bruce mayer, pe registered electrical & mechanical engineer bmayer@chabotcollege

[email protected] • ENGR-45_Lec-14_Metal_MechProp-1.ppt1

Bruce Mayer, PE Engineering-45: Materials of Engineering

Bruce Mayer, PERegistered Electrical & Mechanical Engineer

[email protected]

Engineering 45

Mechanical Mechanical Properties of Properties of

Metals (1)Metals (1)



Learning Goals.1 – Mech PropsLearning 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



Learning Goals.2 – Mech PropsLearning 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



Materials TestingMaterials 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. FormerlyFormerly known as the American Society for Testing and Materials, ASTM InternationalASTM International provides standards that are accepted and used in research and development, product testing, quality systems, and commercial transactions around the globe.



ELASTIC DeformationELASTIC Deformation Apply/Remove a SMALL Force Load to a Specimen

1. Initial 3. Unload

return to initial

2. SMALL load

bonds stretch

F

• F Force Load

(lb or N) Deformation in

Response to the Load (in or m)

F

Linear- elastic

Non-Linear-elastic

ELASTIC means REVERSIBLE



PLASTIC DeformationPLASTIC Deformation Apply/Remove a LARGE Force Load to a Specimen

PLASTIC means PERMANENT

1. Initial 3. Unload

PlanesStillSheared

& planes

2. LARGE load

bonds stretch

shear

F

elastic+plasticplastic

F

linear elastic

linear elastic

plastic



Engineering Stress, Engineering Stress, Normalize Applied-Force to Supporting Area TENSILE Stress, σ

Area, A

Ft

Ft

FtAo

original area before loading

SHEAR Stress,

Area, A

Ft

Ft

Fs

F

F

Fs FsAo

• Engineering Stress Units → N/m2 (Pa) or lb/in2 (psi)



5

• Simple tension: cable

o

FA

• Simple shear: drive shaft

o

FsA

Note: = M/AoR here.

Ski lift (photo courtesy P.M. Anderson)

Common States Of StressCommon States Of Stress

Ao = cross sectional Area (when unloaded)

FF

M

M Ao

2R

FsAc



Canyon Bridge, Los Alamos, NM

6

• Simple COMPRESSION:

Note: These areCOMPRESSIVEstructural members(σ < 0; i.e., a NEGATIVEnumber)

(photo courtesy P.M. Anderson)

Common Stress States cont.1Common Stress States cont.1

Ao

(photo courtesy P.M. Anderson)

Balanced Rock, Arches National Park o

FA



Common Stress States cont.2Common Stress States cont.2 BIAXIAL Tension

z > 0

> 0Pressurized tank(photo courtesyP.M. Anderson)

Tank Surface

HYDROSTATIC Compression

Fish under water(photo courtesyP.M. Anderson)

< 0h

SurfaceElement



Engineering Strain, Engineering Strain,

LATERAL Strain

/2

/2

L/2L/2

Lowo

Lo

L L

wo

SHEAR Strain

Engineering STRAIN Units → NONE (Dimensionless)• To Save Writing Exponents

– µ-in/in– µm/m

TENSILE Strain

90º

90º -

x = x/y = tan

y



Tensile Testing – Cyl SpecimenTensile Testing – Cyl Specimen Std Specimen Tension Tester

3/4

-10

Th

d

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



Linear Elastic DeformationLinear Elastic Deformation Consider a Tension Test With SMALL

loads; Plotting σ vs. ε Find

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

F

Fsimple tension test

Linear- elastic

1E

E



Linear Elastic DeformationLinear Elastic Deformation During a Pull-Test the Material

CONTRACTS Laterally,εL, as it Extends Longitudinally, ε. Plotting

This Data Also Plotsas a Line• Thus εL ε

– The Constant of Proportionality is the Slope,

is “Poisson’s Ratio” as Defined by

F

Fsimple tension test

L

L

1



Shear ModulusShear Modulus Data From

vs. ShearStress Test

• Where– G Modulus of

Rigidity (Shear Modulus)

G Leads to Hooke’s

Law in Pure ShearT

HIN

Wal

led

Cyl

ind

er

http://www.efunda.com/materials/common_matl/Common_Matl.cfm?MatlPhase=Solid&MatlProp=Mechanical#Mechanical

1G

RaLa arctanarctan



Bulk ModulusBulk Modulus Data From

P vs. VTests

Leads to Hooke’s Law in Pure HydroStatic Compression

Pressure Test:

Init. vol =Vo. Vol chg. =

V

P

P P

P

P

V

1-K Vo

OV

VK P

• Where– K Modulus of

Compression (Bulk Modulus) in GPa or Mpsi



Elastic (Hooke’s) RelationsElastic (Hooke’s) Relations Uniaxial Tension Isotropic Material

“Modulus Relations”Eε • Also Poisson’s Ratio 12EG

G Pure Shear

L

OV

VK P

All-Over Compression

213 EK

Steel Properties• E = 190-210 GPa• G = 75-80 GPa• K = 150-160 GPa = 0.27-0.3



Elastic Properties of MetalsElastic Properties of MetalsMetal

Young's ModulusE (Mpsi)

Shear modulus, G (Mpsi)

Bulk Modulus,K (Mpsi)

Poisson'sratio,

Aluminum 10.2 3.8 10.9 0.3Brass, 30 Zn 14.6 5.4 16.2 0.4Chromium 40.5 16.7 23.2 0.2

Copper 18.8 7.0 20.0 0.3Iron (soft) 30.7 11.8 24.6 0.3Iron (cast) 22.1 8.7 15.9 0.3

Lead 2.3 0.8 6.6 0.4Magnesium 6.5 2.5 5.2 0.3Molybdenum 47.1 18.2 37.9 0.3Nickel (soft) 28.9 11.0 25.7 0.3Nickel (hard) 31.8 12.2 27.2 0.3

Nickel-silver, 55CU-18Ni-27Zn 19.2 5.0 19.1 0.3Niobium 15.2 5.4 24.7 0.4

Silver 12.0 4.4 15.0 0.4Steel, mild 30.7 11.9 24.5 0.3

Steel, 0.75 C 30.5 11.8 24.5 0.3Steel, 0.75 C, hardened 29.2 11.3 23.9 0.3

Steel, tool 30.7 11.9 24.0 0.3Steel, tool, hardened 29.5 11.4 24.0 0.3

Steel, stainless, 2Ni-18Cr 31.2 12.2 24.1 0.3Tantalum 26.9 10.0 28.5 0.3

Tin 7.2 2.7 8.4 0.4Titanium 17.4 6.6 15.7 0.4Tungsten 59.6 23.3 45.1 0.3Vanadium 18.5 6.8 22.9 0.4

Zinc 15.2 6.1 10.1 0.2



MetalsAlloys

GraphiteCeramicsSemicond

PolymersComposites

/fibers

E(GPa)

Based on data in Table B2,Callister 7e.Composite data based onreinforced epoxy with 60 vol%of alignedcarbon (CFRE),aramid (AFRE), orglass (GFRE)fibers.

Young’s Moduli: ComparisonYoung’s Moduli: Comparison

109 Pa

0.2

8

0.6

1

Magnesium,Aluminum

Platinum

Silver, Gold

Tantalum

Zinc, Ti

Steel, NiMolybdenum

Graphite

Si crystal

Glass -soda

Concrete

Si nitrideAl oxide

PC

Wood( grain)

AFRE( fibers) *

CFRE*

GFRE*

Glass fibers only

Carbon fibers only

Aramid fibers only

Epoxy only

0.4

0.8

2

4

6

10

20

40

6080

100

200

600800

10001200

400

Tin

Cu alloys

Tungsten

<100>

<111>

Si carbide

Diamond

PTFE

HDPE

LDPE

PP

Polyester

PSPET

CFRE( fibers) *

GFRE( fibers)*

GFRE(|| fibers)*

AFRE(|| fibers)*

CFRE(|| fibers)*

Eceramics > Emetals >> Epolymers



Temperature EffectsTemperature Effects Affect of Temperature on an Aluminum Alloy

In General for Increasing T• E↓

L↑ at Fracture

↓ at Fracture



Some Linear Elastic RelationsSome Linear Elastic Relations UniAxial Tension Simple Torsion, Solid

CylinderM=moment =angle of twist

2ro

Lo

– Material, geometric, and loading parameters contribute to deflection

– Larger elastic moduli minimize elastic deflection

F

Ao/2

L/2

Lowo

FLo

EAo

L

Fw o

EAo

2MLo

ro4G



WhiteBoard WorkWhiteBoard Work 6.66 kN

6.66 kN

Cu380 mm

d

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

bruce mayer, pe registered electrical & mechanical engineer bmayer@chabotcollege

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