1. MECH4301 2008 Lecture 5 Case Studies Ch 61/22 MECH4301 2008 Materials Selection in Mechanical Design Lecture 5 Materials Selection Without Shape (2/2): Case studies Chapters 5 and 6 Cross Sectional Shape is kept constant

2. MECH4301 2008 Lecture 5 Case Studies Ch 62/22 Review of Lecture 4: Materials for a stiff, light beam Chose materials with largest M= Material Index Material choice Area = b 2 What can be varied ? { I = second moment of area: Beam (solid square section) b b L F Function m = mass A = area L = length  = density b = edge length S = stiffness I = second moment of area E = Young’s modulus Stiffness of the beam, S: Constraint Minimise mass, m, where: Goal Eliminate b

3. MECH4301 2008 Lecture 5 Case Studies Ch 63/22 I = second moment of area: Eliminating the free variable 1 2 3 4 5 6

4. MECH4301 2008 Lecture 5 Case Studies Ch 64/22 Demystifying Material Indices (beam, elastic bending) For given shape, the reduction in mass at constant bending stiffness equals the ratio between the reciprocal of the material indices. Same applies to bending strength. mass, Material 1 mass Material 2

5. MECH4301 2008 Lecture 5 Case Studies Ch 65/22 Case studies Chapter 6 Materials for light slender table legs Materials for small/light springs Materials for flywheels Materials for oars Short-term thermal insulation Materials for spark plug insulators This lecture Read these at home

6. MECH4301 2008 Lecture 5 Case Studies Ch 66/22 Materials for lightweight/slender table legs p. 114

7. MECH4301 2008 Lecture 5 Case Studies Ch 67/22 Materials for table legs legs are stiffness- limited, minimum weight, designs Specification leg: light, stiff column Minimum weight; slender Stiffness S specified Cost within reason Toughness adequate Cross-section area Material Material limits, set by constraints Fracture toughness Function Objectives Constraints Free variables Material index, p. 509, set by function/objective Minimise modulus density

8. MECH4301 2008 Lecture 5 Case Studies Ch 68/22 Mass m = A L  (1) Critical condition for buckling p. 483; (n = 1) Maximise M 1 for minimum mass Table legs: Derivation of M. I. for minimum mass Combine (1) and (2) to eliminate A I is the second moment of area Check on p. 509 Failure mode?

9. MECH4301 2008 Lecture 5 Case Studies Ch 69/22 P 509

10. MECH4301 2008 Lecture 5 Case Studies Ch 610/22 Slender legs? Maximise M 2 to minimise cross section Critical condition for buckling p. 483; (n = 1) Solve for R

11. MECH4301 2008 Lecture 5 Case Studies Ch 611/22 Materials for light / slender legs CFRP best option Selection line of gradient 0 Selection line of gradient 2 Foams are a good option !

12. MECH4301 2008 Lecture 5 Case Studies Ch 612/22 Materials for springs Small springs: minimum volume Light springs: minimum mass page 126 Images from: http://www.mech.uwa.edu.au/DANotes/springs/intro/intro.htmlhttp://www.mech.uwa.edu.au/DANotes/springs/intro/intro.html http://www.ftexploring.com/lifetech/flsbws2.html

13. MECH4301 2008 Lecture 5 Case Studies Ch 613/22 Material for a spring of minimum volume Cross section of given shape Volume V = LA A=V/L minimise V for given W….? On E -  chart, select with a line of gradient 2. Search on bottom right corner. Elastic energy W W = ½F  L= ½  A  L = ½  V  L/L = ½  V= ½ V  2 /E Solving for V: F =  A A = V/L  =  /E  L/L =  maximise Goal: minimise V for given amount of elastic energy stored, W F F LL

14. MECH4301 2008 Lecture 5 Case Studies Ch 614/22 Selection line of gradient 2 spring of minimum volume On E -  chart, select with a line of gradient 2. Search on bottom right corner (low E, high  ). CFRP & steels elastomers

15. MECH4301 2008 Lecture 5 Case Studies Ch 615/22 Index ? Solving M light for E: On E/  vs  /  chart, select with line of gradient 2. Search on bottom right corner (low E/ , high  /  ). For minimum mass m =  V Material for a spring of minimum mass Cross section of given shape For minimum Volume V Three materials properties in a single index: separate ?

16. MECH4301 2008 Lecture 5 Case Studies Ch 616/22 spring of minimum mass CFRP Exercise 5.7, Truck suspension On E/  vs  /  chart, select with line of gradient 2. Search on bottom right corner (low E/ , high  /  ). elastomers Metals moved back and down. They are good for small springs, but they don’t get selected for light springs.

17. MECH4301 2008 Lecture 5 Case Studies Ch 617/22 Table B.3 p. 510

18. MECH4301 2008 Lecture 5 Case Studies Ch 618/22 Using CES to sort materials: Exercise 5.3

19. MECH4301 2008 Lecture 5 Case Studies Ch 619/22 From Lecture 4: Materials for a strong, light beam m = mass A = area L = length  = density M f = bending strength I = second moment of area E = Youngs Modulus Z = section modulus Beam (shaped section). Bending strength of the beam M f : Combining the equations for A, M f and Z gives: Chose materials with largest Minimise mass, m, where: Function Objective Constraint L F Area A Eliminate free variable, A

20. MECH4301 2008 Lecture 5 Case Studies Ch 620/22 CES chart density elastic limit Slope 1.5 Search region

21. MECH4301 2008 Lecture 5 Case Studies Ch 621/22 Using CES to sort materials. Q 5.3 light strong beam NamedensityElastic limitStage 1: Index Rigid Polymer Foam (HD)170 - 4701.2 - 12.428.706e-3 Aluminum alloys2500 - 290058 - 5500.012 Flexible Polymer Foam (MD)70 - 1150.43 - 2.950.012 Stainless steel7600 - 8100480 - 22400.013 Rigid Polymer Foam (MD)78 - 1650.65 - 5.10.013 Flexible Polymer Foam (LD)38 - 700.24 - 2.350.016 Bamboo600 - 80036 - 450.017 Titanium alloys4400 - 4800300 - 16250.017 GFRP, epoxy matrix (isotropic)1750 - 1970138 - 2410.017 Silicon carbide3100 - 3210400 - 6100.02 Rigid Polymer Foam (LD)36 - 700.45 - 2.250.02 Polyamides (Nylons, PA)1120 - 114090 - 1650.022 Magnesium alloys1740 - 1950185 - 4750.024 Flexible Polymer Foam (VLD)16 - 350.24 - 0.850.025 Wood, typical along grain600 - 80060 - 1000.026 CFRP, epoxy matrix (isotropic)1500 - 1600550 - 10500.054 Highest M = CFRP & wood Foams=> The good: beam is light, The bad? beam too thick. What makes timber so good? Materials sorted by Index

22. MECH4301 2008 Lecture 5 Case Studies Ch 622/22 The End Lecture 5

23. MECH4301 2008 Lecture 5 Case Studies Ch 623/22 Material for a flywheel -- filament-wound GFRP Case Rotor Burst shield

24. MECH4301 2008 Lecture 5 Case Studies Ch 624/22 Specification for a flywheel Specification Flywheel Maximum energy/wt Must not disintegrate Cost within reason Fr. Toughness adequate Material Function Objectives Constraints Free variables

25. MECH4301 2008 Lecture 5 Case Studies Ch 625/22 Material index and constraints for flywheels Maximise energy/unit weight at maximum velocity Energy Mass Must not fail Energy/mass Maximise Angular velocity Density Strength Moment of inertia Additional constraint: Fracture toughness > 15 MPa.m 1/2 (1) (2) (3) (4) Linear on , quadratic on ω

26. MECH4301 2008 Lecture 5 Case Studies Ch 626/22 Table B.3 p. 510

27. MECH4301 2008 Lecture 5 Case Studies Ch 627/22 Material for flywheels Search region

28. MECH4301 2008 Lecture 5 Case Studies Ch 628/22 Material for flywheels Density (Mg/m 3 ) Strength - Density Additional constraint: K 1c > 15 MPa.m 1/2 Elastic limit (MPa) Search region

29. MECH4301 2008 Lecture 5 Case Studies Ch 629/22 Energy source Gasoline Rocket fuel Flywheels Advanced batteries Lead-Acid battery Springs, rubber bands Comment Oxidation of hydrocarbon - weight or oxygen not included Less than hydrocarbons because oxidising agent forms part of fuel Attractive but not yet proven Battery technology near limit Large weight for acceptable range Much less efficient method of energy storage than flywheel Energy density kJ/kg 20,000 5,000 up to 350 45 - 60 up to 5 Flywheels postscript: Energy density of energy sources

30. MECH4301 2008 Lecture 5 Case Studies Ch 630/22 Potential Use Temperature as a Function of Working Time for Ultra-high Temperature Composites under Simulated Aero Convective Environment (*corresponds to static oxidation test) Y. R. Mahajan, ARC-I, Hyderabad Some possible materials for Exercise 5.9 fin for rocket

31. MECH4301 2008 Lecture 5 Case Studies Ch 631/22 HYPERSONIC TECHNOLOGY DEMONSTRATOR (HSTDV) AUTONOMOUS AIRBREATHING SUSTAINED FLIGHT AT HYPERSONIC SPEED WITH KEROSENE FUEL Mach No. : 6.5 Altitude : 32.5 km Flight duration of cruise vehicle : 20 secs Hypersonic Vehicle consists of : 1. LAUNCH VEHICLE (L.V.) 2. CRUISE VEHICLE (C.V.) CV encapsulated in the payload stage of LV. Y. R. Mahajan, ARC-I, Hyderabad