s 0.009 mm/s 1.0 Table 16: Measurement of the Strain Rate in the Horizontal and Vertical Direction As we can from our results in Table 16 of the strain rate evaluation, there is a greater variance at higher rates of motion for the translation stages than at a slower rate. For
our target strain rate of 1 mm/s, on average, the translation stages in both directions are capable of maintaining that speed. Actuation System: Load Cell To ensure our load cells can translate the force accurately, a simple evaluation has been designed to calibrate and check the accuracy. For our test, we will position the load cells vertically from the table, and weights (20g - 500g) will be hanged from the load cell via a string. Before the evaluation, the slope of the calibration curve or scale factor will be found by hanging the largest weight, 500g, for 10 mins so that the gram- force readings will be as close to the actual weight as possible. For each weight, the process of hanging the weight from the load cell will be done 10 times. The test will allow us to determine whether or not load cells can provide an accurate reading of the grams-force. Horizontal Load Cell Vertical Load Cell Weight (g) Average Measured Weight (g) Standard Deviation (g) Coefficient of Variation (%) Weight (g) Average Measured Weight (g) Standard Deviation (g) Coefficient of Variation (%) 0 0 0 0 0 0 0 0 20 19.85 ±0.43 2.16 20 18.80 ±0.27 1.42 50 50.10 ±0.44 0.88 50 48.38 ±0.24 0.51 100 100.01 ±0.12 0.12 100 98.37 ±0.26 0.26 200 200.13 ±0.05 0.02 200 199.57 ±0.46 0.23 500 499.77 ±0.54 0.11 500 501.35 ±1.14 0.23 Table 17: Average measurement readings of the horizontal and vertical load cells
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Figure 21: Accuracy of the horizontal load cell gram-force readings Figure 22: Accuracy of the vertical load cell gram-force readings From our evaluation tests, we were able to find the scale factors for the load cells, so they can provide a highly accurate gram-force reading. For our horizontal load cell, the scale factor was 1122 and provided weight readings that were very close to the actual weight. For our vertical load cell, the scale factor was 2630, which provided readings that were close to the actual weight value. Table 17 shows the average measurement weight as well as the coefficient of variance between each of the tests for each of the
weight values. Figure 21 and Figure 22 display the actual weight against the average measured weight. Environment Control: Temperature To keep samples in proper physiological conditions in an in vitro environment, the specimen chamber needs to be able to maintain the constant temperature of the medium during the experiment. The validation test will be designed to check how long it will take for the water in the chamber to reach a temperature range of 37.0 ± 1.0°C and maintain it for a long period of time. The readings of the W1209 circuit will be compared to a standard digital thermometer for accuracy. Several settings were adjusted in our W1209 temperature control circuit before we began the test. The target temperature was set to 37.0°C, with hysteresis 0.1°C. The lower limit of the temperature range was to set 35.0°C and the upper limit/relay off was to set to 40.0°C. The temperature reading of the circuit was adjusted (after several trial runs) by +4.0°C to match similar readings of the digital thermometer. Figure 23: Validation test of the temperature control circuit For the starting temperature of the water in the specimen chamber, the thermometer read 29.1°C, while the W1209 circuit read 30.1°C. At the 25 minute mark, the temperature circuit reached 37.0°C. At this point, the temperature was monitored for 40 minutes to check for the circuit's ability to maintain temperature of 37.0 ± 1.0°C. During this time, the circuit was able to maintain range, with the thermometer reading the lowest temperature as 36.5°C and the highest temperature as 37.8°C. It was surmised that the temperature circuit is capable of maintaining a warm environment for the purposes of studies.
Gripping Mechanism: Slippage We evaluated the grip design’s capability of preventing the specimen from slipping during a tensile test. If the sample slips during the tensile test, the overall stress will decrease, either causing the recorded data to be skewed or prevent rupture. A test was designed where five samples will be stretched in the x- and y-direction. The samples will be placed in the gripping mechanism and the region within the grip will be marked (3.8 mm). The samples will be stretched 10 mm 10 times. Each time, a caliper will be used to measure for any grip slippage as well as images will be taken for digital measurement. After performing the evaluation test in the x- and y- directions 10 times, there was no noticeable or measurable slippage of the sample from the grips. Figure 23 displays images from a test done in the x- and y- direction, which shows the samples being stretched to 10 mm and no noticeable slippage occurring, Figure 23: (left) Grip slippage test in the x- direction; (right) Grip slippage test in the y- direction. Strain Measurement: Image Analysis & Strain Mapping The key component to the accuracy of our strain measurement is the quality of the images taken during the experiment. There is a case that the images taken could be distorted at the boundaries due to the lens. To evaluate if there is a distortion in the images at the region of interest by the Tamron M111FM50 lens, three standard checkerboard grids will be used. The dimensions of the squares are 0.5 cm x 0.5 cm, 1.0 cm x 1.0 cm, and 2.0 cm x 2.0 cm. Several images will be taken of each grid, and observed for distortion in the grid’s pattern.
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Figure 24: Checkerboard grid of 0.5 cm x 0.5 cm with undeformed and deformed specimen superimposed.
Figure 25: Checkerboard grid of 1.0 cm x 1.0 cm with undeformed and deformed specimen superimposed.
Figure 26: Checkerboard grid of 2.0 cm x 2.0 cmm with undeformed and deformed specimen superimposed. After several images were taken of each grid, it was confirmed there was no noticeable distortion in the images. This conclusion was made from observing if there was curvature in the grid’s pattern, which was not found. In Figures 24 - 26 , an undeformed and deformed specimen was superimposed onto an image of each grid to show that there is no distortion in the region of interest of our specimen.
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The second evaluation of our strain measurement will pertain to the accuracy of our strain mapping via the GOM Correlate program. We will check for the quality of the speckle pattern, where speckles should be ≥ 3 pixels and pattern density should be 20-40% of the surface area. Once we have verified that our speckle pattern fits the desired requirements, we will test four uniaxial samples in the x- and y- directions until rupture. The polymer mixture that will be used is Sylgard 170 (40%) + Sylgard 527 (60%) + Thinner (20% of Sylgard 170). We will then load the deformation images into the GOM Correlate program and obtain the strain data from the analysis. This data from GOM Correlate and the data from Labview will be graphed in Matlab and compared for accuracy. Figure 27: Comparison of data obtained in GOM Correlate verse LabView
Before we can determine the accuracy of GOM Correlate, we must first understand how the LabView data is used to obtain the Cauchy stress and true strain. The data that is exported from LabView is the force and displacement of the specimen. In Matlab, this data is calculated into the Cauchy stress and true strain. Due the LabView program not being able to provide data on the change of the cross-sectional area, only the Cauchy stress can be calculated from the initial cross-sectional area. The true strain is calculated using the displacement until rupture. In GOM Correlate, we are able to create surface components based on the speckle pattern on the specimen. With this surface component, we are able to obtain data to get the average change in the cross-sectional area and average strain points. This data can be exported to Matlab to obtain the true stress and strain. With this in mind, we can compare the data from GOM Correlate to LabView for its accuracy. The LabView data produced the Cauchy stresses ranging from 1.2 - 1.6 MPa and true strain ranging from 0.65 - 0.7. The GOM Correlate data produced true stresses ranging from 1.0 - 1.2 MPa and true strain ranging from 0.8 - 0.85. From these results, it was concluded that GOM Correlate is capable of producing data within a similar range of the LabView data that is acceptable. Chapter 6: Results and Discussion 6.1 Polydimethylsiloxane, Silicon-Based Organic Polymers Sylgard 184 Polydimethylsiloxane (PDMS) elastomers has been accepted in the field of biomechanics for its ability to replicate the mechanical behaviors of cardiovascular tissue [80]. Sylgard 184, a commonly utilized PDMS for micro-engineering application, was the first elastomer to be used with our system for uniaxial testing. This polymer was produced by Dow Corning and is polymerized by a two-part liquid component kit, a pre- polymer base (part A) and a crosslinking curing agent (part B). The Sylgard 184 elastomer is transparent, which allows for easy inspection for air bubbles and for applying a speckle pattern [80]. According to its technical data sheet, it has a tensile strength of 6.7 MPa (engineering) with a mix ratio of 10:1 [81]. Sylgard 184 began our study into utilizing new polymers to create laboratory models that mimic material properties of arterial tissue. Originally, the initial tests of Sylgard 184 involved uniaxial testing of different mix ratios and secondary curing temperature to see if the polymer’s stress-strain curve could be lowered to our required parameters. Using the original mix ratio of Sylgard 184, 10:1, we tested how different secondary curing temperatures, the first curing temperature being 30°C for all samples, affected the stress-strain curve. For the first curing temperature, the samples were cured for 48 hours and for the secondary curing temperature they were cured for 4 hours.The samples that were used followed the ASTM D412 Type C dimensions for the dumbbell shaped. One of the first notable observations was the Cauchy stress value. The Cauchy stress at each temperature was significantly higher than what was reported in the technical data sheet or in a previous study by Johnston [80,81]. The true strain reported in the study was relatively similar to the values found in our test. Figure 28 displays the stress-strain curves for each curing temperature, while in Table 18 the average Cauchy stress and true strain are recorded from our uniaxial tests. From the uniaxial test, we
found that 50°C and 150°C produced lower Cauchy stresses while at 100°C the Cauchy stress was much higher. As for the true strains, at 50°C and 100°C these values were higher, while with 150°C the true was lower. This could be due to the fact that at higher temperatures the samples are stiffer, and will rupture sooner. Figure 28: Influence of the curing temperature on the Sylgard 184 stress-strain curve. Table 18: The average ultimate Cauchy stress and true strain at the different curing temperature for Sylgard 184 mix ratio 10:1. Once the effect of the curing temperature was studied, we wanted to understand how the curing agent influenced the pre-polymer base. To this end, different mixing ratios were done to find the average Cauchy stress and true strain. All samples followed the same curing procedure of being cured at 30°C for 48 hours and then cured at 100°C for 4 hours. The geometry used was the ASTM D412 Type C dimensions. From the results of our uniaxial test, the original mix ratio of 10:1 had average ultimate Cauchy stress of 34.6 MPa, which is significantly higher than what was reported in the technical
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data sheet and the Johnston study as well [80]. We found that at a lower mix ratio, the Cauchy stress and true strain was lower than the standard mix ratio. At a higher mix ratio, the Cauchy stress was lower, however the true strain was slightly higher. The stress-strain curves of the different mix ratios are graphed in Figure 29 and in Table 19 we can see how the Cauchy stress and true strain lowers greatly from the mix ratio 10:1 to the mix ratio 3:1. Figure 29: Effect of the curing agent on the Sylgard 184 stress-strain curve. Table 19: The average ultimate Cauchy stress and true strain at the different mix ratios for Sylgard 184.
Sylgard 170 Following the initial PDMS, another Dow Corning PDMS was found to be utilized in creating laboratory models to study biological systems, Sylgard 170 [82]. According to the technical data sheet, this elastomer is a black polymer, visually looks dark-gray, that is polymerized by two-part liquid components, a pre-polymer base (part A) and a crosslinking curing agent (part B) [83]. One of the challenging aspects of using Sylgard 170 was the color, as it made it difficult to know if there were air bubbles under the surface of the specimen. To lessen the issue of this occurring, the time where the mixture is placed in vacuum was extended to ensure no air bubbles. The reported tensile strength of Sylgard 170 with original mix ratio of 1:1 was 2.9 MPa (engineering) [83]. Uniaxial tests were done to compare stress strain curves of different mix ratios. All samples followed the same curing procedure, first cured at 30°C for >12 hours and then at 100°C for 4 hours. The geometry used for these samples were ASTM D412 Type D dimensions The results of the uniaxial tests allowed for understanding of how each part of the Sylgard 170 affects the stress-strain curve. For our Sylgard 170 R1:1, the average ultimate Cauchy stress was 3.7 MPa, which is slightly higher than what was reported in the technical data sheet. However, this could be due to the type of geometry used to test the polymer. In the case of the Sylgard 170 R1:5, its stress-strain curve is significantly lower than its counterparts and has an average Cauchy stress of 1.7. This we suspect is not the true value of this ratio as such a significant decrease in the curve could be only attributed to air bubbles that weakened the overall structural integrity of the sample. As for the other two mix ratios, increasing the Part A of the mixture only affects the strain value of the polymer, while Part B effectively decreases the Cauchy stress and increases the strain value. Figure 30 and Table 20 shows the comparison of different mix ratio’s average ultimate Cauchy stress and true strain.
Figure 30: Influence of different ratios on the Sylgard 170 stress-strain curve. Table 20: The average ultimate Cauchy stress and true strain at the different mix ratios for Sylgard 170. Sylgard 527 Sylgard 527 is a silicon based dielectric gel that has been utilized to reduce the overall stress-strain curve of PDMS polymers [84]. This silicone gel is transparent and polymerized by two liquid components, a pre-polymer base (part A) and a crosslinking curing agent (part B) [85]. There were several attempts to conduct uniaxial testing with Sylgard 527 alone, however the material is extremely brittle and will break/damage during removal from the mold. We found in a previous study when Sylgard 184 R1:10 is mixed with Sylgard 527 R1:1 at mass ratios, the overall stress-curve and elastic modulus changes substantially from pure Sylgard 184 R1:10 [84]. To see if it can lower the stress-curve of the polymer would chose to use, Sylgard 170, we compared pure
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Sylgard 170 R1:1 and Sylgard 170 R1:1 plus Sylgard 527 R1:1 with a mass ratio of 40% to 60% or 2:3. From our uniaxial testing, the mixture was capable of lowering the stress- strain values, bringing it closer to the desired values. In Figure 31 , while the true strain remains relatively similar, the average ultimate Cauchy stress decreases from 3.7 MPa to 2.1 MPa. From here, we searched for additional polymers or additives that could lower this stress value even closer to the required parameter. Figure 31: Difference in the stress-curve of Sylgard 170 R1:1 in comparison to Sylgard 170 R1:1 (40%) mixed with Sylgard 527 R1:1 (60%). Table 21: The average ultimate Cauchy stress and true strain of Sylgard 170 R1:1 in comparison to Sylgard 170 R1:1 (40%) mixed with Sylgard 527 R1:1 (60%). Smooth-On Silicone Thinner In our research to find different elastomers to make laboratory models that have tensile strength similar to cardiovascular tissue, we found Smooth-On’s Solaris and Silicone Thinner. While our initial uniaxial test with the Solaris elastomer was promising, the Silicone Thinner was more beneficial in adjusting the stress-strain curves. Silicone
Thinner is a non-reactive silicone fluid that lowers a polymer mixture’s overall tensile strength [86]. The amount of Silicone Thinner added to the polymer mixture is proportional to the total mass of the polymer mixture (Part A &B) [86]. A uniaxial test was performed to evaluate the silicone thinner’s capability of changing the ultimate Cauchy stress and true strain. One set of samples was Sylgard 170 R1:1 , while the other set of samples was Sylgard 170 R1:1 plus Silicone Thinner (20% of Sylgard 170). From our results, while the average ultimate true strain did increase, the average ultimate Cauchy stress did decrease greatly, from 3.7 MPa to 2.2 MPa. With this in mind, we decided to include the Silicone thinner in our current polymer mixture, to see if it could potentially lower the stress-strain curve further. Figure 32: Difference in the stress-curve of Sylgard 170 R1:1 in comparison to Sylgard 170 R1:1 with 20% silicone thinner. Table 22: The average ultimate Cauchy stress and true strain of Sylgard 170 R1:1 in comparison to Sylgard 170 R1:1 with 20% Silicone Thinner. Sylgard 170 (40%) + Sylgard 527 (60%) + Silicone Thinner (20% of Sylgard 170 Mass)
After several trials of uniaxial testing different mass ratios of Sylgard 170 and Sylgard 527, the latest iteration that has yielded the best stress-strain curve closest to our required parameters is the mixture of Sylgard 170 R1:1 (40%), Sylgard 527 R1:1 (60%), and the silicone thinner (20% of Sylgard 170 mass). When comparing pure Sylgard 170 R1:1 to polymer mixture, the average ultimate Cauchy stress has been halved, from 3.7 MPa to 1.8 MPa, which has been closest value to the whole arterial tissue ultimate true stress. The ultimate true strain has maintained a relatively low range, which has been acceptable. For the purposes of this study, we will be using this polymer mixture for our biaxial testing in order to determine if these laboratory models can be used alongside arterial tissue to better understand soft tissue biomechanics. Figure 33: Difference in the stress-curve of Sylgard 170 R1:1 in comparison to Sylgard 170 R1:1 (40%) mixed with Sylgard 527 R1:1 (60%) plus 20% silicone thinner.
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Table 21: The average ultimate Cauchy stress and true strain of Sylgard 170 R1:1 in comparison to Sylgard 170 R1:1 (40%) mixed with Sylgard 527 R1:1 (60%) plus 20% silicone thinner. 6.2 Experimental Design The Cruciform Mold Three cruciform molds (four samples per mold) were designed by Solidworks using ASTM D412 Type C dimensions and cut in the CNC machine. The mold is composed of two plates, a base plate and a top plate. The base plate has the biaxial sample carvings, while the top plate has the wells where the polymer mixture will be injected into molds when the plates are screwed together. Twelve samples can be prepared with the molds, with the two additional samples being prepared incase of impurities in one of the ten initial samples. Polymer Preparation The polymer mixture, Sylgard 170 (40%) + Sylgard 527 (60%) + Silicone Thinner (20% of Sylgard 170 mass), is created by measuring out each part of the polymer by weight and mixing them together. Each part of the polymer mixture is outlined Figure 29 . A precision weight scale is used to measure each part of the mixture and once all parts have been added to the mixing cup, the polymer mixture is stirred for 3 minutes. Once stirring has been completed, the polymer mixture is placed in a vacuum chamber for 15- 30 minutes to remove air bubbles that might be present within it. After it has been verified that no air bubbles are present, the polymer mixture can be injected into the mold’s upper half at a 45 degree angle. This allows for the bottom half of the mold to fill with the polymer, which at this point the molds will be laid flat and have mixture injected from the bottom half. By doing this, there is less of a likelihood of air bubbles forming within the mold. If there is an air bubble, additional polymer mixture can be used to push it to a well to be released. As the polymer mixture settles into the molds, they can be placed in the oven for overnight curing. Figure 29: The current polymer mixture for laboratory model Curing Process The curing process for our laboratory models is completed in two stages. After the procedure of injecting the molds with the polymer mixture and ensuring there are no air bubbles, the molds can be placed in the oven at 30°C for >12 hours. The reason for this is to keep the curing temperature consistent during the initial polymerized period. The following day, the samples will be taken out of the molds and returned to the oven at
100°C for at least 2.5 hours, this curing period allows for the material to stiffen. Once the final curing period is complete, the samples are cooled down and ready for the speckle pattern to be applied. Speckling Patterning For applying the speckle pattern to the specimens, the specimens are placed on a plate within close proximity to each other to ensure an even spread of spray paint can be applied. The spray paint used is a MTN 94 Spray Paint White as the specimen is black. In order to apply fine speckles to the samples, the specimen plate is angled at 45 degrees and the spray paint is held at least 0.3 meters away from the plate. Usually two applications of the spray is enough for a low density of speckles on the sample, however visual inspection of each sample is necessary to ensure that speckle density is sufficient for strain measurement. Once the speckle pattern has been applied, 30 minutes are required for the paint to dry to prevent loss of speckles. Testing To begin the testing procedure the biaxial testing system requires 30 minutes to warm- up as the load cells are temperature sensitive. This warm-up period can be done in conjunction with speckle pattern drying and setting up the LabView software. In the Labview program, we access the biaxial testing system project file and open the main interface and the sub-program for the load cells. In the main interface, the correct file paths are assigned in the preconditioning and biaxial testing tabs as well as camera subsection. Before the testing begins, proper lighting is needed so the images taken of the deforming specimen are of high resolution and the speckle pattern visible. To begin the test, the sample arms need to be placed in the metal grips. About 3.8 mm of the sample’s arm is placed inside the grip and manually tightened without breaking the sample. It is also important that the sample is not curved at the center, but planar as it is necessary for a proper valuation of the force needed to rupture the sample and proper strain mapping. Once the sample is properly set up in the grips, the sample will be preconditioned to prevent hysteresis. There will be ten cycles of loading where the sample stretched 2 mm. After preconditioning has been completed, the rupture test can occur. In the biaxial testing tab, the target displacement for the horizontal and vertical direction is set to 20-25 mm and the load cells must be tared, or set to zero before the machine is activated. Once the system is started, the force, displacement, and images are recorded until the target displacement is reached. This testing procedure is repeated until ten samples in the set have been ruptured and data collected. This data and images will then be processed in Matlab and GOM Correlate to present the true stress and strain. 6.4 Result The biaxial testing system successfully recorded and ruptured ten biaxial samples’ stress-strain curves with strain rate of 1 mm/s. The LabView data of each sample was imported to Matlab, where the Cauchy stress and true strain are calculated by the force (F) and displacement(λ). The data from LabView data can only produce the Cauchy
stress because only the initial cross-sectional area(A 0 ) is known and the change in the cross-sectional area(ΔA) could not be recorded by the program. The Cauchy stress equation: ; The true strain equation: As the forces and displacements of the horizontal and vertical directions are recorded separately, the Cauchy stresses and true strains of each direction are calculated separately as well. In the horizontal direction, the average ultimate Cauchy stress is 0.57 MPa with a true strain of 0.50. In the vertical direction, the average ultimate Cauchy stress is 0.58 MPa with a true strain of 0.51. The calculated overall average ultimate Cauchy stress is 0.575 with a true strain 0.505. Table 23: The average and standard deviation of the ultimate Cauchy stress and ultimate true strain in the horizontal and vertical directions calculated from the LabView data. With the images taken during the biaxial test of each sample, we imported them into GOM Correlate to create a strain map. With the strain map of each sample, it was possible to obtain the change in the cross-sectional area and strain applied to the sample until rupture. The true stress equation can be calculated using the change in the cross-sectional area and the force data from LabView, while true strain is obtained by the average of three strain points across the strain map. The true stress equation: In the horizontal direction, the average ultimate true stress is 0.46 MPa with a true strain of 0.60. In the vertical direction, the average ultimate true stress is 0.58 MPa with a true strain of 0.51. The calculated overall average ultimate true stress is 0.52 with a true strain 0.605.
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Table 24: The average and standard deviation of the ultimate true stress and ultimate true strain in the horizontal and vertical directions calculated from the GOM Correlate data and the force data from LabView.
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Figure 34: Comparison of the stress-strain curve in the horizontal direction from LabView(top) and in GOM Correlate(bottom).
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Figure 35: Comparison of the stress-strain curve in the vertical direction from LabView(top) and in GOM Correlate(bottom).
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Figure 36: Average stress-strain curve in the horizontal/vertical direction from LabView(top) and in GOM Correlate(bottom).
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6.5 Discussion & Conclusion Discussion Discuss the results of the study, in comparison to the wanted values Conclusion This thesis presents the development of the biaxial testing system and methodology used to test and quantify data of laboratory models. As the device has proven to provide accurate mechanical properties for polymer-based laboratory models
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Polymer Type Part A (g) Part B (g) Sylgard 170 (R1:1) 2.4 2.4 Sylgard 527 (R1:1) 3.6 3.6 Silicone Thinner 0.96 g (20% of Syl 170 Mass) Sylgard 170 R1:1 n = 11 Sylgard 170 +527 (40-60) n = 8 Sylgard 170 R1:1 n =11 Sylgard 170 + 20 Thinner n= 6 Sylgard 170 (R1:1) Avg Stress = 3.66 MPa (-0.75 to +.67, Avg Strain = 0.67 (-0.06 to 0.05)
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Sylgard 170 (R1:1) + 20T Avg Stress = 2.18 MPa (-0.6 to +0.77, Avg Strain = 0.76 (- 0.08 to 0.1) Sylgard 170 + 527 Avg Stress = 2.06 MPa (-0.32 to +0.39), Avg Strain = 0.7 (-0.05 to +0.03) Sylgard 170 + 527 + 20T Avg Stress = 1.8 MPa (-0.22 to +0.24), Avg Strain = 0.72 (- 0.06 to +0.05) Sylgard 184 T50 Avg Stress = 23.6 MPa (-4.4 to +6.6), Avg Strain = 0.95 (-0.12 to +0.1) T100 Avg Stress = 28.9 MPa (-3.0 to +1.8), Avg Strain = 1.1 (-0.08 to +0.06) T150 Avg Stress = 23.8 MPa (-5.9 to +4.7), Avg Strain = 0.68 (-0.17 to +0.12) Sylgard 184 R5:1 Avg Stress = 29.1 MPa (-3.2 to +2.0), Avg Strain = 0.84 (-0.05 to +0.03) R10:1 Avg Stress = 34.6 MPa (-1.5 to +1.0), Avg Strain = 1.1 (-0.07 to +0.06) R15:1 Avg Stress = 21.9 MPa (-6.4 to +5.0), Avg Strain = 1.2 (-0.1 to +0.04) R3:1 Avg Stress = 15.5 MPa (-3.5 to +3.0), Avg Strain = 0.83 (-0.11 to +0.09) R4:1 Avg Stress = 17.5 MPa (-3.0 to + 2.6), Avg Strain = 0.84 (-0.09 to + 0.07) Sylgard 170 R1:1 Avg Stress = 3.7 MPa (-0.75 to +0.67), Avg Strain = 0.67 (-0.06 to +0.05) R5:1 Avg Stress = 3.6 MPa (-0.54 to +0.67), Avg Strain = 0.58 (-0.03 to +0.04) R1:5 Avg Stress = 1.68 MPa (-0.21 to +0.20), Avg Strain = 0.61 (-0.05 to +0.05) R1:10 Avg Stress = 2.8 MPa (-0.42 to +0.35), Avg Strain = 0.81 (-0.07 to +0.05) List Of Figures Figure 1: Figure 2: Figure 3: Figure 4: Figure 5:
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Figure 6: Figure 7: Figure 8: Figure 9: Figure 10: Figure 11: Figure 12: Figure 13: Figure 14: Figure 15: Figure 16: Figure 17: Figure 18: Figure 19: Figure 20: Figure 21: Figure 22: Figure 23: Figure 24: Figure 25: Figure 26: Figure 27: Figure 28: Figure 29: Figure 30: Figure 31: Figure 32: Figure 33: Figure 34: Figure 35: Figure 36: Figure 37: List Of Tables
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Table 1: Table 2: Table 3: Table 4: Table 5: Table 6: Table 7: Table 8: Table 9: Table 10: Table 11: Table 12: Table 13: Table 14: Table 15: Table 16: Table 17: Table 18: Table 19: Table 20: Table 21: Table 22: Table 23: Table 24:
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