HW2-Soln-Composite-Materials

HW2-Soln-Composite-Materials - .J" 0 A composite with...

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Unformatted text preview: .J" . 0% A composite with uni-directional fiber reinforcement is made using two unknown constituent materials, Material A which is the fiber and material B which is the reinforcement. The elastic modulus of material A is 150 GPa and the elastic modulus of material B is 10 GPa. ' If material A is 40% of the overall composite by volume, determine the elastic modulus along the direction of the fibers. In addition determine the elastic modulus perpendicular to the main axis of the fibers. - ' 2. F.____—_—-J ._____._———— -—-'> E3: reamTM =— IDGPK _______________. :0. 0 \fi *4 AL on; Na F\BE(L (1" b RELWIBQ) 560mm,: 15';- V: "' Em 147 = (/50)(o»v)+[0/a}/0160) = (00 + (a E == 6.6: GPA COM r- l Q‘DHVDIU’LAm 7:. fig- Fgeg (Z—bzzecr/oidx E0451: EMVF + E: l/m -m /0{0H) + m (M) Emmy-2 3 .. #93”:- Affir- " 1/ + 90 52W.z = /5 W524 1%) Gm“ “112"” EC, = HOGPQ 6 c: '40 M90 SEEL,d=\M, 090 z rmqeooc 53 = 905%; 6 s = 2370 we 09$ '5 {GHQ/"c, Pg? EC: ECVC "' as, Us A": Trf'z 1‘- W9 ‘1: MMMZ AS : 1027-: 0795sz .AC = $,l(4—O.7QS=- 2,555sz Va: 2- 0.75 273% \/g ‘— 5 EC: l)O«O.7§+ZOSrO,?§»= 82,51 51,25 : 155.75% f (5:128 @ = no 6% ~ (.27 (0’5 2. 55w“? + 205- “2740'? 0.793% 1 '3 328.01% 20%? '- 533W \ 40:013*(XC'035)‘~” ' VC‘E—c, ‘ ’ 6 . -6 -G -6 _____._ a, a i“: :10‘0 4 (n' (O "0’ ‘0 )\+ 0.5403? W10 OTISWIO Describe what is meant by the phrase 'critical fiber length'. Explain what happens if the fiber is longer than the critical length and what happens if the fiber is shorter than the critical length. I: "‘ 1,. nclu-Lwc. (it #44,... — I“ #444 72¢— reivrr;aj 7“ /c tit/{0 f/W oux/ «m @Q When in use, a fishing rod can be approximated to act as a cantilevered beam. Assume that the force (P) is applied to the end of the beam by a fish while the other end of the beam is rigidly held by the fisherman. The defamation (A) of the mod is PL3 given by the following equation: A = E] . Assume that the length ofthe rod is fixed (i.e., can not be changed) and the cross section offlie rod is square. The dimensions ofthe cross section can be varied to answer the questions below but the section must remain square. You Should assume the behave as a linearly elastic material. 3) Develop an equation that determines the mass of the fishing rods in terms of the material properties (e. g., elastic modulus and dimension. , section geometry (e.g., cross sectional. length and length), and the design inputs (e.g., load and deformation). L l... on... _ V” lowly L m... was not? war game be en“. fin ’91? a 794:} we: was“ 255 575.6" 172 Am “Pt? 1.3% m “mfg” W ma k?" M M Me) (if) (e) (to fiEm" @ nan) M 7%., AW! afimwfim A... a an!“ flgad IVA-{Md I‘J' firjfla/gnd #2:, _________________ _ _ ’7’? b) Using the data below, detennine which of the materials shouid be used if we wanted to make the lightest rod. assuming that all the rods have the same stiflness c) Using the data "below, determine which ofthe materials should be used if we wanted to make the most economic rod assuming that all the rods have the same stifliaess Nate 1 tonne-'3 1000 kg 83 7g fibéw/ V320 Mwld way/4 7gb {/fimaml {712%qu (1.6- 74er gr M In *‘ “.5 firm.wwfis w W'th :9 N (2.3%”- N Aumtsuvm Au ‘9‘ 3 (3:3 311;: Famwmbnaw g” 9”. ézxm‘fix {la}: wvwmfiaw 2.6m £154 3 (.6. [tidy-83% rad/£3 (fa/gala Adda? Mm fiata’ floifiymaw a} fags?" if? mfiwmq fiwgdmm “7'5 Mdrx/wmtw} @ _ A fishing rod. is formed from a composite material of 0.5 kg of glass fibers embedded in a matrix of 0.5 kg of epoxy resin. The glass fibers are assumed to belong, continuous and unidirectional. To achieve a greater stiffness it is proposed to use a difl'erent composite that is comprised of long continuous carbon fibers that will be . embedded in. a matrix of 0.5 kg of epoxy resin. If the modulus of elasticity ofthe carbon fiber composite is 10% greater than the elastic modulus of the glass fiber composite, estimate the mass of carbon fibers that will be used to make the carbon fiber composite. Assume the applied tensile stress is parallel to the direction of the tong axis of the fibers. The epoxy resin, glass fiber, and carbon. fiber have an elastic modulus of 5, 86, and 350 GPa respectively and a density of 1100, 2500, and 1800 respectively. mm 0: S ‘3 216.53 53:51! ZQBNstrya 2.31m nah? 34M Item can" “PNA‘ /$ “£3 V“ M or: V MW 1%“:ng 23w ka/m’ Vsm‘: a £932. / / o a £3 lax V'f'm‘ae "T" Vague” 4' Vfi’m Véxwa‘éd» MWWWW” em \éwcgé‘mfi :71. Vemeu Vgeewg V a" Saga. 1.: a Viewer“ ‘3 W”! (59 1’2. geWfleeiyfi m Vf‘émfi' $5,455 7" lé’gmv‘ gin“? e: (317.) (away (Mm/)(SMQ g gel/Z» mewsm 3:4 E “m? fiéflfliflf/fiy m 5i} am? 33.526173m m 0‘3“ “WM lific’ {a may; amok praflaadcm A rod made of composite material is placed between rigid-8119mm (TmS could be State two potential advantages of coating fibers before using them in a composite. fi‘fiw ({L'éll; a m flag 7£M 74% (9:) 7g; / (mm/0 m am 4:, flujZaM/ c. e (.1’ nflaar‘ 76 554‘s» 5:; “507%” :i'ékzy [(0794: 73d 24?.» (An/m ' «go (we, Mo/Vch‘m, 76’" «ca. crab /’7l° at) “am #1: 765% a m m 'del’Ow bum] M 4m “K1,, mtxakdxo ® gimiiar to a frp composite bridge deck). At 250 the nod fits perfectly behwecn the rigid supports and there is no stress in the system. What temperature would the composite need to be cooicd to in order for the composite to crack if it has a coefficient ofthonnal expansion of20x10'6 mlmm/C, a $trength of 20 ksi, and an eiastic modulus of 10,000 ksi. Assume the composite behaves as a linear elastic materéal. ...
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