Chapter 8: Mechanical Properties of Metals ISSUES TO ADDRESS... Stress and strain: What are they and why are they used instead of load and deformation? Elastic behavior: When loads are small, how much deformation 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 how do we measure them? Chapter 8-1 Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch Elastic means reversible! δ δ return to initial Linearelastic Non-Linearelastic Chapter 8-2 1
Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload bonds stretch planes & planes still shear sheared δ elastic + plastic δ plastic Plastic means permanent! linear elastic δ plastic linear elastic δ Chapter 8-3 Tensile stress, σ: Engineering Stress t Shear stress, τ: t Area, A o Area, A o s t σ = t = N A o m 2 original cross-sectional area before loading τ = s A o s t Stress has units: N/m 2 Chapter 8-4 2
Common States of Stress Simple tension: cable Ao = cross-sectional area (when unloaded) σ = σ σ A o Torsion (a form of shear): drive shaft A c M 2R M s A o τ = s A o Note: τ = M/A c R here. Ski lift (photo courtesy P.M. Anderson) τ Chapter 8-5 OTHER COMMON STRESS STATES (i) Simple compression: A o Canyon Bridge, Los Alamos, NM (photo courtesy P.M. Anderson) Balanced Rock, Arches National Park (photo courtesy P.M. Anderson) σ = A o Note: compressive structure member (σ < 0 here). Chapter 8-6 3
OTHER COMMON STRESS STATES (ii) Bi-axial tension: Hydrostatic compression: Pressurized tank (photo courtesy P.M. Anderson) σ θ > 0 ish under water (photo courtesy P.M. Anderson) σ z > 0 σ < 0 h Chapter 8-7 Tensile strain: e = δ L o Engineering Strain w o δ/2 L o Lateral strain: - δ e L = L w o Shear strain: θ x δ L /2 γ = Δx/y = tan θ y 90º 90º - θ Strain is always dimensionless. Adapted from ig. 8.1 (a) and (c), Callister & Rethwisch 9e. Chapter 8-8 4
Typical tensile test machine Stress-Strain Testing Typical tensile specimen extensometer specimen ig. 8.2, Callister & Rethwisch 9e. ig. 8.3, Callister & Rethwisch 9e. (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.) Chapter 8-9 Typical tensile test Chapter 8-10 5
Linear Elastic Properties Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law: σ = E e σ E Linearelastic e simple tension test Chapter 8-11 Poisson's ratio, ν Poisson's ratio, ν: e L ν = - el e e metals: ν ~ 0.33 ceramics: ν ~ 0.25 polymers: ν ~ 0.40 -ν Units: E: [GPa] or [psi] ν: dimensionless Chapter 8-12 6
Mechanical Properties Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal ig. 8.7, Callister & Rethwisch 9e. Chapter 8-13 Young s Moduli: Comparison E(GPa) 10 9 Pa 1200 1000 800 600 400 200 100 80 60 40 20 10 8 6 4 2 1 0.8 0.6 0.4 0.2 Metals Alloys Graphite Ceramics Polymers Composites /fibers Semicond Diamond Si carbide Tungsten Al oxide Molybdenum Si nitride Steel, Ni Tantalum <111> Platinum Si crystal Cu alloys <100> Zinc, Ti Silver, Gold Aluminum Glass -soda Magnesium, Tin Concrete Graphite Polyester PET PS PC PP HDPE PTE LDPE Carbon fibers only CRE( fibers)* Aramid fibers only ARE( fibers)* Glass fibers only GRE( fibers)* GRE* CRE* GRE( fibers)* CRE( fibers) * ARE( fibers) * Epoxy only Wood( grain) Based on data in Table B.2, Callister & Rethwisch 9e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CRE), aramid (ARE), or glass (GRE) fibers. Chapter 8-14 7
Elastic Shear modulus, G: τ = G γ Other Elastic Properties τ G γ M simple torsion test Elastic Bulk modulus, K: P = -K Δ V Vo Special relations for isotropic materials: G = E 2(1 + ν) K = P K E 3(1-2ν) ΔV Vo P M P P pressure test: Init. vol =V o. Vol chg. = ΔV Chapter 8-15 Useful Linear Elastic Relationships Simple tension: δ = L o EA o A o δ/2 δ L = - ν w o EA o Simple torsion: α = 2ML o πr o 4 G M = moment α = angle of twist w o L o L o δ L /2 2r o Material, geometric, and loading parameters all contribute to deflection. Larger elastic moduli minimize elastic deflection. Chapter 8-16 8
Ex. 8.1 Copper under elastic loading tension l 0 =305 mm(12 in) s= 276 MPa(40,000 psi) E=110 GPa(16 10 6 psi) l =? Chapter 8 - Ex. 8.2 Brass rod under elastic loading tension d 0 =10 mm(0.4 in) d= 2.5 10-3 mm (10-4 in ) d i = (d 0 - d) E=97 GPa(14 10 6 psi) = 0.34 =? Chapter 8-9
Plastic (Permanent) Deformation (at lower temperatures, i.e. T < T melt/3) Simple tension test: engineering stress,σ Elastic+Plastic at larger stress Elastic initially permanent (plastic) after load is removed e p engineering strain, e plastic strain Adapted from ig. 8.10 (a), Callister & Rethwisch 9e. Chapter 8-19 Shape Memory Materials No permanent deformation Chapter 8-10
since in tension, fracture usually occurs before yield. Hard to measure, in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield. 2016/11/22 Yield Strength, σ y Stress at which noticeable plastic deformation has occurred. when e p = 0.002 σ y tensile stress, σ s y = yield strength Note: for 2 inch sample e = 0.002 = z/z z = 0.004 in e p = 0.002 engineering strain, e Adapted from ig. 8.10 (a), Callister & Rethwisch 9e. Chapter 8-21 2000 Yield Strength : Comparison Metals/ Alloys Steel (4140) qt Graphite/ Ceramics/ Semicond Polymers Composites/ fibers Yield strength, σ y (MPa) 1000 700 600 500 400 300 200 100 70 60 50 40 30 20 Ti (5Al-2.5Sn) W (pure) a Cu (71500) Mo (pure) cw Steel (4140) a Steel (1020) cd Al (6061) ag Steel (1020) hr Ti (pure) a Ta (pure) Cu (71500) hr Al (6061) a Hard to measure, dry PC Nylon 6,6 PET humid PVC PP HDPE Room temperature values Based on data in Table B.4, Callister & Rethwisch 9e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered 10 Tin (pure) LDPE Chapter 8-22 11
Tensile strength, TS (MPa) engineering stress 2016/11/22 TS s y Tensile Strength, TS Maximum stress on engineering stress-strain curve. Adapted from ig. 8.11, Callister & Rethwisch 9e. = fracture or ultimate strength Typical response of a metal strain engineering strain Neck acts as stress concentrator Metals: occurs when noticeable necking starts. Polymers: occurs when polymer backbone chains are aligned and about to break. Chapter 8-23 5000 3000 2000 1000 300 200 100 40 30 20 10 Tensile Strength: Comparison 1 Metals/ Alloys Steel (4140) qt Graphite/ Ceramics/ Semicond W (pure) Ti (5Al-2.5Sn) Steel (4140) a a Diamond Cu (71500) Cu (71500) hr cw Si nitride Steel (1020) Al (6061) Ti (pure) ag Al oxide a Ta (pure) Al (6061) a Si crystal <100> Glass-soda Concrete Graphite Polymers Nylon 6,6 PC PET PVC PP LDPE HDPE Composites/ fibers C fibers Aramid fib E-glass fib ARE( fiber) GRE( fiber) CRE( fiber) wood( fiber) GRE( fiber) CRE( fiber) ARE( fiber) wood ( fiber) Room temperature values Based on data in Table B4, Callister & Rethwisch 9e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered ARE, GRE, & CRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers. Chapter 8-24 12
Ex. 6.3 d 0 = 12.8 mm l 0 = 250 mm ind: 1. E =? 2. Yield strength of strain offset of 0.2%? 3. max =? 4. l =? ; σ = 345 MPa Chapter 8 - Ductility Plastic tensile strain at failure: Engineering tensile stress, σ Adapted from ig. 8.13, Callister & Rethwisch 9e. smaller %EL larger %EL L %EL = Another ductility measure: A A %RA = f x 100 A L o Engineering tensile strain, e o - o f - L o A o L o A f x 100 L f Chapter 8-26 13
Toughness Energy to break a unit volume of material Approximate by the area under the stress-strain curve. Engineering tensile stress, σ Adapted from ig. 8.13, Callister & Rethwisch 9e. small toughness (ceramics) large toughness (metals) very small toughness (unreinforced polymers) Engineering tensile strain, e Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy Chapter 8-27 Resilience, U r Ability of a material to store energy Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to e y U r 1 2 σ y e y ig. 8.15, Callister & Rethwisch 9e. Chapter 8-28 14
Stress 2016/11/22 Elastic Strain Recovery σ yi D σ yo 2. Unload ig. 8.17, Callister & Rethwisch 9e. 1. Load Elastic strain recovery 3. Reapply load Strain Chapter 8-29 Hardness Resistance to permanently indenting the surface. Large hardness means: -- resistance to plastic deformation or cracking in compression. -- better wear properties. e.g., 10 mm sphere apply known force measure size of indent after removing load D d Smaller indents mean larger hardness. most plastics brasses Al alloys easy to machine steels file hard cutting tools nitrided steels diamond increasing hardness Chapter 8-30 15
Rockwell Hardness: Measurement 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. ball, C = diamond HB = Brinell Hardness TS (psia) = 500 x HB TS (MPa) = 3.45 x HB Chapter 8-31 Hardness: Measurement Table 8.5 Chapter 8-32 16
True Stress & Strain Note: S.A. changes when sample stretched True stress True strain Adapted from ig. 8.16, Callister & Rethwisch 9e. Chapter 8-33 Hardening An increase in σ y due to plastic deformation. σ σ y1 σ y0 large hardening small hardening Curve fit to the stress-strain response: σ T = K( e T ) n hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers) true stress (/A) true strain: ln(l/l o ) e Chapter 8-34 17
Design or Safety actors Design uncertainties mean we do not push the limit. actor of safety, N Often N is between 1.2 and 4 Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5. d 1045 plain carbon steel: σ y = 310 MPa Lo 5 TS = 565 MPa d = 0.067 m = 6.7 cm = 220,000N Chapter 8-35 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 σ y. Toughness: The energy needed to break a unit volume of material. Ductility: The plastic strain at failure. Chapter 8-36 18