Do all Probfems(1 05/1 00 Total Points)(1 extra credit for 10 points)Write your answers below the question on this paper. lf extra room isrequired use the back of the page on which a specific questionresides.8-1 (1 0 pts) a) Using a stress-strainhardening means.diagram, €xplain what "strainExam 2a Name: f{ €.vMSEG 302IAv)Q)t{(ho(nIcn(e)(d). tjgr* .$ . Development of strain hardening from the stress_strain diagram. (a) A specimen isstressed beyond th" ri"1d,_r!lg,ngtl, before th-e .ii.r. L iurirro tb) Now the specimen has ah igher yield strength and tensi te-strength, Ori f"*"i O,.iiiiiy. rc, by repeatt ng the procedure, thestrength continues to increase.and ttri or.iiritv.ontin-ri.io o""r""r. untir the aloy becomesvery brittle' (d) Note the-total^strain ano ttr-e ttjitrc itiii-n-L.ou"rv read to remnant prastic strainand (e) if tustration of sprin-gback. fsor*, n"giiiJ iiffineering Matriats t, S&ond Edition, M.F.Ashbey, and D.R.H. Jone, ti . cowtjst?t:t:) l6xiii"dElln"r*"rn. Reprin4d with pemisionfrcm Elsevier Science.)b) Explain why many metallic materials exhibit strain hardening.We obtain strengthening during deformation of a metallic material by increasingthe number of dislocations. Before deformation, the dislocation density is about106 cm of dislocation line per cubic centimeter of metal - a relatively smallconcentration of dislocations. When stress that is greater than the yield strengthis applied dislocations begin to slip. The dislocation density may increase toabout 10" cm of dislocation line per cubic centimeter of metal during strainhardening. The result is an increased strength, but reduced ductility, formetallic materials that have undergone cold working or work hardening.grotatPermanent plastic detbrmation9-2 (10 pts) Suppose that liquid nickel is undercooled untilhomogeneous nucleation occurs. Calculate(a) the critical radius of the nucleus required, and(b) the number of nickel atoms in the nucleus.Assume that the lattice parameter of the solid FCC nickel is 0.356 nm.AT'ar-98ot^ + - a lzSlrrr;' f/."Y,"51+2") ffif ^= @i/soff =l6,tosx,o c,n^JQo-'o,A|Lo nnV = qoS= Ll, 5il8,t/o-2t c*7Vnucler,.S = (qrr/sY 6,Varl0-sc-\3 = l.Zjz xlp-2r o^lNurrnbe/- o4 rrrni* cells' ( r, zr z rto-'t\f(q,s t,fr nto-tt) = /-),\A"lrvms ?r, n{rc\q-us s (q gt-hs/o',/*t\421 ,} c,ettil sf oq crtun'ugf = [2 orr Tlny[AHr AT]Tm 6(K) =273 + Tm(C)TABLE 8-1 I Valuet tor freezing temperature, latent heat af fusion, surtace efisg, and maximamrrndalrcnlling for sr,lrlr;ted materialsFreezingTemperature(T*I$olid'LiquidInlerfacialEneryy(osr)Typical Unducoulingfor Homogsneou$llucleation(Ar)Heat offusion6tr)Metalt'c)(J/cm3){l/cm2)('c)GaBiPbAgCuNiFeNaClCsClHe07690BO250236480420169152404BB5432379651628275617373027132796210851453I 538801645056 x l0-i54 x 10-733 x 10-7126 x 10*7177 x l0*7255 x 10-72M x 10-710-g (10 pts) Write down the Gibbs Phase rule, assuming temperatureand pressure are allowed to change. Explain clearly the meaning of eachterm.2+C * f +pl= *)r nuvnbr of ch,rnicarry inAaganderr* anpnefis ,uruattyatarnar{s or con^Porrn*S, i" -tht Sys{crrF = *),..c- nuiyrb<, o* deqnes o{ .€neodffi , or *Le num9.."'a*rJariabbs (sr^ch as i'e."rEe+^'ar !resstara or co"nposHion),*hat ara a\loh,sA Jo chanlp indegendrr'+ly ."lilh6s6fCM \i n3 -thc- nury\ber s,+ g ha ses i 6 efa,tl ibnu,r, .T : *V nuvn/ o{ pv,aSas pruVyrt>= innpl;ai +h"* bpth *tnryra4ure, anA p*ggE r€ q* aller-rd '{roclvnly,ftl--\!10-4 (10pts) Determine the liquidus temperature, solidus temperature,and freezing range for the following NiO-MgO ceramiccompositions,(a) NiO-30 mol% MgO(c) NiO-60 trrolo/o MgODraw the lines you use to estimate the answers on the figure.dilAAJL = 7-77CI*cT L= ?Lt{s& nCTL= 26fo*cTr 3 ?r?0KT** Ltf,fiofl FK = 180?T$*3e$*o* Fffi* 2to'cT*s ]}S#sC FR * l'40t"L 3 atu t#sdfflsIfr:'L60A5r\../gErFlHEfl2600?AOOMole percentMg0(b) NiO-45 mol% MgO(d) NiO-85 mol% MgO(b)11-5 (20 pts) Gonsider a Pb-l5% Sn alloy. During solidification,determine:the composition of the first solid to formthe liquidus temperature, solidus temperature, solvus temperature,and freezing range of the alloythe amounts and compositions of each phase at 260eCthe amounts and compositions of each phase at 183eCthe amounts and compositions of each phase at 25eCt,/, 5nl-Ar*idu$# 3-q#o{,Soi idus ' ZLlsoC5r;luuS * t?{:*(4l"s-a?,T ranyn t $n*eL'.jrr'f Sn d- ,, lZ,!,Srt,/,L5 Ws(til#/,s lTY,3n *17 ',r/. d *. qE-/,J lf /.5* fm,-p:d ft{et: ,f f,5n Srfou.y' Sn/ d-I -ff$l{fs*} =&71'/,ei" 13ya)b)c)d)e)dililh*-*1pg# zoo{u€)*q)FJlrcrcin un<lcrlicense.p11-6 (10 pts) Consider the binary phase diagram in the figure. ldentify allof the three-phase eutectic and eutectoid reactions that occur. Givetemperature, reaction and type.t tSo " C . n is rlz.clSo,-., oCcars ct I s I' I$+ L Y ?u'i*ec4i(AZD oC : -i*h;g r e. *^c.ln cra sC fr*q-r -f on * tlD y, ffiL; *tr # + tL r.-\#,*0*ss**-'i'g}tp*o C 1 T14 r' g [^* a e &i ern # {: {-{.a,"f*t 'S*t'* trp;-rr*er.hoi&e+fi -'-.+ /Ar 20$I EK}S:fJ;. s0$li.r5'{dcftlHHg 6${}{)t'*40s?s*15,>"{ ',q Sguf 'ah, s, ( ,il. a e" Sr pnL h-b V Ffilht s f aarTron\-l oL +Fc.* ?$'/, fifl ra -t gc*F c-ce* 2rS '/, ts€ur tecttliA*((- w sO C (. *4,,f SFercenf F15-7 (10 pts) Plastic deformation due to dislocation motion is important inmetals; however, this is not a very important consideration for theproperties of ceramics and glasses. Explain.Ceramics contain dislocations and can even be strain-hardened to a small degree.However, dislocations in ceramics are normally not very mobile. Polycrystallineceramics also contain porosity. As a result, ceramics behave as brittle materials andsignificant deformation and strengthening by cold working are not possible. Likewise,covalently bonded materials such as silicon (SD are too brittle to workhardenappreciably. Glasses are amorphous and do not contain dislocations and thereforecannot be strain hardened.MSD-8 (10 pts): Materials Section for Design Screening and RankingDescribe the 4 basic steps for materials selection1. Translation of design requirements into a material specification2. Screening out materials that fail constraints3. Ranking by ability to meet objectives; material indices4. Search for supporting information for promising candidates16-9 (15 points)a) Explain why the degree of polymerization ls not usually used tocharacterize thermosetting polymers?b) Explain the term "glass transition" or Tn. ls this a fixed temperature fora given composition of ceramic or polymer glass?Degree of polymerization is the