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Materials Selection Without Shape - Case Studies. Table legs Flywheels Springs Pressure vessels Precision Devices Buildings. Materials for Table Legs. Aim : cylindrical legs as light and thin as possible constraint : resistance to buckling first eliminate r and get
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Materials Selection Without Shape - Case Studies Table legs Flywheels Springs Pressure vessels Precision Devices Buildings
Materials for Table Legs Aim: cylindrical legs as light and thin as possible constraint: resistance to buckling first eliminate r and get for slenderness
Materials for Flywheels • Flywheel store energy. • Currently made of lead, cast iron, steel, composites - a strange diversity! • Aim: highest stored energy per unit weight, without failing • Stored energy • Mass of flywheel disk
Materials for Flywheels • The quantity to be maximized • The maximum principle stress in a spinning disk of uniform thickness • Eliminating R gives
Materials for Springs • Spring is a device for storing energy • Springs come in many shapes and have many purposes, e.g. axial springs, leaf springs, helical springs, spiral springs, torsion bars, etc.
Materials for Springs • Maximum energy stored in axial spring • For torsion bars • For leaf springs (bending deformation) • The geometry and form of the spring is immaterial to the objective function • For efficient small spring • For efficient light spring
Materials for Safe Pressure Vessels • Daily examples: aerosol can, boiler, etc. • Small vessels are designed to “yield before break”; the distortion easy to detect and the pressure released safely. • Large vessels are designed to “leak before crack”; i.e. critical crack length for unstable propagation is larger than vessel wall thickness; leak is easily detected and releases pressure gradually
Materials for Safe Small Pressure Vessels • The hoop stress of a thin-wall spherical vessel of radius R is • If the vessel contains no cracks or flaws of diameter greater than 2ac, then the stress required for crack propagation is • For “yield before crack”
Materials for Safe Large Pressure Vessels • Number and sizes of cracks in large pressure vessels changes with time due to corrosion and cyclic loading but NDT cannot be done very frequently, therefore the “leak before crack” strategy. • Through-thickness crack must still be stable • The wall thick enough for the pressure without yielding • Eliminate t, gives • Maximize p means
Materials to Minimize Thermal Distortion in Precision Devices • The precision of measuring device is limited by its stiffness and the dimensional change or distortion caused by temperature gradients. • Elastic deflection of the Force Loop is allowed, provided natural vibration frequencies are high! • Expansion is permissible of the Force Loop, provided distortion does not occur!
Materials to Minimize Thermal Distortion in Precision Devices • The temperature can be equalized by heat conduction • The strain related to temperature is • The strain gradient (distortion) • Distortion is minimized by maximizing • To reduce sensitivity to external vibration, the natural frequencies must be high
Materials to Minimize Thermal Distortion in Precision Devices
Materials to Minimize Thermal Distortion in Precision Devices
Structural Materials for Buildings • Roughly half the cost of a house is the cost of materials of which it is made (HK$300/sq. ft in Hong Kong) • The quantities is very large, e.g. around 20000 tonnes for a large apartment block • Structural materials must be stiff, strong and cheap • The critical components in building are loaded either in bending or as columns
Summary • The case studies illustrate how the choice of materials is narrowed • Most designs make certain non-negotiable demands on the material, e.g. operation temperature, corrosion resistance, etc. • The choice is further narrowed by maximizing performance. • Final choice also depends on more detailed information of properties, manufacturing processes, joining, finishing, etc.
