CHAPTER 6: MECHANICAL PROPERTIES ISSUES TO ADDRESS...

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1 CHAPTER 6: MECHANICAL PROPERTIES ISSUES TO ADDRESS... Stress and strain: What are they and why are they used instead of load and deformation? Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? Plastic behavior: At what point do dislocations cause permanent deformation? What materials are most resistant to permanent deformation? Toughness and ductility: What are they and how do we measure them?

2 ELASTIC DEORMATION 1. Initial 2. Small load 3. Unload bonds stretch δ Elastic means reversible! Linearelastic δ return to initial Non-Linearelastic

3 PLASTIC DEORMATION (METALS) 1. Initial 2. Small load 3. Unload bonds stretch planes & planes still shear sheared δelastic + plastic δplastic Plastic means permanent! linear elastic δplastic linear elastic δ

4 ENGINEERING STRESS Tensile stress, σ: Shear stress, τ: t t Area, A Area, A s t σ= t A o original area before loading τ= s A o Stress has units: N/m 2 or lb/in 2 s t

5 COMMON STATES O STRESS Simple tension: cable Ao = cross sectional Area (when unloaded) σ = A o σ σ Simple shear: drive shaft A c M 2R M s A o τ = s A Ski lift (photo courtesy P.M. Anderson) o τ Note: τ = M/AcR here.

6 OTHER COMMON STRESS STATES (1) Simple compression: A o Canyon Bridge, Los Alamos, NM (photo courtesy P.M. Anderson) Balanced Rock, Arches National Park (photo courtesy P.M. Anderson) σ = A o Note: compressive structure member (σ < 0 here).

7 OTHER COMMON STRESS STATES (2) Bi-axial tension: Hydrostatic compression: Pressurized tank (photo courtesy P.M. Anderson) σθ > 0 ish under water (photo courtesy P.M. Anderson) σz > 0 σ < 0 h

8 Tensile strain: Shear strain: θ/2 ENGINEERING STRAIN δ/2 Lateral strain: ε= δ L o ε L = δ L δ L /2 w o δ/2 δ L /2 L o w o π/2 π/2 - θ γ = tan θ θ/2 Strain is always dimensionless.

9 STRESS-STRAIN TESTING Typical tensile specimen Typical tensile test machine load cell Adapted from ig. 6.2, Callister 6e. extensometer specimen moving cross head gauge length = (portion of sample with reduced cross section) Other types of tests: --compression: brittle materials (e.g., concrete) --torsion: cylindrical tubes, shafts. Adapted from ig. 6.3, Callister 6e. (ig. 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.)

10 LINEAR ELASTIC PROPERTIES Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law: σ = E ε Poisson's ratio, ν: ν = ε ε L L ε ε metals: ν ~ 0.33 ceramics: ~0.25 polymers: ~0.40 Units: E: [GPa] or [psi] ν: dimensionless σ -ν 1 E 1 Linearelastic ε simple tension test

11 OTHER ELASTIC PROPERTIES Elastic Shear modulus, G: τ = G γ Elastic Bulk modulus, K: P= -K V Vo τ P -K 1 1 G γ V Vo Special relations for isotropic materials: E E G = K = 2(1+ν) 3(1 2ν) P M P M simple torsion test P pressure test: Init. vol =V o. Vol chg. = V

12 YOUNG S MODULI: COMPARISON E(GPa) 10 9 Pa Metals Alloys Tungsten Molybdenum Steel, Ni Tantalum Platinum Cu alloys Zinc, Ti Silver, Gold Aluminum Magnesium, Tin Graphite Ceramics Semicond Diamond Si carbide Al oxide Si nitride <111> Si crystal <100> Glass-soda Concrete Graphite Polymers Polyester PET PS PC Composites /fibers Carbon fibers only CRE( fibers)* Aramid fibers only ARE( fibers)* Glass fibers only GRE( fibers)* GRE* CRE* GRE( fibers)* CRE( fibers)* ARE( fibers)* Epoxy only Eceramics > Emetals >> Epolymers Based on data in Table B2, Callister 6e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CRE), aramid (ARE), or glass (GRE) fibers PP HDPE PTE Wood( grain) 0.2 LDPE

13 Young s Modulus: Typical Temperature Dependence Melting Point of Al

14 More on Shear Stress A 0 σ = A 0 A A' = S A0 cosθ = sinθ Schmidt actor τ = S A' = sinθ = A0 cosθ A 0 sinθ cosθ = σ sinθ cosθ or uniaxial deformation: maximum shear stress at 45

15 Plastic Deformation σ y = Yield Strength (typically defined at ε = 0.002) Discontinuous Yielding or Yield Point Phenomena Define yield strength at lower yield point Typical metals: plastic deformation onset for strains > Typical σ y : 35 MPa (soft Al); 1400 MPa (high strength steel)

16 Elastic Strain Recovery σ y0 = Yield Strength (typically defined at ε = 0.002) Initial loading σ yi = Yield Strength After unloading and reloading Note: for many metals YS after plastic deformation

17 HARDENING An increase in σy due to plastic deformation. σ σ y 1 σ y 0 unload reload Curve fit to the stress-strain response: σ T = C( ε T ) n true stress (/A) large hardening small hardening ε hardening exponent: n=0.15 (some steels) to n=0.5 (some copper) true strain: ln(l/lo)

18 Tensile Strength Tensile Strength TS Maximum stress Necking Typical TS for metals 50 MPa (soft Al) 3000 MPa = 450,000 psi (high strength steel)

19 Typical Stress-Strain Curves

20 TENSILE STRENGTH: COMPARISON Tensile strength, TS (MPa) Metals/ Alloys Steel (4140) qt W (pure) Ti (5Al-2.5Sn) Steel (4140) a a Cu (71500) Cu (71500) hr cw Steel (1020) Al (6061) ag Ti (pure)a Ta (pure) Al (6061) a Graphite/ Ceramics/ Semicond Diamond Si nitride Al oxide Si crystal <100> Glass-soda Concrete Graphite Polymers Nylon 6,6 PC PET PVC PP LDPE HDPE Composites/ fibers C fibers Aramid fib E-glass fib TS(ceram) ARE( fiber) GRE( fiber) CRE( fiber) wood( fiber) GRE( fiber) CRE( fiber) ARE( fiber) wood( fiber) ~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 ARE, GRE, & CRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers.

21 Brittle and Ductile Materials Ductility % EL = ( l l ) f l % EL = ( l l ) f l % RA = ( A0 Af ) 100 A 0 % RA = ( A0 Af ) 100 A 0 l f = length at fracture A f = section area at fracture Typical Ductility for soft metals %EL 25 75%

22 TOUGHNESS Energy to break a unit volume of material Approximate by the area under the stress-strain curve. Engineering tensile stress, σ smaller toughness (ceramics) larger toughness (metals, PMCs) smaller toughnessunreinforced polymers Engineering tensile strain, ε

23 True Stress and True Strain σ T = A i ε σ ε T T T l = ln l = σ i 0 = ln 1 ( 1+ ε ) ( + ε ) True Stress: Load divided by instantaneous section area A i True Strain: from integration: ε dε = 0 l f l 0 dl l

24 HARDNESS Resistance to permanently indenting the surface. Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties. e.g., 10mm sphere apply known force (1 to 1000g) measure size of indent after removing load D d Smaller indents mean larger hardness. most plastics brasses Al alloys easy to machine steels file hard cutting tools nitrided steels diamond increasing hardness Adapted from ig. 6.18, Callister 6e. (ig is adapted from G.. Kinney, Engineering Properties and Applications of Plastics, p. 202, John Wiley and Sons, 1957.)

25 Hardness

26 Hardness

27 DESIGN OR SAETY ACTORS Design uncertainties mean we do not push the limit. actor of safety, N σ working = σ y N Often N is between 1.2 and 4 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. d 220,000N π d 2 /4 σ working 5 = σ y N 1045 plain carbon steel: σy=310mpa TS=565MPa = 220,000N Lo