Chapter 6: Mechanical Properties

Transcription

1 Chapter 6: Mechanical Properties Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? Stress and strain: What are they and why are they used instead of load and deformation? Plastic behavior: At what point does permanent deformation occur? What materials are most resistant to permanent deformation? Toughness and ductility: What are they and how do we measure them? Chapter 6-1

2 Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch δ Elastic means reversible! F F Linearelastic δ return to initial Non-Linearelastic Chapter 6-2

3 Concepts of stress and strain Tension tests engineering stress engineering strain Compression tests Chapter 6 -

4 Linear Elastic Properties Modulus of Elasticity, E: (also known as Young's modulus) Hooke's Law: σ = E ε σ F Linear- elastic E ε F simple tension test Chapter 6-4

5 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 G raphite Polymers Composites /fibers Polyester PET PS PC PP HDP E PTF E LDPE Carbon fibers only C FRE( fibers)* A ramid fibers only A FRE( fibers)* Glass fibers only G FRE( fibers)* GFRE* CFRE * G FRE( fibers)* C FRE( fibers) * AFRE( fibers) * Epoxy only Wood( grain) 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. Chapter 6-5

6 Mechanical Properties Slope of stress strain plot (which is proportional to the elastic modulus) depends on df/dr Adapted from Fig. 6.7, Callister 7e. Chapter 6-6

7 Concepts of stress and strain (continued) Shear and torsional tests Shear stress Shear strain Geometric considerations of the stress state Chapter 6 -

8 Common States of Stress Simple tension: cable F A o = cross sectional area (when unloaded) σ= F A o F σ σ Torsion (a form of shear): drive shaft Ski lift (photo courtesy P.M. Anderson) Chapter 6-8

9 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= F A o Note: compressive structure member (σ < 0 here). Chapter 6-9

10 Poisson's ratio, ν Poisson's ratio, ν: ε L ν= ε metals: ν ~ 0.33 ceramics: ν ~ 0.25 polymers: ν ~ 0.40 Relation of elastic properties for isotropic materials Tensile strain: Lateral strain: w o ε = δ L o ε δ L = δ/2 L o L w o δ L /2 Chapter 6-10

11 Examples Determine the load required to produce a 2.5x10-3 mm change in diameter. D 0 =10mm, Poisson s ratio for brass is 0.34 Chapter 6 -

12 Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload bonds stretch p lanes & planes still shear sheared δ elastic + plastic δ plastic F F Plastic means permanent! linear elastic δ plastic linear elastic δ Chapter 6-12

13 Plastic (Permanent) Deformation (at lower temperatures, i.e. T < T melt /3) Simple tension test: engineering stress, σ Elastic+Plastic at larger stress Elastic initially permanent (plastic) after load is removed ε p engineering strain, ε plastic strain Adapted from Fig (a), Callister 7e. Chapter 6-13

14 Stress at which noticeable plastic deformation has occurred. when ε p = σ y tensile stress, σ Yield Strength, σ y σ y = yield strength Note: for 2 inch sample ε = = Δz/z Δz = in ε p = engineering strain, ε Adapted from Fig (a), Callister 7e. Chapter 6-14

15 Yield Strength : Comparison Metals/ Alloys Steel (4140) qt Graphite/ Ceramics/ Semicond Polymers Composites/ fibers Yield strength, σy (MPa) Ti (5Al-2.5Sn) W (pure) a Cu (71500) Mo (pure) cw Steel (4140) a Steel (1020) cd Al (6061) ag Steel (1020) hr Ti (pure) Ta (pure) a Cu (71500) hr Al (6061) a Hard to measure, since in tension, fracture usually occurs before yield. dry PC Nylon 6,6 PET PVC humid PP H DPE Hard to measure, in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield. Room T values Based on data in Table B4, Callister 7e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered 10 Tin (pure) LDPE Chapter 6-15

16 Tensile Strength, TS Maximum stress on engineering stress-strain curve. TS σ y engineering stress Typical response of a metal strain engineering strain Metals: occurs when noticeable necking starts. Polymers: occurs when polymer backbone chains are aligned and about to break. Adapted from Fig. 6.11, Callister 7e. F = fracture or ultimate strength Neck acts as stress concentrator Chapter 6-16

17 Tensile strength, TS (MPa) Tensile Strength : Comparison 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) Ti (pure) ag 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 L DPE H DPE Composites/ fibers C fibers Aramid fib E-glass fib A FRE ( fiber) GFRE ( fiber) C FRE ( fiber) wood( fiber) GFRE ( fiber) C FRE ( fiber) A FRE( fiber) wood ( fiber) Room Temp. values Based on data in Table B4, Callister 7e. 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 6-17

18 Plastic tensile strain at failure: E ngineering tensile stress, σ Adapted from Fig. 6.13, Callister 7e. Ductility smaller %EL larger %EL % EL L L = f o Lo L o A o A f x 100 L f Engineering tensile strain, ε Another ductility measure: A A f % RA = x 100 A o - o Chapter 6-18

19 Resilience, U r Ability of a material to store energy Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to U r 1 σ yε y 2 Adapted from Fig. 6.15, Callister 7e. Chapter 6-19

20 Toughness Energy to break a unit volume of material Approximate by the area under the stress-strain curve. Engineering small toughness (ceramics) tensile stress, σ Adapted from Fig. 6.13, Callister 7e. large toughness (metals) very small toughness (unreinforced polymers) Engineering tensile strain, ε Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy Chapter 6-20

21 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 σ y. Toughness: The energy needed to break a unit volume of material. Ductility: The plastic strain at failure. Chapter 6-21