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Special Assignment Add figures/graphics to all slides Use bullets instead of short sentences

Special Assignment Add figures/graphics to all slides Use bullets instead of short sentences For the 15’ presentations use fonts 18 or bigger; however, for the 50’, font sizes 10, 12, 14 are fine. You may use 16 or 18 for titles. Add your summary slide

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Special Assignment Add figures/graphics to all slides Use bullets instead of short sentences

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  1. Special Assignment • Add figures/graphics to all slides • Use bullets instead of short sentences • For the 15’ presentations use fonts 18 or bigger; however, for the 50’, font sizes 10, 12, 14 are fine. You may use 16 or 18 for titles. • Add your summary slide • Graphics should help to explain the topic

  2. CHAPTER 7: MECHANICAL PROPERTIES

  3. CHAPTER 7: MECHANICAL PROPERTIES Stress Strain Elasticity Strength Tensile Elongation Ductile Fracture Tension Flexural Plasticity ISSUES TO ADDRESS... • Stress and strain • Elastic behavior • Plastic behavior • Toughness and ductility • Ceramic Materials

  4. 7.2 STRESS & STRAIN • Tensile stress, s: • Shear stress, t: Stress has units: N/m2 or lb/in2 4

  5. Stress (s) for tension and compression c07f01 Strain (e) for tension and compression Compressive load Tensile load Shear stress Shear strain g = tan q Torsional deformation angle of twist, f

  6. 7.2 COMMON STATES OF STRESS • Simple tension: cable Ski lift(photo courtesy P.M. Anderson) • Simple shear: drive shaft Note: t = M/Ac 5

  7. OTHER COMMON STRESS STATES • Simple compression: (photo courtesy P.M. Anderson) Note: compressive structure member (s < 0 here). (photo courtesy P.M. Anderson) 6

  8. OTHER COMMON STRESS STATES • Bi-axial tension: • Hydrostatic compression: Pressurized tank (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) s< 0 h 7

  9. ENGINEERING STRAIN • Tensile strain: • Lateral strain: • Shear strain: Strain is always dimensionless. 8

  10. 7.2 STRESS-STRAIN TESTING • Typical tensile specimen • Typical tensile test machine Adapted from Fig. 6.2, Callister 6e. • 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

  11. c07f04 Normal and shear stresses on an arbitrary plane Stress is a function of the orientation On plane p-p’ the stress is not pure tensile There are two components Tensile or normal stress s’ (normal to the pp’ plane) Shear stress t’ (parallel to the pp’ plane)

  12. ELASTIC DEFORMATIONS7.3 Stress-strain behavior • Modulus of Elasticity, E: (also known as Young's modulus) • Hooke's Law: s = Ee • Poisson's ratio, n: metals: n ~ 0.33 ceramics: ~0.25 polymers: ~0.40 Units: E: [GPa] or [psi] n: dimensionless 10

  13. c07f05

  14. PROPERTIES FROM BONDING: E • Elastic modulus, E Energy ~ curvature at ro E is larger if Eo is larger. 11

  15. c07f08 c07f08

  16. c07tf01 c07tf01

  17. 7.4 ANESLATICITY Assumed: Time-independent elastic deformation Applied stress produces instantaneous elastic strain Remains constant while elasticity stress is applied At release of load, strain is recovered In real life: Time-dependent elastic strain component: Anelasticity Time-dependent microscopic and atomistic processes For metals is small Significant for polymeric materials: Viscoelastic behavior

  18. 7.5 ELASTIC PROPERTIES OF MATERIALS c07f09 Poisson’s ratio n = -ex/ez = -ey/ez For isotropic materials

  19. YOUNG’S MODULI: COMPARISON Graphite Ceramics Semicond Metals Alloys Composites /fibers Polymers E(GPa) 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. 13

  20. II. MECHANICAL BEHAVIOR—METALS

  21. II. ELASTIC DEFORMATION 1. Initial 2. Small load 3. Unload Elastic means reversible! 2

  22. II. PLASTIC (PERMANENT) DEFORMATION (at lower temperatures, T < Tmelt/3) • Simple tension test: 15

  23. II. PLASTIC DEFORMATION (METALS) 1. Initial 2. Small load 3. Unload Plastic means permanent! 3

  24. 7.6 Tensile properties • YIELD STRENGTH, sy Stress at which noticeableplastic deformation has occurred. when ep = 0.002 16

  25. 7.6 YIELD STRENGTH: COMPARISON 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 17

  26. 7.6 TENSILE STRENGTH, TS Maximum possible engineering stress in tension Adapted from Fig. 6.11, Callister 6e. • Metals: occurs when noticeable necking starts. • Ceramics: occurs when crack propagation starts. • Polymers: occurs when polymer backbones are aligned and about to break. 18

  27. 7.6 TENSILE STRENGTH: COMPARISON 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. 19

  28. 7.6 DUCTILITY, %ELDegree of plastic deformation at fractureBrittle, when very little plastic deformation • Plastic tensile strain at failure: Adapted from Fig. 6.13, Callister 6e. ductility as percent reduction in area • Note: %AR and %EL are often comparable. --Reason: crystal slip does not change material volume. --%AR > %EL possible if internal voids form in neck. 20

  29. c07tf02 c07tf02

  30. c07f14 Stress-strain of iron at several temperatures c07f14

  31. RESILIENCE Capacity to absorb energy when deformed elastically and then upon unloadign, to have this energy recovered Modulus of Resilience For a linear elastic region:

  32. 7.6 TOUGHNESS • Ability to absorb energy up to fracture Usually ductile materials are tougher than brittle ones Areas below the curves 21

  33. 7.7 True stress & strain c07f11 Decline in stress necessary to continue deformation past M Looks like metal become weaker Actually, it is increasing in strength Cross sectional area decreases rapidly within the neck region Reduction in the load-bearing capacity of the specimen Stress should consider deformation

  34. 7.7 True stress & strain HARDENING: An increase insy due to plastic deformation. • Curve fit to the stress-strain response: n = hardening exponent n = 0.15 (some steels) n = 0.5 (some copper) 22

  35. c07tf04 c07tf04

  36. c07f17 7.8 Elastic Recovery After Plastic Deformation

  37. 7.9 Compressive, Shear, and Torsional Deformation Similar to tensile counterpart No maximum for compression Necking does not occur Mode of fracture different from that of tension

  38. III. MECHANICAL BEHAVIOR—CERAMICSLimited applicability, catastrophic fracture in a brittle manner, little energy absorption7.10 FLEXURAL STRENGTH Tensile tests are difficult difficult to prepare geometry easy to fracture ceramics fail at 0.1% strain bending stress rod specimen is used three of four point loading technique flexure test

  39. 7.10 MEASURING STRENGTH • Flexural strength= modulus of rupture = fracture strength = bend strength • Type values: Si nitride Si carbide Al oxide glass (soda) 700-1000 550-860 275-550 69 300 430 390 69 Data from Table 12.5, Callister 6e.

  40. 7.11 Elastic Behavior (for ceramics) Similar to tensile test for metals Linear stress-strain Moduli of elasticity for ceramics are slightly higher than for metals No plastic deformation priorto fracture

  41. 7.12 INFLUENCE OF POROSITY ON THE MECHANICAL PROPERTIES OF CERAMICS Powder as precursor Compaction to desire shape Pores or voids elimination incomplete Residual porosity remains Deleterious influence on elasticity and strength Volume fraction porosity P Aluminum oxide E = Eo(1 – 1.9P + 0.9P2) Eo = modulus of elasticity of the non porous material -Pores reduce the area -Pores are stress concentrators -tensile stress doubles in an isolated spherical pore Aluminum oxide sfs = soe-nP

  42. IV MECHANICAL BEHAVIOR—POLYMERS7.13 STRESS—STRAIN BEHAVIOR Stress-strain curves adapted from Fig. 15.1, Callister 6e. Inset figures along elastomer curve (green) adapted from Fig. 15.14, Callister 6e. (Fig. 15.14 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)

  43. 7.13 T & STRAIN RATE: THERMOPLASTICS • Decreasing T... --increases E --increases TS --decreases %EL • Increasing strain rate... --same effects as decreasing T. 26

  44. c07f25 7.14 Macroscopic Deformation Semicrystaline polymer c07f25

  45. c07f26 7.15 Viscoelasticity Deformation Amorphous polymer: Glass at low T Viscous liquid at higher T Small deformation at low T may be elastic Hooke’s law Rubbery solid at intermediate T A combination of glass and viscous/liquid Viscoelasticity Elastic deformation is instantaneous Upon release, deformation is totally recovered

  46. c07f26 7.15 Viscoelasticity Deformation Totally elastic Load Viscous Viscoelastic c07f26

  47. c07f27 Relaxation Modulus for viscoelastic polymers: Amorphous polystyrene A viscoelastic polymer

  48. Polystyrene configurations c07f29 Almost totally crystalline isotactic Lightly crosslinked atactic Viscoelastic creep Creep modulus Ec(t) amorphous

  49. V. Hardness & Other Mechanical Property Considerations 7.16 Hardness Measure of material resistance to localized plastic deformation Early tests: Mohs scale 1 for talc and 10 for diamond Depth or size of an indentation Tests: Mohs Hardness Rockwell Hardness Brinell Hardness Knoop & Vickers Microindentation Hardness c07f30

  50. c07tf05 c07tf05

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