Anoopoma P. Bhowmik Introduction to Opto-Mechanical Engineering

Transcription

1 Tutoial: Applied Use o Composites in Optical Systems Anoopoma P. Bhowmik Intoduction to Opto-Mechanical Engineeing OPTI 521 Novembe 30, 2009 Abstact The pupose o this pape is to povide a bie discussion o the applied use o composites in optical systems. This pape is meant o the inteested eade in design o optical elements and suppot stuctues, and how composites may be used in both scenaios. Fist, an oveview egading composite theoy is summaized. Secondly, use o composites as optical elements and as suppot stuctues o optical systems is discussed. Thoughout, numeous examples ae used as case studies to illustate application. Intoduction Composite mateials (o composites) o shot ae deined as mateials compised o two essentially dieent engineeed elements. Thei combination can be vaied duing abication and thus allows o unique macoscopic popeties such as the ollowing: The mechanical popeties tend to be othotopic, o deined by the diection o applied load, athe than isotopic, o deined equally in all diections They can exhibit high stength to weight atio, ae lightweight, can maintain a low coeicient o themal expansion (CTE), can be coosion and weathe esistant, etc. Some can be heated and shaped multiple times with little change in mateial popeties Accoding to Yode 1, the most impotant types o composites o optical instument applications ae polyme (esin) matix composites (PMCs) and metal matix composites (MMCs) and will be ocused on in this pape. The pupose o this pape is to investigate the use o composites in optical systems though discussion o design examples and case studies. Section 1 will povide a bie eview o the theoy used to model composite behavio. Section 2 will descibe two case studies that illustate the use o composites in optical elements and suppot stuctues. Finally, Section 3 will descibe some ways composites can ail and potential solutions to impove thei peomance. 1

2 Section 1: The theoy o composite mateials Composites ae geneally composed o two mateials: the einocement mateial (typically aligned ibes, chopped ibes, whiskes, o paticles) and the matix (esin o binde). The einocement mateial povides oveall stength o the mateial in a speciic diection. The esin holds the ibes togethe, potects them om mechanical and envionmental damage, and tanses stess between them. Fabication typically consists o placing the einocing mateial into a mould o the desied shape. Then semi-liquid matix mateial is eithe spayed o pumped into the mold to om the object. Pessue is applied to oce out ai bubbles. Finally, heat is applied to set the composite. 1.1 Pultusion A method o abication called pultusion (om pull and extusion ) stetches the einocement mateial in one paticula diection as the matix is set. This pocess is ideal o manuactuing poducts that ae staight and have a constant coss section, such as suppot beams. Figue 1 below illustates this manuactuing pocess. Figue 1: Schematic o Pultusion Pocess 3 Fo a composite abicated in pultusion, the total density 3 can be calculated using the convesion equation o esin (matix mateial) and ille (einocement mateial) shown in Equation 1: 1 ρ m = (1) W 1 W + ( 1+ H m ) ρ ρ whee ρ m = density o esin-ille mixtue [lb./in 3 ] W = weight action o ille (weight o ille/weight o esin-ille mixtue) ρ = density o ille [lb./in 3 ] 1- W = weight action o esin ρ = density o esin [lb./in 3 ] H m = void action o esin-ille mixtue to the entie matix 2

3 Fo example, a ibeglass composite, with W = 30%, ρ = lb./in 3, ρ = lb./in 3, and H m = 10%, the esulting composite density ρ m is 0.05 lb./in 3. The stength 4 o a composite abicated in pultusion can be appoximated using Equation 2: E A A Em = n + E 1 n (2) Am Am whee E m = Young s modulus o the composite [kpa] n = numbe o bas o ille included E = Young s modulus o the ille mateial [kpa] A = suace aea o the ille mateial [m 2 ] A m = suace aea o the composite [m 2 ] E = Young s modulus o the esin mateial [kpa] Fo example, a ibeglass composite, with n= 4, E = 1.6 E 7 kpa, A = 1.96 E-5 m 2, A m = 3.14 E- 4 m 2, and E = 2 E 7 kpa, the esulting composite Young s modulus is 1.9 E 7 kpa. Now compae the speciic stiness (density/ Young s modulus atio) o the ille mateial and matix mateial. Fo the ibeglass, the speciic stiness o the ibeglass is 0.16 g kpa/cm 3 and o the composite it is 0.68 g kpa/cm 3. This illustates an advantage o the composite ove an isotopic solid. Howeve, Equation 2 does not account o voids in the mixtue and is an appoximation. 1.2 Laminated composite sheets Anothe useul abication pocess is to build sheets o composite mateial to poduce thin stuctues with complex shapes, such as cuved panels. In this pocess, individual sheets o woven ibe einocement mateial ae satuated with the matix ove a molded shape. Once the desied thickness has been established, the entie stuctue is cued. Figue 2 below illustates the use o vaying angles to build a quasi-isotopic stuctue. Figue 2. Two examples o quasi-isotopic laminated composite sheets (a) Eight unidiectional layes (b) Fou bidiectional layes aanged at the indicated angles 3

4 Typically, each unidiectional laye has a thickness between micons, with 127 micons being the most commonly used thickness. The multidiectional layes ae usually between micons thick, with 127 micons also the most common thickness. Figue 3 illustates the geomety used to calculate the laminate sheet s Young s modulus. Figue 3: Unidiectional composite laye with coodinate system (x 1, x 2, x 3 ) whee x 1 is oiented along the einocement ibe diection 5 Equation 4 illustates a theoetical calculation o the mateial popeties 5 o the laminate. E E 1 2 = E = E V V E + E V E + E V,, ν G = V ν + V ν, = G G V G + G V whee E 1 = Young s modulus o the composite along x 1 E 2 = Young s modulus o the composite along x 2 ν 12 = Poisson s atio o the composite in the x 1 -x 2 plane G 12 = Shea modulus o the composite in the x 1 -x 2 plane E = Young s modulus o the ille mateial [kpa] E = Young s modulus o the esin mateial [kpa] V = volume atio o the ille mateial (volume o ille to total volume atio) V = volume atio o the esin mateial (volume o esin to total volume atio) ν = Poisson s atio o the ille mateial ν m = Poisson s atio o the esin mateial Notice this calculation does not conside the thickness o dimensions o the mateial. It assumes a single, bi-diectional lamina ply, theeoe, it is a simple appoximation. 1.3 Metal Matix Composites Some composites can be omed via powde metallugy o in a oam stuctue between two sheets and can thus be machined with the same lexibility as metals to be lightweighted without, (4) 4

5 saciicing stiness, in contast to the uneinoced base mateial. Figue 4 shows a compaison o stess-stain cuves o MCC s as the amount o aluminum alloy is educed. Figue 4: Compaison o stess-stain cuves o inceasing amounts o complex metal alloy (CMA) in a composite with aluminum 6 Table 1 summaizes some chaacteistics o aluminum matix composites. The inomation is compiled om P. R.Yode J., W.R. Mohn, D. Vukobatovich, 10. H. J. Yu, K. H. Chung, S. I. Cha, and S. H. Hong 2, 9, 10 Table 1: Compaison o Aluminum and Silicon Cabide Matix Composite Mateials Popety Instument Gade Optical Gade Stuctual Gade Matix alloy 6061-T T T6 Volume % SiC SiC om Paticulate Paticulate Whiske CTE (x 10 6 K -1 ) Themal conductivity (W/mK) Unknown Young s Modulus (MPa) Density (g/cm 3 ) Image Type/ Mean Paticle Size Optical-light micogaph/ 3.5 micon Unknown/ 8 micon Scanning electon micogaph/ 0.6 micon diamete Sample Image 1.4 Compaison o Composite Mateial Popeties and Applications Table 2 on the next page summaizes some common composite mateials used in optical systems, along with design advantages, disadvantages, and speciic applications. 5

6 Table 2: Compaison o Metal Matix and Polyme Matix Composite Mateials 2 Mateial Advantages Disadvantages Typical Applications Metal Matix Composites SiC/ AL (Discontinuous SiC paticles) B/Al (Continuous boon ibe) Polyme Matix Aamid/ Epoxy (e.g. Kevla o Specta ibes with epoxy matix) Cabon/Epoxy (High-stength ibe) Gaphite/Epoxy (high-modulus ibe) Glass/Epoxy (Continuous glass ibe) Isotopic Lage database 1.5 x modulus and stength o aluminum alloys with the same density High stength vs. weight Low CTE Impact esistant Lowe density than gaphite/epoxy High stength vs. weight Vey high stength vs. weight High modulus vs. weight Low CTE Flight heitage Vey high modulus vs. weight High stength vs. weight Low CTE High themal conductivity Low electical conductivity Well-established manuactuing pocesses Most not weldable Machinable, but esults in high tool wea Lowe ductility than aluminum alloys Limited light heitage Anisotopic Expensive Absobs wate Outgases Low compessive stength Negative CTE Outgasses (matix-dependent) Absobs wate (matixdependent) Low compessive stength Ruptues at low stain Absobs wate and outgasses (matix-dependent) Highe density than gaphite/epoxy Lowe stength and modulus than gaphite/epoxy Tuss ittings Backets Mios and optical benches Tuss membes Shuttle payload doos Sola aay stuctues Radio equency (RF) antenna coves Tuss membes Face sheets o sandwich panels Optical benches Monocoque cylindes Tuss membes Antenna booms Face sheets o sandwich panels Optical benches Monocoque cylindes Pinted cicuit boads Radomes Section 2: Use o composites in optical design Due to thei unique mateial popeties, composites can be used instead o metal o glass o mio substates, as well as o suppoting stuctual components. The ollowing ae some case study examples o using composites in optical design. The eade is encouaged to exploe othe developments by stating with the eeences listed in this pape. 2.1 SXA Mio Example 7, 8 One mio, descibed by Yode in Chapte 13.6, was made om SXA A, an aluminum/silicon cabide metal matix composite (MMC). SXA compises o 2024 aluminum alloy and 30% A SXA is made by Advanced Composite Mateials Copoation, LLC., Gee, South Caolina 6

7 silicon cabide paticulate, by volume. The mio was lage enough to it a beam ootpint 25 cm in diamete and had a inished weight o only 806 gams. SXA was chosen ove glass and beyllium due to its high speciic stength and stiness, good stability, and modeate machining cost. The mio was abicated by a pocess sequence o machining, themal stabilization, electoless nickel plating, polishing, and a high eiciency, lase damage-esistant optical coating. Ate abication, the suace igue was lat to within ~λ/8 powe and ~λ/6 iegulaity ove any 120mm diamete aea. The mio withstood exposue to tempeatues o 160 C without change. 2.2 Silicon Mio and Cesic Stuctue Example IR detectos have diven the eseach to develop mio substates that can be used at cyogenic tempeatues. Silicon glass has both a vey low CTE and high themal conductivity which is avoable o mio applications. A single-cystal electing suace o a silicon mio can be polished to <λ/10 PV at nm wavelength and with micooughness <5Å ms. Howeve, even when combined with a silicon oam-coe stuctue, this pat is still vey agile cannot be machined o mounting. Theeoe, combination with a composite mateial known as Cesic B has been consideed and developed. Cesic is a cabon-ibe-einoced silicon cabide that has a vey close CTE to that o silicon, as well as low density, high stiness, high bending stength, no poosity, no outgassing, isotopy in CTE, themal conductivity, low machining cost, and high chemical, coosion, and abasion esistance. As a inal advantage, Cesic can be machined into astenes that can withstand a high tensile oce appoaching 50,000 N. Theeoe, Cesic is a mateial to be consideed o optical stuctues holding silicon elements due to its simila CTE and othe mechanical popeties. (a) (b) Figue 5: (a) Cesic mount with silicon mio. (b) Compaison o themal peomance o Cesic and Silicon B Cesic is a popietay omulation poduced by ECM Ingenieu-Untenehmen ü Enegie- und Umwelttechnik GmbH, o Munich, Gemany. 7

8 Section 3: Composite ailue 3.1 Design o Composite Stuctues in tems o Stability 11 R.A. Band descibes numeous ailue methods o composites as a way to systematically design stable composite stuctues o lamina composites with potective metal coatings. The key concepts ae summaized hee: Themal stability: achieved by the pope volumetic balance o high-modulus, einocing ibe having a negative CTE, and a matix esin with positive CTE Moistue-induced stability: Expansion can occu when wate diuses into the matix esin causing a volumetic matix change, deined by the coeicient o moistue expansion (CME). The CME is aected by many actos: ibe modulus, ibe volume, tempeatue, elative humidity, diusion constant, equilibium moistue content o the esin, time o exposue, laminate thickness, and law aeas in the potective coveing i thee is one. One appoach is to use a high-modulus ibe and a low moistue-absobing-esin system, such as cyanate este. I a metal coating is added, then the CTE becomes moe positive with inceasing coating thickness, modulus, and CTE o the metal, and the ate o moistue absoption deceases. Design options o dimensional stability in ode o ppm stain change o Maximum (<1 ppm stain change): The laminate has a high modulus ibe, low moistue absobing esin patially satuated with moistue aleady, and metal seal with low law density ( %), thickness such that net CTE is 0.00±0.05ppm/ C. o Excellent (1-2 ppm stain change): nea-zeo CTE laminate combined with a melt-applied eutectic whose moistue is vapoized at high tempeatues. o Modeate (3-5 ppm): High modulus ibes, low moistue absobing esin, lawed ( ~1%) baie/ sealant o Minimal (5-10 ppm): May be the most cost eective appoach. This design uses only a high-modulus ibe and a low-moistue-absobing esin without any potective coating. I the elative humidity (<50%) and tempeatue luctuations can be contolled, then elatively good dimensional stability can still be achieved. 8

9 3.2. Deinition o mechanical ailue modes o composites J. C. Iatidis outlines mechanical ailue o laminate composites in his lectue notes o the ME 257 couse at the Univesity o Vemont 11. The key concepts and some illustative igues ae included hee to pomote undestanding. Deine all ailue modes in tems o: ibe ailue and matix ailue. These ae illustated o a laminate composite in Figue 6 below. Figue 6: Analogy between Buckled Plate and Laminate Load-Deomation Behavio Fo a laminate composite, the pocess o ailue is as ollows: o Deine the loading citeia with bounday conditions at the top and bottom ply o Deine ailue o the ist laye o Deine esulting degadation o the mateial popeties and iteate This pocess is depicted gaphically in Figue 7 on the next page 9

10 Figue 7: Detemination o ibe ailue by an incemental appoach Failue om stess concentations: localized contact stess can lead to ailue and is modeled with geomety shown below in Figue 8. Figue 8: Failue occus when stess (σ n ) at a distance (d 0 ) om edge o discontinuity exceeds the un-notched composite tensile stength F 0 10

11 Failue due to shap cacks: Can use actue mechanics to model and pedict composite ailue as outlined in Equation 5 below. Failue occus at K I exceeds k IC.. K I πaa0 = Yσ πa k IC,1 = F0, a + 2a 0 a k IC, 2 = F0 π a 1 (5) a + d 0 whee K I = Stess intensity acto σ = Applied stess a = Radius o the shap cack k IC,1 = Aveage stess ailue citeion k IC,2 = Stess concentation ailue citeion F 0 = Nominal composite tensile stength without the cack a 0 = Aveage distance om the cack d 0 = Aveage distance om the edge o the cack o It should be noted that composites ae much moe esilient to absobing the enegy o a popagating cack than the isotopic ibe mateials ae. This is due to the matix stess shielding eect such that thee is zeo stess at the cack site. So, as the cack popagates, it encountes ibe, and loses enegy as it inteacts with ibe paticles locally. This allows the composite as a whole to absob a lage amount o stess beoe complete ailue occus. Theeoe, cacks ae a unction o the composite thickness and stess level. Failue in composites occus due to delamination, matix cacking, and ibe ailue Fatigue esistance o composites is geneally vey good. Howeve, atigue lie is complicated by inteaction with actos such as matix cacking, delamination, and impact damage. Conclusion Composites povide many additional design degees o eedom that should be caeully consideed when designing both optical elements and systems. Technology is continually impoving to dive down the cost on available poducts as well as povide eve moe design lexibility. This tutoial has povided a vey bie glimpse o some theoy, uses, and concens associated with using composites. Howeve, much moe detailed FEA and expeimental analysis is highly ecommended pio to use in a developed design. 2 11

12 Reeences 1. D. Ellyad Putting it togethe the science and technology o composite mateials Austalian Academy o Science, Coopeative Reseach Cente o Advanced Composite Stuctues Ltd. Novembe P. R.Yode, J., Opto-Mechanical Systems Design, 3 d Ed., CRC Pess, D. J. Gadne, Pultusion Pocess Adhesion Reseach Goup, Advanced Stuctues and Composites Cente, Univesity o Maine G. Hendeson Behavio o Fibe-Reinoced Polyme (FRP) Composite Piles unde Vetical Loads United States Depatment o Tanspotation - Fedeal Highway Administation. Pub. No. FHWA-HRT J. N. Reddy, Mechanics o laminated composite plates and shells: theoy and analysis 2 nd Ed., CRC Pess, S. Scudino, M. Sakaliyska, K.B. Sueddi, F. Ali, U. Kühn, M. Stoica, N. Matten, H. Ehenbeg, J. Ecket, Metal matix composites einoced with complex metallic alloys, Institute o Complex Mateials, Leibniz Institute o Solid State and Mateials Reseach Desden, Gemany A. Ahmad, D. Vukabatovich, Handbook o Optomechanical Engineeing CRC Pess, 1997, Chapte 5, E. Ulph, Fabication o a metal-matix composite mio, Poc. SPIE 966, 166, W.R. Mohn and D. Vukobatovich, Recent applications o metal matix composites in pecision instuments and optical systems, Opt. Eng., 27, 90, H. J. Yu, K. H. Chung, S. I. Cha, and S. H. Hong Analysis o ceep behavio o SiC/Al metal matix composites based on a genealized shea-lag model, J. Mate. Res., Vol. 19, No. 12, Dec R. A. Band Stategies o stable composite stuctual design Poc. o SPIE Vol. 1752, Cuent Developments in Optical Design and Optical Engineeing, J. C. Iatidis, Failue.ppt and Failue2.ppt ME 257 Composite Mateials, Univesity o Vemont, Disclaime: This tutoial is stictly intended o educational puposes only. I in no way intend to pomote o ault any o the companies, poducts, o technological ideas discussed. I have povided links to many elated Web sites and hope that they ae helpul. Howeve, I cannot accept esponsibility o the accuacy o content o those pages o guaantee ull access to those pages. I have used easonable eots to insue that inomation pesented hee is accuate, but I cannot guaantee that it is accuate o cuent. Fo this eason, any use o this inomation is uged to contact the autho to veiy its accuacy and cuency pio to its use. I assume no liability o inaccuacies contained in the inomation om this pesentation. Fo moe inomation, please contact the autho: abhowmik@optics.aizona.edu 12