CHAPTER 6: Mechanical properties

Transcription

1 CHAPTER 6: Mechanical properties 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 do dislocations cause permanent deformation? What materials are most resistant to permanent deformation? Toughness and ductility: What are they and how do we measure them? 1

2 Elastic deformation 1. Initial 2. Small load 3. Unload bonds stretch δ Elastic means reversible! F F Linearelastic δ return to initial Non-Linearelastic 2

3 Plastic deformation (metals) 1. Initial 2. Small load 3. Unload bonds stretch planes & planes still shear sheared δelastic + plastic δplastic F F Plastic means permanent! linear elastic δplastic linear elastic δ 3

4 Engineering stress Tensile stress, σ: Shear stress, τ: Ft Ft F Area, A Area, A Fs σ= F t A o original area before loading Ft τ= F s A o Stress has units: N/m 2 or lb/in 2 Fs F Ft 4

5 Simple tension: cable F F Ao = cross sectional Area (when unloaded) Common states of stress σ = F A o σ σ Simple shear: drive shaft A c M 2R M Fs A o τ = F s A Ski lift (photo courtesy P.M. Anderson) o τ Note: τ = M/AcR here. 5

6 Other common stress states (1) 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). 6

7 Other common stress states (2) Bi-axial tension: Hydrostatic compression: Pressurized tank (photo courtesy P.M. Anderson) σθ > 0 Fish under water (photo courtesy P.M. Anderson) σz > 0 σ < 0 h 7

8 Tensile strain: ε= δ L o Shear strain: θ/2 Engineering strain δ L /2 w o δ/2 δ/2 δ L /2 L o Lateral strain: ε L = δ L w o π/2 π/2 - θ γ = tan θ θ/2 Strain is always dimensionless. 8

9 Stress-strain testing Typical tensile specimen Typical tensile test machine load cell Adapted from Fig. 6.2, Callister 6e. extensometer specimen moving cross head gauge length (portion of sample with = reduced cross section) Other types of tests: --compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes, shafts. Adapted from Fig. 6.3, Callister 6e. (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.) 9

10 Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law: σ = E ε Poisson's ratio, ν: ν = ε ε L L ε ε -ν 1 metals: ν ~ 0.33 ceramics: ~0.25 polymers: ~0.40 Units: E: [GPa] or [psi] ν: dimensionless Linear elastic properties σ E 1 Linearelastic ε F F simple tension test 10

11 Elastic Shear modulus, G: τ = G γ Elastic Bulk modulus, K: P= -K ΔV Vo Other elastic properties τ P -K 1 1 G γ ΔV Vo Special relations for isotropic materials: E E G = K = 2(1+ν) 3(1 2ν) P M P M simple torsion test P pressure test: Init. vol =V o. Vol chg. = ΔV 11

12 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 Polyester PET PS PC Composites /fibers 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 Eceramics > Emetals >> Epolymers Based on data in Table B2, Callister 6e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers PP HDPE PTFE Wood( grain) 0.2 LDPE 12

13 Simple tension: Ao δ= FL o EA o F Useful linear elastic relations δ L = ν Fw o EA o δ/2 Simple torsion: α= 2ML o π ro 4 G M=moment α =angle of twist δ L /2 w o L o δ/2 δ L /2 2r o Lo Material, geometric, and loading parameters all contribute to deflection. Larger elastic moduli minimize elastic deflection. 13

14 Plastic (permanent) deformation (at lower temperatures, T < T melt /3) Simple tension test: tensile stress, σ Elastic+Plastic at larger stress Elastic initially permanent (plastic) after load is removed εp plastic strain engineering strain, ε 14

15 Stress at which noticeable plastic deformation has occurred. when εp = tensile stress, σ σy Yield strength, σ y εp = engineering strain, ε 15

16 Yield strength, σy (MPa) Yield strength: comparison Metals/ Alloys Steel (4140) qt Ti (5Al-2.5Sn) a W (pure) 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 Graphite/ Ceramics/ Semicond Hard to measure, since in tension, fracture usually occurs before yield. Polymers dry PC Nylon 6,6 PET humid PVC PP HDPE Composites/ fibers Hard to measure, in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield. σy(ceramics) >>σy(metals) >> σy(polymers) Room T values Based on data in Table B4, Callister 6e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered 10 Tin (pure) LDPE 16

17 Tensile strength, TS Maximum possible engineering stress in tension. TS Adapted from Fig. 6.11, Callister 6e. engineering stress Typical response of a metal strain Metals: occurs when noticeable necking starts. Ceramics: occurs when crack propagation starts. Polymers: occurs when polymer backbones are aligned and about to break. 17

18 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) ag Ti (pure) 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 TS(ceram) AFRE( fiber) GFRE( fiber) CFRE( fiber) wood( fiber) GFRE( fiber) CFRE( fiber) AFRE( fiber) wood ( fiber) ~TS(met) ~ TS(comp) >> TS(poly) Room T values Based on data in Table B4, Callister 6e. 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. 18

19 Plastic tensile strain at failure: Engineering tensile stress, σ Adapted from Fig. 6.13, Callister 6e. %EL = L f L o L o smaller %EL (brittle if %EL<5%) larg er %EL (ductile if %EL>5%) Another ductility measure: Ductility, %EL Engineering tensile strain, ε %AR = A o A f A o x100 Note: %AR and %EL are often comparable. --Reason: crystal slip does not change material volume. --%AR > %EL possible if internal voids form in neck. Lo Ao x100 A f 19 Lf

20 Toughness Energy to break a unit volume of material Approximate by the area under the stress-strain curve. Engineering tensile stress, σ smaller toughness (ceramics) larg er toughness (metals, PMCs) smaller toughnessunreinforced polymers Engineering tensile strain, ε 20

21 σ y Resilience Resilience is the capacity to absorb energy in the elastic region Modulus of resilience is the total elastic strain energy per unit volume (Area under elastic portion of σ vs. ε) Stress, σ U U Modulus of resilience (this area) r r y y y σ 1 = Eεdε = E d( σ E) = σdσ E E = σ 0 σ 2 y 2E σ, J/m 3 0 Resilient materials are used in spring applications. They have high yield stress and low modulus of elasticity. σ 0 ε y Strain, ε

22 Elastic properties of spring mtls Material σ y Prop limit E Recov. Normalized (ksi) (ksi) 10 3 ksi strain % Mod. of resil. Ti-55Ni PH MP55N-Co Ti-6Al-4V Beta C Ann Beta C + CW Beta C + CW+ Aged

23 Resistance to permanently indenting the surface. Large hardness means: --resistance to local plastic deformation or cracking in compression. --better wear properties. e.g., 10mm sphere (Brinell Hardness) D apply known force (1 to 1000g) Hardness d measure size of indent after removing load Smaller indents mean larger hardness. most plastics brasses Al alloys easy to machine steels file hard cutting tools nitrided steels diamond increasing hardness Adapted from Fig. 6.18, Callister 6e. (Fig is adapted from G.F. Kinney, Engineering Properties and Applications of Plastics, p. 202, John Wiley and Sons, 1957.) 21

24 An increase in σy due to plastic deformation. σ σ y 1 σ y 0 Strain hardening unload re load Curve fit to the stress-strain response: σ T = C( ε T ) n large hardening small hardening ε Strain hardening exponent: n=0.15 (some steels) to n= 0.5 (some copper) true stress (F/A) true strain: ln(l/l o) 22

25 Design uncertainties mean we do not push the limit. Factor of safety, N σ working = σ y N Often N is between 1.2 and 4 Ex: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below when subjected to a load of 200, 000N. Use a factor of safety of 5. d 220,000N π d 2 /4 Design or safety factors σ working 5 = σ y N 1045 plain carbon steel: σy=310mpa TS=565MPa F = 220,000N Lo 23

26 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. Resilience: Energy absorbed during elastic deformation Ductility: The plastic strain at failure. 24

27 ANNOUNCEMENTS Reading: Chapter Core Problems: Chapter 6, Problems 4, 8, 25, 29, 46 Self-help Problems: Review Example problems 6.2, 6.3, 6.4, 6.4, 6.5 0