Bruce Mayer, PE Registered Electrical & Mechanical Engineer BMayer@ChabotCollege

1. Engineering 45 Mechanical Properties of Metals (1) Bruce Mayer, PE Registered Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. Learning Goals.1 – Mech Props • STRESS and STRAIN: • What they are and why they are they used instead of LOAD and DEFORMATION • ELASTIC Behavior • How Much Deformation occurs when Loads are SMALL? • Which Materials Deform Least

3. Learning Goals.2 – Mech Props • PLASTIC Behavior • Determine the point at which dislocations cause permanent deformation • Which materials are most resistant to permanent deformation • TOUGHNESS and Ductility • What they are • How to Measure them

4. Materials Testing • In The USA the American Society for Testing and Materials (ASTM) Sets Many, Many Materials-Test Standards • Founded in 1898, ASTM International is a not-for-profit organization that provides a global forum for the development and publication of voluntary consensus standards for materials, products, systems, and services. Over 30,000 individuals from 100 nations are the members of ASTM International, who are producers, users, consumers, and representatives of government and academia. In over 130 varied industry areas, ASTM standards serve as the basis for manufacturing, procurement, and regulatory activities. Formerly known as the American Society for Testing and Materials, ASTM International provides standards that are accepted and used in research and development, product testing, quality systems, and commercial transactions around the globe.

5. Apply/Remove a SMALL Force Load to a Specimen 1. Initial 2. SMALL load 3. Unload bonds stretch return to initial d F F Linear- elastic Non-Linear- elastic d ELASTIC Deformation • F  Force Load(lb or N) •   Deformation in Response to the Load (in or m) ELASTIC means REVERSIBLE

6. Apply/Remove a LARGE Force Load to a Specimen 1. Initial 2. LARGE load 3. Unload bonds PlanesStillSheared stretch shear & planes dplastic delastic+plastic F F linear linear elastic elastic d dplastic PLASTIC Deformation PLASTIC means PERMANENT

7. Normalize Applied-Force to Supporting Area F F F t t F A rea, A s A rea, A F s F t F F t t F s = A o original area before loading Engineering Stress,  • TENSILE Stress, σ • SHEAR Stress,  • Engineering Stress Units → N/m2 (Pa) or lb/in2 (psi)

8. Common States Of Stress F F A = cross sectional o Area (when unloaded) M F s A o A c M 2R • Simple tension: cable • Simple shear: drive shaft Ski lift(photo courtesy P.M. Anderson) Note: t = M/AoR here. 5

9. Common Stress States cont.1 A o Balanced Rock, Arches National Park (photo courtesy P.M. Anderson) • Simple COMPRESSION: (photo courtesy P.M. Anderson) Note: These areCOMPRESSIVE structural members (σ < 0; i.e., a NEGATIVEnumber) 6

10. BIAXIAL Tension Pressurized tank Fish under water (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) s< 0 h Common Stress States cont.2 • HYDROSTATIC Compression Tank Surface SurfaceElement

11. g = Dx/y= tan q Engineering Strain,  • TENSILE Strain • LATERAL Strain • SHEAR Strain q x • Engineering STRAIN Units → NONE (Dimensionless) • To Save Writing Exponents • µ-in/in • µm/m y 90º - q 90º

12. Std Specimen 3/4-10 Thd Tensile Testing – Cyl Specimen • Tension Tester • Other Tests • Compression Test for Brittle Materials • e.g.; Concrete → GREAT in Compression, Fractures in Tension/Shear • Torsion (twist) Test • Drive Shafts, Torsion Bars for Vehicle Suspension

13. Consider a Tension Test With SMALL loads; Plotting σ vs. ε Find s F E e 1 Linear- elastic F simple tension test Linear Elastic Deformation • The Data Plots as a Line Through the Origin • Thus σε • The Constant of Proportionality is the Slope, E • E is the “Modulus of Elasticity”, or “Young’s Modulus” • Linear Elastic Materials are said to follow Hooke’s (spring) Law

14. During a Pull-Test the Material CONTRACTS Laterally,εL, as it Extends Longitudinally, ε. Plotting F e L e F -n simple 1 tension test Linear Elastic Deformation • This Data Also Plotsas a Line • Thus εLε • The Constant of Proportionality is the Slope,  •  is “Poisson’s Ratio” as Defined by

15. Data From vs.  ShearStress Test t G g 1 Shear Modulus   THIN Walled Cylinder • Leads to Hooke’s Law in Pure Shear • Where • G  Modulus of Rigidity (Shear Modulus) http://www.efunda.com/materials/common_matl/Common_Matl.cfm?MatlPhase=Solid&MatlProp=Mechanical#Mechanical

16. Data FromP vs. VTests P P P P D V V o -K P 1 Pressure Test: Init. vol =Vo. Vol chg. = DV Bulk Modulus • Leads to Hooke’s Law in Pure HydroStatic Compression • Where • K  Modulus of Compression (Bulk Modulus) in GPa or Mpsi

17. Uniaxial Tension Elastic (Hooke’s) Relations • Isotropic Material “Modulus Relations” • Also Poisson’s Ratio • Pure Shear • Steel Properties • E = 190-210 GPa • G = 75-80 GPa • K = 150-160 GPa •  = 0.27-0.3 • All-Over Compression

18. Elastic Properties of Metals

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 Eceramics>Emetals>>Epolymers E(GPa) 109 Pa Based on data in Table B2, Callister 7e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers.

20. Temperature Effects • Affect of Temperature on an Aluminum Alloy • In General for Increasing T • E↓ • L↑ at Fracture • ↓ at Fracture

21. UniAxial Tension 2 ML FL Fw o d = d = - n  = o o L 4 r p G E A E A o o o F M=moment =angle of twist d /2 A o d /2 L Lo L o w o 2r o Some Linear Elastic Relations • Simple Torsion, Solid Cylinder • Material, geometric, and loading parameters contribute to deflection • Larger elastic moduli minimize elastic deflection

22. d WhiteBoard Work 6.66 kN • Consider this Situation: • Given for Cu • E = 110 GPa (16 Mpsi) • y = 240 MPa (35 ksi) • Find PreLoad/PreStrain Diameter, d, for a PostLoad/PostStrain Axial Extension δ= 0.5 mm Cu 380 mm 6.66 kN