CHAPTER 7: MECHANICAL PROPERTIES

Transcription

1 CHAPTER 7: 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? Ceramic Materials: What special provisions/tests are made for ceramic materials? 1

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

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

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

5 COMMON STATES O STRESS Simple tension: cable Ao = cross sectional Area (when unloaded) σ = A o σ σ Simple shear: drive shaft A c M 2R M s A o τ = s A Ski lift (photo courtesy P.M. Anderson) o τ Note: τ = M/A c R 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 = 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 ish 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 - θ γ = tan θ Strain is always dimensionless. π/2 θ/2 8

9 STRESS-STRAIN TESTING Typical tensile specimen Typical tensile test machine load cell Adapted from ig. 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 ig. 6.3, Callister 6e. (ig. 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 LINEAR ELASTIC PROPERTIES 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 metals: ν ~ 0.33 ceramics: ~0.25 polymers: ~0.40 Units: E: [GPa] or [psi] ν: dimensionless σ -ν 1 E 1 Linearelastic ε simple tension test 10

11 PROPERTIES ROM BONDING: E Elastic modulus, E length, Lo undeformed deformed L cross sectional area Ao L A = E o L o Elastic modulus E ~ curvature at ro Energy unstretched length r o r E is larger if Eo is larger. smaller Elastic Modulus larger Elastic Modulus 11

12 OTHER ELASTIC PROPERTIES Elastic Shear modulus, G: τ = G γ Elastic Bulk modulus, K: P= -K V Vo τ P -K 1 1 G γ V 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. = V 12

13 E(GPa) 10 9 Pa Metals Alloys YOUNG S MODULI: Tungsten Molybdenum Steel, Ni Tantalum Platinum Cu alloys Zinc, Ti Silver, Gold Aluminum Magnesium, Tin COMPARISON Graphite Ceramics Semicond Diamond Si carbide Al oxide Si nitride <111> Si crystal <100> Glass-soda Concrete Graphite Polymers Polyester PET PS PC PP HDPE PTE Composites /fibers 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) Eceramics > Emetals >> Epolymers Based on data in Table B2, Callister 6e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CRE), aramid (ARE), or glass (GRE) fibers. 0.2 LDPE 13

14 Simple tension: Ao δ = L o EA o USEUL LINEAR ELASTIC RELATIONS δ L = ν w 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 2ro Material, geometric, and loading parameters all contribute to deflection. Larger elastic moduli minimize elastic deflection. Lo 14

15 PLASTIC (PERMANENT) DEORMATION (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 engineering strain, ε plastic strain 15

16 Stress at which noticeable plastic deformation has occurred. when εp = tensile stress, σ σy YIELD STRENGTH, σ y εp = engineering strain, ε 16

17 Yield strength, σy (MPa) YIELD STRENGTH: COMPARISON Metals/ Alloys Steel (4140)qt 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 Al (6061)a Graphite/ Ceramics/ Semicond Hard to measure, since in tension, fracture usually occurs before yield. Polymers PC Nylon 6,6 PET humid PVC PP HDPE dry 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 17

18 TENSILE STRENGTH, TS Maximum possible engineering stress in tension. TS Adapted from ig. 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. 18

19 Tensile strength, TS (MPa) Metals/ Alloys Steel (4140)qt W (pure) Ti (5Al-2.5Sn)a Steel (4140)a Cu (71500)cw Cu (71500)hr Steel (1020) Al (6061)ag Ti (pure)a Ta (pure) Al (6061)a TENSILE STRENGTH: COMPARISON 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) ARE( fiber) GRE( fiber) CRE( fiber) wood( fiber) GRE( fiber) CRE( fiber) ARE( 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 ARE, GRE, & CRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers. 19

20 Plastic tensile strain at failure: Engineering tensile stress, σ Adapted from ig. 6.13, Callister 6e. DUCTILITY, %EL smaller %EL (brittle if %EL<5%) larger %EL (ductile if %EL>5%) %EL = L f L o L o Engineering tensile strain, ε Another ductility measure: %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 20 Lf

21 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) larger toughness (metals, PMCs) smaller toughnessunreinforced polymers Engineering tensile strain, ε 21

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

23 MEASURING ELASTIC MODULUS Room T behavior is usually elastic, with brittle failure. 3-Point Bend Testing often used. --tensile tests are difficult for brittle materials. cross section d b rect. R circ. L/2 L/2 Determine elastic modulus according to: x slope = δ δ linear-elastic behavior L 3 Adapted from ig , Callister 6e. δ= midpoint deflection L 3 E = δ 4bd 3 = δ 12πR 4 rect. circ. cross cross section section 23

24 3-point bend test to measure room T strength. cross section b rect. d MEASURING STRENGTH R circ. L/2 L/2 location of max tension Adapted from ig , Callister 6e. lexural strength: fail 1.5 σ fs = σ m = max L bd 2 rect. x max δmax δ = max L πr 3 Typ. values: Material σfs(mpa) E(GPa) Si nitride Si carbide Al oxide glass (soda) Data from Table 12.5, Callister 6e

25 TENSILE RESPONSE: ELASTOMER CASE σ(mpa) 60 x initial: amorphous chains are kinked, heavily cross-linked. brittle failure plastic failure x elastomer Deformation is reversible! ε 8 final: chains are straight, still cross-linked Stress-strain curves adapted from ig. 15.1, Callister 6e. Inset figures along elastomer curve (green) adapted from ig , Callister 6e. (ig is from Z.D. Jastrzebski, The Nature and Properties of Engineering Materials, 3rd ed., John Wiley and Sons, 1987.) Compare to responses of other polymers: --brittle response (aligned, cross linked & networked case) --plastic response (semi-crystalline case) x 25

26 Decreasing T... --increases E --increases TS --decreases %EL Increasing strain rate... --same effects as decreasing T. T AND STRAIN RATE: THERMOPLASTICS σ(mpa) C 20 C 40 C Data for the semicrystalline polymer: PMMA (Plexiglas) 20 to C Adapted from ig. 15.3, Callister 6e. (ig is from T.S. Carswell and J.K. Nason, 'Effect of Environmental Conditions on the Mechanical Properties of Organic Plastics", Symposium on Plastics, American Society for Testing and Materials, Philadelphia, PA, 1944.) ε 26

27 Stress relaxation test: --strain to εο and hold. --observe decrease in stress with time. ε o tensile test Relaxation modulus: E r (t) = σ(t ) ε o TIME DEPENDENT DEORMATION strain σ( t) time Data: Large drop in Er for T > Tg Er(10s) in MPa (amorphous polystyrene) T( C) Tg Sample Tg(C) values: PE (low Mw) PE (high Mw) PVC PS PC rigid solid (small relax) transition region viscous liquid (large relax) Adapted from ig. 15.7, Callister 6e. (ig is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.) Selected values from Table 15.2, Callister 6e. 27

28 Resistance to permanently indenting the surface. Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties. e.g., 10mm sphere HARDNESS apply known force (1 to 1000g) 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 Adapted from ig. 6.18, Callister 6e. (ig is adapted from G.. Kinney, Engineering Properties and Applications of Plastics, p. 202, John Wiley and Sons, 1957.) 28

29 DESIGN OR SAETY ACTORS Design uncertainties mean we do not push the limit. actor 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. Use a factor of safety of 5. d 220,000N π d 2 /4 σ working 5 = σ y N 1045 plain carbon steel: σy=310mpa TS=565MPa = 220,000N Lo 29

30 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. Note: or materials selection cases related to mechanical behavior, see slides 20-4 to