ISSUES TO ADDRESS...

Transcription

1 Chapter 7: Mechanical Properties School of Mechanical Engineering Choi, Hae-Jin Materials Science - Prof. Choi, Hae-Jin Chapter 7-1 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 7-2 1

2 Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch Elastic means reversible! return to initial Linearelastic Non-Linearelastic Chapter 7-3 Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload bonds stretch planes & planes still shear sheared elastic + plastic plastic Plastic means permanent! linear elastic plastic linear elastic Chapter 7-4 2

3 Engineering Stress Tensile stress, : t Shear stress, : t Area, A o Area, A o s = t lb f = 2 A o in original area before loading t or N 2 m = s A o s Stress has units: N/m 2 or lb f /in 2 t Chapter 7-5 Common States of Stress Simple tension: cable Ao = cross sectional area (when unloaded) A o Torsion (a form of shear): drive shaft A c M 2R M s A o s Ao Ski lift (photo courtesy P.M. Anderson) Note: = M/A c R here. Chapter 7-6 3

4 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) A o Note: compressive structure member ( < 0 here). Chapter 7-7 OTHER COMMON STRESS STATES (ii) Bi-axial tension: Hydrostatic compression: Pressurized tank (photo courtesy P.M. Anderson) > 0 ish under water (photo courtesy P.M. Anderson) z > 0 < 0 h Chapter 7-8 4

5 Engineering Strain Tensile strain: Lateral strain: /2 L o w o L o L L L w o Shear strain: x L /2 = x/y = tan y 90º 90º - Adapted from ig. 7.1 (a) and (c), Strain is always dimensionless. Chapter 7-9 Typical tensile test machine Stress-Strain Testing Typical tensile specimen extensometer specimen Adapted from ig. 7.2, Callister & Rethwisch 3e. gauge length Adapted from ig. 7.3, (ig. 7.3 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.) Chapter

6 Linear Elastic Properties Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law: = E E Linearelastic simple tension test Chapter 7-11 Poisson's ratio, Poisson's ratio, : L L L metals: ~ 0.33 ceramics: ~ 0.25 polymers: ~ 0.40 Units: E: [GPa] or [psi] : dimensionless - > 0.50 density increases < 0.50 density decreases (voids form) Chapter

7 Mechanical Properties Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal Adapted from ig. 7.7, Chapter 7-13 Other Elastic Properties Elastic Shear modulus, G: = G G M simple torsion test Elastic Bulk modulus, K: P = -K V Vo P K V Vo Special relations for isotropic materials: G E 2(1 ) K E 3(1 2) P M P P pressure test: Init. vol =V o. Vol chg. = V Chapter

8 Young s Moduli: Comparison E(GPa) 10 9 Pa 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, Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CRE), aramid (ARE), or glass (GRE) fibers. Chapter 7-15 Useful Linear Elastic Relationships Simple tension: Ao L o EA o w o L EA o /2 Simple torsion: 2ML o r o 4 G M = moment = angle of twist w o L o L o L /2 2r o Material, geometric, and loading parameters all contribute to deflection. Larger elastic moduli minimize elastic deflection. Chapter

9 Plastic (Permanent) Deformation (at lower temperatures, i.e. T < T melt /3) Simple tension test: engineering stress, Elastic+Plastic at larger stress Elastic initially permanent (plastic) after load is removed p engineering strain, plastic strain Adapted from ig (a), Chapter 7-17 Yield Strength, y Stress at which noticeable plastic deformation has occurred. when p = y tensile stress, y = yield strength Note: for 2 inch sample = = z/z z = in p = engineering strain, Adapted from ig (a), Chapter

10 Yield Strength : Comparison 2000 Metals/ Alloys Steel (4140) qt Graphite/ Ceramics/ Semicond Polymers Composites/ fibers Yield stre ength, 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, fractu re usually occurs before yield. dry PC Nylon 6,6 PET humid PVC PP HDPE rd to measure, epoxy matrix composites, since e usually occurs before yield. Ha in ceramic matrix and in tension, fracture Room temperature values Based on data in Table B.4, a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered 10 Tin (pure) LDPE Chapter 7-19 Tensile Strength, TS Maximum stress on engineering stress-strain curve. TS y 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 ig. 7.11, = fracture or ultimate strength Neck acts as stress concentrator Chapter

11 Tensile stre ength, TS (MP Pa) 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 20 Graphite 1 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) Room temperature values wood( fiber) Based on data in Table B4, GRE( fiber) a = annealed CRE( fiber) hr = hot rolled ARE( fiber) ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered ARE, GRE, & CRE = aramid, glass, & carbon wood ( fiber) fiber-reinforced epoxy composites, with 60 vol% fibers. Chapter 7-21 Ductility L L o Plastic tensile strain at failure: %EL x 100 L Engineering tensile stress, Adapted from ig. 7.13, smaller %EL larger %EL L o Engineering tensile strain, Another ductility measure: A A %RA = f x 100 A o - o f o A o A f L f Chapter

12 Toughness Energy to break a unit volume of material Approximate by the area under the stress-strain curve. Engineering tensile stress, Adapted from ig. 7.13, small toughness (ceramics) large toughness (metals) very small toughness (unreinforced polymers) Engineering tensile strain, Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy Chapter 7-23 Resilience, U r Ability of a material to store energy Energy stored best in elastic region U r 0 y d If we assume a linear stress-strain curve this simplifies to Adapted from ig. 7.15, U r 1 2 y y Chapter

13 Elastic Strain Recovery yi D yo 2. Unload Stress 1. Load 3. Reapply load Strain Adapted from ig. 7.17, Elastic strain recovery Chapter 7-25 Mechanical Properties Ceramic materials are more brittle than metals. Why is this so? Consider mechanism of deformation In crystalline, by dislocation motion In highly ionic solids, dislocation motion is difficult few slip systems resistance to motion of ions of like charge (e.g., anions) past one another Chapter

14 lexural Tests Measurement of 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 L/2 L/2 d R b rect. circ. Determine elastic modulus according to: 3 L x E 3 4bd slope = 3 L E 4 linear-elastic behavior 12R Adapted from ig. 7.18, = midpoint deflection (rect. cross section) (circ. cross section) Chapter 7-27 lexural Tests Measurement of lexural Strength 3-point bend test to measure room-t flexural strength. cross section b rect. L/2 L/2 Adapted from ig. 7.18, d R circ. location of max tension = midpoint deflection lexural strength: fs 3 f L 2 2bd L f fs 3 R (rect. cross section) (circ. cross section) Typical values: Material fs (MPa) E(GPa) Si nitride Si carbide Al oxide glass (soda-lime) 69 Data from Table 7.2, Chapter

15 Mechanical Properties of Polymers Stress-Strain Behavior brittle polymer plastic elastomer elastic moduli less than for metals Adapted from ig. 7.22, racture strengths of polymers ~ 10% of those for metals Deformation strains for polymers > 1000% for most metals, deformation strains < 10% 29 Chapter 7-29 Influence of T and Strain Rate on Thermoplastics Decreasing T increases E -- increases TS -- decreases %EL Increasing strain rate same effects as decreasing T. (MPa) 80 4 C C 40 C Plots for semicrystalline PMMA (Plexiglas) 20 to C Adapted from ig. 7.24, (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.) 30 Chapter

16 Time-Dependent Deformation Stress relaxation test: -- strain in tension to and hold. -- observe decrease in stress with time. o tensile test strain ( t) Er ( t) o (t) time Relaxation modulus: There is a large decrease in E r for T > T g rigid solid E r (10 s) (small relax) in MPa 10 3 transition 10 1 region 10-1 viscous liquid 10-3 (large relax) T( C) T g (amorphous polystyrene) Adapted from ig. 7.28, Callister & Rethwisch 3e. (ig is from A.V. Tobolsky, Properties and Structures of Polymers, John Wiley and Sons, Inc., 1960.) Representative ti T g values (C): PE (low density) -110 PE (high density) - 90 PVC + 87 PS +100 PC +150 Selected values from Table 11.3, Callister & Rethwisch 3e. 31 Chapter 7-31 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

17 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 (psia) = 500 x HB TS (MPa) = 3.45 x HB Chapter 7-33 Table 7.5 Hardness: Measurement Chapter

18 True Stress & Strain Note: S.A. changes when sample stretched T A i T 1 True stress ln ln1 True strain T i o T Adapted from ig. 7.16, Chapter 7-35 Hardening An increase in y due to plastic deformation. y1 y0 large hardening small hardening Curve fit to the stress-strain response: T K T n hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers) true stress (/A) true strain: ln(l/l o ) Chapter

19 Variability in Material Properties Elastic modulus is material property Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability. Statistics Mean Standard Deviation x n n x n xi s n where n is the number of data points n x Chapter 7-37 Design or Safety actors Design uncertainties mean we do not push the limit. actor of safety, N Often N is y between working 1.2 and 4 N 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 y 1045 plain 220,000N d 2 /4 working 5 N d = m = 6.7 cm carbon steel: y = 310 MPa TS = 565 MPa = 220,000N Lo Chapter

20 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 y. Toughness: The energy needed to break a unit volume of material. Ductility: The plastic strain at failure. Chapter