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Chapter 6

Chapter 6. Mechanical Properties. Load and Deformation. Tensile. Compression. Torsion. Shear. Elastic Deformation. 1. Initial. 2. Small load. 3. Unload. bonds. stretch. return to. initial. d. F. F. Linear-. elastic. Non-Linear-. elastic. d. Elastic means reversible !.

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Chapter 6

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  1. Chapter 6 Mechanical Properties

  2. Load and Deformation Tensile Compression Torsion Shear

  3. Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch return to initial d F F Linear- elastic Non-Linear- elastic d Elastic means reversible!

  4. Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload bonds p lanes stretch still & planes sheared shear d plastic d elastic + plastic F F linear linear elastic elastic d d plastic Plastic means permanent!

  5. Engineering Stress • Tensile stress, s: • Shear stress, t: F F F t t Area, A F s Area, A F s F t F F t s F t = F lb N t s = A = f or o 2 2 in m A o original area before loading  Stress has units: N/m2 or lbf/in2

  6. Common States of Stress F F A = cross sectional o area (when unloaded) F = s s s A o M F s A o A c F s = t A o M 2R • Simple tension: cable Ski lift • Torsion (a form of shear): drive shaft Note: t = M/AcR here.

  7. OTHER COMMON STRESS STATES (1) A o Canyon Bridge, Los Alamos, NM F = s Balanced Rock, Arches A National Park o • Simple compression: Note: compressive structure member (s < 0 here).

  8. OTHER COMMON STRESS STATES (2) Fish under water s > 0 q s< 0 s > 0 z h • Bi-axial tension: • Hydrostatic compression: Pressurized tank

  9. Engineering Strain d /2 d L e = e = L L w L o w o o o d /2 L g = Dx/y= tan q • Tensile strain: • Lateral strain: - d • Shear strain: q x y 90º - q Strain is always dimensionless. 90º

  10. • Typical tensile specimen . specimen extensometer gauge length Stress-Strain Testing • Typical tensile test machine

  11. F • Hooke's Law: s = Ee s E F e simple Linear- tension test elastic Linear Elastic Properties • Modulus of Elasticity, E: (also known as Young's modulus, Linear Elasticity)

  12. eL e e n - L n = - e Poisson's ratio, n • Poisson's ratio, n: metals: n ~ 0.33ceramics: n~ 0.25polymers: n ~ 0.40 Units: E: [GPa] or [psi] n: dimensionless

  13. Mechanical Properties • Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal

  14. Other Elastic Properties M t G simple torsion test g M P • Elastic Bulk modulus, K: P P P D V D V P = - K V o V pressure test: Initial. vol =Vo, Vol change = DV K o • Special relations for isotropic materials: E E = = K G 3(1-2n) 2(1+n) • Elastic Shear modulus, G: t = Gg

  15. Young’s Moduli: Comparison Composites /fibers Polymers 1200 10 00 Diamond 8 00 6 00 Si carbide 4 00 Tungsten Carbon fibers only Al oxide Molybdenum Si nitride E(GPa) Steel, Ni C FRE(|| fibers)* 2 00 Tantalum <111> Si crystal Platinum A ramid fibers only Cu alloys <100> 10 0 Zinc, Ti 8 0 Silver, Gold A FRE(|| fibers)* Glass - soda Aluminum 6 0 Glass fibers only Magnesium, G FRE(|| fibers)* 4 0 Tin Concrete GFRE* 2 0 CFRE * G FRE( fibers)* G raphite 10 8 C FRE( fibers) * 6 AFRE( fibers) * Polyester 4 PET PS Graphite Ceramics Semicond Epoxy only PC Metals Alloys 2 PP HDP E 1 0.8 0.6 Wood( grain) PTF E 0.4 LDPE 0.2

  16. Modulus of Metal

  17. Useful Linear Elastic Relationships 2 ML T FL Fw o d = d = - n a = da = dx o o L 4 JG r p G E A E A o o o F M = moment a = angle of twist d /2 A o d /2 L Lo Lo w o 2ro • Simple tension: • Simple torsion: • Material, geometric, and loading parameters all contribute to deflection. • Larger elastic moduli minimize elastic deflection.

  18. Yield Strength, sy s tensile stress, sy e engineering strain, e = 0.002 p • Stress at which noticeableplastic deformation has occurred. when ep = 0.002 y = yield strength Note: for 2 inch sample  = 0.002 = z/z  z = 0.004 in

  19. Stress-Strain Behavior Typical behavior Yield point phenomenon

  20. Yield Strength : Comparison Graphite/ Metals/ Composites/ Ceramics/ Polymers Alloys fibers Semicond 2 0 00 qt Steel (4140) 10 00 a Ti (5Al-2.5Sn) W (pure) (MPa) 7 00 6 00 cw Cu (71500) 5 00 Mo (pure) a Steel (4140) 4 00 cd y Steel (1020) s , 3 00 ag Al (6061) hr Steel (1020) 2 00 ¨ a Ti (pure) Ta (pure) Hard to measure, hr Cu (71500) Hard to measure in tension, fracture usually occurs before yield. in ceramic matrix and epoxy matrix composites, since since in tension, fracture usually occurs before yield. 100 dry Yield strength, 70 PC 60 Nylon 6,6 a Al (6061) PET 50 humid PVC 40 PP 30 H DPE 20 LDPE Tin (pure) 10 Room T values Based on data in Table B4, Callister 7e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered

  21. Plastic (Permanent) Deformation (at lower temperatures, i.e. T < Tmelt/3) • Simple tension test: Elastic+Plastic at larger stress engineering stress, s Elastic initially permanent (plastic) after load is removed ep engineering strain, e plastic strain

  22. TS F = fracture or ultimate strength Neck – acts as stress concentrator y stress engineering Typical response of a metal strain engineering strain Tensile Strength, TS • Maximum stress on engineering stress-strain curve. • Metals: occurs when noticeable necking starts. • Polymers: occurs when polymer backbonechains are aligned and about to break.

  23. Graphite/ Metals/ Composites/ Ceramics/ Polymers Alloys fibers Semicond 5000 C fibers Aramid fib 3000 E-glass fib 2000 qt Steel (4140) (MPa) A FRE (|| fiber) 1000 Diamond W (pure) GFRE (|| fiber) a Ti (5Al-2.5Sn) C FRE (|| fiber) a Steel (4140) cw Si nitride Cu (71500) hr Cu (71500) Al oxide Steel (1020) 300 ag Al (6061) a Ti (pure) 200 Ta (pure) a Al (6061) Si crystal wood(|| fiber) 100 <100> strength, TS Nylon 6,6 Glass-soda PET PC PVC GFRE ( fiber) 40 Concrete PP C FRE ( fiber) 30 A FRE( fiber) H DPE Graphite 20 L DPE 10 Tensile wood ( fiber) 1 Tensile Strength : Comparison Room Temp. values Based on data in Table B4, Callister 7e. 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.

  24. Ductility - L L = x 100 f o % EL L o smaller %EL E ngineering tensile Ao s stress, Lo larger %EL Af Lf e Engineering tensile strain, - A A • Another ductility measure: = o f % RA x 100 A o • Plastic tensile strain at failure:

  25. 1 @ s e U r y y 2 Resilience, Ur • Ability of a material to store energy • Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to

  26. Toughness small toughness (ceramics) E ngineering tensile large toughness (metals) s stress, very small toughness (un-reinforced polymers) e Engineering tensile strain, • Energy to break a unit volume of material • Approximate by the area under the stress-strain curve. Brittle fracture: elastic energyDuctile fracture: elastic energy+ plastic energy

  27. Elastic Strain Recovery Strain hardening effect– the stress-strain curve will follow EF line when load is reapplied E

  28. Strength of Metal

  29. apply known force measure size e.g., of indent after 10 mm sphere removing load Smaller indents d D mean larger hardness. most brasses easy to machining cutting nitride plastics Al alloys steels file hard tools steels diamond increasing hardness Hardness • Resistance to permanently indenting the surface. • Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties.

  30. Hardness: Measurement

  31. Hardness: Measurement • Rockwell • 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

  32. Hardness Scale Comparison

  33. True Stress & Strain • True stress • True strain

  34. s s large hardening y 1 s y small hardening 0 e hardening exponent: ( ) n n = 0.15 (some steels) s = e K T T to n = 0.5 (some coppers) “true” strain: ln(L/Lo) “true” stress (F/A) Hardening • An increase in sy due to plastic deformation. • Curve fit to the stress-strain response:

  35. Fitting Parameters of Stress-Strain curve

  36. Design or Safety Factors d 1045 plain carbon steel: L o s = 310 MPa y 5 TS = 565 MPa F = 220,000N • 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 = 0.067 m = 6.7 cm

  37. 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 sy. • Toughness: The energy needed to break a unit volume of material. • Ductility: The plastic strain at failure.

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