MATERIALS SELECTION ECONOMIC, ENVIRON., & DESIGN ISSUES

Transcription

1 MATERIALS SELECTION ECONOMIC, ENVIRON., & DESIGN ISSUES 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. Chapter 22-1

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 --Cost of energy used in materials (GJ/ton) processing materials ($/GJ) (g) Al PET Cu steel glass paper PRICE AND AVAILABILITY 237 (17) (b) 103 (13) (c) 97 (20) (b) 20 (d) 13 (e) 9 (f) Energy using recycled material indicated in green. elect resistance propane natural gas oil a a b c d e f g Chapter 22-2

3 Relative Cost ($) RELATIVE COST, $, OF MATERIALS Metals/ Alloys Pt Au Ag alloys Tungsten Ti alloys Cu alloys Al alloys Mg alloys high alloy Steel pl. carbon Graphite/ Ceramics/ Semicond Diamond Si wafer Si nitride Si carbide Al oxide Glass-soda Polymers Nylon 6,6 PC Epoxy PVC PET LDPE,HDPE PP PS Composites/ fibers CFRE prepreg AFRE prepreg Carbon fibers Aramid fibers GFRE prepreg E-glass fibers Wood $ = $/kg ($ /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 = Aramid, Glass, & Carbon fiber reinforced epoxy composites Concrete Chapter 22-3

4 STIFF & LIGHT TENSION MEMBERS L c c F, δ Bar must not lengthen by more than δ under force F; must have initial length L. -- Stiffness relation: -- Mass of bar: F c 2 = E δ L (σ = Eε) M=ρLc2 Eliminate the "free" design parameter, c: specified by application M= FL2 δ ρ E minimize for small M Maximize the Performance Index: (stiff, light tension members) P = E ρ Chapter 22-4

5 L STRONG & LIGHT TENSION MEMBERS c c F, δ Bar must carry a force F without failing; must have initial length L. -- Strength relation: -- Mass of bar: σ f N = F c 2 M= ρlc 2 Eliminate the "free" design parameter, c: specified by application M= FLN ρ σ f minimize for small M Maximize the Performance Index: (strong, light tension members) P = σ f ρ Chapter 22-5

6 L STRONG & LIGHT TORSION MEMBERS Mt 2R τ Bar must carry a moment, Mt ; must have a length L. -- Strength relation: -- Mass of bar: τ τ f N = 2M t πr 3 M=ρπR 2 L Eliminate the "free" design parameter, R: M= ( 2 π NM t ) 2/3 L ρ τ 2/3 f specified by application Maximize the Performance Index: (strong, light torsion members) minimize for small M P = τ 2/3 f ρ Chapter 22-6

7 DATA: STRONG & LIGHT TENSION/TORSION MEMBERS Strength, σf (MPa) 10 4 Ceramics 10 3 Cermets PMCs Steels 10 2 grain Metal alloys 10 Polymers grain 1 Increasing P for strong tension members wood slope = 1 slope = 3/ Density, ρ (Mg/m 3 ) Increasing P for strong torsion members Adapted from Fig. 6.22, Callister 6e. (Fig adapted from M.F. Ashby, Materials Selection in Mechanical Design, Butterworth- Heinemann Ltd., 1992.) Chapter 22-7

8 Strength, σf (MPa) Increasing P for strong 10 4 bending members Ceramics 10 3 Cermets PMCs Steels 10 2 grain Metal alloys 10 Polymers 1 DATA: STRONG & LIGHT grainwood BENDING MEMBERS Maximize the Performance Index: Density, ρ (Mg/m 3 ) slope = 2 P = σ1/2 ρ Adapted from Fig. 6.22, Callister 6e. (Fig adapted from M.F. Ashby, Materials Selection in Mechanical Design, Butterworth- Heinemann Ltd., 1992.) Chapter 22-8

9 DETAILED STUDY I: STRONG, LIGHT Maximize the Performance Index: Other factors: --require σf > 300MPa. --Rule out ceramics and glasses: KIc 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) TORSION MEMBERS ρ (Mg/m 3 ) τ f (MPa) Lightest: Carbon fiber reinf. epoxy (CFRE) member. P = τ 2/3 f ρ too small. P (MPa) 2/3 m 3 /Mg) Data from Table 6.6, Callister 6e. Chapter 22-9

10 DETAILED STUDY I: STRONG, LOW COST TORSION MEMBERS Minimize Cost: Cost Index ~ M$ ~ $/P (since M ~ 1/P) 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) P (MPa) 2/3 m 3 /Mg) $ ($/P)x Data from Table 6.7, Callister 6e. Lowest cost: 4340 steel (oil quench & temper) Need to consider machining, joining costs also. Chapter 22-10

11 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. (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 , June 1995, for more information. 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) Chapter 22-11

12 Applied magnetic field, H: H = N I/L Lorentz "hoop" stress: Magnetic field points out of plane. LORENTZ STRESS & HEATING σ= Iµ o HR A R A σ ( σ f N ) I current I Force length Resistive heating: (adiabatic) T = I2 ρ e A 2 c v t (< T max ) temp increase during current pulse of t = Iµ o H N turns total L = length of each turn elect. resistivity specific heat Chapter 22-12

13 MAGNET COIL: PERFORMANCE INDEX Mass of coil: Applied magnetic field: M = ρ d AL H = N I/L Eliminate "free" design parameters A, I from the stress & heating equations (previous slide): --Stress requirement H 2 M 1 σ f 2 πr 2 Lµ o N ρ d --Heating requirement H t M T max 2π RL 1 ρ d c v ρ e specified by application Performance Index P1: maximize for large H 2 /M specified by application Performance Index P2: maximize for large Ht 1/2 /M Chapter 22-13

14 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 πr 2 Lµ o N σ f ρ d $ H t $ T max 2π RL 1 ρ d $ c v ρ e specified by application Cost Index C1: maximize for large H 2 /$ specified by application Cost Index C2: maximize for large Ht 1/2 /$ Chapter 22-14

15 INDICES FOR A COIL MATERIAL Data from Appendices B and C, Callister 6e: Material 1020 steel (an) 1100 Al (an) 7075 Al (T6) Cu (an) Be-Cu (st) Cu-Ni (hr) Pt Ag (an) Ni 200 units σf MPa ρd $ e g/cm 3 -- cv J/kg-K ρe Ω-m 3 P σf/ρd P <1 2 (cv/ρe) 0.5 C <1 <1 2 P1/$ C <0.1 <0.1 <0.1 <0.1 <0.1 P2/$ 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) ρd P1 P2 C1 C2 Chapter 22-15

16 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. Chapter 22-16

17 Reading: ANNOUNCEMENTS Core Problems: Self-help Problems: Chapter 22-0