530.352 Materials Selection Lecture #11 Materials Selection Software Tuesday October 4th, 2005

Material Selection - the basics: All materials Screening: apply property limits / eliminate those who cannot do the job Ranking: apply material indices / find best candidates Subset of materials Supporting info: Handbooks, software, WWW, etc. Prime candidates Local conditions: in-house expertise or equipment Final Material Choice

Deriving property limits: Simple limits on material properties can be used to eliminate possible materials e.g. Toperating = 250o C Electrically insulating must be available in wire form etc.

Deriving material indices: Combination of material properties Used when component characteristics can be achieved in more than one way: e.g. high stiffness high modulus increasing the cross-section changing the shape

Material indices: Performance = f [F,G,M] p = f [(Functional requirements), (Geometric constraints), (Material properties)]

Function, objective, constraint: what does component do? Objective: what is to be maximized -or- minimized? Constraints: what non-negotiable conditions must be met? what other conditions are desired?

Function, object, constraint ... Tie Beam Shaft Column Objective Minimum cost Minimum weight Maximum energy storage etc. Constraint Stiffness Strength Geometry Corrosion

Procedure for deriving material indices: Define design requirements Develop an equation for the objective in terms of functional requirements, geometry and material properties. Identify the free (unspecified) variables. Develop constraint equations. Substitute for the free variables. Group the variables into three groups and determine: p = f1(F),f2(G),f3(M) Identify the Material Index (M1).

Table legs: Goal: light weight coffee table of daring simplicity: a flat sheet of glass with slender light weight legs. Legs must: be solid be light as possible support a load P without buckling

Table leg design: Design goals Constraint minimize weight maximize slenderness Constraint resistance to buckling

Modeling a table leg: Mass Buckling load m = p r2 l r Pcrit = p 2 EI = p 3Er 4 l2 4l2

Minimizing weight : Mass of legs: m = [4P / p ]1/4 [l]2 [r / E1/2] M1 = E1/2 /r

Criterion for slenderness: Minimum leg radius Pcrit = p 3Er 4 4l2 r = [4P /p3 ]1/4 [l]1/2 [1 / E ]1/4 M2 = E

CES Software: CES software available in the HITS Computing Lab (Krieger 160) or Senior Design Computer Lab. Access it the following way: 1. Click “Start” menu 2. Go to “Programs” ->”Engineering Applications” ->“CES” -> “CES Selector” Why Hawaii ?? thousands of miles of thermally stable ocean. no nearby mountain ranges to roil the upper atmosphere or throw light-reflecting dust into the sky Few city lights Clear, calm and dry 300 nights per year.

Table leg materials: Good : Not good : light weight: slender (stiff) woods ; composites ; ceramics slender (stiff) CFRP ; ceramics Not good : polymers (too compliant) ; metals (too heavy - except Be)

Table leg materials M1 = E1/2 ; M2 = E r Make Modulus-density chart Materials M1 M2 Comment wood 5-8 4-20 cheap, reliable steel 1.8 210 poor M1 CFRP 4-8 30-200 very good, expensive Ceramics 4-8 150-1000 excellent but brittle

Materials for Flywheels : Flywheels store energy Current flywheels are made out of : children’s toys lead steam engines cast iron modern electric vehicles HSLA steels and composites Efficiency measured in “stored energy per unit weight”

Stored energy : For a disc of radius (R) and thickness (t) rotating with angular velocity (w), the energy (U) stored in the flywheel is : U = 1/2 J w2 = 1/4 p r R4 t w2 The mass of the disk is : m= p R2 t r

Stored energy / mass : Energy / mass is : Same for all materials ??? U/m = 1/4 R2 w2 Same for all materials ???

Centrifugal stress : Maximum principal stress in a spinning disk of uniform thickness : smax = [(3+ n)/8] r R2 w2 This sets the upper limit of w ; U/m = [2/(3+n)] [sf / r] M = sf / r [kJ / kg]

Materials for flywheels : Material M [kJ/kg] Comments Ceramics 200-2,000 Brittle in tension. CFRP 200-500 best performance good choice. GFRP 100-400 cheaper than CFRP excellent choice. Steel, Al, Ti, Mg 100-200 Steel cheapest Cast iron 8-10 high density Lead alloys 3 high density

Why use lead and cast iron ?? Children’s toys use these -- why ?? Cannot accelerate to the burst velocity If angular velocity is limited by the drive mechanism (pull string) then : U = 1/4 p r R4 t w2 M2 = r