Mechanical Properties

Transcription

1 Mchanical Proprtis Elastic dformation Plastic dformation Fractur

2 Mchanical Proprtis: Th Tnsion Tst s u P L s s y ΔL I II III For matrials proprtis, rplac load-dflction by strss-strain Enginring strss, s = P/A Enginring strain, = ΔL/L 0 Mchanical proprtis ar rvald in th tnsion tst I. Elastic bhavior II. Plastic dformation III. Plastic instability and fractur

3 Th Enginring Strss-Strain Curv S s u s y T u I II III For a typical ductil mtal: I. Elastic dformation II. Stabl plastic dformation III. Unstabl dformation IV. Fractur Proprtis masurd: Elastic modulus (slop of lastic curv) Yild strngth (s y ) Ultimat tnsil strngth (s u ) Uniform longation ( u ) Total longation ( T ) Rduction in ara (R A = [A 0 -A f ]/A 0 )

4 I. Elastic Dformation s u s sy u T I II III For a typical ductil mtal: I. Elastic dformation II. Stabl plastic dformation III. Unstabl dformation IV. Fractur Strss-strain rlation is linar (Hook s Law) s s = E Strain is rcovrabl rlaxation along th load lin to zro strss

5 II. Stabl Plastic Dformation s sy For a typical ductil mtal: I. Elastic dformation II. Stabl plastic dformation III. Unstabl dformation IV. Fractur s 0.2% p Strss-strain rlation is non-linar Strain is non-rcovrabl Rlaxation is lastic prmannt plastic strain Strain is uniform and stabl - work hardning Plasticity initiats at yild strngth, s y In ductil matrial, s y is not obvious s y is usually dfind by 0.2% offst strain Yild strngth = strss that producs a plastic strain of 0.2%

6 III. Ultimat Tnsil Strngth s s u sy u T I II III For a typical ductil mtal: I. Elastic dformation II. Stabl plastic dformation III. Unstabl dformation IV. Fractur P P L P P L Enginring strss is maximum at s u = ultimat tnsil strngth At s u plastic dformation bcoms unstabl Strain localizs in a nck in th lngth of th spcimn Undr load control, sampl fails at s u Undr strain control sampl longats at lowr load until failur Two common masurs of tnsil strain Uniform longation - u - to ultimat strngth Total longation - T - to fractur (dpnds on gag lngth )

7 Forms of th Enginring Strss-Strain Curv s u sy s u T I II III s Ductil mtal Yild point su su s Brittl solid Elastomr

8 Tru Strss and Strain P P Tru strain is dfind from its diffrntial L L P P V = constant (plastic dformation): V = A 0 L 0 = AL dv = 0 = AdL + LdA ε = dε = dl L = da A L dl L ε = ln L L = ln A 0 A 0 L 0 ε = ln ΔL +1 ε = ln 1+ L 0 ( ) (L/L 0 ) applis whn strain is uniform (A 0 /A) can b usd for non-uniform strain dl L = da A = nginring strain = ΔL L 0 = L L 0 1 Tru strss σ = P A = P A 0 = s L A 0 A L 0 σ = s(1+ )

9 Strss-Strain Rlations ß f Strss-strain rlations ß ß y σ = s(1+ ) ε = ln(1+ ) f s = σ xp( ε) = xp(ε) 1 s u strsss qual for small strain s sy I II III Why us nginring curv? Clarly shows tnsil strngth s u is an important dsign valu No diffrnc in E, s y =σ y

10 Influnc of Tmpratur on Strngth ß y T/T m Thr rgims: Dcras in strngth with T at low T/T m Rlativly constant strngth at intrmdiat T Rapid loss of strngth as T approachs T m Incrasing strain rat is lik dcrasing T Larson-Millr paramtr: T* = Tln(d/dt)

11 High Tmpratur Crp III: n=4-9, Q=Q D ln( γ ) ln( ε ) II: n=2, Q=Q GB I II III I: n=3, Q=Q D t Crp is dformation undr constant load Primary crp Stady stat Trtiary crp to fractur Thrmally activatd procss Stady stat strain rat govrnd by Dorn quation ln(τ) ln(σ) ε = Aσ n xp Q kt

12 Fractur P P L P P L Fractur may rsult from: Elastic instability (buckling, fluttr) Plastic instability (ncking) Crack instability (fractur) Propagation of pr-xisting flaw ß ß a ß T Crack instability Du to strss concntration at crack tip Critical strss rquird to driv crack a r ßa σ c Q 1 K Ic a (Q -1 = gomtric factor) ßa K ic = plan strain fractur toughnss = matrial proprty govrning fractur

13 Th Influnc of Tmpratur on Toughnss Ductil-brittl transition Prominnt in bcc mtals High toughnss, ductil at T>T B Low toughnss, brittl at T<T B T B nar room T in common stls Th transition tmpratur T B Incrass with strngth (s y ) Incrass with strain rat (impact) Incrass with thicknss (constraint)

14 Fatigu Fractur undr cyclic load s s u s l sm s -sm t Fatigu cracks Nuclat Grow to critical siz Propagat to failur Evn at s < s y log(n) Mchanism Cyclic plastic dformation No obvious sign of growth

15 Strss Corrosion Cracking s s u s c Crack Grows by corrosion Rachs critical siz Propagats to failur May caus catastrophic failur No obvious sign of growth t

16 Mchanical Proprtis Elastic dformation Plastic dformation Fractur

17 I. Elastic Dformation S s u s y u T I II III For a typical ductil mtal: I. Elastic dformation II. Stabl plastic dformation III. Unstabl dformation IV. Fractur Strss-strain rlation is linar (Hook s Law) s = E Strain is rcovrabl rlaxation along th load lin to zro strss S

18 Importanc of Elastic Bhavior Enginring dsign Most structurs ar dsignd to rmain blow yild For xampl, s < s y /3 (boilr and prssur vssl cod) s << s y (turbin blads, springs) Elastic failur Utlimat strngth Buckling Fluttr Bridgs, othr structurs Aircraft

19 Th Tnsil Moduli: Young s Modulus and Poisson s Ratio L 0 (1+ z ) D 0 (1+ y ) Assum isotropic matrial Nd two lastic moduli, E and ν Young s modulus: s z = E z Poisson s ratio: x = y = ν z Volum chang: (E = Young s modulus) (ν = Poisson s ratio) ΔV V 0 = (1+ x )(1+ y )(1+ z ) [ ] 1 x + y + z [ ] ΔV V 0 = z (1 2ν)

20 Multiaxial Dformation uniaxial tnsion hydrostatic prssur simpl shar balancd shar Linar lastic strsss ar additiv s x = x = 1 [ E s x ν(s y + s z )] E (1 2ν)(1+ ν) (1 ν) x + ν( y + z ) [ ] Gt y, z, s y, s z by intrchanging x, y, z.

21 Th Physical Moduli: Bulk and Shar Moduli uniaxial tnsion hydrostatic prssur simpl shar balancd shar Fundamntal proprtis ar rflctd in th rspons to Chang of volum (prssur) Chang of shap (shar) E = E 0 (V ) + E conf (E conf from atom arrangmnt at givn V) volum shar bulk modulus (β) shar modulus (G)

22 Physical Basis of Elastic Moduli comprssion E = ν = shar 9βG (G + 3β) 3β 2G 2(G + 3β) Elastic moduli balanc β = rsistanc to volum chang G = rsistanc to shap chang Four cass: β >> G incomprssibl solid E ~ 3G ν ~ 0.5 β ~ 3G normal mtal E ~ 2.7G ν ~ 0.35 β ~ G strong dirctional covalnt E ~ 2.25G ν ~ β << G bond angls prsrvd E ~ 9 β ν ~ -1 (No natural solid has ν < 0)

23 Enginring th Elastic Modulus Elastic proprtis rflct atomic bonding Microstructur manipulation has littl ffct Small composition changs caus ΔE c(e 2 -E 1 ) On xcption is Li in Al Adding Li to Al E, ρ E significantly Al-(1-2.5)Li alloys of intrst for aircraft Composit matrials High-modulus matrials ar usually brittl Add high-modulus fibr or particl to ductil matrix Combin high modulus with usful toughnss Exampls: Fibrglass (glass-poxy) Graphit-poxy SiC-Al

24 Composit Matrials Fibr: E = E 1 f 1 + E 2 f 2 - stiffr lmnt dominats Particulat: 1 E = f 1 E 1 + f 2 E 2 - softr lmnt dominats Fibr composits: ~ uniform strain ( 1 ~ 2 = ) s = P A = s 1 A 1 A A + s 2 2 = (E A 1 f 1 + E 2 f 2 ) Particulat composits: ~ uniform strss (s 1 ~ s 2 = s) E = E 1 f 1 + E 2 f 2 = ΔL = ΔL 1 L 1 + ΔL 2 L 2 = 1 f f 2 = f 1 + f 2 L 0 L 1 L 0 L 2 L 0 E 1 1 E = f 1 E 1 + f 2 E 2 E 2 s

25 Composit Matrials Fibr: E = E 1 f 1 + E 2 f 2 - stiffr lmnt dominats Particulat: 1 E = f 1 E 1 + f 2 E 2 - softr lmnt dominats Fibr composits: High modulus but dirctional proprtis Us in applications whr loading is uniaxial Or, us 2-d or 3-d configurations Lss dirctionality, but lowr modulus Particulat composits: Lowr modulus ffct, but Mor isotropic Rlativly tough and formabl Usd for multiaxial loads

26 Elastic Failurs Lattic instability Th ultimat strngth of a solid (nanoindntation) Failurs in tnsion and shar ( inhrnt ductil-brittl transition) Buckling Bams and buildings Shts (dnts and crushing in automobils) Vibration and fluttr Bridg failurs (fluttr - Tocoma Narrows) Aircraft (fluttr, whirl mod - th Lockhd Elctra) Hovrcraft (flagllation)