Chapter 22-

ISSUES TO ADDRESS...

• Price and availability of materials.

1

• How do we select materials based on optimal performance?

• Applications: --shafts under torsion --bars under tension --plates under bending --materials for a magnetic coil.

CHAPTER 22: MATERIALS SELECTIONECONOMIC, ENVIRON., & DESIGN ISSUES

Chapter 22-2

• Current Prices on the web(a): --Short term trends: fluctuations due to supply/demand. --Long term trend: prices will increase as rich deposits are depleted.

• Materials require energy to process them:--Energy to produce materials (GJ/ton)

AlPETCusteelglasspaper

237 (17)(b)

103 (13)(c)

97 (20)(b)

20(d)

13(e)

9(f)

--Cost of energy used in processing materials ($/GJ)(g)

elect resistancepropanenatural gasoil

2511 9 8

a http://www.statcan.ca/english/pgdb/economy/primary/prim44.htma http://www.metalprices.comb http://www.automotive.copper.org/recyclability.htmc http://members.aol.com/profchm/escalant.htmld http://www.steel.org.facts/power/energy.htme http://eren.doe.gov/EE/industry_glass.htmlf http://www.aifq.qc.ca/english/industry/energy.html#1g http://www.wren.doe.gov/consumerinfo/rebriefs/cb5.html

Energy using recycledmaterial indicated in green.

PRICE AND AVAILABILITY

Chapter 22-3

• Reference material: --Rolled A36 plain carbon steel.• Relative cost, $, fluctuates less over time than actual cost.Based on data in AppendixC, Callister, 6e.AFRE, GFRE, & CFRE = Aramid,Glass, & Carbon fiber reinforced epoxy composites.

$ =

$/kg($/kg)ref material

RELATIVE COST, $, OF MATERIALS

Chapter 22-4

• Bar must not lengthen by more than under force F; must have initial length L.

• Maximize the Performance Index:

F, L c c

-- Stiffness relation: -- Mass of bar:

F

c2=E

δL ( = E) M=ρLc2

• Eliminate the "free" design parameter, c:

M=

FL2

δρE

P =

Eρ

specified by applicationminimize for small M

(stiff, light tension members)

STIFF & LIGHT TENSION MEMBERS

Chapter 22-5

• Bar must carry a force F without failing; must have initial length L.

• Maximize the Performance Index:

F, L c c

-- Strength relation: -- Mass of bar:

M=ρLc2

• Eliminate the "free" design parameter, c:

specified by applicationminimize for small M

P =

σfρ(strong, light tension members)

M=FLN

ρσf

σfN

=F

c2

STRONG & LIGHT TENSION MEMBERS

Chapter 22-6

• Bar must carry a moment, Mt ; must have a length L.

• Maximize the Performance Index:

-- Strength relation: -- Mass of bar:

• Eliminate the "free" design parameter, R:

specified by application minimize for small M

(strong, light torsion members)

τfN

=2Mt

πR3 M=ρπR2L

L 2R Mt

τ τ

M= 2 π NMt( )2/3

Lρ

τf2/3

P =

τf2/3

ρ

STRONG & LIGHT TORSION MEMBERS

Chapter 22-

DATA: STRONG & LIGHT TENSION/TORSION MEMBERS

Increasing P for strong tension members

Increasing P for strong torsion members

0.1 1 10 30

1

10

102

103

104

Density, (Mg/m3)

Strength, f (MPa)

slope = 1

0.1

Metal alloys

Steels

Ceramics

PMCs

Polymers

|| grain

grain wood

Cermets

slope =

3/2

7

Adapted from Fig. 6.22, Callister 6e. (Fig. 6.22 adapted from M.F. Ashby, Materials Selection in Mechanical Design, Butterworth-Heinemann Ltd., 1992.)

Chapter 22-

0.1 1 10 30 0.1

1

10

102

103

104 Cermets

Steels

Density, (Mg/m3)

Str

en

gth

,

f (M

Pa)

slop

e = 2

Increasing P for strong bending members

Metal alloys

Ceramics

PMCs

Polymers

|| grain

grain wood

8

• Maximize the Performance Index:

P =

σ1/2

ρ

Adapted from Fig. 6.22, Callister 6e. (Fig. 6.22 adapted from M.F. Ashby, Materials Selection in Mechanical Design, Butterworth-Heinemann Ltd., 1992.)

DATA: STRONG & LIGHTBENDING MEMBERS

Chapter 22-9

• Other factors: --require f > 300MPa. --Rule out ceramics and glasses: KIc too small.

• Maximize the Performance Index: P =

τf2/3

ρ

• Numerical Data:

• Lightest: Carbon fiber reinf. epoxy (CFRE) member.

material

CFRE (vf=0.65)

GFRE (vf=0.65)Al alloy (2024-T6)Ti alloy (Ti-6Al-4V)4340 steel (oil quench & temper)

(Mg/m3)1.52.02.84.47.8

P (MPa)2/3m3/Mg)7352161511

Data from Table 6.6, Callister 6e.

τf (MPa)11401060 300 525 780

DETAILED STUDY I: STRONG, LIGHT TORSION MEMBERS

Chapter 22-10

• Minimize Cost: Cost Index ~ M$ ~ $/P (since M ~ 1/P)

• Numerical Data:

• Lowest cost: 4340 steel (oil quench & temper)

materialCFRE (vf=0.65)GFRE (vf=0.65)Al alloy (2024-T6)Ti alloy (Ti-6Al-4V)4340 steel (oil quench & temper)

$804015

1105

P (MPa)2/3m3/Mg)7352161511

($/P)x100112769374846

• Need to consider machining, joining costs also.

Data from Table 6.7, Callister 6e.

DETAILED STUDY I: STRONG, LOW COST TORSION MEMBERS

Chapter 22-11

• Background(2): High magnetic fields permit study of: --electron energy levels, --conditions for superconductivity --conversion of insulators into conductors.• Largest Example: --short pulse of 800,000 gauss (Earth's magnetic field: ~ 0.5 Gauss)• Technical Challenges: --Intense resistive heating can melt the coil. --Lorentz stress can exceed the material strength.• Goal: Select an optimal coil material.

(1) Based on discussions with Greg Boebinger, Dwight Rickel, and James Sims, National High Magnetic Field Lab (NHMFL), Los Alamos National Labs, NM (April, 2002).(2) See G. Boebinger, Al Passner, and Joze Bevk, "Building World Record Magnets", Scientific American, pp. 58-66, June 1995, for more information.

Pulsedmagneticcapable of600,000 gaussfield during20ms period.

Fracturedmagnetcoil.(Photostaken at NHMFL,Los AlamosNational Labs,NM (Apr. 2002)by P.M. Anderson)

DETAILED STUDY II: OPTIMAL MAGNET COIL MATERIAL

Chapter 22-12

• Applied magnetic field, H:

H = N I/L

• Lorentz "hoop" stress: • Resistive heating: (adiabatic)

RIA σ =

IμoHRA

( ≤σfN

)

temp increaseduring currentpulse of t

ΔT =I2ρe

A2cv

Δt (<ΔTmax)

Magneticfieldpointsout ofplane.

elect. resistivity

specific heat

current IN turns totalL = length of each turn

Forcelength

=IμoH

LORENTZ STRESS & HEATING

Chapter 22-13

• Mass of coil:

M = dAL

• Eliminate "free" design parameters A, I from the stress & heating equations (previous slide):

• Applied magnetic field:

H = N I/L

H2

M≤

1

2πR2LμoN

σfρd

--Stress requirement

specified by application

Performance Index P1:maximize for large H2/M

H ΔtM

≤ΔTmax2π RL

1ρd

cvρe

specified by application

Performance Index P2:maximize for large Ht1/2/M

--Heating requirement

MAGNET COIL: PERFORMANCE INDEX

Chapter 22-14

• Relative cost of coil:

$ = $ M

• Eliminate M from the stress & heating equations:

• Applied magnetic field:

H = N I/L

--Stress requirement

specified by application

Cost Index C1:maximize forlarge H2/$

specified by application

Cost Index C2:maximize forlarge Ht1/2/$

--Heating requirement

H2

$≤

1

2πR2LμoN

σfρd$

MAGNET COIL: COST INDEX

Chapter 22-15

• Data from Appendices B and C, Callister 6e:Material1020 steel (an)1100 Al (an)7075 Al (T6)11000 Cu (an)17200 Be-Cu (st)71500 Cu-Ni (hr)PtAg (an)Ni 200units

f

395 90572220475380145170462MPa

d

7.852.712.808.898.258.9421.510.58.89g/cm3

$ 0.812.313.4 7.951.412.91.8e4271 31.4 --

cv

486904960385420380132235456J/kg-K

e

1.600.290.520.170.573.751.060.150.95-m3

P1

50 33204 25 58 43 7 16 52 f/d

P2

2 21 15 5 3 1 19 <1 2 (cv/e)0.5

d

C1

63 315 3 1 3<1<1 2P1/$

C2

2.5 1.7 1.1 0.6<0.1<0.1<0.1<0.1<0.1P2/$

Avg. values used. an = annealed; T6 = heat treated & aged;st = solution heat treated; hr = hot rolled

• Lightest for a given H: 7075 Al (T6)

• Lightest for a given H(t)0.5: 1100 Al (an)

• Lowest cost for a given H: 1020 steel (an)• Lowest cost for a given H(t)0.5: 1020 steel (an) C2

C1

P2

P1

INDICES FOR A COIL MATERIAL

Chapter 22-16

• Material costs fluctuate but rise over the long term as: --rich deposits are depleted, --energy costs increase.• Recycled materials reduce energy use significantly.• Materials are selected based on: --performance or cost indices.• Examples: --design of minimum mass, maximum strength of: • shafts under torsion, • bars under tension, • plates under bending, --selection of materials to optimize more than one property: • material for a magnet coil. • analysis does not include cost of operating the magnet.

SUMMARY

Chapter 22-

Reading:

Core Problems:

Self-help Problems:

0

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