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Chapter 6: Mechanical properties of metals Outline Introduction Concepts of stress and strain Elastic deformation • Stress-strain behavior • Elastic properties of materials Plastic deformation • • • • Yield and yield strength Ductility Resilience Toughness Concepts of stress and strain Tension, compression, shear, and torsion 1 Stress-strain testing Tension tests σ= F • engineering stress A0 • engineering strain ε= li − l 0 l0 = Δl l0 extensometer specimen Gauge length Compression tests Shear stress Shear and torsional tests • Shear stress τ = F = Gγ A0 • Shear strain γ = Δx/y = tan θ Δx 90º - θ y 90º Geometric considerations of the stress state 2 Elastic deformation 1. Initial 2. Small load 3. Unload bonds stretch return to initial δ F F Linearelastic Elastic means reversible! Non-Linearelastic δ Linear elastic properties Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law: σ=Eε σ F E ε Linearelastic F simple tension test 6 3 Stress-strain behavior Stress-strain for linear elastic deformation Stress-strain for non-linear elastic deformation Stress-strain behavior(continue) Modulus of elasticity E is proportional to (dF/dr)r Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal 4 Other elastic properties M τ Elastic Shear modulus, G: G simple torsion test γ τ=Gγ M Elastic Bulk modulus, K: P=- K P P ΔV ΔV Vo P Vo K P pressure test: Init. vol =Vo. Vol chg. = ΔV Special relations for isotropic materials: E E G = K = 2(1 + ν) 3(1 − 2ν) Comparison of Young’s moduli 1200 1000 800 600 400 E(GPa) 200 100 80 60 40 Diamond Tungsten Molybdenum Steel, Ni Tantalum Platinum Cu alloys Zinc, Ti Silver, Gold Aluminum Magnesium, Tin Si carbide Al oxide Si nitride Carbon fibers only CFRE(|| fibers)* <111> Si crystal Aramid fibers only <100> A FRE(|| fibers)* Glass -soda Glass fibers only GFRE(|| fibers)* Concrete GFRE* 20 10 8 6 4 2 1 0.8 0.6 0.4 0.2 CFRE* GFRE( fibers)* Graphite Polyester PET PS PC CFRE( fibers) * AFRE( fibers) * Epoxy only PP HDP E PTFE Wood( grain) LDPE 5 Comparison of yield strength Metals/ Alloys 200 Ti (5Al-2.5Sn)a W (pure) Cu (71500)cw Mo (pure) Steel (4140)a Steel (1020)cd Al (6061)ag Steel (1020)hr Ti (pure)a Ta (pure) Cu (71500)hr 100 70 60 50 40 30 Al (6061)a 20 10 Tin (pure) ¨ dry PC Nylon 6,6 PET PVC humid PP HDPE Hard to measure, 700 600 500 400 300 in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield. Yield strength, σy (MPa) 1000 Steel (4140)qt Hard to measure, since in tension, fracture usually occurs before yield. 2000 Graphite/ Ceramics/ Polymers Composites/ fibers Semicond LDPE Elastic properties of materials Poisson’s ratio ν =− ε εx =− y εz εz metals: ν ~ 0.33 ceramics: ν ~ 0.25 polymers: ν ~ 0.40 Units: E: [GPa] or [psi] ν: dimensionless 6 Plastic Deformation (Metals) 1. Initial 2. Small load bonds stretch & planes shear 3. Unload planes still sheared δplastic δelastic + plastic F F Plastic means permanent! linear elastic linear elastic δplastic δ Plastic deformation: yield and yield strength Yielding Proportional limit Yield strength 7 Tensile strength TS σy engineering stress Tensile strength: the stress at the maximum on the engineering stress-strain curve Metals: occurs when noticeable “necking” starts Ceramics: occurs when crack propagation starts Polymers: occurs when polymer backbones are aligned and about to break Typical response of a metal engineering strain Plastic (permanent) deformation (At lower temperature: T< Tmelt/3) Simple tension test: Elastic+Plastic at larger stress engineering stress, σ Elastic initially permanent (plastic) after load is removed εp engineering strain, ε plastic strain 8 Elastic and plastic deformations Stress-strain relations under uniaxial loading Ceramics Polymeric material Ductility Ductility: a measure of the degree of plastic deformation that has been sustained at fracture 9 Mechanic properties of typical metals Resilience Resilience: is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered. Resilience 10 Toughness Energy to break a unit volume of material Approximate by the area under the stress-strain curve Engineering tensile stress, σ small toughness (ceramics) large toughness (metals) very small toughness (unreinforced polymers) Adapted from Fig. 6.13, Callister 7e. Engineering tensile strain, ε Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy Summary • Stress and strain: These are size-independent measures of load and displacement, respectively. • Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G). • Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches σy. • Toughness: The energy needed to break a unit volume of material. • Ductility: The plastic strain at failure. 11