Block 3 –Materials/Structural IntegrityThree purposes to this block of lectures:1. To allow you to understand limits on stressesthat a structure can carry: 1-D and multiaxial –in order to design2. To allow you to understand the origins (andlimits) of the strength in the different classes ofmaterial –identifying “unobtainium”, origins andlimitations on models for strength3. To allow you to select materials for specificfunctions, understand design process.Note: “Failure” occurs when a structure cannot meetits design requirements. Does not necessarilycorrespond to material “failure” – e.g buckling. We willfocus on material aspects here.Materials can behave in a variety of ways accordingto the loading. Examples:1. a piece of metal wire (paper clip):Can “twang” it – elastic deformationBend it - leading to permanent deformationCyclic loading – rupture into two pieces (fatigue)2. A piece of aluminum foil:Load it up and it “necks down” before fracturePut a notch in it and it tears3. A balloon (pressurized aircraft fuselage)Stick a pin in it and it explodes – catastrophicfailure4. e.g piece of solder wire with a weight hanging fromit under a bright light - creepWe will examine four types of failure in Unified; Yield(ductile failure), Fracture (brittle failure), Fatigue(cyclic loading) and creep (time/temperaturedependent failure) – necessarily brief. Read Ashbyand Jones for more details.M15 Yielding and PlasticityReading: Ashby and Jones ch. 8, 11Characteristic stress-strain curve and materialresponse for a ductile metal under uniaxial loadingUnloading and reloading is elastic, permanent strain:u[Load-extension curve for a bar of ductile metal(e.g. annealed copper) pulled in tension.FFFAF = 0F = 0 F = 0F = 0AoI0FuFF FImage adapted from: Ashby, M. F., and D. R. H. Jones. Engineering Materials 1. Pergamon Press, 1980.Slope ETensionFuReversible elastic deformationPermanent plastic deformationImage adapted from: Ashby, M. F., and D. R. H. Jones. Engineering Materials 1. Pergamon Press, 1980.Most engineering alloys have an initial linear elasticregion followed by yield and non-linear plasticity:Key features of stress-strain response:Yield stress, syTensile strength stsPermanent strain after unloadingLinear elastic unloading-reloadingWork hardening (increasing yield stress withincreasing plastic strain).Image adapted from: Ashby, M. F., and D. R. H. Jones. Engineering Materials 1. Pergamon Press, 1980.snsTSsysnf∈∈Final fractureOnset of neckingsTSTensile strength (Plastic strain after fracture,0.1% Strain0.1%Proof stress0.1%Yieldstrength)Slope is Young's modulus, EUp to now we have not distinguished betweencompressive and tensile response of materials. Needto be careful with large plastic strains:Apparent difference between compression andtension due to increase in cross-sectional area incompression vs. reduction in tension. Modifydefinitions of stress and strain to account for this:Image adapted from: Ashby, M. F., and D. R. H. Jones. Engineering Materials 1. Pergamon Press, 1980.Al0A0CompressionFFF = 0F = 0FuTrue stress,st: Load/actual cross-sectional area: st=F/A (vssnominal =F/A0)True strain,etdefined incrementally:de=dul=dllfi de=dllHence strain developed from an initial length l to afinal length l0 is given by:et=dlll0lÚ= lnll0ÊËÁˆ¯˜Also, in a plastic deformation volume is conserved(material is incompressible). Hence, if the elasticdeformation is negligible, A =A0l0l . Hence,st=FA=FlA0l0Rearranging we obtain:st=sn1+en()et= ln 1+en()Replot stress-strain curves, appear symmetric:Work is done causing plastic deformation – it is anirreversible process:Upl=sdeÚ-s22EExplains why tools, metal heat up during metalworking. Also why frictional sliding generates heatImage adapted from: Ashby, M. F., and D. R. H. Jones. Engineering Materials 1. Pergamon Press, 1980.,Area = plasticwork dissipated per unit volume incausing a permanent plastic strainsxxFinal fractureNecking beginsTensionsand in centre of neck∈∈∈∈Compression“Necking” – tensile instabilityCan examine onset of necking using true-stress-truestrain definitions:From tensile nominal stress- nominal strain curveknow that: Ast= F = constantThenAdst+stdA = 0Or:dstst=-dAABut volume is conserved during plastic flow, so:-dAA=dll= detImage adapted from: Ashby, M. F., and D. R. H. Jones. Engineering Materials 1. Pergamon Press, 1980.A Al+dll+ dA - dASection AreaSection Area Section AreaAssssssThe formation of a neck in a bar of material which is being deformed plastically.dstst= detfidstdet=stSubstituting for nominal stresses and strains:dsnden= 0The necking point is important because it defines alimit on how thin one can roll or draw metalsheets/foils or draw wires in a single pass.Materials can have a wide range of values of yieldstress and ultimate tensile strength:Image adapted from: Ashby, M. F., and D. R. H. Jones. Engineering Materials 1. Pergamon Press, 1980./MN m-2/MN m-2Yield Strength, , Tensile Strength, , and Tensile Ductility, fMaterialDiamond 50000000000000000000Silicon carbide, SiC 10000Silicon nitride, Si3N48000Silica glass, SiO27200Tungsten carbide, WC 6000Niobium carbide, NbC 6000Alumina, AI2O35000Beryllia, BeO 40004000400040004000400036003000180-2000 500-2500 0.01-6680-2400 0.02-0.31500-2000 0.3-0.6760-1280725-17300.45-0.65400-2000 0.01-0.6400 0.651510 0.01-0.6665-1650 0.01-0.36300-1400 0.06-0.3500-1880 0.2-0.3400-1100 0.01-0.4400-12000-0.18250-1000400900670-640230-890300-700200500-800200-500410240-440430200125-380100-300380-62022011030-1200.02-0.100.50.03-0.050.01-0.550.550.020.01-0.70.05-0.30.50.15-0.250.1-1.00.0200.24-0.370.18-0.250.30.06-0.201500-1900286-500200-1600560-1450180-1320260-1300330-1090220-103060-96060400-90070-640100-62740240-400160-421200-350100-3652205080-30034-27660-11030-10052-9040701000500-1980MulliteTitanium carbide, TiCZirconium carbide, ZrCTantalum carbide, TaCZirconia, ZrO2Soda glass (standard)Magnesia, MgOCobalt and alloysLow-alloy steels (water-quenched and tempered)Pressure-vessel steelsStainless steels, austeniticBoron/epoxy composites (tension-compression)Nickel alloysNickel TungstenMolybdenum and alloysTitanium and alloysCarbon steels (water-quenched and tempered)Tantalum and alloysCast ironsCopper alloysCopper Cobalt/tungsten carbide cermetsCFRPs (tension-compression)Brasses and bronzesAluminium alloysAluminium Stainless steels, ferriticZinc alloysAlkali halidesZirconium and alloysMild steelIronMagnesium
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