Chapter 8: Mechanical Properties of Metals

Transcription

1 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? AMSE 205 Spring 2016 Chapter 8-1

2 Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch Elastic means reversible! δ F F δ return to initial Linearelastic Non-Linearelastic AMSE 205 Spring 2016 Chapter 8-2

3 Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload bonds stretch planes & planes still shear sheared δ elastic + plastic δ plastic F F Plastic means permanent! linear elastic δ plastic linear elastic δ AMSE 205 Spring 2016 Chapter 8-3

4 Tensile stress, σ: Engineering Stress Ft Shear stress, τ: Ft F Area, A o Area, A o Fs σ = F t Ft = N A o m 2 original cross-sectional area before loading τ = F s A o Fs F Ft Stress has units: N/m 2 AMSE 205 Spring 2016 Chapter 8-4

5 Common States of Stress Simple tension: cable F F Ao = cross-sectional area (when unloaded) σ = F A o σ σ Torsion (a form of shear): drive shaft A c M 2R M Fs A o τ = F s A o Ski lift (photo courtesy P.M. Anderson) τ AMSE 205 Spring 2016 Chapter 8-5

6 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 = F A o Note: compressive structure member (σ < 0 here). AMSE 205 Spring 2016 Chapter 8-6

7 OTHER COMMON STRESS STATES (ii) Bi-axial tension: Hydrostatic compression: Pressurized tank (photo courtesy P.M. Anderson) σ θ > 0 Fish under water (photo courtesy P.M. Anderson) σ z > 0 σ < 0 h AMSE 205 Spring 2016 Chapter 8-7

8 Tensile strain: = δ L o Engineering Strain w o δ/2 L o Lateral strain: L = - δ 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 Fig. 8.1 (a) and (c), Callister & Rethwisch 9e. AMSE 205 Spring 2016 Chapter 8-8

9 Typical tensile test machine Stress-Strain Testing Typical tensile specimen extensometer specimen Fig. 8.2, Callister & Rethwisch 9e. Fig. 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.) AMSE 205 Spring 2016 Chapter 8-9

10 Linear Elastic Properties Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law: σ = E σ F E Linearelastic F simple tension test AMSE 205 Spring 2016 Chapter 8-10

11 Poisson's ratio, ν: Ratio between radial and axial strains ν =- L metals: ν ~ 0.33 ceramics: ν ~ 0.25 polymers: ν ~ 0.40 Poisson's ratio, ν L -ν Units: E: [GPa] or [psi] ν: dimensionless > 0.50 density increases = 0.50 no volume change < 0.50 density decreases (voids form) AMSE 205 Spring 2016 Chapter 8-11

12 Mechanical Properties Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal Fig. 8.7, Callister & Rethwisch 9e. AMSE 205 Spring 2016 Chapter 8-12

13 Other Elastic Properties Elastic Shear modulus, G: τ = G γ τ G γ M simple torsion test M Special relations for isotropic materials: G = E 2(1 + ν) AMSE 205 Spring 2016 Chapter 8-13

14 Young s Moduli: Comparison E(GPa) 10 9 Pa Metals Alloys Tungsten Molybdenum Steel, Ni Tantalum Platinum Cu alloys Zinc, Ti Silver, Gold Aluminum Magnesium, Tin Graphite Ceramics Semicond Diamond Si carbide Al oxide Si nitride <111> Si crystal <100> Glass -soda Concrete Graphite Polymers Composites /fibers Polyester PET PS PC PP HDPE PTFE Carbon fibers only CFRE( fibers)* Aramid fibers only AFRE( fibers)* Glass fibers only GFRE( fibers)* GFRE* CFRE* GFRE( fibers)* CFRE( fibers) * AFRE( 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 (CFRE), aramid (AFRE), or glass (GFRE) fibers. 0.2 LDPE AMSE 205 Spring 2016 Chapter 8-14

15 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 p engineering strain, e plastic strain Adapted from Fig (a), Callister & Rethwisch 9e. AMSE 205 Spring 2016 Chapter 8-15

16 Yield Strength, σ y Stress at which noticeable plastic deformation has occurred. when p = σ y tensile stress, σ y = yield strength Note: for 2 inch sample = = z/z z = in p = engineering strain, e Adapted from Fig (a), Callister & Rethwisch 9e. AMSE 205 Spring 2016 Chapter 8-16

17 Typical stress-strain behavior for a metal Typical stress-strain behavior for steels AMSE 205 Spring 2016 Chapter 8-17

18 2000 Yield Strength : Comparison Metals/ Alloys Steel (4140) qt Graphite/ Ceramics/ Semicond Polymers Composites/ fibers Yield strength, σ y (MPa) 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) Ta (pure) a Cu (71500) hr Al (6061) a Hard to measure, since in tension, fracture usually occurs before yield. dry PC Nylon 6,6 PET humid PVC PP HDPE Hard to measure, in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield. 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 AMSE 205 Spring 2016 Chapter 8-18

19 y Tensile Strength, TS Maximum stress on engineering stress-strain curve. TS engineering stress Typical response of a metal strain engineering strain Metals: occurs when noticeable necking starts. Polymers: occurs when polymer backbone chains are aligned and about to break. Adapted from Fig. 8.11, Callister & Rethwisch 9e. F = fracture or ultimate strength Neck acts as stress concentrator AMSE 205 Spring 2016 Chapter 8-19

20 Tensile strength, TS (MPa) Tensile Strength: Comparison Metals/ Alloys Steel (4140) qt W (pure) Ti (5Al-2.5Sn) Steel (4140) a a Cu (71500) Cu (71500) hr cw Steel (1020) Al (6061) Ti (pure) ag a Ta (pure) Al (6061) a Graphite/ Ceramics/ Semicond Diamond Si nitride Al oxide 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 AFRE( fiber) GFRE( fiber) CFRE( fiber) wood( fiber) GFRE( fiber) CFRE( fiber) AFRE( 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 AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers. AMSE 205 Spring 2016 Chapter 8-20

21 Ductility Plastic tensile strain at failure: Engineering tensile stress, σ Adapted from Fig. 8.13, Callister & Rethwisch 9e. smaller %EL larger %EL %EL % elongation = L o L f - L o A o L o A f x 100 L f Engineering tensile strain, Another ductility measure: A A f %RA = x 100 A o - % reduction in area o AMSE 205 Spring 2016 Chapter 8-21

22 Toughness Energy to break a unit volume of material Approximate by the area under the stress-strain curve. Engineering tensile stress, σ Adapted from Fig. 8.13, Callister & Rethwisch 9e. small toughness (ceramics) large toughness (metals) very small toughness (unreinforced polymers) Engineering tensile strain, Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy AMSE 205 Spring 2016 Chapter 8-22

23 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 y Fig. 8.15, Callister & Rethwisch 9e. AMSE 205 Spring 2016 Chapter 8-23

24 True Stress & Strain S.A. changes when sample stretched Adapted from Fig. 8.16, Callister & Rethwisch 9e. AMSE 205 Spring 2016 Chapter 8-24

25 True Stress & Strain vs. Engineering Stress & Strain True stress True strain AMSE 205 Spring 2016 Chapter 8-25

26 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( ) n T hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers) true stress (F/A) true strain: ln( / o ) AMSE 205 Spring 2016 Chapter 8-26

27 Elastic Strain Recovery σ yi D σ yo Stress 2. Unload 1. Load 3. Reapply load Strain Fig. 8.17, Callister & Rethwisch 9e. Elastic strain recovery AMSE 205 Spring 2016 Chapter 8-27

28 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 AMSE 205 Spring 2016 Chapter 8-28

29 Rockwell Hardness: Measurement No major sample damage Each scale runs to 130 but only useful in range 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 (MPa) = 3.45 x HB AMSE 205 Spring 2016 Chapter 8-29

30 Table 8.5 Hardness: Measurement AMSE 205 Spring 2016 Chapter 8-30

31 Design or Safety Factors Design uncertainties mean we do not push the limit. Factor 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 plain carbon steel: σ y = 310 MPa TS = 565 MPa Lo d = m = 6.7 cm F = 220,000N AMSE 205 Spring 2016 Chapter 8-31

32 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. AMSE 205 Spring 2016 Chapter 8-32