Transcript Chapter 6
PLASTIC (PERMANENT) DEFORMATION (at lower temperatures, T < Tmelt/3) • Simple tension test: Proportional limit Chapter 6- 14 YIELD STRENGTH, y • Stress at which noticeable plastic deformation has occurred. when ep = 0.002=0.2% tensile stress, (just a rule of thumb or conventio y engineering strain, e ep = 0.002 Chapter 6- 15 YIELD STRENGTH: COMPARISON y(ceramics) >>y(metals) >> y(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 Chapter 6- 16 TENSILE STRENGTH, TS • Maximum possible engineering stress in tension. Adapted from Fig. 6.11, Callister 6e. Work Example Problem 6.3 • Metals: occurs when noticeable necking starts. • Ceramics: occurs when crack propagation starts. • Polymers: occurs when polymer backbones are aligned and about to break. Chapter 6- 17 TENSILE STRENGTH: COMPARISON TS(ceram) ~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 AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers. Chapter 6- 18 DUCTILITY, %EL L f Lo x100 • Plastic tensile strain at failure: %EL Lo Adapted from Fig. 6.13, Callister 6e. Ao A f • Another ductility measure: %AR x100 Ao • Note: %AR and %EL are often comparable. --Reason: crystal slip does not change material volume. --%AR > %EL possible if internal voids form in neck. Chapter 6- 19 Effect of Temperature on the StressStrain Diagram Chapter 6- 19 RESILIENCE 1 1 y y modulus of resilience U r ye y y 2 2 E 2E 2 Resilient materials, with high yield strength and low modulus of elasticity, are used in spring applications. Chapter 6- 19 TOUGHNESS • Energy to break a unit volume of material • Approximate by the area under the stress-strain curve. • Toughness can be measured with an impact test (Izod or Charpy) smaller toughness (ceramics) Engineering tensile stress, larger toughness (metals, PMCs) smaller toughnessunreinforced polymers Engineering tensile strain, e Chapter 6- 20 TOUGHNESS Toughness can be measured with an impact test (Izod or Charpy) Chapter 6- 20 TRUE STRESS & TRUE STRAIN li F True Stre ss T , True Strain e T ln Ai l0 Instantaneous area Instantaneous gauge length If volume of material is conserved during deformation: Ai li=A0 l0 Then (1 e ), e ln(1 e ) TT necking valid until necking point Chapter 6- 22 EXAMPLE PROBLEM 6.4 A cylindrical specimen of steel having an original diameter of 12.8mm (0.505 in) is tensile tested to fracture and found to have an engineering fracture strength f of 460 MPa (67,000 psi). If its cross-sectional diameter at fracture is 10.7mm (0.422 in). Determine: a) The ductility in terms of percent reduction in area b) The true stress at fracture Chapter 6- 22 HARDENING • An increase in y due to plastic deformation. • Curve fit to the stress-strain response: strain K K and n can be found from tables or tensile tests Chapter 6- 22 HARDNESS • Resistance to permanently indenting the surface. • Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties. Adapted from Fig. 6.18, Callister 6e. (Fig. 6.18 is adapted from G.F. Kinney, Engineering Properties and Applications of Plastics, p. 202, John Wiley and Sons, 1957.) Chapter 6- 21 P HARDNESS Brinell, uses 10 mm sphere of steel or tungsten carbide 2P HB D D D 2 d 2 Rockwell and Superficial Rockwell, uses a diamond cone (Brale indenter) or steel spheres Vickers microhardness, uses a diamond pyramid HV 1.854P / d12 Knoop microhardness, uses a diamond pyramid HK 14.2P / l 2 Chapter 6- 21 HARDNESS and TENSILE STRENGTH There is a linear relation between the tensile strength and hardness of a metal (especially for cast iron, steel and brass) For most steels: TS ( MPa) 3.45 HB TS ( psi) 500 HB Chapter 6- 21 DESIGN OR SAFETY FACTORS • Design uncertainties mean we do not push the limit. • Factor of safety, N Often N is between y working 1.2 and 4 N • 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. working 220,000N d2 / 4 y N 5 Chapter 6- 23 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. Note: For materials selection cases related to mechanical behavior, see slides 22-4 to 22-10. Chapter 6- 24