Write your answers to Probfems on this Handout!See Last Page for equations and other needed info! Tear this off as a reference.(12011 00 Total Points)3-1 (1 0 points)EXAilr #1 (A)MSEG 3023t15106Name:Determine the Miller Indices of the planes:u)Draw and index 2 planes that arecrystallographically equivalent rothe shaded plane in A. Use theblank unit cell to draw the planesand list their respective Millerindices below.N(r"dIndex the drawn directionsin the cubic unit cellsl,Or\ ad'O/\,''aFt t, '(--c,o, ol, -[ t'/'(0,0,0)azilrcl?'t33P.ltq4-1 (10 pts) a) what are the three general types of impeffections ordefects in a crystalline materlal? b) Discuss each type.?olnt Da-Stc+a i uMtch in c luds va can cias, ;nkrs-$i *.Jc t o"{,,44 s, <r,&Sc,rb s-{n *q*i .yo\ atws, ,n{*o&tacc LornT"vss;Uq. o. ]<',s;ln s{o,i€ a&t +ha+ d.l s{r"rb r4*- a\n-ri(. q, r r qrtaprnen*s r,-t JA{-St^rrutn$11 3.y *1, Aa- q rc;u l{, dis\o.i+l o',s canp* eos;lv s lipi n *l"rr--)rtftaC-n- [Jq*(ctS '. I.rcl..dt ttrein b.r^nclqri €s " P.od,S'nno.\\ Io.*.^ j*-i,-.-j: st;nr, l;l"ffi{T,} T**",polnf &{rcts o.."A ru s*.e4r71n-ot lo+.t,," naol<.iqr ir inere.p).Linq" Dr$<.+x ( o' D,r l...*h'un$ : br\',\ a{vca. r,s qpfi,,ad -r.r3o\ n"-e'fa[t\ 'a.toltrio\ naovQ.s o,^al Oatrgts or rne*sllic rtclt^,el fodo{".n"'.4'2 (10 pts) Why is the theoretical strength of metals much higher thanthat observed experimentally?b;s \ oca+.i on s Cauin Sl ;? , St;p ar f lqrln so{ rrq+.\\S i5 ftiuc-Vt loa:c, *lno-m+"{tn4 {4\e Aa-+qll,'c borncl. Ifq -1+ny {--achon o{ .r\r nte{-ctric bo^d s q.c,a s si".kr€a C-L f\,tc.A +* b4 brn lc-e-t a+ a{Lyoq.q *-',r44,or'.4 -+4< -6.rc. re 7,^,]nerJ. -{- &*Gr.r" -+LL n".r{* t i sSnnalL,tt"enSrt"p "*Ai c\td\on\y{4a-*hy {d{.-+{q rJ c- lvrAsli/ oo.-s,,?5L5-2 (10 pts) A lmm thick by 100 cm x 100 cm sheet of iron is used tocontain nitrogen in a heat exchanger at 1200C. The concentration on theinside is 15 x 10E N2 atoms/cmt. The outside concentration is 1 x ro6 -atom/cm3. Assume that the heat exchanger has been in operationalcontinuously.a) Galculate the concentration gradientb) Calculate the diffusion coefficientc) Calculate the flux.d) Calculate the totalnumbqr of atoms per unit timei x lO6a\r.rrs Ne &^t- l5 x IOB a{}nn r N z, /c*3\Acq\ &=-.-l,V Y iOro a-bq.4f{i; u, crv]O, i Gn"ril D =bo q*r[: izoouc(- e/er\= lq-7i KGd.eaX\ 4rFIICIU-J=hb r- (0" s03qqeyr.z/*-\ erFtu,boc /C(r.qsilrqrr))D 3 2.50 xl0*8 crn\*,_Dz.So xlD I e^Trsc[,Ll xlOto tbf t nt"\C^3'cYt, )lrhtrns / +rhq. =-lx kreqz3SO 1T:it" x \oocrn x lort crhCnrr2'g{= 35o #?sz5-3(10 pts) consider Ficks 2nd Law for a semi-infinite slab. The surfaceis subjected to a gas with concentration C" of atoms that wilt diffuseinto the slab. The slab does not have any initial concentration ofthese atoms. The diffusion coefficient otihis gas into the slab is 4x10'15cm?s at 1150oG. After thr (s600s) the dJsired concentrationprofile has been achieved.a) Write down boundary and initial conditionsb) sketch the evolution of the concentration gradientsc) How long will it take to aehleve the same c-oncentration profileat 1715oG if the diffusion coefficient is 6x10-11 cm?s"\Tni.4te,t Co"dr+on\ :Co =O(s = C'ons{qnt$ oh^d*7 Cri-,dt'lt{ o"E l34t ri - J.n$;""{e s\ebCw=O-riltt , = I)z.tz( q x f o - l rc,*' 7t\ (S (g Co t)=pgr+Dis4on@, x6-4 (1Opts) A 850.1b force is applied to a 0.1S-in. diameter nickel wirehaving a yield strength,of 4s,000 psi and a tensite strength of s5,000 psi.Determine (a) whether the wire will plastically deform anA 6; whether thewire will experience necking...r- = F/a = ?5o tb'/cnlrr\Co'tr)z = QE,too f s;A &.or5" s.- i s lnco{tr *|,a,-r t\[ y O i lA S+'vn${n of c{ q o00 /"i ,tLa t^lir\c uriti plas-ficofiy oU-h.rn. (YESb\ Bocau:r' 0'- is \oss J'tae', *t'. &,,ntJta t*"tn$'la of 5s u'oP"j)ns fucbi,+5 r^rit\ occ{-^,r. ( ruO\(10pts) A polymer bar's dimensions are 1 in.4 2 in.4l5 in. long. Thepolymer has a modulus of erasticity of eoo,oob p"i. wn"t force isrequired to stretch the bar elasticaily to tS.ZS iri.eS+a,{n € = ( ls,zr -rs) /,r =o,a3 tGbl3*"e.rs r = EG = (bcro,ooo p*;)Co,otour\ = lo,0oorosifi>rcr, F =trA = (rc,ooo Pt;Y z;^)( t ;.) = Zs,ooo tb.6-5?556'6 (10 pts) The following data were collected from a standard 0.505 in.diameter test specimen of a copper alloy (initial length (lo) = 2.0 in.):Load(tb)03,0006,0007,5009,00010,50012,00012,40011,400Gage Length Stress(in.) (psi)2,00000 02.00167 l sroors2.00333 70 to0o.0041T Ba t f?o2.0090 QS,Doo3'.2t0 lt,ffi:2.50 (max load) bz,otlo3.O2 (fracture) 6"7,11119EngineeringStrain(in./in.)o,oO,()c>o?3;;O"Cr9 llskS-65r,0OZOSfo'coqr0,t)2c), t3ouero,s1 iAfter fracture, the gage length is 3.014 in. and the diameter is 0.374 in.Calculate the engineering stress and strain the table. Plot this data (out to2o/o straln) and calculate(a) tensile strength = (pz,or>o psi(b) modulus of elasticity E o t3qo,p-d/C o,oorrr6f -d) = lt x lD@fs'(c) engineering strain at fracture LA/J6 = o.ff(d) true stress at fracture =,lt,.{rro tU.'/tn/q)(o,zzu)z = lo}, -t7,ops;(e) true strain at fracture = )n (Broa / z) '.'9i U,z fn, /in,-)DboCsDsa\r#iu2DOIDg\<Td\'so;415x588o<i aa-;6d6(i^/,')DESr-'\-=1-eTBo.iEBFBqq<; d'o' o' d o g a$o{a$r*i"b"DZw6Tl'* luXth o{ +t'q in{ezn e\ $a,': s ; s 2o, , o.o rj )n .Ot^r r\on-dlscrtrc*iva .{ts+ Cq^ &{e c} €fa^-s0,c f in.11 t ,Y tftt-'-l S tl*X t (rthichle *qu;^od .i s n.>+ Srnaller +t"Gn +1,LAS Srnell qScri*j e* I7'7 (10 pts) A ceramic matrix composite contains internat flaws as targeas 0.001 cm in length. The plane strain fracture toughness of the compoiiteis 45MPa {m and the tensile strength is 550 MPa. Will the flaw cause thecomposite to fail before the tensile strength is reached? Assume that f = l,Remember the definition of an internal fraw versus surface flaw.?.a..0,OO I crn = O,0O oO lrr\qtO"OOoOOSrnKc""€g'-ffi or tr=' /'r-tc / (Gcr4(un/tn P-16.)l(il(@= ll,3s-z tqP^TI.& agp r;aA S*,e-ss ru7u;rwd, .6. {Lr crccK +D ccruie {eil,,ai s rnuch lara4r * ha^ *h,- fcn sire S Mr .tr. of s go th\a ,F la,^r L^"', ll Nq1- e ausA Lomprcs;le -h" -G;\,7-a (1Opts) A ceramic pan for a Jet engine has a yield strength of 75,000psi and a plane strain fracture toughness of 5,000 psi y' in. To be sure thatthe part does not fail, we plan to assure that the maximum applied stress isonly one third the yield strength. We use a nondestructive test that willdetect any internal flaws greater than 0.0s in. long. Assuming that f = 1.4,does our nondestructive test have the required sensitivity? Explain.Cf r ('zr)(:S,o00 ps;\ = j Eooo pria