Chapter 22 Avi

8/3/2019 Chapter 22 Avi

1/17

Chapter 22-

ISSUES TO ADDRESS...

Price and availability of materials.

1

How do we select materials based on optimalperformance?

Applications:--shafts under torsion--bars under tension

--plates under bending--materials for a magnetic coil.

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


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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 producematerials (GJ/ton)

AlPETCu

steelglasspaper

237 (17)(b)103 (13)(c)97 (20)(b)20(d)13(e)9(f)

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

elect resistancepropanenatural gas

oil

25119

8a 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 recycled

material indicated in green.

PRICE AND AVAILABILITY


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Chapter 22- 3

Reference material:

--Rolled A36 plaincarbon steel.

Relative cost, $,fluctuates lessover time than

actual cost.

Based on data in AppendixC, Callister, 6e.AFRE, GFRE, & CFRE = Aramid,Glass, & Carbon fiber reinforcedepoxy composites.

$$/kg

($ /kg)ref material

RELATIVE COST, $, OF MATERIALS


4/17

Chapter 22- 4

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

Maximize the Performance Index:

-- Stiffness relation: -- Mass of bar:

F

c2 E

d

L(s = Ee) M Lc

2

Eliminate the "free" design parameter, c:

MFL2

d

E

P

E

specified by applicationminimize for small M

(stiff, light tension members)

STIFF & LIGHT TENSION MEMBERS


5/17

Chapter 22- 5

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


-- Strength relation: -- Mass of bar:

M Lc2

Eliminate the "free" design parameter, c:

specified by applicationminimize for small M

P s f

(strong, light tension members)

M FLN

sf

s f

N

F

c2

STRONG & LIGHT TENSION MEMBERS


6/17

Chapter 22- 6

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


-- Strength relation: -- Mass of bar:

Eliminate the "free" design parameter, R:

specified by application minimize for small M

(strong, light torsion members)

f

N2Mt

R3

M R2L

M 2 NMt 2 /3

L

f2 /3

P f2 /3

STRONG & LIGHT TORSION MEMBERS


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Chapter 22-

DATA: STRONG & LIGHTTENSION/TORSION MEMBERS

Increasing Pfor strongtension

members

Increasing Pfor strong

torsion members

0.1 1 10 30110

102103

104

Density, (Mg/m3)

Strength, sf(MPa)

0.1

Metalalloys

SteelsCeramicsPMCs

Polymers|| grain

grain

Cermets

7

Adapted from Fig. 6.22,Callister 6e. (Fig. 6.22 adaptedfrom M.F. Ashby, MaterialsSelection in MechanicalDesign, Butterworth-

Heinemann Ltd., 1992.)


8/17

Chapter 22-

0.1 1 10 300.1110

102103104

CermetsSteels

Density, (Mg/m3)

S

trength,sf(MPa)

Increasing Pfor strong

bending members

Metalalloys

CeramicsPMCs

Polymers|| grain

grain

8

Maximize the Performance Index: P s1/2

Adapted from Fig. 6.22,Callister 6e. (Fig. 6.22 adaptedfrom M.F. Ashby, MaterialsSelection in MechanicalDesign, Butterworth-Heinemann Ltd., 1992.)

DATA: STRONG & LIGHTBENDING MEMBERS


9/17

Chapter 22- 9

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

Maximize the Performance Index: P f2 /3

Numerical Data:

Lightest: Carbon fiber reinf. epoxy

(CFRE) member.

materialCFRE (vf=0.65)GFRE (vf=0.65)Al alloy (2024-T6)

Ti alloy (Ti-6Al-4V)4340 steel (oil

quench & temper)

(Mg/m3)1.52.02.8

4.47.8

P (MPa)2/3m3/Mg)735216

1511

Data from Table 6.6, Callister 6e.

f (MPa)11401060300

525780

DETAILED STUDY I: STRONG, LIGHTTORSION MEMBERS


10/17

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)

$80

40151105

P (MPa)2/3m3/Mg)73

52161511

($/P)x100112

769374846

Need to consider machining, joining costs also.

Data from Table 6.7, Callister 6e.

DETAILED STUDY I: STRONG, LOWCOST TORSION MEMBERS


11/17

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 exceedthe material strength.

Goal: Select an optimal coil material.(1) Based on discussions with Greg Boebinger, Dwight Rickel, and James Sims, National HighMagnetic 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 during

20ms period.

Fracturedmagnetcoil.(Photos

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

DETAILED STUDY II: OPTIMALMAGNET COIL MATERIAL


12/17

Chapter 22- 12

Applied magnetic field, H:

H = N I/L

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

s IoHR

A(

sf

N)

temp increaseduring current

pulse of Dt

DT I2e

A2cv

Dt ( DTmax )

Magneticfieldpointsout ofplane.

elect. resistivity

specific heat

Force

length IoH

LORENTZ STRESS & HEATING


13/17

Chapter 22- 13

Mass of coil:

M = dAL

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

Applied magnetic field:

H = N I/L

H2

M

1

2R2LoN

sf

d

--Stress requirement

specified by application

Performance Index P1:maximize for large H2/M

H Dt

M

DTmax

2 RL

1

d

cve


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

--Heating requirement

MAGNET COIL: PERFORMANCE INDEX


14/17

Chapter 22- 14

Relative cost of coil:

$ = $M

Eliminate M from the stress & heating equations:

Applied magnetic field:

H = N I/L

--Stress requirement


Cost Index C1:maximize forlarge H2/$


Cost Index C2:maximize forlarge Ht1/2/$

--Heating requirement

H Dt

$

DTmax

2 RL

1

d$

cve

H2

$

1

2R2LoN

sf

d$

MAGNET COIL: COST INDEX


15/17

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

sf395

90572220475

380145170462MPa

d7.852.712.808.898.25

8.9421.510.58.89g/cm3

$0.8

12.313.4

7.951.4

12.91.8e4271

31.4--

cv486904960385420

380132235456J/kg-K

e1.600.290.520.170.57

3.751.060.150.95

W-m3

P15033

2042558

4371652

sf/d

P22

2115

53

119


16/17

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


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Chapter 22-

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Core Problems:

Self-help Problems:

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