CHAPTER 20: OPTICAL PROPERTIES

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Transcript CHAPTER 20: OPTICAL PROPERTIES

CHAPTER 20: MATERIALS SELECTION AND DESIGN CONSIDERATIONS ISSUES TO ADDRESS...

• Price and availability of materials .

• How do we select materials based on optimal performance?

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

PRICE AND AVAILABILITY

• Current Prices on the web are depleted.

(a) : --Short term trends: fluctuations due to supply/demand.

--Long term trend: prices will increase as rich deposits • Materials require energy to process them: --Energy to produce materials (GJ/ton) --Cost of energy used in processing materials ($/GJ) (g) Al PET Cu steel glass paper 237 103 97 20 (17) (13) (20) (d) 13 (e) 9 (f) (b) (c) (b) Energy using recycled material indicated in green.

elect resistance propane natural gas oil 25 11 9 8 a http://www.statcan.ca/english/pgdb/economy/primary/prim44.htm

a http://www.metalprices.com

b http://www.automotive.copper.org/recyclability.htm

c http://members.aol.com/profchm/escalant.html

d http://www.steel.org.facts/power/energy.htm

e http://eren.doe.gov/EE/industry_glass.html

f http://www.aifq.qc.ca/english/industry/energy.html#1 g http://www.wren.doe.gov/consumerinfo/rebriefs/cb5.html

RELATIVE COST,

, OF MATERIALS

 $ /kg ($ /kg) ref material

• Reference material: --Rolled A36 plain carbon steel.

• Relative cost, $ , fluctuates less over time than actual cost.

Based on data in Appendix C, Callister, 6e .

AFRE, GFRE, & CFRE Glass, & Carbon fiber reinforced epoxy composites.

= Aramid, 3

STIFF & LIGHT TENSION MEMBERS

• Bar must not lengthen by more than

under force F; must have initial length L.

-- Stiffness relation: -- Mass of bar:

F 2  E d L

(

= E

)

  Lc 2

• Eliminate the "free" design parameter, c :

M  FL 2 d  E

minimize for small M specified by application • Maximize the Performance Index : (stiff, light tension members)

P  E 

STRONG & LIGHT TENSION MEMBERS

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

-- Strength relation: -- Mass of bar:

s f  F N c 2   Lc 2

• Eliminate the "free" design parameter, c :

 M  FLN

specified by application

s f

minimize for small M • Maximize the Performance Index : (strong, light tension members)

P  s f 

STRONG & LIGHT TORSION MEMBERS

• Bar must carry a moment, M t must have a length L.

; -- Strength relation: -- Mass of bar:

 f  2M t N  R 3   R 2 L

• Eliminate the "free" design parameter, R :

M   2  NM t

specified by application

 2 / 3 L   f 2 / 3

minimize for small M • Maximize the Performance Index : (strong, light torsion members)

P   f 2 / 3 

DATA: STRONG & LIGHT TENSION/TORSION MEMBERS

Strength,

f (MPa) 104 Ceramics Increasing P for strong tension members 103 102 10 1 0.1

Cermets PMCs || grain Steels Metal alloys Polymers 0.1

grain 1 Density,



Increasing P for strong torsion members 10 30 (Mg/m3) Adapted from Fig. 6.22, Callister 6e. (Fig. 6.22 adapted from M.F. Ashby, Materials Selection in Mechanical Design Ltd., 1992.) , Butterworth-Heinemann 7

DATA: STRONG & LIGHT BENDING MEMBERS

• Maximize the Performance Index :

P 

104 103 102 10 1 || grain Increasing P for strong grain Ceramics PMCs Steels Metal alloys Polymers bending members Cermets Adapted from Fig. 6.22, Callister 6e. (Fig. 6.22 adapted from M.F. Ashby, Materials Selection in Mechanical Design, Butterworth-Heinemann Ltd., 1992.)

s 1/ 2 

0.1

1 Density,



10 30 (Mg/m3) 8

DETAILED STUDY I: STRONG, LIGHT TORSION MEMBERS

• Maximize the Performance Index • Other factors: --require

f > 300MPa.

--Rule out ceramics and glasses: K Ic • Numerical Data: material CFRE (v f =0.65) GFRE (v f =0.65) Al alloy (2024-T6) Ti alloy (Ti-6Al-4V) 4340 steel (oil quench & temper)



(Mg/m 3 ) 1.5

2.0

2.8

4.4

7.8



f (MPa) 1140 1060 300 525 780 :

P   f 2 / 3 

too small.

P (MPa) 2/3 m 3 /Mg) 73 52 16 15 11 Data from Table 6.6, Callister 6e. • Lightest: Carbon fiber reinf. epoxy (CFRE) member.

DETAILED STUDY I: STRONG, LOW COST TORSION MEMBERS

• Minimize Cost: • Numerical Data: material CFRE (vf=0.65) GFRE (vf=0.65) Al alloy (2024-T6) Ti alloy (Ti-6Al-4V) 4340 steel (oil quench & temper) Cost Index ~ M $ ~ $ /P (since M ~ 1/P) P (MPa) 2/3 m 3 /Mg) 73 52 16 15 11 $ 80 40 15 110 5 ( $ /P)x100 112 76 93 748 46 Data from Table 6.7, Callister 6e. • Lowest cost: 4340 steel (oil quench & temper) • Need to consider machining, joining costs also.

DETAILED STUDY II: OPTIMAL MAGNET COIL MATERIAL

• 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.

Pulsed magnetic capable of 600,000 gauss field during 20ms period.

Fractured magnet coil.

(Photos taken at NHMFL, Los Alamos National Labs, NM (Apr. 2002) by P.M. Anderson) (1) High Magnetic Field Lab (NHMFL), Los Alamos National Labs, NM (April, 2002).

(2) Based on discussions with Greg Boebinger, Dwight Rickel, and James Sims, National See G. Boebinger, Al Passner, and Joze Bevk, "Building World Record Magnets", Scientific American, pp. 58-66, June 1995, for more information.

LORENTZ STRESS & HEATING

• Applied magnetic field, H: H = N I/L • Lorentz "hoop" stress:

s 

Magnetic field points out of plane.

I  o A HR (  s f N )

• Resistive heating: (adiabatic) elect. resistivity

D T  I 2  e A 2 c v D t (  D T max )

temp increase during current pulse of

t specific heat

Force  I  o H

MAGNET COIL: PERFORMANCE INDEX

• Mass of coil: • Applied magnetic field: M =



d AL H = N I/L • Eliminate "free" design parameters A , I stress & heating equations (previous slide) from the : --Stress requirement

H 2 M  1 2  R 2 L  o N s f  d

--Heating requirement

H M D t  D 2 T  max RL 1  d c  v e

specified by application Performance Index P 1 : maximize for large H 2 /M specified by application Performance Index P maximize for large Ht 2 : 1/2 /M 13

MAGNET COIL: COST INDEX

• Relative cost of coil: • Applied magnetic field: $ =

$

M H = N I/L • Eliminate M from the stress & heating equations: --Stress requirement --Heating requirement

H 2 $  1 2  R 2 L  o N s f  d

H $ D t  D T max 2  RL 1  d

c v  e

specified by application Cost Index C 1 : maximize for large H 2 /$ specified by application Cost Index C 2 : maximize for large Ht 1/2 /$ 14

INDICES FOR A COIL MATERIAL

• Data from Appendices B and C,

Callister 6e

: Material 1020 steel (an) 1100 Al (an) 7075 Al (T6) 11000 Cu (an) 17200 Be-Cu (st) 71500 Cu-Ni (hr) Pt Ag (an) Ni 200 units

f 395 90 572 220 475 380 145 170 462 MPa



d 7.85

2.71

2.80

8.89

8.25

8.94

21.5

10.5

8.89

g/cm 3 $ 0.8

12.3

13.4

7.9

51.4

12.9

1.8e4

271 31.4

- c v 486 904 960 385 420 380 132 235 456 J/kg-K



e 1.60

0.29

0.52

0.17

0.57

3.75

1.06

0.15

0.95

-m 3 P 1 50 33 204 25 58 43 7 16 52

f /



d P 2 2 21 15 5 3 1 19 <1 2 (c v /



e ) 0.5



d 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) P 1 P 2 C 1 C 2 C 1 63 3 15 3 1 3 <1 <1 2 P 1 / $ P C 2 2.5

1.7

1.1

0.6

<0.1

2 / $ 15

THERMAL PROTECTION SYSTEM

• Application: Space Shuttle Orbiter Fig. 23.0, Callister 5e. (Fig. 23.0 courtesy the National Aeronautics and Space Administration.

• Silica tiles (400-1260C) --large scale application : Fig. 19.2W, Callister 6e. (Fig. 19.2W adapted from L.J. Korb, C.A. Morant, R.M. Calland, and C.S. Thatcher, "The Shuttle Orbiter Thermal Protection System", Ceramic Bulletin, No. 11, Nov. 1981, p. 1189.) --microstructure: ~90% porosity!

Si fibers bonded to one another during heat treatment.

Fig. 19.3W, Callister 5e. (Fig. 19.3W courtesy the National Aeronautics and Space Administration.

Fig. 19.4W, Callister 5e. (Fig. 219.4W courtesy Lockheed Aerospace Ceramics Systems, Sunnyvale, CA.) 16

THERMAL

• Space Shuttle Tiles: --Silica fiber insulation offers low heat conduction .

Fig. 19.0, Callister 6e.

(Courtesy of Lockheed Missiles and Space Company, Inc.) • Thermal Conductivity of Copper: --It decreases when you add zinc!

Adapted from Fig. 19.4W, Callister 6e. (Courtesy of Lockheed Aerospace Ceramics Systems, Sunnyvale, CA) (Note: "W" denotes fig. is on CD-ROM.) Adapted from Fig. 19.4, Metals, 1979, p. 315.) Callister 6e.

(Fig. 19.4 is adapted from Metals Handbook: Properties and Selection: Nonferrous alloys and Pure Metals, Vol. 2, 9th ed., H. Baker, (Managing Editor), American Society for 17

SUMMARY

• 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. 18