Presentation on theme: "Chapter 6: Mechanical Properties"— Presentation transcript:
1 Chapter 6: Mechanical Properties ISSUES TO ADDRESS...• Stress and strain: What are they and why arethey used instead of load and deformation?• Elastic behavior: When loads are small, how muchdeformation occurs? What materials deform least?• Plastic behavior: At what point does permanent deformation occur? What materials are most resistant to permanent deformation?• Toughness and ductility: What are they and howdo we measure them?
2 Elastic Deformation d F F d 1. Initial 2. Small load 3. Unload bondsstretch3. Unloadreturn toinitialFLinear-elasticElastic means reversible!Non-Linear-elasticd
3 Plastic Deformation (Metals) 1. Initial2. Small load3. UnloadplanesstillshearedFdelastic + plasticbondsstretch& planesshearplasticFdlinearelasticplasticPlastic means permanent!
4 Engineering Stress s = F A F t s = A m N or in lb • Tensile stress, s: original areabefore loadings=FtAo2fmNorinlbArea, Ao• Shear stress, t:Area, AoFts=Ao Stress has units: N/m2 or lbf /in2
5 Common States of Stress • Simple tension: cableAo= cross sectionalarea (when unloaded)Fos=FAsSki lift (photo courtesy P.M. Anderson)• Torsion (a form of shear): drive shaftMAo2RFscot=FsANote: t = M/AcR here.
6 OTHER COMMON STRESS STATES (i) • Simple compression:AoBalanced Rock, ArchesNational Park(photo courtesy P.M. Anderson)Canyon Bridge, Los Alamos, NMos=FANote: compressivestructure member(s < 0 here).(photo courtesy P.M. Anderson)
7 OTHER COMMON STRESS STATES (ii) • Bi-axial tension:• Hydrostatic compression:Fish under waterPressurized tank(photo courtesyP.M. Anderson)(photo courtesyP.M. Anderson)sz> 0qs < 0h
8 Engineering Strain L w e = d L - d e = w q g = Dx/y = tan • Tensile strain:d/2Low• Lateral strain:e=dLo-deL=wodL/2• Shear strain:q90º90º - qyxg = Dx/y = tanStrain is alwaysdimensionless.Adapted from Fig. 6.1(a) and (c), Callister & Rethwisch 8e.
9 Stress-Strain Testing • Typical tensile test machine• Typical tensile specimenAdapted from Fig. 6.2,Callister & Rethwisch 8e.gaugelengthspecimenextensometerAdapted from Fig. 6.3, Callister & Rethwisch 8e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.)
10 Linear Elastic Properties • Modulus of Elasticity, E:(also known as Young's modulus)• Hooke's Law:s = E esLinear-elasticEeFsimpletensiontest
11 Poisson's ratio, n eL e -n e n = - • Poisson's ratio, n: Units: metals: n ~ 0.33 ceramics: n ~ 0.25 polymers: n ~ 0.40Units:E: [GPa] or [psi]n: dimensionless > density increases < density decreases (voids form)
12 Mechanical Properties Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metalAdapted from Fig. 6.7,Callister & Rethwisch 8e.
13 Other Elastic Properties simpletorsiontestMtGg• Elastic Shearmodulus, G:t = G g• Elastic Bulkmodulus, K:pressuretest: Init.vol =Vo.Vol chg.= DVPP = -KDVo• Special relations for isotropic materials:2(1 + n)EG=3(1 - 2n)K
14 Young’s Moduli: Comparison GraphiteCeramicsSemicondMetalsAlloysComposites/fibersPolymers0.280.61Magnesium,AluminumPlatinumSilver, GoldTantalumZinc, TiSteel, NiMolybdenumGraphiteSi crystalGlass-sodaConcreteSi nitrideAl oxidePCWood( grain)AFRE( fibers)*CFREGFRE*Glass fibers onlyCarbonfibers onlyAramid fibers onlyEpoxy only0.40.824610001200TinCu alloysTungsten<100><111>Si carbideDiamondPTFEHDPLDPEPPPolyesterPSPETCFRE( fibers)FRE( fibers)*FRE(|| fibers)*E(GPa)Based on data in Table B.2,Callister & Rethwisch 8e.Composite data based onreinforced epoxy with 60 vol%of alignedcarbon (CFRE),aramid (AFRE), orglass (GFRE)fibers.109 Pa
15 Useful Linear Elastic Relationships • Simple tension:• Simple torsion:a=2MLor4GM = moment= angle of twist2roLod=FLoEAdL=-nFwoEAFAod/2LLow• Material, geometric, and loading parameters allcontribute to deflection.• Larger elastic moduli minimize elastic deflection.
16 Plastic (Permanent) Deformation (at lower temperatures, i.e. T < Tmelt/3)• Simple tension test:Elastic+Plasticat larger stressengineering stress, sElasticinitiallypermanent (plastic)after load is removedepplastic strainengineering strain, eAdapted from Fig. 6.10(a),Callister & Rethwisch 8e.
17 Yield Strength, sy y = yield strength sy • Stress at which noticeable plastic deformation hasoccurred.when ep = 0.002tensile stress,sengineering strain,esyep= 0.002y = yield strengthNote: for 2 inch sample = = z/z z = inAdapted from Fig. 6.10(a),Callister & Rethwisch 8e.
18 Yield Strength : Comparison Graphite/Ceramics/SemicondMetals/AlloysComposites/fibersPolymersYield strength,sy(MPa)PVCHard to measure,since in tension, fracture usually occurs before yield.Nylon 6,6LDPE7020406050100103020030040050060070010002000Tin (pure)Al(6061)aagCu(71500)hrTa(pure)TiSteel(1020)cd(4140)qt(5Al-2.5Sn)WMo (pure)cwHard to measure,in ceramic matrix and epoxy matrix composites, sincein tension, fracture usually occurs before yield.HDPEPPhumiddryPCPETRoom temperature valuesBased on data in Table B.4,Callister & Rethwisch 8e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & tempered
20 Tensile Strength, TS TS engineering stress strain engineering strain • Maximum stress on engineering stress-strain curve.ystrainTypical response of a metalF = fracture orultimatestrengthNeck – acts as stress concentratorengineeringTSstressengineering strainAdapted from Fig. 6.11, Callister & Rethwisch 8e.• Metals: occurs when noticeable necking starts.• Polymers: occurs when polymer backbone chains arealigned and about to break.
21 Tensile Strength: Comparison Si crystal<100>Graphite/Ceramics/SemicondMetals/AlloysComposites/fibersPolymersTensilestrength, TS(MPa)PVCNylon 6,6101002003001000Al(6061)aagCu(71500)hrTa(pure)TiSteel(1020)(4140)qt(5Al-2.5Sn)WcwLDPEPPPCPET203040200030005000GraphiteAl oxideConcreteDiamondGlass-sodaSi nitrideHwood( fiber)wood(|| fiber)1GFRE(|| fiber)( fiber)CFREAFRE( fiber)E-glass fibAramidfibRoom temperature valuesBased on data in Table B.4,Callister & Rethwisch 8e.a = annealedhr = hot rolledag = agedcd = cold drawncw = cold workedqt = quenched & temperedAFRE, GFRE, & CFRE =aramid, glass, & carbonfiber-reinforced epoxycomposites, with 60 vol%fibers.
22 Ductility x 100 L EL % - = • Plastic tensile strain at failure: Lf Ao Adapted from Fig. 6.13, Callister & Rethwisch 8e.Engineering tensile strain, eEngineeringtensilestress, ssmaller %ELlarger %ELLfAoAfLo• Another ductility measure:100xARA%of-=
23 Toughness • Energy to break a unit volume of material • Approximate by the area under the stress-strain curve.very small toughness(unreinforced polymers)Engineering tensile strain, eEngineeringtensilestress, ssmall toughness (ceramics)large toughness (metals)Adapted from Fig. 6.13, Callister & Rethwisch 8e.Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy
24 Resilience, Ur 2 1 U e s @ Ability of a material to store energy Energy stored best in elastic regionIf we assume a linear stress-strain curve this simplifies toyr21Ues@Adapted from Fig. 6.15, Callister & Rethwisch 8e.
26 Hardness • Resistance to permanently indenting the surface. • Large hardness means:-- resistance to plastic deformation or cracking incompression.-- better wear properties.e.g.,10 mm sphereapply known forcemeasure sizeof indent afterremoving loaddDSmaller indentsmean largerhardness.increasing hardnessmostplasticsbrassesAl alloyseasy to machinesteelsfile hardcuttingtoolsnitrideddiamond
27 Hardness: Measurement RockwellNo major sample damageEach scale runs to 130 but only useful in rangeMinor load kgMajor load (A), 100 (B) & 150 (C) kgA = diamond, B = 1/16 in. ball, C = diamondHB = Brinell HardnessTS (psia) = 500 x HBTS (MPa) = 3.45 x HB
29 True Stress & Strain Note: S.A. changes when sample stretched True strainAdapted from Fig. 6.16, Callister & Rethwisch 8e.
30 ( ) Hardening s e s s • An increase in sy due to plastic deformation. large hardeningsy1sysmall hardeninge• Curve fit to the stress-strain response:sT=Ke()n“true” stress (F/A)“true” strain: ln(L/Lo)hardening exponent:n =0.15 (some steels)to n =0.5 (some coppers)
31 Variability in Material Properties Elastic modulus is material propertyCritical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability.StatisticsMeanStandard DeviationAll samples have same valueBecause of large variability must have safety margin in engineering specificationswhere n is the number of data points
32 Design or Safety Factors • Design uncertainties mean we do not push the limit.• Factor of safety, NOften N isbetween1.2 and 4• Example: Calculate a diameter, d, to ensure that yield doesnot occur in the 1045 carbon steel rod below. Use afactor of safety of 5.1045 plaincarbon steel:sy= 310 MPaTS = 565 MPaF = 220,000NdLo5d = m = 6.7 cm
33 Summary • Stress and strain: These are size-independent measures of load and displacement, respectively.• Elastic behavior: This reversible behavior oftenshows a linear relation between stress and strain.To minimize deformation, select a material with alarge elastic modulus (E or G).• Plastic behavior: This permanent deformationbehavior occurs when the tensile (or compressive)uniaxial stress reaches sy.• Toughness: The energy needed to break a unitvolume of material.• Ductility: The plastic strain at failure.