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Chapter 7: 機械性質 ( Mechanical Properties)

Chapter 7: 機械性質 ( Mechanical Properties). Tensile & Hardness Testing; Macroscopic Behavior; Elastic Deformation; Elastic Modulus; Proportional Limit; Poisson's Ratio; Plastic deformation; Yielding and Yielding Strength; Tensile Strength; Fracture Strength; Ductility; Resilience;

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Chapter 7: 機械性質 ( Mechanical Properties)

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  1. Chapter 7:機械性質(Mechanical Properties) • Tensile & Hardness Testing; • Macroscopic Behavior; • Elastic Deformation; • Elastic Modulus; • Proportional Limit; • Poisson's Ratio; • Plastic deformation; • Yielding and Yielding Strength; • Tensile Strength; • Fracture Strength; • Ductility; • Resilience; • Toughness • Property Variability; • Design Safety Factors. 1

  2. c07f01 7.2 應力和應變(Stress and Strain)的觀念 c07f01

  3. c07f03 c07f03 拉力試驗

  4. 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 • Torsion (a form of shear): drive shaft Note: R × t×Ac= M here. 4

  5. OTHER COMMON STRESS STATES (i) A o Canyon Bridge, Los Alamos, NM (photo courtesy P.M. Anderson) F = s Balanced Rock, Arches A National Park o • Simple compression: Note: compressive structure member (s < 0 here). (photo courtesy P.M. Anderson) 5

  6. OTHER COMMON STRESS STATES (ii) Fish under water s > 0 q s< 0 s > 0 z h • Bi-axial tension: • Hydrostatic compression: Pressurized tank (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) 6

  7. Engineering Stress • Tensile stress, s: • Shear stress, t: F F F t t Area, Ao F s Area, Ao 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 7

  8. Engineering Strain d /2 - d d L e = e = L L w L o w o o o d /2 L • Shear strain: q g = Dx/y= tan x q y 90º - q 90º • Tensile strain: • Lateral strain: Strain is always dimensionless. Adapted from Fig. 7.1 (a) and (c), Callister & Rethwisch 3e. 8

  9. c07f04 c07f04

  10. c07f05 c07f05 彈性變形(Elastic Deformation) 7.3 應力-應變行為(Stress-Strain behavior)

  11. Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch return to initial d F F Linear- elastic Elastic means reversible! Non-Linear- elastic d 11

  12. Linear Elastic Properties F • Hooke's Law: s = Ee s E F e simple Linear- tension test elastic • Modulus of Elasticity, E: (also known as Young's modulus) 12

  13. Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload bonds planes stretch still & planes sheared shear d plastic d elastic + plastic F F linear linear elastic elastic d d plastic Plastic means permanent! 13

  14. c07f06 c07f06

  15. c07f07 c07f07

  16. Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal Adapted from Fig. 7.7, Callister & Rethwisch 3e. 16

  17. c07f08 c07f08

  18. c07tf01 c07tf01

  19. Young’s Moduli: Comparison 1200 10 00 Diamond 8 00 6 00 Si carbide 4 00 Tungsten Carbon fibers only Al oxide Molybdenum Si nitride 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 Epoxy only PC 2 PP HDP E 1 0.8 0.6 Wood( grain) PTF E 0.4 LDPE 0.2 Graphite Ceramics Semicond Metals Alloys Composites /fibers Polymers E(GPa) Based on data in Table B.2, Callister & Rethwisch 3e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers. 109 Pa 19

  20. c07f26 7.4 滯彈性(Anelasticity) c07f26

  21. c07f09 c07f09 7.5 材料的彈性性質(Poission’s Ratio)

  22. Poisson's Ratio, n eL e L n = - e e -n • Poisson's ratio, n: metals: n ~ 0.33ceramics: n~ 0.25polymers: n ~ 0.40 Units: E: [GPa] or [psi] n: Dimensionless •  > 0.50 density increases •  < 0.50 density decreases (voids form) 22

  23. 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: Init. vol =Vo. Vol chg. = DV K o • Special relations for isotropic materials: E E = = K G 3(1-2n) 2(1+n) • Elastic Shear modulus, G: t = Gg 23

  24. c07prob c07prob

  25. Mechanical Properties: Macroscopic Behavior; Elastic Deformation; Elastic Modulus; Proportional Limit; Poisson's Ratio; Plastic deformation; Yielding and Yielding Strength; Tensile Strength; Fracture Strength; Ductility; Resilience; Toughness. 7.6 拉力性質(塑性變形) c07f10ab c07f10ab

  26. Plastic (Permanent) Deformation Elastic+Plastic at larger stress permanent (plastic) after load is removed ep plastic strain (at lower temperatures, i.e. T < Tmelt/3) • Simple tension test: engineering stress, s Elastic initially engineering strain, e Adapted from Fig. 7.10 (a), Callister & Rethwisch 3e. 26

  27. Yielding and Yield Strength, y 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 Adapted from Fig. 7.10 (a), Callister & Rethwisch 3e. 27

  28. c07f11 c07f11

  29. Tensile Strength, TS TS F = fracture or ultimate strength Neck – acts as stress concentrator y stress engineering Typical response of a metal strain engineering strain • Maximum stress on engineering stress-strain curve. Adapted from Fig. 7.11, Callister & Rethwisch 3e. • Metals: occurs when noticeable necking starts. • Polymers: occurs when polymer backbonechains are aligned and about to break. 29

  30. c07f33 c07f33

  31. Yield Strength : Comparison Graphite/ Metals/ Composites/ Ceramics/ Polymers Alloys fibers Semicond 2000 qt Steel (4140) 1000 a Ti (5Al-2.5Sn) W (pure) 700 (MPa) 600 cw Cu (71500) 500 Mo (pure) a Steel 400 (4140) cd y Steel (1020) s 300 , ag Al (6061) hr Steel 200 (1020) ¨ 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) 50 PET humid PVC 40 PP 30 H DPE 20 LDPE Tin (pure) 10 Room temperature values Based on data in Table B.4, Callister & Rethwisch 3e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered 31

  32. Tensile Strength: Comparison 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 Room temperature values Based on data in Table B4, Callister & Rethwisch 3e. 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. 32

  33. c07f13 Ductility(延性) c07f13

  34. Ductility - L L = x 100 f o % EL L o smaller %EL E ngineering Ao tensile Lo Af Lf stress, s larger %EL Adapted from Fig. 7.13, Callister & Rethwisch 3e. Engineering tensile strain, e - A A • Another ductility measure: = o f % RA x 100 A o • Plastic tensile strain at failure: 34

  35. c07f14 c07f14

  36. c07tf02 c07tf02

  37. c07f15 c07f15 Resilience(彈性能, 回彈性), Ur

  38. Resilience, Ur Ability of a material to store energy Energy stored best in elastic region 1 @ s e U r y y 2 If we assume a linear stress-strain curve this simplifies to Adapted from Fig. 7.15, Callister & Rethwisch 3e. 38

  39. Toughness(韌性) small toughness (ceramics) E ngineering tensile large toughness (metals) stress, s very small toughness (unreinforced polymers) Engineering tensile strain, e • Energy to break a unit volume of material • Approximate by the area under the stress-strain curve. Adapted from Fig. 7.13, Callister & Rethwisch 3e. Brittle fracture: elastic energyDuctile fracture: elastic + plastic energy 39

  40. c07f16 7.7 真應力與真應變 c07f16

  41. c07tf04 c07tf04

  42. c07f17 c07f17 7.8 塑性變形期間之彈性回復

  43. Elastic Strain Recovery Elastic strain recovery D syi syo 2. Unload Stress 3. Reapply load 1. Load Strain Adapted from Fig. 7.17, Callister & Rethwisch 3e. 43

  44. c07f18 c07f18 7.10 Fexural Strength of Ceramics)

  45. Mechanical Properties of Ceramics 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 45

  46. Flexural Tests – Measurement of Elastic Modulus F cross section L/2 L/2 d R b d = midpoint rect. circ. deflection • Determine elastic modulus according to: F (rect. cross section) x F slope = d (circ. cross section) d linear-elastic behavior • Room T behavior is usually elastic, with brittle failure. • 3-Point Bend Testing often used. -- tensile tests are difficult for brittle materials. Adapted from Fig. 7.18, Callister & Rethwisch 3e. 46

  47. Flexural Tests – Measurement of Flexural Strength F cross section L/2 L/2 d R b location of max tension d = midpoint rect. circ. deflection • Typical values: • Flexural strength: s Material (MPa) E(GPa) fs Si nitride Si carbide Al oxide glass (soda-lime) 250-1000 100-820 275-700 69 304 345 393 69 (rect. cross section) (circ. cross section) Data from Table 7.2, Callister & Rethwisch 3e. • 3-point bend test to measure room-T flexural strength. Adapted from Fig. 7.18, Callister & Rethwisch 3e. 47

  48. c07f19 c07f19

  49. c07f20 c07f20

  50. c07f21 c07f21

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