THE MECHANICAL BEHAVIOR OF HIGH PERFORMANCE POLYMER FIBERS by JOHN EDWARD MOALLI B.S. Civil Engineering Northeastern University 1987 SUBMITTED TO THE DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF SCIENCE at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 1992 © Massachusetts Institute of Technology 1992 All Rights Reserved Signature of Author Department of Materials Science And Engineering May 1, 1992 Certified by P-f&fesso ederick J. McGarry Thesis Supervisor Accepted by Linn W. Hobbs Professor Of Materials Science Chairman, Departmental Committee on Graduate Students ARCHIVES MASSACHUSETTS INSTITUTE OF TcrwJnl nry JUL 3 0 1992 UBRAHIES The Mechanical Behavior of High Performance Polymer Fibers by John E. Moalli Submitted to The Department of Materials Science and Engineering on May 1, 1992 in partial fulfillment of the requirements for the Degree of Doctor of Science. Abstract The mechanical behavior of high performance polymer fibers In order to better characterize the was investigated. mechanical properties of these fibers several novel test methods were developed and improvements were made on older A device which simplifies fiber cutting for the ones. tensile recoil test was constructed. A new method to evaluate the transverse strength index of single fibers has The index is found to be similar among a been devised. variety of fibers suggesting that lateral properties depend more on interfibrillar morphology than interchain properties. The same instrument can also be modified to perform three This permitted the point bending tests on single fibers. determination of flexural stiffness and compressive modulus. The compressive modulus is found to be considerably less than the tensile modulus for most high performance polymer fibers. Compressive failure of high performance polymer fibers is Using the modeled by buckling of fibril structural units. compressive modulus from three point bending tests, fibril diameters from scanning electron microscopy and single mode Euler's from several methods, fibril buckling lengths equation is employed to predict the compressive strength of experimental data is single fibers. Agreement with reasonable and the model is shown to be especially useful for predicting relative compressive strength among fibers of processing subjected to different similar composition conditions. Based on the modeling of fibril buckling initiating compressive failure, a new method is introduced to improve compressive strength in which rigid ceramic coatings are Aluminum oxide coatings applied to the fiber exterior. applied by physical vapor deposition are shown to increase compressive strength well beyond that predicted by a rule of Alumina coatings also are shown to reduce the mixtures. radial thermal expansion coefficient by a factor of two. Thesis Supervisor: Frederick J. McGarry Title: Professor of Materials Science and Engineering 2 Dedicated to the memory of my Grandfather, Luciano Moalli whose courage and ambition brought my family into this country, and whose morals and ethics will always be with me. 3 Acknowledgments I would first like to thank Professor Frederick McGarry whose guidance, friendship and support made this work possible. The long discussions, often not related to science, and constant advice have had an influence on my professional Many development and character that cannot be measured. other faculty members are acknowledged for their input and limited to: Professor David advice, including but not Roylance, Professor Michael Rubner, and Professor Peggy Cebe. For the financial support of Dow Chemical, and the fruitful Many thanks to discussions with its employees I am grateful. Dr. Steve Allen of DuPont for supplying Kevlar® and PPTA fibers, and for encouraging input on this work. The staff at MIT has also been instrumental to the completion machining and design done by Arthur and Steven of this work: Rudolph was nothing short of spectacular and my time spent in Mike Frongillo provided their lab is most memorable. microscopy instruction and advice with humor and style that Rich Perilli's help with PVD and equipment are unparalleled. John Martin rovided acquisition is greatly appreciated. (and The constant help surface lab. great help in the haressment) from Maria Raposo often pushed me over those barriers we all encounter. And what would have I done without the UROP's ? Those who contributed substantially to this project are: Betty Chang, Amy Chiang, Maureen Fahey, Francis Lee, Rafy Levine, Troy Morrison, Rodrigo Rubiano, Shari Schuchmann and Becky Wittry. The company and friendship of UROP's on other projects is also recognized: Lynore Abbott, Nate Getrich, Mike Groleau, Daphne Karydas and Helen Shaugnessy. I would also like to thank the brothers of Phi Gamma Delta for their friendship. My fellow graduate students have also provided help and friendship that was so important: Haskell Beckham, Francois Billaut, Jeff Carbeck, Mary Chan, Hans Foulger, Sue James, Sun-Wook Kim, Georgios Margaritis, Susan Noe, Ambuj Sagar, There are many Ramnath Subramaniam and the entire PPST clan. others who are not mentioned but are definitely remembered. My most special friend, Shari, has provided unselfish love The happiness and enjoyment she has added to and friendship. my life have made MIT much more enjoyable. Finally, my family must be acknowledged: Mom, Dad, Glenna, George, Grandma's, Michelle, Dan and Mary Ann, Maria, Pam and Mike, Andrea and Dave have always been there with support and Thank you all so much. love. 4 A bstract ................. ..................... .2 Acknowledgements .......... ..................... .4 List Of Figures ............ List Of Tables ............. .......................... 1 1 Chapter 1. Introduction ...... 12 Chapter 2. General Mechanical Behavior of High Performance Fibers......... .......................... 21 ............................ 2.1.Anisotropic Elasticit 21 2.1.1.The Cylindric illy Orthotropic Fiber ....... 23 2.1.2.The TransversE ely Isotropic Fiber .......... 24 2.2.Consequences Of Anisc)tropic Elasticity ............ 24 Chap,ter 3. Measurement of Fit Per Mechanical Properties .... 26 26 3.1.Axial Compressive Sti ength ........................ 3.2.Transverse Strength.. ............................. 28 3.3.Compressive Modulus.. ............................. 2 9 3.4.Experimental......... .......... ................... 29 3.4.1.Axial Compress;ive Strength ................ 29 3.4.1.1.Recoil Testing ..................... 29 3.4.1.2 .Composiite Testing .................. 32 3.4.2.Transverse Sti:ength ...................... 36 3.4.3.Compressive Mc)dulus .............. ...... 44 3.4.3.1.RectancTular Model .................. 50 3.4.1.2.CirculE ir Model ..................... 54 3.5.Results and Discussic)n ....... ...... ... ........ 63 3.5.1.Axial Compresssive Strength .............. 63 3.5.1.1.Recoil Testing .................... 63 3.5.1.2 .Composiite Testing .................. 63 3.5 2.Transverse Str:ength 3.5.3.Compressive Modulus 5 ....................... 64 ....................... 68 ...... .y Chapter 4. Modeling of Fiber Compressive Failure 4.1.E .virneP f Firil B:llcl ........ n 76 ..76 4.2 . 4odeling with Euler Buckling ................... ... 78 4.3.IResults and Discussion ......................... .. 88 Chapter 5. Improving Fiber Compressive Strength ...... 5.1. lethods of Improvement ......................... 5.1.1.Chemical Methods ....................... 5.1.2.Rigid Coatings ...................... 5.1.2.1. * . .97 ... 97 ... .97 .. 98 Coating Selection ............. .. .100 5.2 .E Experimental................................. .. 103 5.2.1.Coating Deposition ..................... ...103 5.2.2.Property Evaluation .................... ... 106 5.3.R Results and Discussion ......................... .. .109 5.3.1.Effect of 5.3.2.Effect of 5.3.3.Effect of 5.3.4.Mechanism Coatings on Fiber Strength ... .. .109 Coatings on Fiber CTE ........ ...112 Coatings on Flexural Behavior .. .119 of Improvement .............. ...123 5.3.4.1.Rule of Mixtures ................ ...123 5.3.4.2.Lateral Restraint ............... ... 124 5.3.5.Effect of External Stresses on Residual Strength of Coated Fiber ..................... ...126 Chapter 6. Conclusions .................. ............. 132 Appendix ........................................... 37 References ......................................... 140 6 List of Figures Figure Page Figure 1-1. Aromatic Polymers Spun Into High Performance Fibers . .................................. 13 Figure 1-2. SEM Micrograph of Split PBO Fiber Showing Fibrillar Morphology in Fiber Interior .................... 15 Figure 1-3. SEM Micrograph of Split PPTA Fiber Showing Fibrillar Morphology in Fiber Interior ..................... 15 Figure 1-4. SEM Micrograph of Split Polyethylene Fiber Showing Fibrillar Morphology in Fiber Interior ............. 16 Figure 1-5. SEM Micrograph of Kink Band In PBO Fiber ...... 16 Figure 1-6. Anisotropy in Mechanical Behavior of High Performance Polymer Fibers ................................. 17 Figure 1-7. Anisotrcpy in Thermal Expansion Behavior of High Performance Polymer Fibers ............................ 18 Figure 2-1. Polar Coordinates For A Single Fiber ....... 22 Figure 3-1. Lateral compression of a single fiber between parallel plates .............................. 30 Figure 3-2. Schematic of Spike in Load During Tensile Recoil Testing Caused by Shearing Action of Scissors ....... 33 Figure 3-3. Schematic of spike in load during tensile recoil testing caused by unsymmetrical cutting.............34 Figure 3-4. Photograph of FI-RE-CUT device ................ 35 Figure 3-5. Schematic of Mini-composite manufacturing procedure..................................................38 Figure 3-6. Cross section of mini-composite ............... 39 Figure 3-7. Schematic of lateral splitting test of single fiber. ............................................ 40 Figure 3-8. Optical Micrograph of Single Fiber Three Point Bend Specimen ................................. 41 Figure 3-9. Schematic of Instrument Used For Transverse Testing and Three Point Bending ............................ 42 Figure 3-10. Photo of device used for transverse testing and three point bending .................................. 7 43 Figure 3-11. Photo of device used for transverse testing .................................. and three point bending 43 Figure 3-12. Schematic of three point bend device .......... 46 Figure 3-13. SEM micrograph of fiber support block. Span is about 950 um ....................................... 47 Figure 3-14. SEM Micrograph of single fiber being tested in three point bend configuration .......................... 48 Figure 3-15. SEM Micrograph of single fiber being tested ....................... in three point bend configuration. 48 Figure 3-16. Rectangular cross-section around the neutral axis ............................................... 51 Tension-Compression Stress-Strain Diagram Figure 3-17. For Material With Unequal Tensile and Compressive Moduli Subjected to a Bending Moment .............................. Figure 3-18. Circular Cross-Section ....................... 51 55 Circular Segment ............................. 55 Figure 3-20. Compressive Modulus versus Tensile Modulus for Fibers With Normalized Flexural Rigidities ............ 59 Figure 3-21. Flexural rigidity versus compressive modulus for different cross section ........................ 60 Figure 3-22. Normalized bending stiffness for fibers of different tensile modulus ................................. 61 Figure 3-23. Compressive Modulus as a Function of Fiber Radius for a Measured Flexural Rigidity .................... 62 Figure 3-24. Stress-Deflection plot from compression .......................... testing of mini-composites 66 Figure 3-25. Load-Deflection plot from three point bending on single glass fibers ............................. 69 Figure 3-26. Load-Deflection plot from three point bending on single Kevlar® fibers .......................... 72 Figure 3-27. Load-Deflection plot from three point bending on single Kevlar® 149 fiber. ...................... 73 Figure 3-28. Load-Deflection plot from three point bending on single PBO fibers ............................... 74 Figure 3-19 - 8 Figure 4-1. SEM Micrograph of Single PBO Fiber split with micromanipulator . ........................ 77 Figure 4-2. 79 Schematic of Simply Supported Column .......... Figure 4-3. SEM Micrograph of single Kevlar® 49 fibril from a fiber split with a micromanipulator ................. 82 Figure 4-4. SEM Micrograph of sheath of fibrils peeled from Kevlar® 49 fiber as shown in schematic . ........... 83 Figure 4-5. SEM Micrograph of sheath of fibrils peeled from Kevlar® 49 fiber. .................................... 84 Figure 4-6. Method of determination of buckled (arc) length of single fibril .................................. 86 Figure 4-7. SEM Micrograph of Arrays Of Buckled Rows In The Skin of a PBO Fiber Which Has Been Peeled Off The Core ....................................................... 87 Figure 4-8. SEM Micrograph of Arrays Of Buckled Rows In The Skin of a PBO Fiber Which Has Been Peeled Off The Core ....................................................... 87 Figure 4-9. Eulers Curve.... eoee Figure 4-10. SEM Micrograph of Kink Band Initiating on Exterior of PBO Fiber....... .f Pits Along Kink Boundary Q9 J, ... 93 Figure 4-11. SEM Micrograph of Pits Along Kink Boundary in Plasma Etched PBO Fiber.. .f Pits Along Kink Boundary. .... 94 Figure 4-12. SEM Micrograph of Pits Along Kink Boundary in Plasma Etched PBO-6 Fiber .... 94 Figure 4-13. SEM Micrograph (of Pits Along Kink Boundary in Plasma Etched PBO-5 Fiber .... 95 Figure 4-14. SEM Micrograph <of Pits Along Kink Boundary in Plasma Etched PBO-4 Fiber 95 .... Figure 5-1. Modification of IFibril Model To Consider Lateral Support By An Elasticc Foundation ................. 99 Figure 5-2. Schematic of FoIrces on Thin Rigid Coating Applied to Fiber. .......................................... 101 Figure 5-3. Radizal CTE as a Function of Coating Modulus Generated By Finit:e Element Model .......................... 104 Figure 5-4. Radizal CTE as a Function of Fiber Transverse IModu liis Generated By Finite Element Model ...... 9 105 Figure 5-5. SEM Micrograph of lumina Coating on PBO Fiber Applied by Physical Vapor Deposition ............... 107 Figure 5-6. SEM Micrograph of Alumina Coating on Glass .............. Fiber Applied by Physical Vapor Deposition 107 Figure 5-7. SEM Micrograph of Failed Alumina Coated PBO Good Adhesion of Coating is Evident............. . .111 Fiber. Figure 5-8. SEM Micrograph of Failed Alumina Coated PBO Good Adhesion of Coating is Evident............. . . .111 Fiber. Ultimate Compressive Strength versus Figure 5-9. Alumina Coatina Thickness For PBO Fibers ................ ... 113 Cumulative Distribution Function Of Figure 5-10. Ultimate Load For Uncoated and Alumina Coated PBO Fibers in Tension............................................ ...114 Figure 5-11. SEM Micrograph of Alumina Coated PBO Fiber Heated In-Situ to 4000 C ................................. ... Percent Change in Fiber Diameter With Figure 5-12. Temperature For Uncoated and Alumina Coated PBO Fibers.. 116 ... 117 Figure 5-13. Percent Change in Fiber Diameter With 49 Temperature For Uncoated and Alumina Coated Kevlar Fibers .................................................. .. .118 For Uncoated and Load Deflection Plot Figure 5-14. Alumina Coated PBO-5 Fibers ............................ ... 121 Figure 5-15. Load Deflection Plot For an Alumina Coated ... E-Glass Fiber...................................... 122 UCS vs. Coating Thickness: measured data Figure 5-16. and values calculated from rule of mixtures........... ..... 125 Figure 5-17. Circumferential Cracks in Coating on PBO Fiber From Tensile Loading ............................ ..... 129 Figure 5-18. UCS vs. Coating Thickness in PBO Fiber both Unloaded and After a 60g Tensile Preload ......... UCS vs. Coating Thickness in PBO Fiber Figure 5-19. Before and After Heating in Air....................... ..... 130 ..... 131 Variation in compressive modulus for PBO Figure A-1. fibers of the same lot .................................. 138 Variation in compressive modulus for PBO Figure A-2. fibers of the same lot .................................. 139 10 List of Tables Table Pag Table 3-1. Compressive Strength From Tensile Recoil Test ............................................... 65 Table 3-2. Compressive Strength of Fibers From MiniComposites ................................................. 65 Table 3-3. Transverse Strength Index for Several High Performance Fibers ......................................... 67 Table 3-4. Compressive Modulus for Several High Performance Fibers ......................................... 71 Table 4-1. Euler Analysis of Single Fibrils Using Sheath Peeling and R4 methods .............................. 89 Table 4-2. Euler Analysis of Single Fibrils Using Plasma Etching Method For Single Mode Buckling Length ............. 96 Table 5-1.Mechanical Properties of Alumina Used For Rigid Coating on Fibers ........................... 108 11 Chapter 1. High Introduction performance fibers are those described as having strength and moduli many times that of glass fibers. Almost since their inception, high performance provoked much excitement: with their benefits low for specific The fibers have their tensile properties, combined gravity, structural applications. polymer promise composites, performance of extraordinary especially many aircraft, in mobile missiles, land vehicles and boats could be measurably improved by using structural with materials Unfortunately this has not higher specific proved out properties. in practice; the low compressive strengths of the fibers have severely constrained their utility since relatively few structural components or systems function exclusively under tension. Most high performance fibers polymers. Figure 1-1: phenylene A are derived from rigid aromatic few of the more common ones are illustrated in poly(p-phenylene benzobisoxazole), benzobisthiazole), terepthalamide), PPTA. The PBT; former two PBO; poly(p- poly(p-phenyleneare experimental fibers while the latter is produced by Dupont under the trade name Kevlar®. Extended chain poly 12 (ethylene) has also been N 33~OO~~f PBO ~ n t(S9\/S 3PBT n H N Q I NC H Figure 1-1. j 0 Aromatic PPTA PPTA C1 n Polymers Fibers. 13 Spun Into High Performance made into high performance fibers by Allied Signal under the trade name Spectra®. The aromatic polymers form liquid crystalline solutions in strong solvents and are dry jet wet spun from these solutions at low concentrations into fibers. The alignment of chains during spinning results in fibers with a high degree of axial order 1 . Heat treatment further increase order aliphatic polymers chains and polymer good fibers under tension are and gel axial resultant a properties. spun which results alignment. display is then employed to All unique The in extended high performance fibrillar morphology, illustrated for the above systems in Figures 1-2 to 1-4 which are SEM micrographs of split fibers. This fibrillar behavior. morphology Under axial leads to anisotropic mechanical tension, the fibers are very strong but under axial compression the fibrils buckle and form kink bands as shown in Figure 1-5. Since the fibrils are held together only by weak secondary forces, the lateral tensile strength of the fibers is also low. also itself manifests behavior: negative direction typically high coefficients and very in of large Axial chain alignment anisotropic performance thermal polymer expansion positive ones 14 thermal in in the expansion fibers have the axial transverse SEM Micrograph of Split Figure 1-2. Fibrillar Morphology in Fiber Interior. SEM Micrograph of Split Figure 1-3. Fibrillar Morphology in Fiber Interior. 15 PBO Fiber Showing PPTA Fiber Showing SEM Micrograph of Split Polyethylene Figure 1-4. Showing Fibrillar Morphology in Fiber Interior. Figure 1-5. SEM Micrograph of Kink Band In PBO Fiber. 16 Fiber -ePW4 *-( ,--- 0)- Excellent L · L r- - III--- Axial Tensioa _ns =- - 0e Poor I I, L~ _ ,, I I .l ..... . |_ Ik i Axial Compression 4 ( Poor -?-C g , Is s- r 0 * Transverse Tension Figure 1-6. Anisotropy Performance Polymer Fibers in Mechanical 17 Behavior of High - ( P7 3 - -1 ---I · Is - -· -bB rr 0 + A T Fiber Shrinks Axially And Expands Radially r # f I ,' I, , 4' Figure 1-7. Anisotropy in Thermal High Performance Polymer Fibers 18 Expansion Behavior of direction. These anisotropic characteristics are schematized in Figures 1-6 and 1-7. The need to compressive correct this strength, deficiency, has been chemical in nature, increase the apparent many efforts to do so have been made. been to for axial some time, and Principally these have seeking to provide primary bonding transversely across the fiber 2 . The motivating idea was, and still is, that if the axially aligned polymer chains could be crosslinked in some way, their failure would be increased. the failure indeed, fiber mechanism resistance to compressive (Implicit is the assumption that is by buckling of the chain and, there have been attempts to quantitatively model the behavior laterally this stabilize buckling load: improve. on the changes in chain the compressive These Despite the basis 3) attempts apparent fiber and crosslinks thereby strength of have not achievement compressive The of been increase the very have its fiber would successful. crosslinking, strength would been modest reported often at the expense of tensile strength. This research compressive find a to failure way to produce properties. sought to in elucidate high with In Chapter 2, specific mechanism of performance delay it with the fibers the polymer and hope of discovering methods less anisotropic an overview of the 19 fibers mechanical anisotropic In order to effectively assess any improvements presented. Chapter them. properties mechanical some and of describes novel tensile testing the is in developed to measurement of be to fibers single including axial and axial strength on older test methods are Improvements compressive modulus. made 3 lateral strength, compressive had methods properties, mechanical evaluate microstructure fiber the from resultant elasticity techniques are developed. Chapter 4 describes a new method of modeling the compressive failure of high performance to measured properties. failure and introduces of high a the modeling performance Chapter from polymer the fibers the Chapter 4, compressive using rigid 5 strength coatings on Effects of rigid coatings on the thermal expansion behavior of the fibers highlights correlates the model Based on observations of compressive new method to improve the fiber exterior. 6 and fibers findings of suggestions for future work. 20 is also discussed. the research and Chapter makes Chapter 2. General Mechanical Behavior of High Performance Fibers 2.1. Anisotropic Elasticity The fibrillar performance structure polymer by covalent axial fibers mechanical behavior. carried and chain manifests polar itself in bonds while those coordinate system, applied (transverse or axial loads). however, if loads on the r and dissimilar responses. identically, the system is The more general case, the fiber orthogonal responses possess axes. to peculiar If we examine a one with fiber will react differently to loads invoke high transversely r, 0, and shown in Figure 2-1, it is not difficult to realize axes of Loads applied axially to the fiber are are held by weaker secondary forces. in a alignment that the imposed on the r and z axes ( radial and hoop) will the r ana 0 planes behave said to be transversely isotropic. symmetry applied z axes as It is not entirely clear, If though, These fiber is the orthotropic one, with two respect systems forces as thorough discussion on this topic, Allen4 . 21 to three produce very described below. where mutually different For a the reader is referred to z 0 KN\ r Figure 2-1. Polar Coordinates For A Single Fiber. r=Radial and =Hoop directions. 22 Z=Axial, 2.1.1. A The Cylindrically Orthotropic Fiber completely anisotropic material has It constants. only 9 of be can shown for the that are constants these 21 independent elastic case orthotropic The independent. stiffness matrix then becomes EI Er Ez 0 Ez 0 Er Eg E O Ez EOz E 0 O 0 Goz 0 0 0 and Oz terms will produce indicates some then of the of hydrogen forces stresses of of the hoop indeed has direction these interactions system is the result. 23 If the cylindrically been shown to sheets 5. Van an be This related Der covalent bonding; differ, forces on chain be to loads axial stiffness would be axial direction to of both in the fiber. is based example, radial direction bonding, and the magnitudes The presence application will for (2.1) radially oriented hydrogen bonded implies that the to GrO 0 system systems Kevlar®, orthotropic. composed 0 that radial and hoop mechanical behavior only, 0 0 0 0 O0 0 are the principal moduli. where Eij's rz 0 0 0 0 O 0 Grz Waals as the orthotropic 2.1.2. The Transversely Isotropic Fiber If mechanical behavior is based on fibril interactions, then the radial and hoop directions should be indistinguishable and the stiffness matrix becomes where K = exist. in Err E 0 Er Eo Er Er0 Erz E Ezz 0 0 0O 0 0 0 0O 0 0 0 0 G 0 0 0 G 0 0 0 K 0 0 0 0 0 0 (Err - ErO)/ 2 , and only (2-1) 5 independent constants This type of model does not consider any differences radial or hoop properties that may be derived from a orthotropic system skin/core structure in the fiber. 2.2. Consequences Of Anisotropic Elasticity It has been shown6 that a cylindrically will produce radial and hoop stresses when an axial load is applied. This implies that axial compression on a fiber may produce transverse tension, a combination of forces that is obviously detrimental to the transversely axial isotropic fibrillar structure. system, and other directions. Chapters, this research no coupling As will offers be exists evident evidence that For the between in later fibril interactions control mechanical behavior, hence all analysis are conducted assuming transverse isotropy in the fibers. 24 It must structure Kevlar®) constant also be pleated in anisotropy depending on the fibers compressive moduli. would may sign have supramolecular fiber the result can Specifically, matrices the example (for that recognized sheet arrangement in single of a the different in elastic applied tensile load. and This would imply that separate stiffness have to be compressive loadings. 25 compiled for tensile and Chapter 3. Measurement of Fiber Mechanical Properties 3.1. Axial Compressive Strength As described previously, rigid rod polymer axial compressive strengths; measure this. Most of them mark failure strength is low by the onset of They include the elastica loop matrix shrinkage 8 and beam bending compressive have several methods are available to visible kink band formation. test 7, fibers calculated 3 9 . , In these tests from the product of the tensile modulus and the critical strain for kinking, thus it is assumed that the fiber behaves in a linear elastic fashion to compressive moduli are uncertainty axial failure and that identical. so a compressive more These assumptions direct strength the tensile and compressive cause measurement is desirable. tension to various levels and then single The tensile test developed by Allen is such a method1 0 . in of substantial cut surface and cause compressive recoil Fibers are loaded and the recoil stresses created from tensile failure reflect grip fiber damage in the elastic from the fiber. is assumed that no damping occurs during reflection It such that the magnitude of the resulting compressive stress is equal to the tensile stress determined by at failure. fracturing a The compressive number of tensile strength is specimens at different stress levels to find the minimum value which just 26 initiates tensile kink band failure at formation. different Obviously stress this levels requires and several cutting techniques have been developed for the purpose. include spot etching, heat cutting, mechanical damage, and scissor cutting 1 0 . the is first undesirable shearing a poor increases action. symmetrical gives three in the A new accurate applied localized Reproducibility in scissor device cutting of the more and prior They cutting induces stress because has been of the developed for fiber during recoil testing which assessment of the axial compressive strength. Another method compressive fiber have may be strength is by using is available, compression which which to evaluate composites. If fiber sufficient a high quality composite can be made and tested. been used The composite shown to must substantially strength in unidirectional composites. be free reduce of voids compressive Fiber alignment must also be perfect as strength and modulus decrease rapidly with increasing misalignment of fibers. If these met, can the fiber compressive strength micromechanical disadvantages. differential theories, Among the thermal perfect alignment. fiber compressive method latter are shrinkage Poisson's Ratio effects, of a conditions are be calculated using which matrix effects, has hardening many and differential specimen end friction and difficulty Also failure it is very difficult details 27 in such to monitor assemblages, compared to a single fiber specimen. methods are desirable as they Nonetheless, composite provide properties during end use applications. has been developed which allows for data for fiber Hence, a new method the construction of highly aligned void free composites for compression testing. 3.2. Transverse Strength The transverse very low. strength Several by produces strength of rigid rod polymer researchers have measured the lateral tension compression on the of midplane procedure is shown in Figure 3-1. test which Such is fiber are condition is tend which Furthermore, fiber crushing developed forces the at to to of the Therefore, opening mode polymer a test which This by frictional low load unless lateral state, attenuation all of a strength. in the In order to avoid such has been forces deformation. stress desirable to perform lateral testing on fibers. transverse fiber. during assumed of determine is A major deficiency of this the nature also fiber1 1 single fiber base exacerbated exact difficult the change is a and the resultant elastic constants are known. it is fibers the fiber effects free standing developed in which an crack is propagated axially in high performance fibers. The crack initiation force measure of a transverse fiber mechanical property. 28 provides a 3.3. Compressive Modulus The most modulus comnon is technique with for evaluating unidirectionally fiber compressive reinforced thermosetting polymer matrixl 2, usually with a 13 composites, . The fiber modulus is calculated through application of micromechanical theories to composite disadvantages as properties, mentioned a method which has previously. Other researchers have used cantilever bending on large diameter fibers 500 um) to calculate fiber compressive many modulus1 4. (250 To the authors knowledge, no such flexural tests have been performed on high performance polymer fibers which typically have .; diameters from development of 10 a um to single 20 um. This fiber three research presents point bending test the for evaluation of fiber compressive modulus. 3.4. Experimental 3.4.1. Axial Compressive Strength 3.4.1.1. Recoil Testing The analysis of the tensile recoil test has been presented by Allen1 0 . Since zero attenuation of the reflected wave is desirable and the amplitude of the reflected wave is given by (Pm Cm- Pf cf) (PAe +ncm f cf) 29 (3.1) __ * s __ wI S I -u,-...., - iber - -- -- -- - - - ,, Parallel Plates - - - , , , - , E'///////////////////// A-- P Figure 3-1. Lateral compression of a single fiber between parallel plates. 30 where the wave velocity, ci is ci Pi and E is the modulus and p is the density, it is obvious that the fiber and gripping medium must have different impedances. This is readily accomplished by placing the -fiber ends in epoxy resin which typically has modulus values 40 to 80 times less than that of the fiber. The epoxy is used to mount the fibers onto cardboard tabs, the center of which is a hole of the desired gauge length. The fiber/tab assembly is placed in a tensile testing machine (Instron 4505 with 2000 g load cell at 20 g full scale load) and gripped. The edges of the tab are then cut away such that only the fiber is loaded. The most difficult part of the test is finding a suitable method to cause tensile failure in the fibers. is not done with great care, applied load will occur. large increases If breaking (spikes) in the If the spikes are too large, the test is invalid because the exact stress state in the fiber becomes unknown. surgical scissors problems exist Although some researchers have can provide with this shearing action, and as reasonable technique. found that reproducibility, The blades cut by a shown schematically in Figure 3-2, this imposes a twist on the fiber causing an increase in the applied load. Another problem arises when the blades do not cut symmetrically: both blades do not come in 31 contact with the fiber at the same time. The fiber is displaced laterally, as in Figure 3-3, shown which also causes a spike in the Both of these effects are more pronounced as the fiber load. modulus increases. To remedy these (FIber-REcoil-CUTter) shown in Figure 3-4. a was a photograph made, device named problems FI-RE-CUT of which is It employs scalpel blades mounted on blocks which are supported by linear bearings. The blades avoiding any shearing action. The blocks remain co-planar, are connected to a drive rod with opposing left and right handed threads; when the rod is rotated it brings the blades together smoothly at The entire device is a uniform rate. mounted on a micrometer substage which facilitates precision centering of the fiber between the blades and prevents unsymmetrical cutting. 3.4.1.2. Composite Testing The method developed for composite manufacture, similar to that of Piggot 13 is a pultrusion technique. Four inch lengths of fibers were cut and placed on top of a small wire. After a sufficient number of fibers were in place the wire was looped over the fibers which were pulled by the wire into a hollow glass tube of 20 mm diameter. A smaller glass tube (5 mm) lined with rubber was then placed over the wire just above the fibers. Next, epoxy resin (Dow Tactix 123) was 32 I I C.__. Tensile Force Time Figure 3-2. Schematic of Spike in Load During Tensile Recoil Testing Caused by Shearing Action of Scissors. 33 I I II - I I I I I CO ;fL Tensile Force Time Figure 3-3. Schematic of spike in load during recoil testing caused by unsymmetrical cutting. 34 tensile S. Figure .- 4. Photograph of FI-RE-CUT 35 device. poured into the (Figure assembly glass small placed 3-5) the resin degassing, tube over the large tube and a in fibers and the entire After oven. vacuum soaked fibers were pulled through the Void free, cured. high fiber volume fraction composites were produced using this method. A cross section of a typical composite is shown in Figure 3-6. Composites were cut to 12.5 mm lengths with a diamond saw in a specially designed jig to ensure that specimens ends were Specimens parallel. loaded were unsupported, end on, in direct compression in an Instron 4505 at a crosshead speed of Teflon was placed between the loading platens and 1 mm/min. the specimen ends to minimize frictional end constraints. Transverse Strength 3.4.2. The poor lateral integrity of rigid rod polymer fibers makes that a fiber of It was observed from handling. them susceptible to damage cross circular could section easily be flattened with tweezers or other instruments. Then if the end was split, the force transverse strength. required could give some idea of the Using a micromanipulator , one end of a fiber which is a few centimeters in length is flattened. vee shaped segment is removed defining two A ligaments (usually this operation is easily performed on the rigid rod polymer fibers because of their high orientation and directionality; with other less oriented fibers such as nylon it may be more difficult). This whole procedure is sketched 36 in Figure 3-7 and, experimentally, made with a micromanipulator. in Figire 3-8. The extremely small and loads such specimens have been An optical micrograph is shown involved in splitting difficult to measure. fibers are To determine the critical crack propagating force an instrument which operates with dead weights has been constructed; in Figure 3-11. 3-9 and photographs are The operation notched fiber is movable grip (it is quite placed in a a given schematic is shown in Figures simple: fixed grip 3-10 and one ligament of the and the is necessary to keep the axis specimen approximately perpendicular to the the two grips and the weighing splitting of the fiber). movable supported weights grip shaft. are is The placed. a of the fiber line defined by to ensure successful The moveable grip is supported by a gas bearing which eliminates the cable, other in a friction effects. cable running cable ends at [Since loads the a over Attached to a bucket gas in required bearing which for the crack propagation are in the milligram range, the gas bearings are critical: frictional forces in conventional bearings easily exceed the loads of the test.] testing, the entire device is end causing Weights are position. the movable added until To balance the system before slightly elevated on the right grip the to displace movable grip is to in the a left. neutral Then the fiber is inserted into the grips and more weights are added until the fiber splits. 37 The entire test I Rubber Tube Small Glass Tube Wire Resin Fibers I Large Glass Tube lubber Stopper Fiaurna *- procedure. ouIIleUman C Ot Mini-composite 38 manufacturing Figure 3-6. Cross section of mini-composite showing good distribution of fibers and fiber volume fraction of 50 percent. 39 +I I A B C Figure 3-7. Schematic of lateral splitting test of single fiber. a) Flattening of. fiber end b) Creating notch in flattened portion c) Pulling ligaments apart d) Propagating crack 40 D Ig Figure 3-8. Optical micrograph of single fiber which has been flattened and then had a notch created in it using a micromanipulator. 41 Vz 0 -g z £b hn 0 b c - rq ,.c a c I3 Go Lt p xE U) , 0a p0 "dU I -I.4 rl ,. Figure 3-10. Photo of device testing and three point bending. used Figure 3-11. Photo of device used testing and three point bending. 43 for for transverse transverse procedure is observed with an optical measured on and accurate a easy chemical to diameter of the fiber split, the balance which Their value, use. equipped The incremental weights with a closed circuit video system. are microscope is inexpensive, divided by the provides a number to represent lateral integrity of the fiber: the opening mode axial crack initiating force, normalized by diameter. In recognition of the fact that this test does not measure the true transverse tensile strength of micro fracture toughness test) (it is actually a kind this number has been named the Transverse Strength Index (TSI). Compressive Modulus 3.4.3. The apparatus also can be used for single fiber three point bending tests. The fixed grip is replaced by a fiber support A hooked probe is attached to the movable grip. block. A fiber is placed on the platform with the hooked probe beneath it. When weights are added to the bucket the hooked probe loads the with a fiber at video its midpoint. micrometer and Deflections are measured kept small so that linear behavior occurs. A schematic of the bending device is given in Figure 3-12. A micrograph of the fiber support block is shown in Figure 3-13 and micrographs of a fiber being loaded are given in Figures 3-14 and 3-15. 44 If the angle of rotation of the fiber, small, then the basic differential (Figure 3-12), equation for is bending holds: 2 ax2 EI (3.2) where 6 is the deflection, x is the distance along the fiber, M is the bending moment, E is the modulus and I is the moment of inertia. The equation of the load deflection curve can be derived by double integration of equation 3.2 p=48EI 8 L3 (3.3) where P is the load and L is the span. Integration of equation 3.2 gives the angle of rotation of the fiber 6 = P L2 16 E I If is large (tan 0), then derive equation 3.3 is not valid. the (3.4) analysis employed to Typical fiber diameters in the three point bend test are 10 - 30 um. The span is 800 - 1100 um and loads 5 mN. typical rotation values is are usually less than entered into sufficiently equation small analysis. 45 to 3.4, employ With such the basic angle of elastic P Figure 3-12. Schematic diagram of three point bend device 46 Figure 3-13. SEM micrograph of fiber support block. about 950 um. 47 Span is Figure 3-14. SEM Micrograph of single tested in three point bend configuration. fiber being Figure 3-15. SEM Micrograph of single fiber being Deflection tested in three point bend configuration. is about 100um. 48 Equation 3.3 assumes that all deformation is due to flexure only; shear effects are not considered. Modified for shear deformation, equation (3.3) becomes p=48EI 6( 1+ where d is )(3.5) the fiber diameter and G is the shear modulus. Typical values of G are about two orders of magnitude less than E um 8. and However, since the span in this case is about 950 the fiber diameter is typically comparison of equation 3.3 and 3.5 10 show that to 20 um, shear effects are negligible for this particular testing geometry. Equation 3.3 cannot be solved directly for the modulus as the moment of unknown. neutral one, inertia with respect to the neutral axis is When the tensile and compressive moduli differ, the axis and the of the fiber shifts expression for the away from the fiber centroidal bending stiffness becomes: (EI)f =EcI + ETIT (3.6) Where the subscripts f, c and T refer to fiber, compression and tension. The moment of inertia for each of the latter two is with reference to the displaced neutral axis and the magnitude of its displacement from the centroidal one is a function of the relative magnitudes of Ec and ET. Thus, if ET is known from another test, a tensile one, then Equation 3.6 49 but the algebra involved in contains only one unknown, Ec, for Ec an expression obtaining becomes quite complicated, especially if the beam cross section is circular rather than Such rectilinear. the is case many with fibers, so the details of the solution are presented below. In working out the solution for the anisotropic beam, a fiber with a circular cross section, it was also of interest to see how well this could be approximated by a rectilinear cross either a square circumscribed about the circle section, one or This was motivated by the relative inscribed within it. simplicity of the squares analyses. Recalling equation 3.6, since If=It+Ic, 3.6 can be simplified to: EfIf = (Et - E) It + EcIf With the flexural rigidity measured (3.7) from the three point bending test and the tensile modulus evaluated from a tension test, we can solve 3.7 for the compressive modulus if the appropriate moments of inertia are known. 3.4.3.1 If the Rectangular Model cross section of the fiber is rectangle which circumscribes the circle moments of inertia for the 50 three approximated (Figure 3-16), rectangular by a the sections b =2r ...w ~~~~~~~~~~ F_ - l "" _1 - I -- I II~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ h 1 Neutral Axis A h =2r w - - - , d _ .. I . Centroidal Axis .. . h2 I Figure 3-16. axis r L Rectangular cross-section around the neutral G £2 e Figure 3-17. Tension-Compression Stress-Strain Diagram For Material With Unequal Tensile and Compressive Moduli Subjected to a Bending Moment 51 (total section, compressive section and tensile section) can be found by the parallel axis theorem (3.8) and the equation for the moment of inertia of a rectangle around its centroid (3.9): I, = I,,x + Ad 2 where Ixc (3.8) Ix is the moment of inertia of a section about axis x, is the centroidal moment of inertia of the section and A is the area. For rectangular shapes Ix = bh 12 (3.9) Thus, the for the moment of inertia of the cross section around neutral section , axis, It, If, and the the moment moment of section around the neutral axis, If 4 of inertia inertia of the of the tensile compressive Ic we obtain: + 4r2 d2 3 (3.10) It= 24r(r-d)3 (3.11) 2r + d Ic= 3 (3.12) shift measured, another method the is beam in the neutral axis, Since the subjected must be to a used to positive 52 d, cannot be determine bending directly it. If moment, for equilibrium the shaded two areas stress-strain Hence curve (Figure 3-17) must be equal. at C = the under c E2 2 2 (3.13) From Hooke's Law : (Ft = Etl ac= Ec2 £1 = -hl E2 = -Kh (3.14) also : 2 (3.15) where K is the curvature. (3.15) into equation Substituting equations (3.13), (3.14) and gives: E t h2 = Ech (3.%6) Which can also be expressed as: =(r+d d = d 2 +2rd + r2 Et = Ec h2 (r-d)2 d2 -2rd+r 2 (3.17) Collecting terms, gives: 53 1 2 E +2)rd+t- 1)r2=0 (3.18) Solving equation 3.18 for d, using the quadratic formula, yields: fp+ (3.19) (note that the root selected is the one for which Substitution of equations (3.10)-(3.12) and d < r) (3.19) into equation (3.6) gives the flexural rigidity : EfIf=21 3 4 (Et-E)( 1- z) +3E( 3 1+ 3z2) (3.20) where Appropriate+ can be used to evaluate (3.20) Appropriate numerical methods can be used to evaluate (3.20) for Ec. 3.4.3.2 Circular Model The same analysis as applied to a rectangular section can be applied to a section which is circular (Figure 3-18). 54 h xis Figure 3-18. Circular Cross-Section dis 0 Figure 3-19 - Circular 55 Segment For a circle: If= 4 + r4z 2 (3.21) For It we use a circular segment (Figure 3-19). Applying the parallel axis theorem we find that It=4 (2a8Asin6a + sin 2a)(1 + a-2sin3acosa)_ sin o- cos sin 2a) a 9 2a + (2 2 ~~ic~~ [ 6a-4- sin sin2orIJ 3 sin (3.22) Where: a = cos-1 dr = Cos- z (3.23) Substituting (3.21) - (3.23) into (3.7) we arrive at the expression for the flexural stiffness of an anisotropic beam with a circular cross section Ef If E - E) sin + a2 -sin 2a1 T(2a-si · 8sin cosaa a 9 2a -sin sin2a r2(2a - sin 2a[ , -c o s o a) 2 L %6o[a 3 sin 2o } +E4t4+ (3.24) 56 4Z2) Again, appropriate numerical methods can be used to evaluate Equation 3.24 for Ec. A validity check of the analysis is shown in Figure 3-20. Here each curve represents a single value of the normalized bending stiffness, (EI)f/r 4 , and shows how the tensile and compressive moduli vary as the stiffness The curves are symmetrical about the remains constant. 450 diagonal as they should be, hence the validity check. Figure 3-21 compressive shows modulus a plot for circumscribed square is of flexural different rigidity cross versus sections. seriously in error and while The it is not shown, the inscribed one is also; the magnitudes of the errors change, depending on analyzed, but they are always square cross section having the particular significant. the fiber being In contrast, a same area as the circular cross section gives a nearly identical solution, at least for the case presented. How broadly this equivalence can be generalized or extended is not known, but for the fibers of interest it seems to be a good approximation. Figure 3-22 shows the fiber compressive modulus as a function of the fiber normalized bending stiffness, radius. plotted: Curves for two (EI)f/r4 , where r is the fiber tensile moduli are 124 GPa (18 Msi) is typical for Kevlar® 49 and 276 57 GPa (40 Msi) section represents PBO. fibers expressions and shown. both Both refer to circular cross- can This be fit presentation by the of polynomial the analysis is convenient for interpreting experimental measurements made on fibers: to obtain a measured value of compressive modulus one simply takes (EI), divides into the expression of this Figure 3-22 does imply one very sensitive whole compressive modulus: to the approach to magnitude Use of measurement a fiber's errors in the fiber diameter are raised of the is radius an SEM error is recommended. associated for a with shown in Figure 3-2315: can lead to almost uniform cross section The potential improper radius a 0.5 um difference in 100 compressive modulus in some cases. need determining fourth power, so accuracy in this measurement is very important. the and substitutes it derived from the tensile modulus of the fiber of interest. feature by r4 it the percent error in This also emphasizes the in the analysis invoked. For a more detailed description of error sources in the three point bending Finally, a test the validity reader check on is referred the three to Appendix point bend I. test procedure was made: glass fibers which are isotropic and well characterized were tested. the identical glass fibers A measured flexural modulus to the tensile indicate a satisfactory testing process. 58 modulus for would 400 0 300 0 X 200 rI 100 V. OP 0 0 100 200 300 '400 Tensile Modulus (Gpa) Figure 3-20. Compressive Modulus versus Tensile Modulus for Fibers With Normalized Flexural Rigidities Typical of Kevlar® (11.8) and PBO(13.4). 59 Comparison of Anisotropic Section Models - - 2.5 2.0 a rIM 0 rW4 e4 'ircumscribed Square [qual Areas Circle 1.5 C 1.0 0.5 0.0 0 50 100 150 Ec (Gpa) Figure 3-21. Flexural rigidity versus for different cross section 60 compressive modulus ran 5WU 250 co CL 200 t = 276 Gpa (40 Msi) c = 124 Gpa (18Msi) 150 Q0 Sm 100 C0 Et = 124 Gpa 50 Et = 276 Gpa 0 0 5 10 15 (EI)f / r ^4 Figure 3-22. 20 25 (Pa x ElO) Normalized bendingq stiffness for fibers of different tensile modulus. 61 300 I m 200- r0 r- 100 _= -r -- I-- W1 o 0u 04.0 I I I 5.0 6.0 Radius . - . 7.0 (microns) Figure 3-23. Compressive Modulus as a Function of Fiber Radius for a Measured Flexural Rigidity, EI, Typical of PBO Fibers. 62 3.5. Results and Discussion 3.5.1. Axial Compressive Strength 3.5.1.1. Recoil Testing It has been found that using FI-RE-CUT the success rate for correctly cutting fibers is nearly 100 percent for Kevlar 49 and about fibers, 80 percent compared respectively, compressive for with using PBO and about other 80 other stiff percent methods. and Typical strength from the tensile recoil experimental 30 percent, values of test are the given in Table 3-1. 3.5.1.2. Composite Testing A typical Stress - displacement curve for a mini-composite is given in onset of nonlinear behavior. Figure 3-24. Specimen failure is defined as the This is also marked by visible failure in the composite by formation of a global kink band. Compressive strengths mixtures approach exhibited linear for fiber failure were which obtained using assumed behavior well (this was that a simple the beyond the epoxy strains rule of matrix required verified by compression testing neat epoxy samples). The results are in for PBO and Kevlar® reasonable agreement with 63 fibers, single given fiber in Table 3-2 compressive The Kevlar® strengths obtained from tensile recoil testing. are values also manufacturer 1 6. similar caused by the reported those by the The increase in fiber compressive strengths composite data over from to increased those from recoil testing may be support lateral provided by the matrix to the composite fibers. Transverse Strength 3.5.2. Table 3-3 presents the results from lateral testing. The various PBO fibers listed have the same composition but were The difference in the processed under different conditions. transverse strength index (TSI) between these fibers indicate in processing that the TSI can be used to evaluate changes exists any relationship between TSI and fiber compressive strength. It parameters. It does not appear that there is interesting to note that PBO-1 and Kevlar® 49 have similar TSI values. strength, one If the would TSI were expect the based on Kevlar® intermolecular 49, a polyamide capable of hydrogen bonding, to have a higher value than PBO. Since this is properties are intermolecular lateral not the more case, likely strength. (and compressive) one can conclude that based Hence, on interfibrillar attempts strength by at than improving introducing primary valence bonding in the transverse direction 64 lateral (interchain) will Table 3-1. Compressive Strength From Tensile Recoil Test Fiber Compressive Strength [MPa(Ksi)] PBO-1 PBO-2 PBO-3 PBO-4 PBO-5 PBO-6 Kevlar® 29 Kevlar® 49 172 414 152 324 227 165 365 379 Table + 5 4 + 6 ± 5 + 6 ± 6 + 10 ± 10 f (25) (60) (22) (47) (31) (24) (53) (55) 3-2. Compressive Strength of Fibers From Mini-Composites Fiber Compressive [IPa (Ksi) PBO-1 Kevlar~ 4 9 220 448 65 11 13 Strength (32) (5) 800 600 400 r2 200 0 0.00 0.10 0.20 0.30 Displacement (mm) Figure 3-24. Stress-Deflection plot from compression testing of mini-composites 66 Table 3-3. Transverse Strength Index for Several High Performance Fibers Fiber Designation Fiber Diameter (um) Transverse Strength Index [N/m (lb/in)] Spectra Kevlar® 49 PBO-1 PBO-3 PBO-4 PBO-5 PBO-6 35 12 24 16 17 24 27 349 519 491 272 278 285 339 ± ± ± ± ± ± ± 44 42 47 21 24 15 38 (1.99) (2.96) (2.80) (1.55) (1.59) (1.63) (1.93) Note: PBO-2 was not included in this study as an insufficient quantity of it was available for TSI evaluation. 67 be ineffective unaffected. interactions interfibrillar will be This has been the case in several studies5Z. Compressive Modulus 3.5.3. Figure as 3-25 shows the single glass fibers. results for three point bending of Since the glass fibers are isotropic, equation 3.3 can be solved directly for Ef. using a least squares analysis line fit This is done by to the load data . The slope of the line of the load - deflection curve is then given by Slope = 48 E I L3 (3.22) which is solved for E since I and L are known. The result is an average flexural modulus of 75.8 GPa (11 Msi) which is in good agreement with literature values for the tensile modulus of E-glass. Figure 3-26 shows flexural data for Kevlar® fibers. The least squares fit for the Kevlar® 149 fibers uses the first three data points only as the fibers exhibited non-linear behavior at higher loads as shown in Figure 3-27, result of kink band formation. most likely as a Figure 3-28 shows the three The difference in the slopes point bending for PBO fibers. of the curves comes from the variation in fiber diameter. 68 Vetrotex Glass P103-24 h Am~. in 1.50e-3 Z 1.QOe-3 T,oi 011 Pk 5.o0e-4 0.00e+O O.00e+O 1.00e-5 2.00e-5 Deflection 3.00e-5 (m) Figure 3-25. Load-Deflection plot from three point bending on single glass fibers 69 the Using modulus values analysis for described, several are fibers of tensile moduli the values given in employed in the of compressive Table All 3-4. calculations are those provided by the manufacturers. Tensile moduli were not explicitly measured in this study. As can be seen, in all cases the values of the compressive modulus are less than the and in one instance, greatly so. tensile ones While there has arisen the assumption that the two should be equal3 The microstructure fact just the opposite is to be expected. of these chains fibers are probably is highly is not perfect and while the polymer fibrillar the oriented along in fiber nor uniform. axis, the Thus, alignment at the chain level, a pull will tend to improve the alignment and a push, to reduce have and it. It is also clear if the molecules involved a non symmetric potential well that different tensile compressive limit absolute microstructure tension, will moduli of zero will be expected, strain. Further, exhibits a pleated sheet1 7 open and flatten, when compressed, except the in the Kevlar® form which, under becoming stiffer, whereas, it will fold more closed and decrease in stiffness. Another interesting feature of the data sensitivity of the compressive modulus. is the apparent The two PBO cases, while identical in composition, underwent somewhat different processing in the fiber drawing stage and this was reflected 70 Table 3-4. Compressive Modulus for Several High Performance Fibers Fiber PBO-1 PBO-2 Kevlar® 29 Kevlar® 49 Kevlar® 149 Assumed Tensile Modulus, Et [GPa(Msi)] Compressive Modulus, Ec [GPa(Msi)] Ratio E/Et 276 (40) 276 (40) 96 (14) 124 (18) 179 (26) 40 240 90 90 55 0.15 0.87 0.94 0.73 0.31 71 (6) (35) (13) (13) (8) ____ 5.000e-4 0 Kevlar 49 O Kevlar 49 o Kevlar 49 4.000e-4 ZCu 3.000e-4 o Kevlar 149 O Kevlar 149 O Kevlar 149 0 ,- 2.000e-4 1.000e-4 O.000e+O 0.00e+0 2.00e-5 4.00e-5 Deflection 6.00e-5 8.00e-5 (m) Figure 3-26. Load-Deflection plot from three point bending on single Kevlar® fibers 72 Kevlar 149 Z o 0~ C 0.OOe+0 2.00e-5 4.00e-5 6.00e-5 8.00e-5 Deflection (m) Figure 3-27. Load-Deflection plot from three point bending on single Kevlar® 149 fiber. 73 _ Ads_ 1.00e-3 8.00e-4 Z 6.00e-4 co 4.00e-4 2.00e-4 .00e+0 O.00e+O 1.00e-5 2.00e-5 3.00e-5 4.00e-5 Deflection (m) Figure 3-28. Load-Deflection plot from three point bending on single PBO fibers 74 in the compressive modulus values. By other methods, the microstructural and morphological changes difference be the revealed can that the explored, two mechanical properties; but fibers accompanying the simple had marked bending test differences this was confirmed by differences in in compressive strength behavior also (Table 3-1). Some other interesting three point bending experiments can be envisioned: experimentation with shorter spans which will produce significant shear deformations is being conducted; it may be possible to determine the shear modulus directly in this manner. Finally, another feature of the single fiber bending test is proving to failure. can be be interesting: its use to study compressive Bending fibers until visible kink band formation a strength. useful method for determination of compressive The current loading geometry makes this difficult, however, because the loading probe is located at the point of maximum stress and tends to make kinks difficult to see. A four point bending configuration would be more suitable for a compressive strength test and it is under development1 5. 75 Modeling of Fiber Compressive Failure Chapter 4. 4.1. Evidence of Fibril Buckling It is well known that high performance polymer fibers fail in by compression described kink a as band buckling microstructural scales: formationl8,3 . failure on Kinking has been different several Deteresaet a1 3 developed a model for kink formation based on the buckling of single polymer chains while Cohen buckling and Thomasl 9 described The entity. former microfibrils model concludes as the that the compressive strength should be equal to the shear modulus and although this has not proven to be the case, data exists that show a correlation between linear recognized the fibril as the the buckling two. Although entity, the they latter researchers made no attempt to model the compressive strength of fibers as a discussed viable function of fibrillar microstructure. fibril mechanism buckling but to explain concluded that similarities in it Kumar 20 was not a compressive strength among PBO fibers with different tensile moduli. Figure 4-1 split with is a SEM micrograph of a PBO fiber which has been a micromanipulator ; the fibrillar the fiber is evident on the split surface. 76 structure of The rear surface Figure 4-1. SEM Micrograph of Single PBO Fiber split with micromanipulator. 77 of the fiber is in compression and kink bands have formed. buckled These kinks have propagated through the fiber and fibrils are also visible on the split surface. evidence (along with that from others1 7 ,1 8 ), Such visible which is clearly indicative of fibril failure within the kink, has motivated by fibril buckling modeling of compressive failure in this research. 4.2. Modeling with Euler Buckling The most simple model for buckling is that given by Euler 2 1. a column is defined as the The critical buckling load for load applied to the column which, when column not to return to its original removed, causes position. At the loads higher than the critical value, the column becomes unstable and will collapse by bending. Examining Figure 4-2, see that greater this than will occur when the restoring the applied moment moment (M). EI i =-M ax2 (4.1) Setting this equal to the external moment gives EI 2y +Py=O ax2 78 (P*y) is Assuming deformations, the internal moment, M, is given by (4.2) we can small x x P1 P x IX I I I I I I I I I I I I I I I I a I I, Y Figure 4-2. y Schematic of Simply Supported Column 79 Y which is a second order homogeneous linear differential equation and can be solved to yield p = n 2 X 2 EI L2 (4.6) where n is the number of half sine waves or buckling modes. The smallest value of the buckling force is given when n=l, Obviously, no lateral loading of the fibril is considered in the Euler analysis. transversely This isotropic implies (Chapter exists between axial and radial orthotropic stress system could have develop on the fibrils 2) that and that stresses. substantial as a the fiber no is coupling A cylindrically lateral consequence tensile of axial compressive loading, and the critical buckling load would be greatly reduced. With respect to fibril buckling, the parameters necessary for prediction of critical buckling loads are the fibril compressive modulus, Ec, the fibril moment of inertia, I, and the fibril single mode buckling length L. The compressive modulus is obtained from single fiber three point bending tests described in Chapter 3. Here it is assumed that the individual fibrils have the same compressive 80 The fibril moment of inertia is modulus as the bulk fiber. given by 4 where no shift in the neutral axis is considered for axial fibril The loading. is diameter found by splitting individual fibers and measuring the diameters with an SEM. A typical micrograph is shown in Figure 4-3. The single mode buckling length for a single found in a number of different ways. The fibril can be first has been performed on Kevlar® 49 fibers and entails peeling a sheath of fibrils from the fiber as shown in Figure 4-4. The high curvature at the peel point causes the fibrils to buckle. micrograph composite Figure 4-5. of a sheath of fibrils is given A in The single mode buckling length L, or arc length of the buckled fibril, is easily calculated by measuring the chord length, chord as 2b, shown in and the departure, Figure 4-6. ,of the arc from the Using this method on 10 different buckled Kevlar® 49 fibrils from Figure 4-5 gives an average buckled length of 1510 nm with a standard deviation of 224 nm. Another method for determination of the buckled length has In this process a section of been employed on PBO fibers. the skin is peeled from the fiber. In PBO, the skin buckles in regular arrays as shown in Figures 4-7 and 4-8. 81 4-3. SEM Micrograph of single Kevlar® Figure fibril from a fiber split with a micromanipulator. 82 49 Peel ( 00-0000Compression Surface iber Figure 4-4. SEM Micrograph of sheath of fibrils peeled from Kevlar® 49 fiber as shown in schematic. Buckling of fibrils in high curvature region is evident. 83 Figure 4-5. SEM Micrograph of sheath of Kevlar® 49 fiber. 84 fibrils peeled from This R4t effect Kevlar® fibers. skin buckle seems to be more prominent in PBO than If it is assumed that the fibrils behind the over the same length periodic spacing of the R4 effect as the skin then the can be used as the single mode buckling length. The buckling length can also be determined by plasma etching of previously DeTeresa compressed et.al that fibers. fibers It which are formation and subsequently placed in or reversal 0 2 CF 4 of plasma, kinks8 . small If these pits appear shown in Figure 4-11. failure causes an increase buckled region is etched formation. The Since diameter in shown compressed to by kink tension show unfolding fibers are etched with an at kink the fibril a the length of the buckled fibril. been boundary 22 as fibrillation during compressive at of has higher pits are surface rate area, the causing pit indicative of the Since the ultimate pit size is a function of etchant and exposure time, this method can only be used qualitatively for comparison of fibers exposed to similar conditions. t This is called the R4 effect since it was first observed by an undergraduate research student: Rodrigo R. Rubiano's Ripples. 85 'I R b NJ I] II 0 1 L ii A e R= 2+ b 2 26 .4 L = R * 20 = sin- b R Figure 4-6. Method of determination of buckled (arc) length of single fibril. 86 Figure 4-7. SEM Micrograph of Arrays Of Buckled Rows In The Skin of a PBO Fiber Which Has Been Peeled Off The Core. Figure 4-8. Same as Above, Higher Magnification. 87 4.3. Results and Discussion Table 4-1 presents the results of the Euler buckling analysis applied to Kevlar@ 49 and PBO fibrils. The single mode buckling length was found by the sheath peeling and R4 method for Kevlar® strength is and PBO respectively. calculated strength by the ratio The fiber by multiplying of fiber to the fibril compressive single area fibril (number of fibrils). It is clear that the predicted load for compressive failure overestimates the measured one. A number of reasons are available to explain this: 1) The size of the fibril is not single valued. Actually a distribution of fibril diameters exists. 2) The compressive deformation in the fibrils is not elastic as assumed in the Euler analysis. The analysis is based on long stability considerations and is valid for slender columns. The slenderness ratio of fibrils is very low, on the order of about 20 - 25. the (The slenderness ratio is the length of the column ,L,divided by the radius of gyration ,R, of the cross section in the plane of buckling). ratio which above The Eulers value of formula estimated by R)min =i\ 88 UCs the slenderness applies can be Table 4-1. Euler Analysis of Single Fibrils Using Sheath Peeling and R4 methods. Fiber Fibril Diameter (nm) Kevlar 49 160±20 PBO-1 220±30 Calc. Measd Fibril Length (nm) Comp. Modulus (GPa) Compress Strength IMPa) Compress. Strength (MPa) 1510±220 1400±200 90 40 620+205 620±276 345±35 207±35 Note: Measured Compressive Strength From Tensile (Fiber Diameters: Kevlar® 49=12um, PBO-1=18um) 89 Recoil. which conservatively assumes that non -linear behavior For Kevlar® and PBO occurs after compressive failure. this value is 50. about Examination of 4-9 Figure indicates that the Euler analysis will overestimate the compressive strength for typical fibrils. This overestimation is derived from the fact that crushing is also involved in fibril failure. In order to consider this type of behavior, the compressive stress - strain curve for a single fibril/fiber would have to be known. The agreement observations is of the with model encouraging: it other postulates experimental that the kink band initiates on the fiber surface, where the low degree of lateral support leads to small critical buckling loads. Kink bands do start on the fiber surface as can be seen in Figure 4-10. Perhaps the best use of the model is in the investigation of processing variations on the mechanical properties of a fiber of given composition. One such study was conducted on four types of PBO fibers, each subjected to different processing conditions. O2CF 4 plasma length. The fibers were simultaneously subjected to an for 20 minutes to obtain the fibril buckling Figures 4-11 to 4-14 are SEM micrographs of the pits created from plasma The etching. similar to kink lengths lengths of the pits are in PBO fibers measured by others 2 3. 90 Split fibers were used to measure fibril diameters. presents the results aforementioned uncertainty (section 3.5.3), are given on of the in analysis. the plasma Due The to etching the predicted fiber compressive a ranked basis only. Table 4-2 the method strengths fibril peel and R4 methods measure actual buckling entities and hence are more accurate. Nonetheless, the relative measurement provided by the plasma etching is effective: compressive strength is in the predicted rank excellent agreement in the with the measured one, indicating the merit of the model. Despite the fact that the model is useful in ranking ultimate compressive strength of single fibers, its utility in determining the absolute ultimate compressive strength may be limited. fibril To improve the model compressive fibril-fibril for axial stress--strain interactions, lateral would require knowledge of and the interaction, Szo. items would allow for more behavior, the nature of compliance coefficient Identification of these exact modeling of these complex systems. 91 ---5000 4000 u 3000 0 1000 0 0a0 o 0 20 40 60 80 100 Slenderness Ratio Figure 4-9 Eulers Curve for Fiber with Compressive Modulus of 89.5 GPa 92 4-10 SEM Micrograph Figure Exterior of PBO Fiber 93 of Kink Band Initiating on Figure 4-11. SEM Micrograph of Pits Boundary in Plasma Etched PBO Fiber. Along Figure 4-12. SEM Micrograph of Pits Along Boundary in Plasma Etched PBO-6 Fiber. Kink 94 Kink SEM Micrograph of Pits 4-13. Figure Boundary in Plasma Etched PBO-5 Fiber. Along Figure 4-14. SEM Micrograph of Pits Along Kink Boundary in Plasma Etched PBO-4 Fiber. 95 Kink Table 4-2. Euler Analysis of Single Fibrils Using Plasma Etching Method For Single Mode Buckling Length. Fibril Diameter Fibril Length Measured UCS Measured Rank in Predicted Rank in Fiber (nm) (nm) [MPa (ksi) ] UCS UCS PBO-3 PBO-4 PBO-5 PBO-6 220 230 180 250 590 350 360 660 152 324 214 165 4 1 2 3 4 1 2 3 96 (22) (47) (31) (24) Chapter 5. Improving Fiber Compressive Strength 5.1. Methods of Improvement 5.1.1. As Chemical Methods discussed in Chapter 4, several researchers have recognized that buckling of polymer chains 3 or fibrils 19 is responsible for the compressive failure in high performance polymer fibers. the introduction Others predicted that of lateral covalent bonding between chains would delay buckling and improve the compressive strength. introduced flourene moieties Bhattacharya et. al. into Poly(p-phenylene benzobisthiazole) (PBT) fibers 2 for lateral crosslinking while Chuah et. al. crosslinked PBT copolymers via labile methyl groups 2 4. Both studies compressive strength; reduced' because showed minimal improvement in in fact, the axial tensile strength was of the reduction in packing ability. The lack of improvement from interchain crosslinking is further indication that compressive fibrillar morphology, properties are governed by thus a method to laterally reinforce the fibrils was sought. 97 5.1.2. Rigid Coatings Examination of the model developed in section 4.2 indicates that lateral restraint of a column will increase its critical buckling load. elastic If the model is modified to include support, as shown in Figure 5-1, the lateral, critical buckling load is2 5 PI, -2 EI n 2 L2 where is the other variables modulus are as of + n2n4 E the elastic given previously. (5.1) foundation and all By choosing a high modulus material for the foundation, the buckling load can be increased by n2Ei percent. 00 Note, however that by increasing condition at which Pn= (5.2) there is a < Pn=2 i.e 1+ =4+ 4 EI p 4/x4 E (5.3) =4 '4 EI (5.4) Thus if only stability is considered, the maximum increase in single mode buckling strength is 500 percent. initiates on the fiber exterior where 98 Since kinking X t Figure 5-1. Modification of Fibril Model To Consider Lateral Support By An Elastic Foundation. Each spring has a spring constant k. The modulus of the foundation, , is given by i = k / b 99 the lateral support is minimal, application of a rigid coating to the fiber surface should increase the compressive strength. 5.1.2.1. Coating Selection Equation 5.1 indicates that any material of finite modulus applied the to strength. fiber should increase its compressive However, the coating itself also carries an axial load so a high modulus is desirable to prevent buckling of it. Strength of materials calculations indicate that the coating will carry an axial load given by Pc = applied * EfA ECA + ) (5.5) EfAf where P is force, E is the modulus, A is the cross sectional area and the fiber. are subscripts This shows desirable for that c and f refer to the coating and coating materials with high moduli lateral support (equation 5.1) but they will acquire a higher proportion of the applied axial forces which may lead to their premature buckling. A schematic of some of the forces on the coating is given in Figure 5-2. The lateral forces come from fibrils attempting to buckle and the hoop forces are derived from the lateral expansion of the fiber. If the coating and the fiber have different thermal expansion coefficients, residual 100 Axial Force From A1 T -- d aLU.U ,A Hoop Force From Poisson Effects Lateral Force From Kink B Figure 5-2. Schematic of Forces on Thin Rigid Coating Applied to Fiber (Fiber Not Shown). 101 stresses will result from temperature excursions. These forces are given by p=(a1 a is by and fiber the either coefficient, AT as is the defined can be found by dividing sectional cross coating or are subscripts the appropriate stress The previously. expansion thermal temperature in change the (5.6) EAf EAcP where AT 1 Xj area. To coating materials with thermal expansion minimize the stress, coefficients similar to those of the fiber are desirable. Good adhesion for necessary the fiber and the the coating between reinforcing concept to be surface effective. is If the outer fibrils are not constrained and can start to bend, they support from the fiber if only coating the Similarly, buckle. will two the lateral derives are adhered. well Absent good adhesion, the coating idea is not effective. A rigid coating also reduces the thermal expansion 40 greater than is so low, the (CTE) ppm/ 0 C. high fiber radial coefficient of is which the Since modulus very large, fiber transverse coating restrains Finite element calculations performed by Jao2 fiber with thickness of a transverse modulus 1 percent of the of 4 GPa the modulus fiber. show that for a and fiber diameter the 102 typically a coating radial CTE is significantly reduced with high modulus coatings. results are reduction shown in Figure in transverse will not higher radial CTE modulus. It also by the be reduced fiber element 5-3. modulus calculations is in a strong 5-4 rigid coating even of that direction. that shows that the function indicates that show Figure if These the the fiber axial because of CTE the Finally, finite coating cracks the axially at 450 intervals around the fiber circumference, the radial increases CTE only by a few percent if the coating remains well adhered to the fiber surface. 5.2. Experimental 5.2.1. Coating Deposition High modulus physical ceramic coatings vapor (PVD) were deposition applied to techniques fibers as using outlined in United States Patent 502125827. The PVD process is unique in that high melting point the polymer substrate it permits materials deposition without of subjecting appreciable temperature differentials. beam evaporator with special fixtures A for A1 2 0 3 ) most The literature 2 8 of the bulk are study was properties given of in Table Temescal used. aluminum oxide alumina 5-1. to electron designed to rotate the fibers for uniform coating deposition was used ceramic The ceramic (alumina or obtained from The properties the listed are for crystalline a-alumina which was the evaporant source. 103 60 - I _ _ meter 0 50 E' 40d 30 .I 0 . 200 I . I 400 . 600 800 Coating Modulus ( Gpa ) Figure 5-3. Radial CTE as a Function Generated By Finite Element Model. 104 of Coating Modulus 70 60 . s -- -- - O 50 - 5U 1-1 0 U 40 - 30 - "a 20 - r Diameter Coating Modulus = 414 upa 10 IP .1 · ·· .1 10 1 -- 10 Fiber Transverse Modulus -1 00 1000 ( Gpa ) Figure 5-4. Radial CTE as a Function of Fiber Transverse Modulus Generated By Finite Element Model. 105 However, X-ray was deposited material indicated studies diffraction that of SEM observations amorphous. the the coatings showed they are homogeneous and uniform both axially (Figure 5-6). (Figure 5-5) and circumferentialy Figure 5-6 shows frozen in liquid glass the was to produce the illustration coating thickness on The to prepare.) which fiber fiber was used for this placed adjacent to slides fractured and nitrogen is easier it glass coated alumina (A glass surface shown. because an fibers during deposition was used to measure the coating thickness on the fibers. glass provided slides a on substrate flat which a The Dektak® profilometer was used to measure the thickness. 5.2.2. Property Evaluation The compressive the tensile fibers were strength of recoil bending test. The with radial fibers Flexural test. determined coated the thermal evaluated by was of coated three point properties single fiber observed by expansion was using a hot stage in an SEM and measuring the change in fiber diameter with heating. Fibers were dried under vacuum prior to testing to avoid dimensional No composites were made with changes from water expulsion. coated thousands of fibers required for a be coated by the fibers 106 the many single specimen could not batch electron beam process times periods. as in reasonable Figure 5-5. SEM Micrograph of Alumina Coating on PBO Fiber Applied by Physical Vapor Deposition. Coating is Smooth and Homogeneous. Figure 5-6. SEM Micrograph of Alumina Coating on Glass Fiber Applied by Physical Vapor Deposition. Coating is Uniform Around Fiber Circumference. 107 Table 5-1. Mechanical Properties of Alumina Used For Rigid Coating on Fibers Modulus Of Elasticity 372 GPa (54 Msi) Compressive Strength 2.4 GPa (350 Ksi) Tensile Strength 207 MPa (30 Ksi) Coefficient of Thermal Expan-sion 7 ppm/°C .... .. .. .. . . .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 108 5.3. Results and Discussion Effect of Coatings on Fiber Strength 5.3.1. A range of coating thicknesses was applied to both single PBO 49 and Kevlar® fibers 29 . strength ultimate compressive The versus coating thickness for PBO is given in Figure 5-9. A fit linear well correlates to the line the strength compressive almost exactly to the extrapolates back and data strength of the PBO is more than doubled with a coating thickness of 8000 A. SEM in Figures 5-7 of micrographs and failed coated fibers are given Kink 5-8. compressive The of the uncoated fiber. are bands In fact, the coating and the excellent adhesion is apparent. adhesion was so engineering traditional adhesion was not polymers to unique were made to attempts good that to be certain and acrylonitrile that good fibers. poly-methylmethacrylate, polywas adhesion poly-ethylene: of A study was initiated to investigate excellent in all cases. the more flat plates Alumina .coatings were successfully applied to styrene coat high performance polymer poly-styrene, poly-carbonate, failed the beneath discernible source of the adhesion and preliminary secondary ion mass spectrometry indicate alumina that and conclusive interface and x-ray primary the as the caused bonding valence polymers. minute The volume analytical between existed studies fraction difficulties. 109 data spectroscopy photoelectron of were not the fully ceramic/polymer It is suspected that the atomic oxygen which is known to be present electron beam evaporation of alumina 3 0 is responsible during for he formation of primary bonds. The improvements not as in compressive strength for Kevlar® consistent Kevlar® fibers strength and as those observed for PBO. would other show times large almost determined that the reason for the poor adhesion between the Sometimes the increases none. 49 were in compressive Eventually it was inconsistent behavior was fiber and coating. Morgan 31 et al found large amounts of residual sulfur and sodium in Kevlar® while Penn3 2 confirmed the et al found presence of stearic and palmitic sulfur and sodium acids. by a We neutron activation study. The stearic and palmitic acids are used as lubricants processing weak during boundary layer coating adhesion. were obtained from on the and their fiber presence surface PPTA fibers made without DuPont indicate that improvements and the limited which 110 a inhibits such lubricants data in their compressive similar to those observed in PBO. creates obtained strength are Figure Fiber. 5-7. SEM Micrograph of Failed Alumina Coated PBO Good Adhesion of Coating is Evident. Figure 5-8. SEM Micrograph of Failed Alumina Coated PBO Fiber. Good Adhesion of Coating is Evident. 111 Since the rigid existed that, ceramic coating in tension, failure of the occur. The data fiber. is brittle, some concern its fracture would cause premature Figure 5-10 shows indicate no significant that this does not difference between the two. Well adhered rigid ceramic coatings significantly improve the compressive strength of PBO fibers. This improvement is not accompanied by a decrease in tensile strength as was found in the other studies cited2 ,2 4 . It has also been observed by Chang3 3 that cracking in the coating caused by tensile loading or by thermal compressive cycling strength does not provided degrade the the improvement coating remains in well adhered. 5.3.2. Effect of Coatings on Fiber CTE Uncoated fibers and coated fibers 250 C to 400 ° C at about were heated in a SEM from 250 C/min. A micrograph of a coated fiber at 4000 C is given in Figure 5-11. The axial cracking is a of large result critical thickness. be used to the cracking radial expansion of temperature This cracking is the dependent fiber; the on coating at elevated temperatures can also indicate adhesion: a poorly adhered coating will show a single axial crack and spall free while a well adhered one will give multiple cracks, while remaining in place. 112 600 I 4 500 S ;- Ut w 400 D * rA 300 ._W r> C6 E 4) 200 14- 100 0 2000 4000 6000 8000 10000 Coating Thickness (A) Figure 5-9. Ultimate Compressive Strength versus Alumina Coating Thickness For PBO Fibers. 113 -- A 1.0 ' 0 O A 0.8O =1 a0 eC 0 0.60 .0 O Uncoated A Coated O A [] 0.4- C: 0 [] 0] 0.2- 0.0 I 60 [] ~- . i - 80 Ultimate . -- 1 00 Tensile -- -- L- 120 s 140 Load (g) Figure 5-10. Cumulative Distribution Function Of Ultimate Load For Uncoated and Alumina Coated PBO Fibers in Tension. 114 Figure 5-12 presents the percent change in fiber diameter for PBO fibers, both uncoated and coated with 6000A (3% of fiber All data were fit linearly by the least diameter). The slope method. radial CTE in ppm / in radial CTE by a coated fibers at of the lines m, divided by 100, C. squares is the The coated fibers show a reduction factor of 2. begins Cracking the in about 250 ° C, but no substantial deviation finite in expansion is observed, in good agreement with the element predictions. Figure 5-13 presents the percent change in fiber diameter for Kevlar® 49 fibers both uncoated and coated with 3500A (3% of fiber diameter). The more than three fold decrease in radial CTE is more dramatic in the Kevlar® system. Since less axial cracking was observed in the Kevlar® system its adhesion was worse than that of the PBO. This indicates that good adhesion is not as critical in reduction of radial CTE's as it is for improvement of compressive strength. It is encouraging to observe that a problem long associated with high performance polymer fibers, large radial solved by the application of rigid coatings. 11 CTEs, can be Figure 5-11. SEM Micrograph Fiber Heated In-Situ to 4000 C. of 116 Alumina Coated PBO 7 6 5 cm =so 4 .0 3 2 B0 0 0 100 200 300 Temperature ( 400 500 600 C) Figure 5-12. Percent Change in Fiber Diameter With Temperature For Uncoated and Alumina Coated PBO Fibers. (m=slope). 117 3 L( 2 Cu *-i .0J 0 100 200 Temperature ( 300 C) Figure 5-13. Percent Change in Fiber Diameter With Temperature For Uncoated and Alumina Coated Kevlar 49 Fibers. (m=slope). 118 400 5.3.3. The Effect of Coatings on Flexural Behavior presence neutral EI. axis This of of a high a modulus beam will produces lower material increase its deflections the flexural behavior. determine the transformed coated shows fiber The in-situ flexural rigidity for uncoated and coated with 8000 A of alumina. of from the same the load. load-deflection plot for PBO fibers Figure 5-14 is a flexural rigidity distant increase modulus of the can the The increase in improvement also coating be used by use of in to a section method in which the coating is virtually transformed into a mechanically equivalent area of the fiber. Recognizing that the axial force on the coated fiber section must be zero it follows . ydA + Ef ydA =O (5.7) If n, the modulus ratio, is defined as n=Ec Ef (5.8) then equation 5.7 can be rewritten as nydA+ ydA=O (5.9) 119 cross where A is area and Equation 5.9 remains is the y distance to the neutral axis. indicates that the position of the neutral axis unchanged multiplied by n. single material if each area element of coating the is the coated fiber can be modeled as a Hence, (fiber) with a moment of inertia I (d+ 2 n t)4 64 (5.10) where d is the fiber diameter, and t is the coating thickness. The anisotropic nature of the high performance polymer fibers creates uncertainties in the appropriate fiber modulus to be used in equation involved: 5.8 since three different Et,fiber,Ec,fiber and Ecoat. Instead, moduli three are point bend tests were conducted on coated glass fibers since glass is an isotropic material. A plot of the load-deflection data for a 24 um diameter E-glass fiber is given in Figure 5-15. From the slope of the linear fit, inertia from equation 3.22 known. ratio we can find the moment of since the modulus and span are Equation 5.10 can then be since the coating thickness solved for the modulus is known. Using this method, the in-situ modulus of the coating was found to be 310 GPa (45 Msi) to 345 GPa (50 Msi) which is in reasonable agreement with the modulus of the bulk material ( 372 GPa [54 Msi]) reported previously. 120 A ~ A 4.u0e-3 3.00e-3 O Uncoated O Coated 2.00e-3 o Pk 1.00e-3 0.00e+0 0.00e+0 1.00e-5 2.00e-5 Deflection Figure 5-14. Coated PBO-5 Load Deflection Plot Fibers. (m=slope). 121 3.00e-5 4.00e-5 (m) For Uncoated and Alumina 0.003 0.002 Z 3- 0so L, ex 0.001 0.000 .00e+O 1.00e-5 2.00e-5 Deflection 3.00e-5 (m) Load Deflection Plot For an Alumina Coated EFigure 5-15. Glass Fiber. (m=slope). 122 5.3.4. The Mechanism of Improvement motive restraint for of the the rigid outer coating fibrils was and compressive strength of the fibers. to provide thereby lateral increase the It is possible, however, that the high modulus coating simply takes load away from the fiber thus rule of allowing the mixtures system to (ROM) type of sustain a behavior. higher This load; a alternate explanation of its action had to be explored. 5.3.4.1. Rule of Mixtures Equation 5.5 345 GPa shows that for a coating of 4000A thickness Modulus on compressive modulus of the load is the fiber thickness is it occurring. a fiber 20 um increased coating. by unlikely more that Alternatively, it a Since the than 80 ROM type levels 5.5, The load either analysis required the thickness. study fiber 70 GPa strength of percent of at was chose coating properties to reach or the the ultimate coating for a Figure 5-16 displays the results: 123 Using examine stress coating and then stress given is coating follow a ROM. conducted to this behavior in the fiber and in the coating for different moduli. the an and is possible to find a modulus value such that the system does equation diameter (typical of PBO) approximately 29 percent borne by the is of and found level in coating measured values of coated fiber ultimate compressive (On the figure, the coating generated by using equation 5.5. modulus, Ec, and strength, The analysis shows GPa.) Sc, strength and the data are given for each line in that in order to obtain behavior similar to that which was measured, the coating must have a 950 of more than modulus strength of 3.8 GPa GPa the represented by set These are much higher than (551 Ksi). Much closer to the known values their known, in-situ values. is and a compressive (138 Msi) the triangle (A), which is This casts below the experimentally measured data. far strong doubt on the relevance of the simple rule of mixtures to the system; either a more complicated rule is required , true action of the coating against constraint is to provide buckling. The the latter or the stabilizing appears more probable. 5.3.4.2. Lateral Restraint Implementing is hypothesis restrains a model difficult. kink controls), to then formation the validate If we until the lateral assume it appropriate fails model the coating (coating failure that would be a shell supported on foundation. This shell would be loaded as in Figure 5-2. also attempt to model the thin interior by an elastic cylindrical could its restraint outer fibrils as We columns supported by an elastic foundation as depicted in Figure 5-1. 124 --bUU 500- 0 Ec--551 Sc=2 A Ec=345 Sc=2x Ec=950 Sc=3.8 Measured Values X 0 X X x x xM CL a 400 " E*-A 200- 0XX 00 00 D xx 00 00000 00A A xAA 0 O"AAA 100 0 2000 4000 0 0000 0 AAAA 6000 8000 10000 Coating Thickness (A) Figure 5-16. Ultimate Compressive Strength vs. Coating Thickness: measured data and values calculated from rule of mixtures (Ec=Coating Modulus, Sc=Coating Compressive Strength) Units:Gpa 125 Unfortunately, magnitudes since of the the lateral restraint forces conditions imposed by the and the kinks are unknown, predicting the coated fiber behavior based on these models would assumptions degenerate play out into in the seeing now results. It the starting would not be conclusive. At this point the it is believed that the correct explanation of coating effect compressive There is is its buckling. abundant mechanism is crosslinking stiffening of the This derives evidence fibril between that kink bands at fiber coating coating a stiff functions temperature excursions reinforcement dimensions even action of essential to fibrils. its Good function, it localized, adhesion since it is why failure chemical The surface of the delays tensile crack factors. ineffective. surface though is very is is or near the on the may several compressive which chains buckling initiates and the buckling, polymer from surface against it. The preloading extensively; or the consistent with the of the coating is attached to only one side of the fibril rather than entirely surrounding it. 5.3.5. Effect of External Stresses on Residual Strength of Coated Fiber Since the coating is brittle, in work done by Chang3 3 cracked extensively, to near its either by loading the breaking point or 126 by fiber heating it it was in tension such that significant differential thermal expansion occurred. The fibers used PBO with a baseline compressive strength of about 80 Mpa as measured by the tensile recoil method. were coated with various uniform thicknesses pulled to about 80% of their breaking The fibers of ceramic and load, producing uniformly spaced circumferential cracks as shown in Figure 517. Then results data, these shown the improvement in were tested Figure in 5-18. tensile Within precracked fibers as uncracked ones, did thicker coatings. the recoil with scatter the same showed the the of the strength especially with the Though cracked, the coating remained well adhered to the fiber, with no spalling evident, and the width of the crack cracks was very small, width buckling same is much fibril order elements of less elements buckling remain of the order than in the fibrils observed by by cracks. This suggests that it elements that which observed A length PBO observed by us constrained we 15,000 of 2500 A. is but This of the on the others 2 3. The the coating the larger scale buckling control despite the the compressive strength. Using coated fibers exposed to minutes in elevated air. No from the same population, temperatures: special steps 150 0 C fibers to rates contract number were 2500 C and accompanied specimens were simply removed from the oven. the a cooling; 127 30 the Heating caused axially and expand radially, different from the ceramic coating, for and the both at result was a series of axial cracks as seen in Figure 5-11. occurred and the radial thermal cracked coating expansion of the continued to fiber. No spalling inhibit When these the fibers were tested in tensile recoil, the compressive strengths were nearly the same as for the uncracked coated fibers as shown The axial cracks were narrow, about 2500 A, in Figure 5-19. and followed a circuitous path on that scale they were irregular not perfectly straight. path apparently The combined of dimension; small to gap and the preserve constraining action of the coating on the fibril elements. 128 the Figure 5-17. Circumferential Cracks PBO Fiber From Tensile Loading. 129 in Coating on ___ uu --- 2 100 *050 0 2000 4000 Coating Thickness 6000 8000 (A) Figure 5-18. Ultimate Compressive Strength vs. Coating Thickness in PBO Fiber both Unloaded and After a 60g Tensile Preload. 130 200 . I - -- --· ---- [ 0 a A 150[ O aqa 100- A 0 U 0 A I" Uncylcled Preheated to 150 °C Preheated to 250 °C E I 0 ' 2000 I 4000 Coating Thickness ' I I 6000 8000 (A) Figure 5-19. Ultimate Compressive Strength vs. Coating Thickness in PBO Fiber Before and After Heating in Air.. 131 Chapter 6. Conclusions have been developed to evaluate the mechanical New methods fibers. polymer high performance of properties A device which simplifies recoil testing by symmetrical cutting of the fiber was made and it gives a more accurate measurement of Load spikes created by non- the axial compressive strength. symmetric cutting are nearly eliminated in Kevlar® fibers and greatly reduced for PBO fibers. To evaluate the transverse strength of single fibers, was developed in which an opening mode a test crack is propagated axially in the fiber. The crack initiation force normalized by the fiber diameter provides a fiber mechanical property. The loads weights was an force which instrument Gas constructed. involved are extremely To determine critical crack small and difficult to measure. propagating measure of a transverse operates were bearings with used on dead all translational parts to minimize frictional forces. Because the tensile test does not measure the true transverse strength the numbers obtained have been termed the Transverse Strength changes the TSI Index (TSI). The TSI in processing parameters. and the fiber can used to evaluate No relationship between compressive 132 be strength is evident. Values TSI the of strong with fibers for obtained (aramids) are similar to those without intermolecular bonding (PBO) suggesting that the lateral properties are more likely based on interfibrillar than intermolecular strength. A fibers. Load deflection curves single three point bending of enables apparatus testing the transverse to modification are generated by adding incremental weights and measuring the deflection corresponding Analysis video micrometer. a with shows that shear effects are minimal and basic elasticity is section were derived. numerically tested to for the They and check are were High ones. were and in of excellent The to for Kevlar® conditions: it 149 is conditions from 0.15 tensile PBO 0.31. showed to moduli is 29 Ec/Et fibers The ratio of Future bending to with it compressive failure, thus work A 133 for of different Ec/Et should Kevlar® ranged focus on four point bending a single fiber can be tested replacing the test. processing under ratios shorter spans to examine shear effects. test has been developed; to 0.94 while processed similar effects: 0.87. sensitive is values compressive had moduli that were less than their tensile ones. compressive were agreement with the fibers performance fibers device. the both solved glass Isotropic performance glass modulus published complex graphically. the moduli tensile and compressive different with cross a material of circular for bending of The equations valid. cumbersome recoil fiber compressive modeling of The of buckling fibrils the has been behavior through a simple The fibril successful. diameters are determined from SEM observation of fibers split The a micromanipulator. with of the assumed to be that point bend fiber as obtained from the fibril The test. compressive modulus fibril buckling have lengths is three been determined in several ways: plasma etching, buckled peels and the strength but it in The effect. R4 of fibers overestimates model compressive fiber is useful in ranking the compressive behavior the same composition to subjected processing variations which alter their fibrillar morphology. coupled with the observation of external kink band The model, initiation, be could suggested improved When coatings. physical using by that was applied improvement compressive from about to the deposition, strength improved significantly. coating thickness fiber application the alumina vapor the of rigid exterior fiber surface, the fiber compressive linear with The increase is 1000 A strength The observed to 8000 A. exceeds that predicted by the rule of mixtures, indicating that the coating does restrain fibril buckling and does not also simply carry load away from the fiber. reduces, thermal by a factor of 2, the radial The coating coefficient expansion of the high performance fibers. of Cracks in the coating from tensile preloading or from high temperature 134 exposure do not significantly degrade the improved compressive performance. Further work should be done to examine effects of different coatings (of both higher and lower moduli) compressive, flexural and thermal characteristics. 135 on fiber Appendix Error In Single Fiber Bending Experiments 136 The for potential bending experiments is in deflections to related 3-23, Figure moment the dependent on quickly. Hence, it is It measured accurately. fiber section of the critical is is error but, sources of largest is is which errors in the propagate fiber diameter the imperative that also are order fourth tend to that the is cross This can length. uniform along its as fiber properties flexural the small point Inaccurate measurements inertia of diameter, the the Since evaluation. diameter are both three fiber single the significant. load and in exemplified in error be a significant problem in experimental fibers made in batch A processing. caused by which nonuniform cross shows of PBO the for the same SEM: their test minimized and useful of fibers length the data. single For a reader is referred to shows group is given the fibers of in Figure A-i, been omitted. calculated fiber It.is three thorough 137 series large and compressive been they have The compressive section scatter is modulus evident then, that careful point discussion [15]. is calculated after a for nonuniform cross with a have statistically significant. execution the The scatter lot. error potential of calculated compressive modulus Figure A-2 screened in an over sections from the same fibers unacceptable. modulus illustration good bending on this can yield topic the 1__ 4UU 350300pi V 250- ; 200- ~0~~0 S 00 * ;0 0 150$00 0 50 o00 2 I I I 4 6 8 10 I I I I 12 14 16 18 20 Test Number Figure A-1. Variation in compressive modulus for PBO fibers of the same lot. included.. Fibers with nonuniform cross sections are 138 IAA 4UU 350_J 300- - 250- 0 o-_ 150 · a 0 0 · S 5 6 I 100x 200 - 0 1 2 3 4 7 Test Number Figure A-2. Variation in compressive modulus for PBO fibers of the same lot. Fibers with nonuniform cross sections have been omitted.. 139 References 1 Chatzi, E.G. and Koenig, L.J., 26, 229 (1987) 2 Bhattacharya S., Chuah, H.H, Dotrong, M., Wei, K.H., Wang, C.S., Vezie, D., Day, A., Adams, W.W., Procs. A.C.S. Div. Poly. Mats. Sci. and Eng., 60, 512 (1989) 3 Deteresa, S.J., Porter, R.S., and Farris, R.J., Sci., 20, 1645 (1985) 4 Allen, S.R., PhD Thesis, UMASS, 1983 5 Dobb,M.G., Johnson,D.J., and Saville,B.P, J. Polym. Sci., Polym. Symp., 58, 237 (1977) 6 Likhnitskii, S.G, Theory of Elasticity of an Anisotropic Body, MIR Publishers, Moscow (1981) 7 Sinclair, D.J., 8 Deteresa, S.J., Allen, S.R., Farris, R.J., and Porter, R.S., J. Mat. 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