4020-F-2011-HW-13 (1) - HSE Wt? \F- 20H @. Creep modulus...

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Unformatted text preview: HSE Wt? \F- 20H @. Creep modulus (psi) Acetal, whose duPont trade name is Delrin, is used to make cams, gears, and bearings because of its strength, good I frictional properties, and abrasion resistance. It also has good resistance to attack by solvents, but is attacked by strong acids and also by sunlight. , Acme Corporation of Worcester, Massachusetts, a manufac~ turer of industrial robots, is interested in manufacturing their pneumatic actuators by molding the components with Delrin. One of the parts is a thin—walled cylinder with closed ends. It will be subjected to compressed air at 100 psig. The operating temperature ranges from 40°F to 170°F. These products must last for 10 years. \\ a) Construct a master curve and determine the shift factor ' a(T) as a function of temperature (see Fig. V1.13). . j; b) If the maximum allowable hoop strain ‘is 0.01, determine .3- the maximum r/t ratio for the cylinder. c) Determine the 7/)? ratio of the cylinder if the part is subjected to 40°F for 8 hr/day and to 170°>F for 16 hr/day for 10 years. 5x|O5 4x|05 3x105 N x 5 UI 1x105 | IO IOO IO IO IO Time (hr) Fig. Vl.13 Creep modulus of duPont Delrin 500 (poly‘acetal). Creep modulus is 1/]0 (Plotted from data taken from ‘Modern Plastics Encyclopedia, ” vol. 43, 1966.) NJ ® midis?) tit/i C M" {M‘ {W 02067 7’0 U9 Wile Lei/J ire, flat] étfl/Jififfi i M; aivmmwmnifrfirm, The palatal“. t»de is W M {Wire This is (“$0068 Pro/o {am to 4692‘- yaw LWW MW V; 0*? Mite/(lam Mia (“seafl- giimafmw Her fly WW “(mtfitfiéwgfir N at wahib whim {6 Proof) 0%”? QWEI J A manufacturer of plastic advertising signs in Los AngelesP receives a complaint from a customer in the Imperial Valley near the Mexican border, who claims that several signs installed only 3 months earlier are badly distorted and about to fall down. The manufacturer, who has had similar signs in ‘ Los Angeles in use for 3 years, is suspicious of the customer’s claim. The signs are made from polymethylrnethacrylate (PMMA). The mean summer daytime temperature in Los I Angeles is 80°F, with less than ten days above 95°F, and the mean daytime temperature during the 3 months in the Imperial Valley has been 105°F, with 15 days above 115°F, and maximum temperatures of 12 0°F. Using the data given in ' Figs. V1.14: and, V1.16 for the modulus and the shift factor \ given in Problem V1.9 for PMMA, determinewyvhether the customer’s claim is reasonable. Your discussion should be as quantitative as possible. You may assume that the IOads are the same in both cases. . Log a (T) O ShIf-t factor for PMMA 4o 60 so 100 120140 I Temperature(°C) ‘ Log Er m ('dynes/cmz) -IO —5 4. Log! ( hr,a$ II5°C) '- aster curve for PMMA, constructed from the data in Fig. d A. V. Tobolsky, j. Colloid. Sci., vol. 7, p. 555, 1952.) Fig. V|.16 Relaxation modulus m VI.14. (From J. R. McLaughlin an Log Er (t) (dynes/cm2 ) |35°C .00L .0: .I' | F0 100 I000 10.900 hr Fig. V1.14 Relaxation modulus for unfracfionated polymethyl methacrylate (PMMA). (From I. R. McLaughlin and A. V. Ta-bolsky, J. Colloid. Sci., vol. 7, p. 556' 7952.) Over a limited temperature range, from Tg to Tg + 100°C, the I following universal function for the shift factor a(T) for all glassy polymers is found to exist: ~17.4(T _ T loga(T) = g) , —~————~ (v1.17) » t - 51.6 + (T -ITg) ‘ where the temperatures are given in degrees centigrade. Equation (V1.17) is known as the WLF (Williams—Landel-Ferry) equation.'l' The WLF equation was originally determined empirically. W CW Mot thug QWH ~§3mcxiw 7cm“ P H M 1": Caggmggfg M +0 V g F {,1}; & lfifim‘rifitiéf gm“ W WM, D I}; W M @th 2 WWW ) Shift factor for PMMA W40 60 80 Temoem’rure (°C) La) kmwzwm» [21/th “A support rod in a boiler carries a constant tensile stress of 10,000 psi. If the. rod is made from the medium-carbon’steel for which creep data are given in Fig. VII.3, .What is the expected lifetime for the rod before it elo ~~~50 n§ates 10%? l Maw I Ann‘s I_- The operating temperature of the boiler is IOOOOF. Strain rate (hr-'l IO 0 EA . 55 so 65 ZO~«\ZS ‘ao "85xl0 Reciprocal temperature , I/T ‘( R Fig. Vl|.3 Creep rate for medium-carbon forged5steel. (Data from Ref. 7, p. 636..) . V ; I TABLE Vil.1 Boltzmann's Constant . g3, k = 1.38 X 10'16 erg/OK .=1.38 X 10‘23 Joule/OK =&Mle5€NFK=&leW”hmmFR “X Nets ‘é'l/ml- the Wm; 552 We? as? was vaklfiefl é” g; £639 3 . T ‘ ' WWOW‘EM I W e VEEEDQG/‘ij KT “ _, _ i m}? . ,I, J?” i I {AM {gamma 11-1 mm, wafflxiimfim M Ma; Rama me M? w {7% mfimmaflfi (3”! {Lug C »m Maia, . fem-Wm! L 617 FM? am gmmmw fl if \ m \ 6 cf" gaff? Q“, g " 0mm" a’g‘mmg’ "fig/5M 3; 755"; M m“ gm“? WW WW1; v - .21" (5 NHL 44) ‘ngf Y5 5" m. “g *E” 1;; h ) W V e? m. a, m 4,9 Jfiweyw. afflflvfxfiw {M 051/5413.) {fl REM. OWMW ka’www’mfl Mm 5mm? (him i w Wfi mm W mfg-wwwgimir if W 02"!” E} 3 {’W’Q’C": Wfiil‘mfi CL 3 g («man ngm mm L Zr ' , a r . ~ , 4? ’2” 1M fig“? Wu ‘3’ c- ...
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This note was uploaded on 12/05/2011 for the course MSE 4020 at Cornell University (Engineering School).

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4020-F-2011-HW-13 (1) - HSE Wt? \F- 20H @. Creep modulus...

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