Chapter 8: Mechanical Properties of Metals

1 Chapter 8 -AMSE 205 Spring 20161 ISSUES TO Stressand strain: What are they and why arethey used instead of load and deformation? Elasticbehavior: When loads are small, how much deformation occurs? What materials deform least? Plasticbehavior: At what point does permanent deformation occur? What materials are most resistant to permanent deformation? Toughnessand ductility: What are they and howdo we measure them? Chapter 8: Mechanical Properties of Metals Chapter 8 -AMSE 205 Spring 20162 Elastic means reversible!Elastic Deformation2. Small loadF bonds stretch1. Initial3. Unloadreturn to initialF Linear-elasticNon-Linear-elasticChapter 8 -AMSE 205 Spring 20163 Plastic means permanent!Plastic Deformation ( Metals )F linear elasticlinear elastic plastic1.

2 Initial2. Small load3. Unloadplanesstill shearedF elastic + plasticbonds stretch & planes shear plasticChapter 8 -AMSE 205 Spring 20164 Stress has units:N/m2 Engineering Stress Shearstress, :Area, AoFtFtFsFFFs =FsAo Tensilestress, :original cross-sectional area before loading =FtAom2N=Area, AoFtFtChapter 8 -AMSE 205 Spring 20165 Simpletension: cable Common States of Stresso =FAo =FsA MMAo2 RFsAc Torsion(a form of shear): drive shaftSki lift(photo courtesy Anderson)Ao= cross-sectional area (when unloaded)FF Chapter 8 -AMSE 205 Spring 20166(photo courtesy Anderson)Canyon Bridge, Los Alamos, NMo =FA Simplecompression:Note: compressivestructure member( < 0 here).(photo courtesy Anderson)OTHER COMMON STRESS STATES (i)AoBalanced Rock, Arches National ParkChapter 8 -AMSE 205 Spring 20167 Bi-axialtension: Hydrostaticcompression:Pressurized tank < 0h(photo Anderson)(photo Anderson)OTHER COMMON STRESS STATES (ii)Fish under water z> 0 > 0 Chapter 8 -AMSE 205 Spring 20168 Tensilestrain: Lateralstrain:Strain is Strain Shearstrain: 90 90 - y x = x/y= tan = LoAdapted from Fig.

3 (a) and (c), Callister & Rethwisch 9e. /2 Lowo- L=Lwo L/2 Chapter 8 -AMSE 205 Spring 20169 Stress-Strain Testing Typical tensile test machineFig. , Callister & Rethwisch 9e.(Taken from Hayden, Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.)specimenextensometer Typical tensile specimenFig. ,Callister & Rethwisch 8 -AMSE 205 Spring 201610 Linear Elastic Properties Modulus of Elasticity, E:(also known as Young's modulus) Hooke's Law: = E Linear-elasticE FFsimple tension testChapter 8 -AMSE 205 Spring 201611 Poisson's ratio, Poisson's ratio, :Ratio between radial and axial strainsUnits:E: [GPa] or [psi] : dimensionless > density increases = no volume change < density decreases (voids form) L - =-L Metals : ~ : ~ : ~ 8 -AMSE 205 Spring 201612 Mechanical Properties Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metalFig.

4 , Callister & Rethwisch 8 -AMSE 205 Spring 201613 Elastic Shearmodulus, G: G = G Other Elastic PropertiessimpletorsiontestMM Special relations for isotropic materials:2(1+ )EG= Chapter 8 -AMSE 205 Spring 201614 MetalsAlloysGraphiteCeramicsSemicondPoly mersComposites/fibersE(GPa)Based on data in Table ,Callister & Rethwisch data based onreinforced epoxy with 60 vol%of alignedcarbon (CFRE),aramid (AFRE), orglass (GFRE) s Moduli: ,AluminumPlatinumSilver, GoldTantalumZinc, TiSteel, NiMolybdenumGraphiteSi crystalGlass -sodaConcreteSi nitrideAl oxidePCWood( grain)AFRE( fibers) *CFRE*GFRE*Glass fibers onlyCarbon fibers onlyAramid fibers onlyEpoxy alloysTungsten<100> <111>Si carbideDiamondPTFEHDPELDPEPPP olyesterPSPETCFRE( fibers) *GFRE( fibers)*GFRE(|| fibers)*AFRE(|| fibers)*CFRE(|| fibers)* Chapter 8 -AMSE 205 Spring 201615(at lower temperatures, T< Tmelt/3)Plastic (Permanent) Deformation Simple tension test:engineering stress, engineering strain, eElastic+Plastic at larger stress pplastic strainElastic initiallyAdapted from Fig.

5 (a),Callister & Rethwisch (plastic) after load is removedChapter 8 -AMSE 205 Spring 201616 Stress at which noticeableplastic deformation p= Yield Strength, y y= yield strengthNote: for 2 inch sample = = z/z z= inAdapted from Fig. (a),Callister & Rethwisch stress, engineering strain, e y p= 8 -AMSE 205 Spring 201617 Typical stress-strain behavior for a metalTypical stress-strain behavior for steelsChapter 8 -AMSE 205 Spring 201618 Room temperaturevaluesBased on data in Table ,Callister & Rethwisch = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & temperedYield Strength : ComparisonGraphite/ Ceramics/ SemicondMetals/ AlloysComposites/ fibersPolymersYield strength, y(MPa)PVCHard to measure, since in tension, fracture usually occurs before 6,6 LDPE702040605010010302003004005006007001 0002000 Tin (pure)Al(6061)aAl(6061)agCu(71500)hrTa (pure)Ti (pure)aSteel(1020)hrSteel(1020)cdSteel(4 140)aSteel(4140)qtTi ( )aW (pure)Mo (pure)Cu(71500)cwHard to measure, in ceramic matrix and epoxy matrix composites, sincein tension, fracture usually occurs before Chapter 8 -AMSE 205 Spring 201619 Tensile Strength, TS Metals :occurs when noticeable neckingstarts.

6 Polymers:occurs when polymer backbone chainsarealigned and about to from Fig. , Callister & Rethwisch 9e. ystrainTypical response of a metalF= fracture or ultimate strengthNeck acts as stress concentratorengineering TSstressengineering strain Maximum stress on engineering stress-strain 8 -AMSE 205 Spring 201620 Tensile Strength: ComparisonSi crystal<100>Graphite/ Ceramics/ SemicondMetals/ AlloysComposites/ fibersPolymersTensilestrength, TS(MPa)PVCN ylon 6,6101002003001000Al(6061)aAl(6061)agCu( 71500)hrTa (pure)Ti (pure)aSteel(1020)Steel(4140)aSteel(4140 )qtTi ( )aW (pure)Cu(71500)cwLDPEPPPCPET203040200030 005000 GraphiteAl oxideConcreteDiamondGlass-sodaSi nitrideHDPE wood ( fiber)wood(|| fiber)1 GFRE(|| fiber)GFRE( fiber)CFRE(|| fiber)CFRE( fiber)AFRE(|| fiber)AFRE( fiber)

7 E-glass fibC fibersAramid fibBased on data in Table B4,Callister & Rethwisch = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & temperedAFRE, GFRE, & CFRE =aramid, glass, & carbonfiber-reinforced epoxycomposites, with 60 vol% temperaturevaluesChapter 8 -AMSE 205 Spring 201621 Plastic tensile strain at failure :Ductility Another ductility measure:100xAAARA%ofo-=x 100 LLLEL%oof-=LfAoAfLoAdapted from Fig. , Callister & Rethwisch tensile strain, Engineering tensile stress, smaller %ELlarger %EL% elongation% reduction in areaChapter 8 -AMSE 205 Spring 201622 Energy to break a unit volume of material Approximate by the area under the stress-strain fracture: elastic energyDuctile fracture: elastic + plastic energyAdapted from Fig.

8 , Callister & Rethwisch small toughness (unreinforced polymers) Engineering tensile strain, Engineering tensile stress, small toughness (ceramics)large toughness ( Metals ) Chapter 8 -AMSE 205 Spring 201623 Resilience, Ur Ability of a material to store energy Energy stored best in elastic regionIf we assume a linear stress-strain curve this simplifies toFig. , Callister & Rethwisch 9e. yChapter 8 -AMSE 205 Spring 201624 True Stress & changes when sample stretchedAdapted from Fig. , Callister & Rethwisch 8 -AMSE 205 Spring 201625 True stressTrue strainTrue Stress & Strain vs. Engineering Stress & Strain Chapter 8 -AMSE 205 Spring 201626 Hardening Curve fit to the stress-strain response: T=K T()n true stress (F/A) true strain: ln( / o)hardening exponent:n = (some steels) to n = (some coppers) An increase in ydue to plastic deformation.

9 Large hardeningsmall hardening y0 y1 Chapter 8 -AMSE 205 Spring 201627 Elastic Strain RecoveryFig. , Callister & Rethwisch Reapplyload2. UnloadDElastic strainrecovery1. Load yo yiChapter 8 -AMSE 205 Spring 201628 Hardness Resistance to permanently indenting the surface. Large hardness means:-- resistance to plastic deformation or cracking better wear , 10 mm sphereapply known force measure size of indent after removing loaddDSmaller indents mean larger hardnessmost plasticsbrasses Al alloyseasy to machine steelsfile hardcutting toolsnitrided steels diamondChapter 8 -AMSE 205 Spring 201629 Hardness: Measurement Rockwell No major sample damage Each scale runs to 130 but only useful in range 20-100. Minor load 10 kg Major load 60 (A), 100 (B) & 150 (C) kg A = diamond, B = 1/16 in.

10 Ball, C = diamond HB = Brinell Hardness TS (MPa) = x HBChapter 8 -AMSE 205 Spring 201630 Hardness: MeasurementTable 8 -AMSE 205 Spring 201631 Design uncertainties mean we do not push the limit. Factor of safety, NOften and 4 Example:Calculate a diameter, d, to ensure that yield doesnot occur in the 1045 carbon steel rod below. Use a factor of safety of or Safety Factors51045 plain carbon steel: y= 310 MPa TS = 565 MPaF= 220,000 NdLod= m = cmChapter 8 -AMSE 205 Spring 201632 Stressand strain: These are size-independentmeasures of load and displacement, respectively. Elasticbehavior: This reversible behavior oftenshows a linear relation between stress and minimize deformation, select a material with alarge elastic modulus (Eor G).