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Development of Failure Criterion for Materials Exposed to Multiaxial Tensile-Torsion Testing

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Development of Failure Criterion for Materials Exposed to Multiaxial Tensile-Torsion Testing
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Millar, David William
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Multiaxial fatigue tests permit advances in the basic understanding of materials behavior that might be utilized in the processes of declaring component service lives. To accurately predict how a material will behave when exposed to multiple sources of stress, we set out with the intent to develop testing methods that can be applied to the testing of brittle and ductile materials in one comprehensive failure test that will yield accurate failure criterion for combined tensile stress and torsional forces. To do this we studied the current failure criterion methods of a specific material (ABS plastic) to accurately describe and predict behavior of this material in between areas of pure shear and pure tension, i.e. multiaxial failure. Individual tensile and torsion tests were run to establish a baseline for the material's failure criterion, then multiaxial tests were run and compared to the established criterion. The behavior observed and the placement of the mixed tensile and torsional stress on the material's established failure graph allowed us to see that the test method worked, and accurate results were achieved. ( en )
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Awarded Bachelor of Science in Mechanical Engineering, magna cum laude, on May 8, 2018. Major: Mechanical Engineering
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College or School: College of Engineering
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Advisor: Peter Ifju. Advisor Department or School: Mechanical and Aerospace Engineering

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Copyright David William Millar. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.

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DEVELOPMENT OF FAILURE CRITERION FOR MATERIALS EXPOSED TO MULTI AXIAL TENSILE TORSION TESTING By DAVID WILLIAM MILLAR AN HONORS THESIS PRESENTED TO THE COLLEGE OF MECHANICAL AND AEROSPACE ENGINEERING AT THE UNIVERSITY OF FLORIDA IN PART IAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF BACHELOR OF SCIENCE WITH HIGH HONORS UNIVERSITY OF FLORIDA 2018

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2 2018 David William Millar

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3 To Maya for staying by my side and believing in me, no matter what.

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4 ACKNOWLEDGEMENTS I want to express my gratitude to Dr. Peter G. Ifju and Mattlock Mennu for supervising my research work. Dr. Ifju sparked my interest in Mechanics and Materials and has always encouraged me to get involved and learn more ab Ph.D. students. Without his encouragement and motivation for me to succeed, this project may not have happened or gotten as far as it did. I am grateful for all his help and look forward to wor king Florida. And without the helpful assistance of Mattlock, the testing portion of this project could not have happened. Lastly, I want to thank my famil y and friends at UF for their support and constant encouragement throughout this process.

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5 TABLE OF CONTENTS 8 17 21 28 33 APPENDIX 37 8 41

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6 LIST OF TABLES TABLE II: Pure Tension 1 TABLE III: Pure Torsion TABLE IV: Multiaxial Failure 32 33

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7 LIST OF FIGURES Figure 2: Tres Figure 6: Model of System Setup w Figure 10: Figure 13: Degree of Twist vs. Torque Multiaxial { Figure 17: Def Figure 20: Deflection vs. Ratio of Load to Torque 2

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8 Figure A Figur e A Figure A Figure B 1: Dogbone Failure Figure B 2: Dogbone Failure F igure B 3: Dogbone Failure Figure B 4: Dogbone Failure

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9 LIST OF ABBREVIATIONS & SYMBOLS Abbreviations UTM = Universal Testing Machine ABS = Acrylonitrile, Butadiene, and Styrene EDM = Electrical Discharge Machining DAQ = Data Acquisition Symbols = Shear stress Y = Yield (as in stress) U = Ultimate (as in stress) P = Load T = Torque M = Moment = Degree of Twist J = Polar Moment of Inertia C = radius of test specimen

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10 Abstract of Thesis Presented to the College of Mechanical and Aerospace Engineering at the University of Florida in Partial Fulfillment of the Requirements of Graduating with High Honors DEVELOPMENT OF FAILURE CRITERION FOR MAT ERIALS EXPOSED TO MULTIAXIAL TENSILE TORSION TESTING By David William Millar April 2018 Chair: Dr. Peter Ifju Major: Mechanical Engineering Multiaxial fatigue tests permit advances in the basic understanding of materials behavior that might be utilized in the processes of declaring component service lives. To accurately predict how a material will behave when exposed to multiple sources of stress, we set out with the intent to develop testing methods that can be applied to the testing of brittle and ductil e materials in one comprehensive failure test that will yield accurate failure criterion for combined tensile stress and torsional forces. To do this we studied the current failure criterion methods of a specific material (ABS plastic) to accurately descri be and predict behavior of this material in between areas of pure shear and pure tension, i.e. multiaxial failure. Individual tensile and torsion tests were run to d compared to the established criterion. The behavior observed and the placement of the mixed tensile and worked, and accurate results were achieved.

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11 SECT ION I INTRODUCTION & MOTIVATION Uniaxial testing methods, such as pure tensile, pure compression, or pure torsion tests, are implemented into real world applications, materials are often exposed to more than just uniaxial forces. Because of this, multiaxial fatigue tests permit advances in the basic understanding of materials behavior that might be utilized in the processes of declaring component service lives [1] Sim ilar to uniaxial testing methods, multiaxial testing applies loading to a single specimen, but uses several actuators to directly apply a multiaxial load [2] Multiaxial Tension/Torsion Testing On e of the most common multiaxial tests involves tensile torsi on testing, or combined axial and torsional loading [ 3 ]. Common to composites testing applications, tension torsion testing can replicate anticipated or recorded service loading conditions that involve combinations of axial or linear loading with torsional or rotary loading [ 3 ]. W hen a specimen is loaded into a uniaxial testing machine, it is subjected to uniaxial stress or strain; essentially the specimen is either being pulled or pushed in one direction (the 11 direction) while all other components (i.e 12, 21, 32, etc.) of stress and strain are zero [4]. For an isotropic material, the stress and stain experienced can be characterized by the following matrices: ; (1) us for uniaxial stress, (1) can simply be written as: ; (2)

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12 While (1) and (2) are useful in determining stress and stain of a material in a single direction, they fail to account for stresses experienced in the auxiliary directions. Therefore, multiaxial tests are u seful in that they can characterize behavior over a wide range of loading ratios and conditions [3]. For example, high force / torque machines, such as the TestResources 300 Series Universal Testing Machine (UTM), can be used to generate constitutive modeli ng o f tubular test specimens [3]. These types of machines can generate large plastic strains on test specimens without complications to the stress state that occur when necking begins to take place [5]. During these combination tests, the state of stress i n the torsion test consists of pure shear, with equal tensile and compressive stresses at 45 to the shear stresses; a variation in the stress state can be achieved if axial forces, tensile or compressive, are superimposed on the twisting moment [5]. Howev disadvantage of the torsion component of the test is that stress, strain, and strain rate can significantly vary from the axis to the outer fiber of a solid cylindrical specimen [5]. Despite this, accurate measurements and characteristics can still be determined by using hollow cylindrical specimen with a relatively thin wall thickness [5]. Development of Failure Criterion Ductile Materials As stated previously, multi axial testing methods can be used to quantify component service life. Another way service life can be maximized is by studying the failure (yield) criterion of the test material, or the relationship among the stresses which predict the yielding of the mate rial [6]. There are two yield criteria that are commonly used by engineers in industry: Tresca criterion also called maximum shear stress theory, and von Mises yield criterion also called distortion

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13 energy criterion [6]. Each of these studies when plas tic deformation will occur in material s to develop material specific yield criteria. The Tresca criterion focuses on shear stress in a material. According to Beer et. al., Tresca criterion is based on the observation that yield in ductile materials is ca used by slipping of material along surfaces and caused by shearing stresses [7]. Tresca criterion further states that a specimen will not fail if the maximum shear stress (i.e. max ) remains smaller than the corresponding shear stress in a tensile test spe cimen of the same material as the specimen starts to yield [7]. In other words, where (3) In (3), a a n b are the principal stresses. If the principal stresses have the same sign, the Tr esca criterion gives (4); if the principal stresses have opposite signs, Tresca criterion gives (5). (4) (5) The von Mises criterion focuses on normal stress in a material. According to Beer et. al., von Mises criterion is based on the determination of the distortion energy in a material [7]. According to this criterion, a specimen will not fail if the maximum value of the distortion energy per unit volume in that material remains smaller than the distortion energy per unit volume required to cause yield in a tensile test specimen of the same material [7]. In other words, ( 6 ) In ( 6 ), a and b are the principal stresses. When a specimen starts to yield, von Mises gives (7); the limit of the von Mises yield criterion is given by (8).

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14 a Y b = 0 ( 7 ) ( 8 ) To better understand failure criterion, values from both the Tresca and von Mises criterion can be plotted along ax e s of principal stresses, as seen in Fig. 1 and Fig. 2 Any given state of stress can be represented by a point of coordinates a b If a stress point falls within the boundary lines of either stress criterion, the specimen will not fail; conversely, if the point falls outside the boundary lines of either stress criterion, the specimen will fail as a res ult of yield in the material [7]. shearing stress criterion (left); von Mises surface based on the maximum distortion energy criterion (right) [7].

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15 Fig. 2 Comparison of the Tresca hexagon and von Mises surfa ce for failure criterion [7]. Development of Failure Criterion Brittle Materials While Tresca and von Mises can establish failure criterion for most materials there are additional failure criterion for brittle materials. When subjected uniaxial testing brittle materials such as Acrylonitrile, Butadiene, and Styrene (ABS) plastic rupture (or fracture) with little to no plastic deformation before failure [7]. When a brittle specimen is under uniaxial stress, the normal stress causing failure is equal to the ultimate tensile strength ( U ) [7]. maximum normal maximum normal stress reaches the ultimate strength ( U ) obt ained from the tensile test of a specimen of the same material [7]. In other words, the material will not fail as long as: (9) lly, as seen in Fig. 3. If a stress point falls within the boundary lines, the specimen will not fail; conversely, if the point falls outside the boundary lines, the specimen will fail [7].

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16 Fig. 3 normal stress criteri on [7]. Focus on Testing Prevent Slipping with EDM Another disadvantage with multiaxial tensile torsion testing is slipping of the test specimen during testing. Slipping can cause inaccurate data to be collected and, therefore, inaccurate failure crite rion can be established. To better accommodate such testing, specialized grips can be manufactured to better grab the specimen and prevent slippage. One such way the grips can be modified is through the use of electrical discharge machining (EDM). EDM has been in use in industry for about 50 years [8]. In standard EDM, an electrical spark is created between an electrode and the part to be machined, usually a steel/metallic alloy. The spark is carefully controlled and localized and can reach intense heat, w ith temperatures reaching 8,000 12,000 C [9]. To control the process, the workpiece is typically placed in the dielectric (electrical insulator) of deionized water; the water acts as a conductor and a good coolant to flush away the eroded metal particles [9]. When special contours need to be cut that a spark

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17 the conductors and the electrical current is run through it; the wire is then used to cut a programmed contour in a workpiece typically using CNC machines [8 9]. Motivation When attempting to establish failure criterion for a material, the type of test and material being used must be considered. Often, ductile materials will require different testing meth ods than brittle materials due to their unique behaviors when exposed to stress. Additionally, to gain a more comprehensive idea of failure criterion, multiple tests of different failure modes, such as tensile and torsion al stress will need to be tested. Because of this, failure testing of materials, in either research or industry, is often cost prohibited, in terms of both time and money. The degree of ineffectiveness of multiple failure tests of a single material is usually determined from how often a f ailure test needs to be conducted for a single material. Attempts to remedy this can still be considered ineffective due to the extra cost associated with specialized multiaxial testing equipment. Therefore, we intend to develop testing methods that can be applied to the testing of brittle and ductile materials in one comprehensive failure test that will yield accurate failure criterion for combined tensile stress and torsional forces. To do so, we first intend to study current failure criterion methods of a specific material (ABS plastic) to accurately describe and predict behavior of this material in between areas of pure shear and pure tension, i.e. multiaxial failure. Once we have established accurate proof of accurate testing and failure criterion, the goal will be to test with a variety of new materials before establishing and verifying the new testing method.

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18 SECTION II PROCEDURES Pre Experimentation Before multiaxial testing c ould commence, possible causes of error in the testing procedure needed to be eliminated, starting with the test specimen and chuck grips. The original chuck grips for the TestResources 300 Series UTM, as seen in Fig. A 1, have a very small contact area, meaning that slipping is likely to occur during any of the tests. To minimi ze the risk of slipping, the contact area needed to be expanded on both the specimen and grips so the resultant force and moment generated mimic the behavior of a wrench when tightening a bolt, as seen in Fig. 4. Fig. 4. Behavior of a wrench twisting a bolt. The resultant forces on either face of the bolt head help in generate a moment on the bolt and assist in twisting. To accomplish this, models of the specimen and chuck grips were generated in Solidworks. T he specimens were designed to be hexagonal dogbone in shape ; additionally, three of the circular inclusions, as seen in Fig. A 3. The chuck grips were modified to contain an extruded semi as seen in Fig. A 2. Once the designs for each were finalized, the chuck grips were shipped to

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19 Triad EDM, a local manufacturing company that specializes in wire EDM. Wire EDM was used to cut the face of grips down to match the designed faces in Fig. A 2. While the grips were being machined, the specimens needed to be manufactured; therefore, a test material needed to be chosen. To accommodate for the timeline of the project, but still of the specimens were printed in the UF MAE 3D Printing Lab using ABS plastic. Relevant material properties for ABS plastic are given by Table I. TABLE I Mechanical Properties of ABS Plastic Property Symbol Value Density 3.79E 02 lb. / in 3 Rockwell A Hardness HR A 102 Ultimate Tensile Strength U 5.54 ksi Yield Tensile Strength Y 5.99 ksi E 305 ksi Flexural Yield Strength bend 9.28 ksi Flexural Modulus E bend 319 ksi *All values in Table I were found using [10]. Experimentation & Analysis With the specimens printed and the grips modified, test ing commenced. The newly to the actuators. As seen in Fig. 5, t he specimen wa s loaded into the chuck, where the three grips were 6 the test specimens were test ed under three different loading conditions: {1} pure tension, {2} pure to rsion, and {3} multiaxial tension and torsion. For test {1} appropriate testing rates in inches/second were applied; for test {2} appropriate testing rates in degrees/second were applied.

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20 Fig. 5. Physical t est specimen loaded into grips (r ight); Fig. 6. Model of specimen loaded into grips (only bottom grips shown), with testing conditions indicated. Test {3} is a combination of {1} and {2} shown above (left). After each test, the data recorded by the SADI data acquisition (DAQ) device was exported to an Excel spreadsheet; on each spreadsheet, appropriate data for each test was analyzed to generate stress vs. strain or tor que vs. degree of twist curves. For test {3} material data from the curves generated from tests {1} and {2} were used to generate updated testing rates for the two tests being run simultaneously. Equations (10) and (1 1 ) were used to determine the updated testing rates to ensure that failure for the pure tension and pure torsion tests would occur at or around 120 seconds. (1 0 ) (1 1 )

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21 After several trials of test {3}, the data recorded by the SADI DAQ was exported to an Excel spreadsheet; on these spreadsheets, the ratio of tensile load (P) to torsional torque (T) was plotted against deflectio n. This data, along with the previous curves from tests {1} and {2} was then used to determine if the failure behavior witnessed accurately describe d theoretical behavior of this material in between areas of pure shear and pure tension

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22 SECTION III EXPE RIMENTATION AND RESULTS In Fig. 7 through Fig. 9 the data from the pure tension test of the ABS plastic specimen was analyzed to yield appropriate stress v s. strain curve s The data that resulted exhibited properties of a brittle material, as expected. T his can be seen by the fact that the graph reaches the failure point without entering a plastic deformation region. This behavior can also be seen in the failure mode exhibited by the physical specimen in Fig. B 1 Fig. 7 Strain (in/in) vs. Stress (psi ) curve for the pure tension test of the ABS test specimen at a testing speed of 7.00 inches/second. Fig. 8 Strain (in/in) vs. Stress (psi) curve for the pure tension test of the ABS test specimen at a testing speed of 0.05 inches/second. 0 500 1000 1500 2000 2500 3000 0 0.01 0.02 0.03 0.04 0.05 Stress, (psi) Strain, (in/in) 0 500 1000 1500 2000 2500 0 0.01 0.02 0.03 0.04 0.05 Stress, (psi) Strain, (in/in)

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23 Fig. 9 St rain (in/in) vs. Stress (psi) curve for the pure tension test of the ABS test specimen at a testing speed of 0.025 inches/second. In Fig. 10 and Fig. 1 1 the degree of twist and torque data from the pure torsion tests of the ABS plastic specimen are plott ed against each other. The data that resulted from subjecting the specimen to a pure torsion force exhibited properties of a brittle material, as expected. This can be seen by the fact that the graph reaches the failure point without entering a plastic def ormation region. This behavior can also be seen in the failure mode exhibited by the physical specimen in Fig. B 2 Fig. 10 Degree of Twist (deg) vs. Torque ( lb. in ) curve for the pure tension test of the ABS test specimen at a testing speed of 0. 2 5 de grees/second. 0 500 1000 1500 2000 2500 0 0.01 0.02 0.03 0.04 0.05 Stress, (psi) Strain, (in/in) 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 Torque, T (lb in) Degree of Twist, (deg)

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24 Fig. 1 1 Degree of Twist (deg) vs. Torque ( lb. in ) curve for the pure tension test of the ABS test specimen at a testing speed of 0.5 0 degrees/second. In Fig. 1 2 through Fig. 20 the stress/strain, torque/twist, and combined data are plot ted. All three multiaxial failure trials were run at simultaneous rates of 0.000293 inches/second and 0.1495 degrees/second, as calculated using (10) and (11). The material failed with two distinct failure modes; the first was flat, which is typical of br ittle materials when exposed to pure tension (see Fig. B 1 ), and the second was perpendicular (about 45 ) to the shaft axis (see Fig. B 2 ). This combined behavior can be seen in the failure mode exhibited by the physical specimen in Fig. B 3 through Fig. B 4 Fig. 1 2 Strain (in/in) vs. Stress (psi) curve for the multiaxial tension torsion test of the first (blue) ABS test specimen. 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 Torque, T (lb in) Degree of Twist, (deg) 0 200 400 600 800 1000 1200 1400 1600 1800 0 0.005 0.01 0.015 0.02 0.025 0.03 Stress, (psi) Strain, (in/in)

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25 Fig. 1 3 Degree of Twist (deg) vs. Torque ( lb. in ) curve for the multiaxial tension torsion test of the first (blue) ABS test specimen. Fig. 1 4 Deflection (in) vs. Ratio of Load to Torque (in 1 ) curve for the multiaxial tension torsion test of the first (blue) ABS test specimen. 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 Torque, T (lb in) Degree of Twist, (deg) 0 2 4 6 8 10 12 0 0.005 0.01 0.015 0.02 0.025 Ratio of Load to Torque, P/T (in 1 ) Deflection, (in)

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26 Fig. 1 5 Strain (in/in) vs. Stress (psi) curve for the multiaxial tension torsion test o f the second (grey) ABS test specimen. Fig. 1 6 Degree of Twist (deg) vs. Torque ( lb. in ) curve for the multiaxial tension torsion test of the second (grey) ABS test specimen. 0 200 400 600 800 1000 1200 1400 1600 1800 0 0.005 0.01 0.015 0.02 0.025 0.03 Stress, (psi) Strain, (in/in) 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 Torque, T (lb in) Degree of Twist, (deg)

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27 Fig. 1 7 Deflection (in) vs. Ratio of Load to Torque (in 1 ) curve for the multiaxial tension torsion test of the second (grey) ABS test specimen. Fig. 1 8 Strain (in/in) vs. Stress (psi) curve for the multiaxial tension torsion test of the third (red) ABS test specimen. 0 1 2 3 4 5 6 7 8 9 0 0.005 0.01 0.015 0.02 0.025 Ratio of Load to Torque, P/T (in 1 ) Deflection, (in) 0 200 400 600 800 1000 1200 1400 1600 0 0.005 0.01 0.015 0.02 0.025 Stress, (psi) Strain, (in/in)

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28 Fig. 1 9 Degree of Twist (deg) vs. Torque ( lb. in ) cu rve for the multiaxial tension torsion test of the third (red) ABS test specimen. Fig. 20 Deflection (in) vs. Ratio of Load to Torque (in 1 ) for the multiaxial tension torsion test of the third (red) ABS test specimen. 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 Torque, T (lb in) Degree of Twist, (deg) 0 1 2 3 4 5 6 7 8 9 10 0 0.005 0.01 0.015 0.02 0.025 Ratio of Load to Torque (in 1 ) Deflection, (in)

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29 SECTION IV DISCUSSION OF EXPERIM ENTATION AND RESULTS During the testing of pure tension, the first test was run at an initial speed of 7.00 inches per second. This yielded in the robust curve as seen in Fig. 7 Therefore, for the remaining tests run for pure tension, the testing rate was reduced to 0.05 and 0.025 inches per second, so the data would be more precise and yield consistent data. This same approach was also applied to the pure torsion tests; here the testing rates started small at 0.25 degrees per second and gradually increa sed to 0.5 degrees per second to generate a faster testing period while keeping data precise. The failure modes of the pure tension and pure torsion tests matched expectations of brittle failure. B rittle failure in tension experiences minimum plastic defo rmation so the surface is typically flat. and was completely flat, as seen in Fig. B 1. In fact, if we were to attempt to piece the parts back together, the two would fit perfectly with very little material missing. If any material was missing, this could have been caused by a high testing rate that caused the material to violently rupture and get thrown from the specimen. Additionally, and differences in failure mode or st ress values, such as the increased yield stress observed in test {1}, could also be attributed to increased strain or testing rate, or stress concentration conditions formed during the 3D printed process. Brittle failure due to torsional loading occurs alo ng planes perpendicular to the direction where tension is a maximum, typically along surfaces at 45 failure surface after the pure torsion tests matched this expectation and contained a 45 notch, as seen in Fig. B 2. A ll three specimens failed in the same direction; however, if any failed in the notch, this could be attributed to stress concentration conditions inadvertently formed during the 3D printed process.

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30 Based on in formation available regarding brittle failure in tension and torsion, we expected that the failure mode of the combined loading tests to contain a mixture of both types of failure torsio n test matched this expectation, containing both a flat failure surface and a 45 notch. However, while the blue notches surrounding an additional flat surface. The difference between these two types of multiaxial failure observed could be attributed to print quality of the specimens (the grey had several visible defects and cavities) or the testing rates used. Based on the data collected during the tests that examin ed pure tensile failure behavior, the following yield and ultimate stress values were determined for the specimens used. It should be noted that since the material used (ABS plastic) is a brittle material, the yield stress and ultimate stress are the same. Furthermore, when comparing the stress results to those in Table I and gathered previously by Cantrell et. al, the yield and ultimate strengths found in t his experiment were significantly lower. Cantrell et. all tested ABS specimens in different orientatio ns to determine mechanical properties; the yield stress and ultimate stress found fo specimens were 4,337 and 4,487 psi, respectively [1 1] The difference in stress properties can likely be attributed to the print quality of the specime ns, specifically the percent fill difference between Cantr ell s standard dogbone specimens and the ci rcular/hexagonal dogbone specimens used in the experiment.

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31 TABLE II Pure Tension Yield and Ultimate Stress Test {1} 2,498 psi Test {2 } 2,249 psi Test {3} 2,237 psi Average 2,328 psi Similarly, based on the data collected during the tests that examined pure torsional failure behavior, the original data, and (12) and (13) were used to calculate the yield and ultimate stress values for the specimens used. In (12), T Y is the torque value where yielding first occurs, C is the outside radius of the cross section area of the circular test area only, and J is the polar moment of inertia of a hollow cylinder. In (13), D and d are the outer and inner diameters of the cross section area of the circular test area, respectively. (10) (11) TABLE III Pure Torsion Yield and Ultimate Stress Test {1} Yield 2,936 psi Test {2 } Yield 2,904 psi Average Yield 2,920 psi Test {1} Ultimate 3,394 psi Test {2 } Ultimate 3,406 psi Average Ultimate 3,400 psi Taking these average data values for pure tensile failure and pure torsional failure, we can accurately compare the failure criterion established by von Mises and Tresca in Fig. 2 to the failure criterion in Fig. 2 1

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32 Fig. 2 1 Failu re criterion based on average yield and ultimate data for the pure tension and pure torsion tests of the ABS specimens. With the failure criterion established for pure tension and pure shear, we can begin to examine if the tests conducted accurately esta blished where and when multiaxial failure would occur. To determine if the multiaxial tests accurately predicted or matched the failure criterion established in Fig. 2 1 the yield and ultimate stress values experience during the tension torsion tests were found and complied into Table IV. TABLE IV Multiaxial Failure Yield and Ultimate Stress Test {1} Tension Yield 1,664 psi Ultimate 1,695 psi Test {1} Torsion Yield 1,831 psi Ultimate 2,111 psi Test {2} Tension Yield 1,590 psi Ultimate 1,632 psi Test {2} Torsion Yield 1,923 psi Ultimate 2,094 psi Test {3} Tension Yield 1,462 psi Ultimate 1,488 psi

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33 TABLE IV Multiaxial Failure Yield and Ultimate Stress Test {3} Torsion Yield 1,748 psi Ultimate 1,971 psi Average Tension Yield 1,572 psi Ultimate 1,605 psi Average Torsion Yield 1,834 psi U ltimate 2,059 psi It should be noted that due to the combine loading, the yield and ultimate stress values were noticeably less than when the specimens were run under pure tension/torsion. The combined loading effects caused this dip due to the materia l being exposed to stress in every direction along its failure surface. Taking these average data values for multiaxial tensile/torsional failure, we can compare the pure tension/torsion failure criterion established in Fig. 2 1 to the combined failure crit erion in Fig. 2 2 Fig. 2 2 Failure criterion based on average yield and ultimate data for the multiaxial tension/torsion tests of the ABS specimens, compared to failure criterion established from average yield and ultimate data for the pure tension and pure torsion tests.

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34 SECTION V CONCLUSION AND FUTURE WORK In this thesis, we set out with the intent to develop testing methods that can be applied to the testing of brittle and ductile materials in one comprehensive failure test that will yield accurate failure criterion for combined tensile stress and torsional forces. To do this we studied the current failure criterion methods of a specific material (ABS plastic) to accurately describe and predict behavior of this material in between areas of pure shear and pure tension, i.e. multiaxial failure. ABS plastic was chosen as the testing material because of its predictable material properties and failure modes. To study the material, individual tensile and torsion tests were run to establish a baseline for th established criterion. The behavior observed and the placement of the mixed tensile and torsional the test method worked, and accurate results were achieved. Despite the success of this experiment, several aspects need to be improved before other materials can be tested. One major problem encountered was misaligned chucks on the UTM; as the specimens were tightened into the grips, slight bending was observed wh ich could have altered how or when the specimen failed. Another significant issue was poorly printed test specimens. Typical printing of the specimens took about 5 6 days; however, due to the timeframe of this experiment, some of the specimens had to be pr inted within 2 3 days. This rush could have caused significant cavities to form, resulting in stress concentrations that made the specimens fail faster than normal. Before testing can be carried to other materials, these two issues need to be corrected.

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35 A PPENDIX A SOLIDWORKS MODEL DRAWINGS Figure A 1 Solidworks drawing of the original tension torsion chuck grip.

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36 Figure A 2. Solidworks drawing of the desired modified tension torsion chuck grip.

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37 Figure A 3. Solidworks drawing of the hexagonal dog bone test specimen.

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38 APPENDIX B TEST SPECIMEN PICTURES Fig. B 1 (a) (c). Dogbone specimen after failing during the pure tension test. The behavior exhibited is that of a brittle material due to the sudden rupture of the specimen without the presence of any plastic deformation, such as necking.

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39 Fig. B 2 (a) (c). Dogbone specimen after failing during the pure torsion test. The behavior exhibited is that of a brittle material since the specimen failed along surfaces 45

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40 Fig. B 3 (a) (c). Blue d og bone specimen after failing during the multiaxial tension torsion test The behavior exhibited is that of a brittle material and failed in tension (flat area) and torsion (45

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41 Fig. B 4 (a) (c). Red d o g bone specimen after failing during the multiaxial tension torsion test The behavior exhibited is that of a brittle material and failed in tension (flat area) and torsion (45

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42 LIST OF REFERENCES [1] Filippini, M., Foletti, S. and Pasqu ero, G. (2010). Assessment of multiaxial fatigue life prediction methodologies for Inconel 718. Procedia Engineering (2), pp.2347 2356. [2] Nierenberger, M., Poncelet, M., Pattofatto, S., Hamouche, A., Raka, B. and Virely, J. (2011). Multiaxial Testing of Ma terials Using a Stewart Platform: Case Study of the Nooru Mohamed Test. Experimental Techniques (38), pp.74 83. [3] Test Types. (2018). Axial Torsion Test [online] [4] Brannon, R. (2012). Distinction between uniaxial stress and uniaxial strain [online] [5] Kuh n, H. (1968). Stress State in the Combined Stress Torsion Test Philadelphia: Drexel Institute of Technology Department of Metallurgical Engineering. [6] Chandramouli, R. (n.d.). Plasticity Thanjavur, India: SASTRA University. [7] Beer, F., Johnston, Jr., E., D eWolf, J. and Mazurek, D. (2015). Mechanics of Materials 7th ed. New York: McGraw Hill Education. [8] Donohue, B. (2018). How it Works Wire EDM | [online] Todaysmachiningworld.com. [9] Xactedm.com. (2018). What Is EDM? How Does Elec trical Discharge Machining Work? : XACT. [online] [10] Matweb.com. (2018). MatWeb The Online Materials Information Resource [online] [11] Cantrell, J., Rohde, S., Damiani, D., Gurnani, R., DiSandro, L., Anton, J., Young, A., Jerez, A., Steinbach, D., Kroese, C. and Ifju, P. (n.d.). Experimental Characterization of the Mechanical Properties of 3D Printed ABS and Polycarbonate Parts Gainesville: UF Mechanical and Aerospace Engineering.

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43 BIOGRAPHICAL SKETCH Mr. David William Millar was born and raised up in Plantation, Florida, a suburb of Ft. Lauderdale, FL. He attended high school at South Plantation High School in Plantation and graduated in 2013. He continued his education at Broward College, graduate with his Associates of Arts degree in May 2015. After Broward College, David transferred to the Univer sity of Florida Research Opportunity Program. In the program, he worked u nder Dr. Bogdan Epureanu on a dissimilar materials Performance Prediction f or Ultrasonic Spot Welded Aluminum Stainless Steel Specimens Exposed t o Harmonic Loads a nd Material Degradation In addition to his research, David also participate d in a professional internship program at Walt Disney World. In this program, David worked at the Epcot Engineering Services department assisting current Imagineers with facilitating the design and installation of a maintenance bridge for the support team at the Frozen Ever After attraction as well as enhancing ride components for the Test Track ride vehicles David will be graduating magna cum laude from the University of en continue