NONDESTRUCTIVE EVALUATION OF FIBERGLASS USING CHOLESTERIC LIQUID CRYSTALS: REVIEW OF TECHNIQUES AND INDUSTRIAL APPLICATIONS by TOMAS A. GONZALEZ SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY (May 1980) Signature of Author.....v. ........................ . ... . ........ Department of Mechanic4>ingine ring, 5-9-80 Certified by. Accepted by. . - . ...................... Thesis Supervisor - q e.... . Cl airman, Mecha 0* 0000......................................... ,.-nginering Department Committee vpmlc TECHNOLOYCRNES ARCHIVES JUN 241980 LIBRAp!ES NONDESTRUCTIVE EVALUATION OF FIBERGLASS USING CHOLESTERIC LIQUID REVIEW OF TECHNIQUES AND CRYSTALS: INDUSTRIAL APPLICATIONS by TOMAS AGUSTIN GONZALEZ SUBMITTED TO THE DEPARMENT OF MECHANICAL ENGINEERING ON MAY 9, 1980, IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING Abstract Based fiberglass with test for the evaluation mography and designed and fiberglass lighting conditions. determination minute flaws of the The equipment optimal in liquid crystal ther- Equipment heat built will flux for A special was under different specimens in fiberglass specimens using cholesteric liquid crystals. paper construction. fiberglass built to test This hulls. boat involved specimen of crystals can provide a simple fiberglass of various techniques the reviews colesteric liquid evaluation nondestructive investigation, this on also aid the thermal in detection the of testing with fiberglass panel with 108 flaws of known size and location was built to help establish the lower limit of resolution of different crystal blends and thermal test procedures. This research was exploratory and initiatory. The equipment and specimens built for this research should help in the refineIt is hoped that the ment of this thermal testing technique. project will be continued until a suitable field test nondestructive evaluation of fiberglass is developed. Thesis supervisor: James H. Williams, Jr. Associate Professor of Mechanical Engineering for the - 3 FOREWORD Composites enable the design of unique materials which combine high strength and high stiffness to an extent unattainable through conventional posites have a high metallurgical strength/weight practices. ratio which Fiber com- makes them attractive materials where increased performance can be achieved through weight reduction, such as in boat building. composites used in boat construction are Most fiber fiberglass layups. However, high performance sailboats and powerboats are currently being built with kevlar, dynel, graphite and other sophisticated and expensive fiber materials. performance applications and The capital investment Their use is restricted to high is done by very few manufacturers. necessary to manufacture boats with fiberglass is lower than that previously needed to build a boat out of wood or aluminum. impact on the boating allows it to be tions. As a consequence, industry. molded it has had a great The versatility of to many shapes and material fiberglass specifica- This, combined with the relative ease of manufacture, has attracted many builders to the boat industry. Today some 2500 - 3000 builders build pleasure crafts which range in size from 9 100 feet inboards, and are classified outboards, into various inboard-outboards, categories, ATV's, such airboats, as sail- boats, houseboats, custom boats, and canoes and kayaks. 1 There are no enforceable federal regulations regarding construction of the fiberglass lay-up for pleasure boats. the Guide- - 4 lines are set by the American Bureau of Shipping2 and the American Boat and Yacht Council 3, but both of these are quite general and only specify that the builder submit for review, a fabrica- tion process description before the lay-up is commenced. the lack of regulations large variations Due to in the qulity of design and construction of pleasure crafts exists. Deviation in proper- ties for greater composite than materials that on considered multiple acceptable tests for is somewhat established metal technology. Under the Federal Boat Safety Act of 1971, the Coast Guard is given the power to require the contains a safety defect to necessary repairs at the manufacturer notify all of a boat which purchasers and make the manufacturer's expense. The obstacle to effective enforcement regarding structural major integrity is the lack of quantitative inexpensive NDE techniques which can be broadly required by the Coast Guard. Pleasure boat manufacturers and the boating simple cost-effective method for assessing the grity of fiberglass pleasure craft may be unable to niques which composite sold or establish are transferred quantitative employed structures craft. are by as public structural expensive, inte- governmental aircraft agencies Most NDE industry complicated and are tech- to test equipment- intensive. What this research project aims to establish is: 1) no Consequently, substandard regulations. the have A cost-effective NDE technique for boat manufacturers prior to craft delivery; 2) A procedure to assist governmental agencies in establishing quantitative structural criteria for pleasure craft; 3) A technique to aid marine surveyors in conducting "Condition Surveys" which form an important basis for craft insurability; 4) A simple test for boat owners for assessing the structural integrity of their boats; 5) Laboratory apparatus and techniques which will meet the aims listed above. help - 6 INTRODUCTION The purpose easily of this utilized research was to develop an nondestructive evaluation (NDE) inexpensive test for the evaluation of fiberglass structures. Most defects common to composite layups such as voids, delaminations, uncured matrix, improper interface bonds, improper resin-matrix ratio and even the are internal in nature and are usually undistinguishable from an neglect of Nondestructive undamaged composite. reinforcing evaluation (NDE) layers, techniques must be used to detect the presence of potentially hazardous defects. Methods for establishing the quality of the manufactured composite by NDE must be developed to a high level of assurance for all types of fiber-matric composite layups. Although the science of NDE is very broad, certain categories, each containing a number of NDE techniques, offer characteristic capabilities which are likely to be of essential value in revealing the types of flaws which are most prevalent method selection is in generally based composite materials. on part NDE geometry and com- position, defect size, location, orientation and availability of test equipment. Very often more than one NDE method because different conditions and defects are revealed. methods which are likely to prove most valuable is used Some NDE in evaluating fiber composites are summarized in Table 1. The first step in the nondestructive evaluation is the visual - 7 inspection of the fiber composite layup. The method for identi- fication and classification of visual defects in glass reinforced allowable defects and their laminates is covered in ASTM D2563; to have be All composite parts included in table 2. acceptance levels are with conformance for inspected and dimensions Critical areas are defined tolerances specified of the drawings. by ASTM as those areas in which the presence of imperfections is considered to be most detrimental, these areas shall be free of all defects listed in Table 2. which content, nature, by The defects in noncritical or not do frequency areas affect serviceability of the part are designated as allowable defects. 2. in Table described comply must defects Allowable The the with presence acceptance these of defects levels must be The type of test I am aiming indicated in the product drawings. for is one that can be used at any remote location, such as a dry a boat dock or trailer users boat and as a variety of This would result in a test which can environmental conditions. aid and under 1.), (see fig. to a supplement visual inspection for analyzing the structural integrity of fiberglass boats. Nondestructive evaluation of fiber composites with cholesteric liquid process for crystals the is a cheap, evaluation of accurate fiberglass easily utilized structures. Previous and research using cholesteric liquid crystals have found them to be successful tools in the analysis of bonds, leak detection, penetrant detection, thermal definition of cracks and the analysis of honeycomb composites. The chemical properties of the - 8 liquid crystals are discussed in Appendix B. The first step of the research was to develop techniques and equipment for a field test that can be used for the thermographic evaluation of commercial formed and the I have per- The experiments fiberglass structures. equipmment I built for this project should be extremely useful for the quantitative analysis of the variety of defects and material properties that can be obtained from such techniques. My broken research down equipment, crystal those into in three specimen system. doing thermography. liquid components, design I hope further crystal this research and thermography (LCT) the and test jig construction thesis can serve in the area of and as can recording the liquid a guide liquid be for crystal 9 - - EXPERIMENTAL PROCEDURE when LCT, detection for allows rapidly changing departures at the simultaneous a large number of The area which can be tested effectively depends on the points. area of executed, properly over which monitored. constant The test illustrated in intensity heat can stand which I built figure 2. This jig be applied for this is and research is designed for the irradiation of large surface ares with a uniform intensity light. The angle and intensity of the lights and the size of the uniform test area can be controlled by moving the lamps relative to the area to be tested. The lights used on this jig are Smith Victor Model 750/1000 watt quartz-iodine studio lamps and are mounted on a set of rails that allows them to be placed anywhere within the shaded area in figure 2. The flexibility provided by this light jig can aid, in later research projects, to find the optimal heat flux pattern for the detection of minute flaws in fiberglass specimens. Another objective of this experimental set-up was to accommodate specimens of many sizes. Liquid crystal thermography (LCT) can evaluation whose thermal of be material a useful tool for the of any material response is significantly altered by the presence discontinuities, to the point where it becomes present at the surface as a variation in the thermal map. of the specimens tested were others consisted of flat panels 1" (7" x 12" x 7"). strips of Some fiberglass, The specimen holder - 10 - consists of a highly articulated adjustable microscope (fig. 3) mount built by American Optical Instrument Company. Specimens are held on a plane which can be placed and secured in a large to be unmounted or of positions without having number touched. This is extremely convenient for LCT since you avoid disturbing the liquid crystal The mounting plate is 4" x 19" and can also be used or adjusted. to layer whenever the specimen needs to be moved thermometer stopwatches, hold identification and probes labels. The open design of the test stand permits observation of the from LCT many Permanent angles. thermograms can be made on color records of liquid considerations Several film. crystal must be made in color film selection as they have different film Higher film speeds resolution and color response. speed, (ASA) allow the use of higher F-stops that provide a greater depth of High ASA films should be used if the application involves field. curved surfaces that are difficult to focus entirely or where the light sources are located film speeds lose Higher more 3' than though resolution enough to affect thermogram interpreation. heat up Kodachrome ASA 100 is adequate. project is a Nikon FM with a 135 mm from the not thermogram. significantly For monitoring during The camera used for this f/2.8 Autopromaster lens. There are a couple of drawbacks to this photographic set-up: 1) The promaster lens does light meter so that not automatically not couple with the Nikon f-stop changes on the lens are sensed by the light meter, thus - - 11 correct exposure has to be set manually. The 135 mm lens is too long, so it does not allow for 2) specimen. close-up photos of the sug- A couple of gestions on the recording equipment are to get a 50 mm NIKON MACRO Lens and a motor drive for the camera. In addition to the photographic recording equipment we used a digital portable thermometer (Precision Digital 521) Model to monitor the temperature of the specimen surface during the test. The probe used was Thermistor Probe). cup, epoxy backed. surface an attachable It consists Series (YSI probe 700 stainless steel of a 3/8" dia. The time constant of the probe is 1.1 sec- onds. The time constant is a standard measure of probe response time; it is the time required for a probe to read 63% of a newly impressed temperature. The next step in temperature monitoring will be to connect the thermometer to an X-Y plotter so that we get vs. time advise using temperature every of graphs I would also test. accurate measure- an air temperature probe to get ments of the effects of ambient temperature on LCT. Specimen Design The fiberglass specimens used in this research were dupli- cates of the lay-up used in the construction of single skin hulls 4 for high performance yachts . The main objective of the specimen was to introduce location, current to LCT a number determine test. The the of flaws lower of limit specimen was known of type, size and of our resolution built of seven layers of - 12 - glass in a mold shaped as a scale model of popular deep-vee hull 6 This shape was useful in analyzing the designs (fig. 4)6. usefulness of for LCT testing of surfaces and sizes different The construction of fiberglass panels is described orientations. (fig. 5) panel contains 108 flaws made The main in Appendix A. to represent small air voids or cracks in the interior of a boat The flaws come in six sizes (.20 - hull. of flaws internal previous that interface the between the glass layers flaws are made from micropipettes are more These fiberglass of than the air (fig. crystals can be used voids directly without applied 6). representative The panel was built with a black gel tests. liquid groups of The location of the flaws varies also; they are on the panel. at in .80 - 3/4" - 1/2" depending on their location six with lengths of 1" - located .63 - .56 - and are built into the specimen mm diameter) 1.05 .28 - in coat so a backup Molded fiber glass, whether in a boat, car body, furni- paint. ture or other items, is easily repaired with polyester resin and fiber glass mat and/or cloth. Sometimes the secondary bond between the patch and the hull is not perfect and may fail while in operation. LCT can be useful for the detection of air gaps in the secondary bond as well as internal cracks which may have gone undetected. significantly thermal The presence of voids weaken the in adhesive bonds which may structure will diffusivity of the bond line. coated with also decrease the local As the surface, which is the liquid crystals, is heated, the face sheet (over areas with poorer heat transfer) will heat more rapidly than the - 13 - adjacent well-bonded areas. Since thermal of temperature surface the undergoing a material is only a few degrees above room temperature a testing direct photographic method cannot be used to detect the temperature differences because no photographic material exists which is the long wavelength sensitive to stroms) region (8000 Angstroms - Thermal in question. 10,000 Ang- gradients can be detected and evaluated by various methods most common of which are the use of thermal focused sensitive coatings attention on the our use of We inspection. infra-red and temperature-sensitive cho- lesteric liquid crystals for the evaluation of thermal gradients associated with material discontinuities. Liquid Crystals Liquid crystals are described in Appendix B. with the cholerteric evaluation liquid crystals can be odd-shaped of surfaces, particularly useful and irregular which cannot be assessed by other NDE methods. thermography can be useful any material as long as painted with black paint. for monitoring the surface Thermal testing is in contours Liquid crystal thermal smooth gradients and has in been With liquid crystals it is possible to make direct observations in high ambient light of small thermal gradients near room temperature. Their simplicity, high sensi- tivity and speed of response make them readily adaptable to the varied requirements vestigations. of laboratory and process development in- - 14 - Liquid crystals should be sprayed uniformly over the surface of the specimen. Potting depths slow response time and wash out resolution considerably, and therefore, one must avoid touching the surface affect of a coated specimen response the of the since streaks and marks also crystals. Liquid crystals can be washed off with acetone, Ajax or any similar detergent; make sure all the old crystals are washed off before applying a new coat. Specimens should be dry and free of dust particles before they are coated with crystals, as these will also adversely affect the response of the blends. can be used left on the Once a specimen is coated the same blend repeatedly approximately 25 times. specimen for several damaged by dust or wind exposure. days as long The coat can be as it is not - 15 - CONCLUSIONS AND RECOMMENDATIONS nondestructive specimens method for the thermography can be a useful Liquid crystal evaluation prepared in of this equipment and designed to conduct re- The fiberglass. thesis are search to develop a field test for the evaluation of boat hulls. A variable heat areas has been source that built (and is can apply uniform heat over large now in 3-365). This test stand should be used to find the optimal heat flux for the detection of very small flaws in fiberglass. The jig has been designed so A fiberglass panel with that it is easily adjusted and serviced. 108 flaws of known size and location was also built and The present flaws, those system was only capable of the outermost layers. of detecting 8 of testd. these The light jig and fiber- glass panel can be used quantitaviely to rate the effectiveness of different crystal blends under different test conditions. I hope this research is continued and that this thesis can serve as a good starting point and guide for future research projects in Liquid Crystal Thermography. - Building a fiberglass specimen. APPENDIX A. The construction - 16 that factors the affect or lay-up, is an attention to a large number elaborate process requiring careful of panel, a fiberglass of of quality the Fiberglass panel. specimens can be built of any size, shape and strength with good as consistency long as the is up lay carefully planned and There are two basic types of fiberglass panels: single executed. Construction of sandwich panels skin and sandwich construction. is more difficult than single skin because of the steps necessary to ensure a good bond between the skins and core. There are three (1) Those incorporat- basic core materials in general use today: ing light weight cores of foam or balsa, in which the bending is almost resisted core. modulus of the effective by entirely in bending, (2) the such as plywood, which has incorporating the very low a modulus of For this type the design of the panel must be based on the lower Those to Those incorporating cores which are elasticity similar to that of FRP. (3) due skins, strength thin FRP webs of the plywood. to separate the faces. This type of construction permits the use of thinner panels since the shear strength of the webs is far higher than that of foam or balsa. The voids between the shear webs are generally filled with low density foam (2 pounds per square foot) both to provide a mold buckling surface for laying of the webs and to prevent their 6 These are illustrated in figure 7. For a material of equal - - 17 stiffness, a sandwich panel will be both lighter and require less Sandwich construction is depth than a single skin with frames. generally limited to large flat surfaces such as decks, bulkheads The stiffness of sandwich panels is particularly and cabin tops. flexi- surfaces where the constructing walking in advantageous bility of thin single skin FRP panels would be unacceptable. Single skin panels are made successive of layers of glass Common layups consist of reinforcement soaked in a resin matrix. alternate layers of mat and woven roving repeated 3 or 4 times. Mat or chopped mat, consists of randomly oriented chopped glass fibers bonded sheets into with mat Chopped adhesive. a light comes in various weights (1/2, 3/4, 1, 1 1/2, 2 oz./sq. ft.) and fiber lengths 1, (3/4, 1 3/4, 2 in.), usually comes it and is commonly bought by the square yard. handling careful to embedded in the skin. prevent the rolls Chopped mat requires fibers glass in from becoming The women roving (rov) or fiberglass cloth It consists of long bundles of glass fibers woven into a cloth. comes in several commonly used weights in hull (10-40 construction repairs a lighter cloth -- oz./sq. being 12-16 oz. -- yard), the the 24 oz. one most size; for is preferable. Mold Preparation The first step in the construction of a fiberglass panel the design and construction of a mold. two ways: is A panel may be built in into a female mold or onto a male mold. In both cases the construction is basically the same, the only difference being - 18 - Molds can be made in whether you begin or end with the gel coat. out wood, of to work only requirement I preferred with. proper application of a gel coat. applied should surface is the polished smooth be coat; since polished it should be waxed several times and then sprayed with a mold for the With a female mold, the first application before any scratches the or pits Once a mold surface of the panel. appear on the outer will gel outer female to work with aluminum molds be cause we did not have the necessary equipment layer is (so that they don't deform during lay-up) and that they be stiff easy the or fiberglass; aluminum, is (using ceara mold wax) sure release, making to keep the mold clean and free from dust until you are ready to apply to gel coat. Preparation of the surface is all-important. If it is done right, you will never have to do it again...so take you time and work carefully. The panel is built from the outside in. (4 mats, ply construction boat builders for made flat; craft 3 rov) I selected a seven- similar to that used by most from 20-60 ft. The first panels were more recent panels were scale models of single skin power boat hulls. I strongly recommend that one practice with small flat panels before attempting to build a complex specimen. Flaw Design The key to a successful specimen construction is organization and practice. First, the materials for the selected and arranged in their proper sequence. panel The have to be reinforcing 19 - - the correct At this point one should also design and flaws that will be introduced in the specimens. record should be kept of the flaw types, included be will analyzing flaws in accurate the thermographs. consistent and There specimen fiberglass a this specimen; the in in to prevent (with paper between the layers sequence separation of fibers). prepare the stacked scissors and can be cut to size using long material few to Initial flaws voids made by cutting out a section or several when introduce can them of later help are many ways but results. locations that sizes, will A produce consisted of sections out of the layers and creating an air void in the lay-up. This approach has several drawbacks: 1) resin flows in the vacant area filling up the void unless one pre-cures the boundaries of the flaw; 2) easily detectable with although this type of flaw is liquid crystals it is unlikely that it ever occurs in real situations. Using this technique I placed voids of only one ply thickness (approximately 1/20") and was able to detect them successfully at depths of up to 3/16". Another technique for introducing flaws of known location is to use small glass tubes, micropipettes. size and The tubes are first measured to determine the internal diameter, then they are cut to specific lengths and sealed with wax. I noticed that the tubes tend to fill with resin by capillary action rendering them useless as flaws; this is why I seal the ends with wax. - There are several - 20 such tubes as flaws, advantages to using glass as: 1) ease of construction, 2) variety and consistency of size (0.2-1 mm.), 3) cut to any size and placed at any interface, 4) their precise size and location can be recorded as they are placed in the lay up. The drawbacks are: 1) they tend to fill up with resin, 2) they break easily when handlng and during lay-up. Glass tubes can be used to model small air bubbles and hair line tubes was that glass than One of inside a composite. cracks the of any they were flaws which the reasons available smaller sizes much in previously were I chose to use detected using resolution for our colicry hence we could set a lower limit of test as well as a goal for further research in the area. one can either choose polyester or epoxy Polyester resin will do a fine job under most conditions resins. and matrix, the For is most resin Epoxy economical. costs more, but offers greater adhesion and superior strength where needed for special conditions. adding to In addition, there are coloring agents available for the resin polyester or tinting Special pigment pigments should are be used used with difference is the setting times. for epoxy premixed colors A maximum of 1 oz. of normally added to the finish coat only. coloring the one (1) quart systems. of Another resin. major Polyester resins can harden in - be and minutes five 21 fully cured (which are usually used - within an hour; resins epoxy in large boat construction) require at least 4 hours to set and up to 24 hours to be fully cured. Where to Work Work should be done under cover, out-of-doors. degrees ferred. If Fahrenheit, working when the if possible, or shaded if is below 60 shop is temperature a well-ventilated and heated pre- DO NOT WORK IN DIRECT SUNLIGHT, as this accelerates the curing of the resin and can cause a distortion of the finish. A temperature of 70 to 80 degrees Fahrenheit is ideal. The mold or other surfaces you are working on should also be at this temperature. Getting Ready Make sure the mold has been waxed the lay-up. any resin. and sprayed before doing Prepare all your tools and materials before mixing This should include: 3 pairs of plastic gloves (at least) 3 beakers 500 or 1000 ml; have one for mixing resin, one with acetone and 1 spare. 2 brushes, 1 1/2" wide with brush hair cut to 3/4" length 1 flat roller 1 grooved roller 1 mold (waxed and sprayed) 5 mats (cut to size) (one extra) - 3 rovings - 22 (cut to size) epoxy resin -hardener -- DER 331 or similar VERSAMID 140 or similar pigments and mixing rod paper towels wax paper flaws and notepads If you are working with apply the "gel coat" first epoxy resin, as and let it I did, dry overnight. you should A gel coat usually consists of tougher epoxy resin and is the outer layer of a boat, a pigmented epoxy resin was used for our specimens since gel coats are expensive and very difficult to work with. On cold days, use more hardener to insure curing; on warm days, cut down on the hardener to keep the resin from curing too soon. When applying the gel coat use equal amounts of resin and hardener. along This accelerates the cure inclined mold surfaces. and lessens The "gel flow of coat" should be brushed on the mold with long even strokes making sure all removed. resin bubbles are Allow the epoxy to settle for a few minutes then remove any additional bubbles. It usually takes several coats of resin to cover the mold properly. specimen remove excess resin If you are making a curved or angled from corners or grooves; in addi- tion, watch out for thinning out in inclined areas. If you are working with a polyester resin you will have to be more careful since bubbles may never get a chance to escape during the curing process and tend to get trapped at the surface. - Do not mix the hardener with time Begin will the resin until you are be with small changed when batches until using resin in larger approximately 100 ml for the gel coat -For the actual lay-up use about 400 ml. You will need 1 1/2 sq. foot panel. (for a seven-ply 1 square Do not attempt to re-brush an area, particularly after the resin has begun to harden. of amounts. you have gotten experience with the lay-up process and the application of resin. foot specimen). ready to Never mix more than one quart at a time since apply the resin. gel - 23 thickening, discard If the resin it and mix in your can another batch. shows signs After the Resin is hard when your fingernail will not make an indentation complete layup is finished, allow resin harden. to in the surface. Once the "gel coat" has dried you should clean it thoroughly with soap and water to remove any oil or dust that may damage the bond with the rest of the specimen. Begin the lay-up by mixing a batch of resin (2 Resin:1 Hardener), making sure it is well mixed and that no bubbles are in the mixture. Apply a coat of resin to The mat the mold and then place a layer of chopped mat on it. should first be rolled, using wax paper to prevent sticking fibers onto the roller, and then coated with more resin. Avoid clumping, air gaps, resin pools for these will affect the quality of your specimen. To apply resin start from center and work out with short rapid brush strokes. The wet finish coat on top of the first layer of mat acts as "bedding" coat for the first layer of cloth. The cloth is applied while the resin is wet. Each - 24 - layer is saturated from the bottom in this way, and from the top with additional coats of resin. Starting at one end of the mold, the cloth smoothly working out wrinkles as you go; now wet out Use squeegee to smooth cloth if you prefer, but do with resin. wash hands frequently in bucket of to use hands; afraid not be unroll the cloth, applying detergent and water or acetone (or simply put on new gloves). cloth the Roll out evenly to remove air bubbles, note all that the cloth is much easier to roll than the mat since it will not have clump been trapped mat in the or any air that may below. layers Repeat this Trim and sand off all whiskers, lumps and extra The smoother each layer is, cloth. remove Finish up with one or two layers procedure for all the layers. of chopped mat. to pressure apply extra up, the smoother the entire job will be. Let the fiberglass job stand for at least three days; "blushing" or loosening of coating may develop if the water placed in too soon. Should air bubbles develop, sand through bubbles after resin has hardened, then fill area with finish coat. Should air bubbles or pockets develop due to the cloth pulling away from the gull (surface not clean), you can cut out the entire area and patch with cloth and resin. Resin, chopped mat, roving, pigments, etc., from Allied Resin Weymouth, Mass. Corporation, 02189; Tel: Weymouth can be purchased Industrial (617) 337-6070. Park, East - - 25 Liquid Crystals APPENDIX B. Cholesteric Liquid Crystals Liquid crystals are substances which over a clearly defined temperature range appear to possess the flow characteristics of a liquid while retaining much of the molecular order of a crystalline liquid to according lesteric their cho- Cholesteric long whose molecules or smectic structures. molecular have parallel crystals nematic, can be crystals Liquid solid. axis lies along very thin planes. The molecular layers in a cholesteric substance are very thin (approximately 3 Angstroms) with the long axes of the molecules parallel to the plane of the are essentially flat, with a individual molecules The layers. side chain of methyl groups (CH3) projecting upward from the plane of each molecule. This unusual configuration of direction the causes the long axes of the molecules in each layer to be displaced slightly from the cor- layers. This displacement, which averages about 15 minutes or arc per layer, is cumulative overall displacement responding successive through traces out in direction adjacent layers, a helical path. so that the pitch The of the helical path is usually temperature-dependent, and the temperature dependence may be postive or negative. structure can be in the cholesteric molecular The twist observed in the optical characteristics of homogeneously ordered layers. The molecular architecture of cholesteric liquid crtystals - gives - 26 rise to anumber of peculiar optical properties. As polar- ized light transmitted perpendicularly to the molecular layer the the electric vector direction of of the light will be rotated progressively to the left along a helical path, thus the plane of direction through poropagation of an angle that transmitting material. rotate light the electric vector and the is determine by polarization which is also will be to proportional to rotated the the thickness left, of the Optically active materials, those which in this fashion, such as certain types of quartz, rotate the plane of polarization about 20 degrees per millimeter An optically active cholesteric and are considered very active. substance, on the other hand, rotates the plane of polarization through an angle of as much as 198,000 degrees, or 50 rotations Liquid crystals of this kind are by far the most per millimeter. optically active substances known. Another strictly crystalline optical property cholesteric liquids is circular dichroism. light is directed separated into at two a cholesteric components, one by When ordinary white material, with exhibited the the light electric is vector rotating clockwise and the other with the electric vector rotating counter-clockwise. Depending on the material, one of these is transmitted and the other that gives color when combination the is reflected. cholesteric phase it is illuminated of colors depends on its characteristic by white and the angle of the incident beam. It is this property light. the material, The the iridescent particular temperature - cholesteric Each carbon of number over range perature only exhibit in ester cholesteric The acid the group, a fraction of the the the tem- determine and colors they may go Liquid spectrum according to their structure. through the full the crystals may spectrum or color to structure, Liquid transition. this responses unique has which the crystals exhibit during exhibited colors atoms - crystal liquid variations. temperature 27 crystals can be blended to scatter light over a temperature range -20 from degrees to 250 Centigrade. degrees The color-play range (temperatures over which colors are given) can vary from 50 to 1 degree Centigrade, the response time is of the order of 0.1 a with sec. resolution 0.1 liquid crystals literature on ture7. of degree Centigrade. The in the patent is covered best litera- The important parameters that control a liquid crystal's usefulness in non-destructive testing are: 1) availability and cost, 2) ease of application, 3) resistance to wind and UV exposure, 4) dust resistance, 5) long shelf life, 6) reliable color play range, at relevant temperatures. Prepared Liquid liquid Crystal crystal Biosystems, can be blends Inc., 26101 purchased Miles Road, from LCB, Cleveland, Ohio 44128. These are available in spray cans and come in four color play ranges: 30-33 degrees Centigrade, 31-34 degrees Centigrade, - 33-36 Centigrade, degrees 32-35 28 - degrees blends The Centigrade. are satisfactory for LCT but are not effective for testing thick panels or performing tests where the relevant thermal differences occur above 36 degrees Centigrade. with made several organic Liquid crystal blends can be available chemicals from Kodak and I experimented with a system of cholesteryl oleyl other sources. carbonate and cholesteryl nonanoate and was able to duplicate the response the blends produced by LCB. color I also be prepared blends to operate at the 50 and 60 degrees Centigrade range. temperature room range of canned blends temperature and hence The just a few degrees above is is quite vulnerable to air currents and other forms of convective cooling that affect the accuracy of a test. Blends should be applied evenly over the entire area tested, the thickness of the layer should be about to be 1 mil, a thinner layer should be used at first, then if the color response was not adequate more crystals should be sprayed on. open area newspapers. for spraying When and place the specimen flat Select an on some spraying avoid covering an area too thickly, use fast strokes from 12-18 inches depending on the spay pattern. When using your own blends be extremely careful with the atomized solvent (hexane, petroleum ether); they are extremely volatile and should not be used indoors, unless there is good ventilation. Blends for field testing will wind and intense light. amount have to be able to withstand Using thin crystal films will reduce the of distortion when exposed to wind. The use of ultra- - violet stabilizers such as 29 PABA - (P-amino benzoic acid) can protect the blends from destruction by UV and can increase their shelf life substantially 7 The cost of liquid crystal blends varies but tively cheap compared to other NDE tests. is still rela- Cholesteryl nonanoate is available from Eastman Kodak for 19.05 for 25 g, cholesteryl oleyl carbonate 25 g $49.50. The crystal blends are the most important part of the test and further research should definitely be conducted fiberglass. to develop suitable blends for field testing of - - 30 REFERENCES 1. Communications with Boating Safety Devision, USCG, First Coast Guard District, Boston, Mass. Spring, 1977 - Fall, 1977. 2. Rules for Building and Classing Reinforced Plastic Vessels 1978, American Bureau of Shipping, N.Y., N.Y. 3. American Ave., 4. Boat and Yacht P.O. Box 806, 190 Ketcham Amityville, N.Y. (Standards and Recommended Practices). Photography Prosystem Inc., 5. Council, of Liquid Crystal Thermograms, Liquid Crystal Cleveland, Ohio. Survey of Boat Manufacturers, on Materials and Building Stan- dards, Prof. J. H. Williams, Fall, 1977 (for fiberglass layup procedure and quality control) 6. Fiberglass Boat Design & Construction, Robert J. Scott, Tuckahoe, N.Y., J de Graff, 1973. 7. Williams, Edward L. "Liquid Crystals and Electronic Applica- tions, Chemical Technology Review, No. 46. Liquid Crystals and Their applications -- Patent Literature on a very useful text. - 31 - Liquid Crystals REFERENCES, APPENDIX B. "Cholesteric Liquid Crystals for Nondestructive Brown, Shelba P., Testing." Materials Evaluation, Aug., Frederick Davis, "Liquid 1968, Crystals: A search/Development, June, 1967, p. 24 - G. D. "Cholesteric Dixon, p. 163 - 166. New in Testing" Materials Evaluation, June, 1977, p. 51 - J. L. "Liquid Crystal" Fergason, No. 2, Aug., J. L. pp. 77 - 1964, "Liquid Fergason, Applied Optics, Vol. D. R. Green, Ceramics." D. J. for and Re- Nondestructive 55. Scientific American, Vol. 211, 85. in Crystals Nondestructive 7, No. 9, Sept., 1968, pp. 1729 - "Thermal NDT" 27. Crystals Liquid Tool Infrared Testing of Testing" 1737. Composites and Materials Evaluation, Nov., 1971. Hagemaier, H. J. McFaul and J. T. Parks,, "Nondestructive Testing Techniques for Fiberglass, Graphite Fiber and Boron Fiber Composite Aircraft Structures." Materials Evaluation, Sept., 1970. D. J. Hagemaier, H. J. McFaul and D. Moon, "Nondestructive - 32 - Materials Evaluation, Testing of Graphite Composite Structures." June, 1971. G. Edmund Wunchwind. Journal Kenneth II, Henneke Thermography -- Wayne and Reifsnider W. An NDI Method for Damage Detection, September Metals, of L. 1979, p. 11 - 15 (video- thermography) . E. W. Kitzscher, K. H. Zimmerman and J. L. Bothin, "Thermal and Infrared Methods for Nondestructive Evaluation of Adhesive-Bonded Structures." Materials Evaluation, July, 1968. Eugene Sprow, "Liquid-Crystals, Design, Feb. 1969. W. E. Aug., W. E. with 1968, p. 149 - Woodmansee, Liquid Crystals. 1721 - and Woodmansee Discontinuities 1727. pp. 34 - H. L. Liquid a film in Your Future." Machine 41. Southworth, Crystals." "Detection Materials of Material Evaluation, 154. "Aerospace Thermal Mapping Applications of Applied Optics, Vol. 7, No. 9, Sept, 1968, pp. - Figure 1. drawing 33 - Field testing with cholesteric liquid crystals. illustrates testing. a possible A--Regulated B--Camera. tective tent. frequency C--Technician. F--Boat. equipment and set-up amplitude D--Portable for light generator. This on-site source. E--Pro- G--Instrument box with light controls. w w ?AN 7: L-/A 4. H~~~ Figure 2. filament. Light jig (top view) this section. M FAT AA$ Taken at mid- Shows the rails built for this research which permit quick adjustments on the location of the studio lamps. areas show possible locations for light filaments. ------- - Shaded - 35 - TABLE 1 APPROPRIATE NONDESTRUCTIVE EVALUATION METHODS FOR COMPOSITE MATERIALS DEFECT FIBERGLASS BORON FIBER GRAPHITE FIBER Disbonds Sonic Ultrasonic Thermal (thin sections only) Sonic Ultrasonic Thermal (thin sections only) Eddy-Sonic Sonic Ultrasonic Delaminations Eddy-Sonic Sonic Ultrasonic Sonic Ultrasonic Thermal (thin sections only) Eddy-Sonic Thermoluminescent Thermoluminescent Coatings Coatings Sonic Ultrasonic Thermal (thin sections only) Eddy-Sonic Thermoluminescent Coatings Fiber-Orientation Back-lighting (magnified) (Tape) -X-ray (low kv) Back-lighting (magnified) X-ray (low kv) X-ray (low kv) FIber-Orientation X-ray Microscope (Laminate) (edge) X-ray Microscope (edge) Microscope (edge) Inclusions X-ray Ultrasonic X-ray Ultrasonic X-ray Ultrasonic Crushed X-ray Ultrasonic (through transmission) X-ray Ultrasonic (through transmission) Eddy-Sonic X-ray Ultrasonic (through transmission) Eddy-Sonic Resin-rich and resin-starved areas X-ray Ultrasonic X-ray Ultrasonic X-ray Ultrasonic Hicromechanic studies Acoustic emission Acoustic emission Thickness gaging Micrometer Ultrasonic Micrometer Ultrasonic Porosity and cracks (internal) Ultrasonic X-ray (thin sections only) Ultrasonic X-ray (thin sections only) Ultrasonic X-ray (thin sections only) Porosity and cracks (external) Penetrant Penetrant Penetrant Honeycomb Core Adhesive disbonds joint * Acoustic emission .Hicrometer Ultrasonic Pulse Echo Pulse Echo Pulse Echo (Also, see disbords and dela-minations above.) - 36 Visual Acceptance Levels Name Definition Level I + a small piece broken off an edge or surface none Crack an actual separation of the laminate, visible on opposite surfaces, and extending through the thickness crack existing only on the surface of the laminate fine cracks at or under the surface of a laminate Delamination, edge separation of the layers of material at the edge of a laminate Delamination, inter- separation of the layers of material in a laminal nate Dry-spot area of incomplete surface film where the reinforcement has not been wetted with resin metallic particles included in a laminate Foreign inclusion which are foreign to its composition (metallic) Crazing Foreign inclusion (nonmetallic) Fracture Air bubble (void) Blister Burned Fish-eye Lack of fillout Level II Level +----------4 Chip Crack, surface - nonmetallic particles of substance included in a laminate which seem foreign to its composition rupture of laminate surface without complete penetration air entrapment within and between the plies of reinforcement, usually spherical in shape rounded elevation of the surface of a laminate, with boundaries that may be more or less sharply defined, somewhat resembling in shape a blister on the human skin showing evidence of thermal decomposition through some discoloration, distortion, or destruction of the surface of the laminate small globular mass which has not blended completely into the surrounding material and is particularly evident in a transparent or translucent material an area, occurring usually at the edge of a laminated plastic, where the reinforcement has not been wetted with resin Table 2. Ill _____________________________________ none maximum dimension of break, 3.0 mm (/ in.) none maximum dimension of break, 6.5 mm (!4 in.) none none maximum length, 3.0 mm ('6.in.) maximum lngth 6.5 mm (, none none maximum dimension of crazing, 13 maximum dimension of crazing, 25 mm mm () in.) (I in.) frequency and location to be determined by customer maximum dimension, 3.0 mm (N in.) maximum dimension, 6.5 mm (%gin.) none none none maximum diameter, 9.5 mm (% in.) none none, if for electrical use; maximpm none, if for electrical use; maximum dimension, 0.8 mm 042 in.), 1/0.09 dimension, 1.5 mm (Y4, in.), 1/0.09 m' ( ft'), if for mechanical use n 2 (I W), if for mechanical use maximum dimension, 0.8 mm ("Ma in.), maximum dimension, 1.5 mm (%a in.); 1/0.09 m2 (I ft') 1/0.09 M2 (I ft) none in.) none maximum diameter, 14 mm (9/e in.) none maximum dimension, 21-mmn (Ij6 in.) maximum immension, mm 29 none none maximum diameter, 1.5 mm (Ye in.); maximum diameter, 3.0 mm (% in.); 2/in.' 4/in.' maximum diameter, 3.0 mm (%.Jin.); maximum diameter, 6.5 mm (4 in.); height from surface not to be outside height from surface not to be outside drawing tolerance drawing tolerance none none none none maximum diameter, 9.5 mm (% in.) maximum diameter, 13 mm (.1- in.) none maximum diameter, 6.5 mm (i4 in.) maximum diameter, 9.5 mm (h in.) Allowable defects. ASTM 2563. (lh in.) 1 CD - 37 - Visual Acceptance Levels Name Definition Orange-peel Pimple Pit (pinhole) Porosity (pinhole) uneven surface somewhat resembling an orange peel small, sharp, or conical elevation on the surface of a laminate small crater in the surface of a laminate, with its width approximately of the same order of magnitude as its depth none maximum diameter, 14 mm (?J6 in.) none none none presence of numerous visible pits (pinholes) none maximum diameter, 0.4 mm (4 in.); maximum diameter, 0.8 mm (2 in.); depth less than 20 percent of wall depth less than I percent of wall thickness thickness frequency and location to be determined by customer maximum of 25 pits (pinholes) in po- maximum of 50 pits (pinholes) in porous area of size listed in Level Ill rous area of size listed in Level II maximum dimension, 13 mm (I in.); maximum dimension, 6.5 mm (% in.) height above surface not to be outside height above surface not to be out drawing tolerance side drawing tolerance an unintentional extra layer of cured resin on part of the surface of the laminate (This condition does not include gel coats.) an apparent accumulat,itin of excess resin in a Resin-pocket small localized area within the laminate insufficient reinforcing material at the edge of Resin-rich edge molded laminate Shrink-mark (sink) depression in the surface of a molded laminate where it has retracted from the mold Pre-gel Wash Wormhole Wrinkles Scratch Short Level III Level II [Level I area where the reinforcement of molded plastic has moved inadvertently during closure of the mold resulting in resin-rich areas elongated air entrapment which is either in or near the surface of a laminate and may be covered by a thin film of cured resin in a laminate, an imperfection that has the appearance of a wave molded into one or more plies of fabric or other reinforcement material shallow mark, groove, furrow, or channel caused by improper handling or storage in a laminate, an incompletely filled out condition NOTE-this may be evident either through an absence of surface film in some areas, or as lighter unfused particles of material showing through a covering surface film, possibly accompanied by thin-skinned blisters Table 2 (cont.). none | maximum diameter, 29 mm (11- in.) maximum diameter, 3.0 mm (Li in.) none maximum diameter, 3.0 mm (!' in.) maximum diameter, 6.5 mm (Ij in.) none none maximum, 0.4 mm (4 in.) from thi edge maximum diameter, 9.5 mm (% in.) depth not greater than 25 percent o wall thickness maximum dimension 21 mm (1%6 in.) maximum, 0.8 mm (362 in.) from the edge maximum diameter, 14 mm (ia in.); depth not greater than 25 percent of wall thickness maximum dimension 29 mm (4 in.) none maximum diameter, 3.0 mm (I in.) maximum diameter, 6.5 mm (!/ in.) none none none none maximum length surface side, 13 mn (1i in.); maximum length opposit side, 13 mm (M in.); depth less tha 10 percent of wall thickness maximum length, 25 mm (1.0 in.); maxi mum depth, 0.125 (0.005 in.) none Allowable defects. maximum length surface side, 25 mm (I in.); maximum length opposite side, 25 mm (I in.); depth less than 15 percent of wall thickness maximum length, 25 mm (1.0 in.); maximum depth, 0.255 (0.010 in.) none ASTM 2563. - 38 - U eZx4" L&H ~ FeAM= Figure 3. Specimen holder. This settings for the specimen holder. drawing shows the !5(PPCW T range of - 39 - Aiuminum/ Storage Pock FRP Bonding A Portable Plywood Panel Foam Reinforcement -Plywood Stringer Covered with FRP -Plywood Girder Covered with FrP led-in Spray Strip Reinforcement Inboard/Outboard Power Cruiser Figure 4. Deep vee hull section.' (6 I I III I I II II I I II II I Ii j*4t3 Ii I f 42 ~, Sb~ 1.1 100 188 ~- to 0 -. to - 1* -w I I0 I Io 00 I', 1. -1 2. I0 ~-1 *2.0 r 2.0 I -2. ia3 ____ S0 k~?l 1 ~~0 2.0 -1oo 10 100 -roe vimA4 noe -I--- 4OZ Figure 5. & zo as 1bIcA1-5- r.Ao2 ZO.m Z=.2'9rmm hA.) :(ITr 1.5 6 mm I ..b3mm 0 z.20 o m / 00 /. .05mm Fiberglass panel showing approximate flaw locations. I - 41 - 'I' ===I _ MAT #3 ~ I1-~ MAT Novo T___7_A tions. Interface coding sequence L ---. M ol.. ggg; Figure 6. W1 4t used to record flaw loca- - Foam 42 End Grain Balsa Plywood Foam Mandrils Shear Webs - Vertical Figure 7. Shear Webs - Truss Core materials. - 43 - .70 - .50 Ee 40 .30 .20 0 20 30 40 50 60 70 s0 Length on Waterline. L Table 3. Typical hull thickness. 90 to - - 44 Number of Plies or Pairs vs Larninate Thickness in Inches Laminate 1-1/2Low 112o.Mt Glass Content (Percent)J 2 3 4 5 Number of Plies or Pairs 10 9 8 7 6 11 12 13 14 15 .060 .120 .180 .240 .300 .360 .420 20 Low High .076 .152 .228 .304 .380 .456 .532 .480 .608 .540 .684 .600 .760 .660 .836 .720 .912 .780 .940 .900 .988 1.064 1.140 .045 .090 .135 .180 .225 .270 .315 25High .061 .122 .183 .244 .305 .366 .427 .360 .488 405 .549 .450 .610 .495 .671 .540 .732 .585 .793 .630 .854 .245 .350 .280 .400 .315 .450 .350 .500., 1.100 1.260 .900 1.070 .750 .910 .450 .610 .380 .540 .320 .480 .270 .420 .230 .380 .385 .550 1.210 1.386 .990 1.177 .825 1.001 .475 .671 .418 .594 .352 .528 .297 .462 .253 .418 .420 .600 1.320 1.512 1.080 1.284 .900 1.092 .540 .732 .456 .648 .384 .576 .324 .504 .276 .456 .455 .650. 1.430 1.638 1.170 1.391 .975 1.183 .585 .793 .494 .7012 .416 .624 .351 .546 .299 .494 .400 .701a 1.540 1.764 1.260 1.498 1.050 1.274 .630 .854 .532 .756 .448 .672 .378 .588 .322 .532 .140 .175 .210 30 Low .035 .070 .105 Il 0'0.100 .150 .200 .250 .300 30 Low .110 1220 .330 .40 .550 .660 High .126 .252 .378 .504 .630 .756 Composite Laminate (Alternate Plies of 35 Low .090 .180 .270 .360 .450 .540 High .107 .214 .321 .428 .535 .642 1-1/2 oz. Mat and 40 Low .075 .150 .225 .300 .375 .450 24 oz. WR) 40High .091 .182 .273 .364 .455 .546 40 Low .045 .090 .135 .180 .225 .270 40High .061 .122 .183 .244 .. 305 .366 .228 45 Low .038 .076 .114 .152 .190 High .05 4 .108 .162 .216 .270 .324 Rvig 0Low .0 32 .064 .096 .128 .160 .192 24oz Wve .048 .096 .144 .192 .240 .288 24High .054 .081 .108 .135 .162 55 Low .027 High .042 .084 .126 .168 .210 .252 .069 .092 .115 .138 Low .023 .046 High .038 .076 .114 .152 .190 .228 Table 4. .770 .880 .990 .882 1.008 1.134 .630 .720 .810 .749 .856 .963 .525 .600 .675 .637 .728 .819 .315 .360 .405 .427 .488 .549 .266 .304 .342 .378 .432 .486 .224 .256 .288 .336 .384 .432 .189 .216 .243 .294 .336 .378 .161 .184 .207 .266 .304 .342 .67 .915 .525 .750 1.650 1.890 1.350 1.605 1.125 1.365 .675 .915 .570 .810 .480 .720 .405 .630 .345 .570 - - 45 Number of Plies or Pairs vs. Laminate Weight Pounds Per Square Foot Laminate 1-1/2 oz. Mat Composite Laminate (Alternate Plies of 1-1/2 oz. Mat and 24 oz. WR) 24 oz. Woven Roving Glass Content (Percent) 1 2 3 20 Low .439 High .499 25 Low .345 High .405 .878 .998 .690 .810 30 Low .283 High .343 .566 .686 1.32 1.50 1.04 1.22 .849 1.03 2.47 2.74 2.10 2.37 1.82 2.09 1.21 1.29 30 Low High 35 Low High 40 Low High .823 .913 .700 .789 .606 .696 1.65 1.83 1.40 1.58 1.21 1.39 40 Low .403 High .430 .806 .860 45 Low .357 High .383 .714 .766 50 Low .320 High ..347 .640 .694 55 Low .290 High .316 .580 .632 60 Low .265 High .292 .530 .584 4 1.76 2.00 1.38 1.62 1.13 1.37 3.29 3.65 2.80 3.16 2.42 2.78 1.61 1.72 1.07 1.43 1.15 1.53 .960 1.28 1.04 1.39 5 2.20 2.50 1.73 2.03 1.42 1.72 4.12 4.57 3.50 3.95 3.03 3.48 2.02 2.15 1.79 1.92 1.60 1.74 Number of Plies or Pairs 6 7 8 10 9 2,63 2.99 2.07 2.43 1.70 2.06 4.94 5.48 4.20 4.73 3.64 4.18 2.42 2.58 2.14 2.30 1.92 2.08 .870 1.16 1.45 1.74 .948 1.26 1.58 1.90 .795 1.06 1.33 1.59 .876 1.17 1.46 1.75 Table 5. 3.07 3.49 2.42 2.84 1.98 2.40 5.76 6.39 4.90 5.52 4.24 4.87 2.82 3.01 2.50 2.68 2.24 2.43 2.03 2.21 1.86 2.04 3.51 3.99 2.76 3.24 2.26 2.74 6.58 7.30 5.60 6.31 4.85 5.57 3.22 3.44 2.86 3.06 2.56 2.78 2.32 2.53 2.12 2.34 3.95 4.49 3.11 3.65 2.55 3.09 7.41 8.22 6.30 7.10 5.45 6.26 3.63 3.87 3.21 3.45 2.88 3.12 2.61 2.84 2.39 2.63 11 12 13 14 4.39 4.83 5.27 5.71 6.15 4.99 5.49 5.99 6.49 6.99 3.45 3.80 4.14 4.49 4.83 4.05 4.46 4.86 5.27 5.67 2.83 3.11 3.40 3.68 3.96 3.43 3.77 4.12 4.46 4.80 11.5 8.23 9.05 9.88 10.7 9.13 10.0 11.0 11.9 12.8 7.00 7.70 8.40 9.10 9.80 5.89 8.68 9.47 10.3 11.0 6.06 6.67 7.27 7.88 8.48 6.9G 7.66 8.35 9.05 9.74 4.03 4.43 4.84 5.24 5.64 4.30 4.73 5.16 5.59 6.02 3.57 3.93 4.28 4.64 5.00 3.83 4.21 4.60 4.98 5.36 3.20 3.52 3.84 4.16 4.48 3.47 3.82 4.16 4.51 4.86 2.90 3.19 3.48 3.77 4.06 3.16 3.48 3.79 4.11 4.42 2.65 2.92 3.18 3.45 3.71 2.92 3.21 3.50 3.80 4.09 15 6.59 7.49 5.18 6.08 4.25 5.15 12.3 13.7 10.5 11.8 9.09 10.4 6.05 6.45 5.36 5.75 4.80 5.21 4.35 4.74 3.98 4.38