# Material Study

### MATERIALS SELECTION AND DESIGN

### Q1

A material is required for the windings of an electric air furnace capable of temperatures up to 1000oC. Think about what attributes a material must have if it is to be made into windings and function properly in a furnace.

### Answer 1

### Attributes of the material is:

Function

Wire winding for furnace

Constraints

Heat and shock resistance up to 1000oC

Easy to fabricating joining and forming

Objective

Maximum thermal conductivity

Maximum conductor of electricity

Minimum cost

High corrosion resistant

Free Variables

Choice of material

Candidate material

Copper alloys ( Cu alloys )

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### Q2

A furnace is required to sinter powder-metal parts. It operates continuously at 650oC while the parts are fed through a moving belt. You are asked to select a material for furnace insulation to minimize heat loss and make the furnace as energy efficient as possible. For reasons of space the insulation is limited to a maximum thickness of

x = 0.2 m.

### Answer 2

Function

Furnace insulation

Constraints

Heat resistance and Insulator up to 650oC

Insulator maximum thickness (x = 0.2 m)

Objective

Minimum thermal conductivity

Minimum heat storage

Minimum conductor of electricity

Minimum cost

Maximum corrosion resistant

Maximum heat reflectance

Maximum energy efficiency

Free Variables

Low Weight

Choice of material

Candidate material

### Q3

The standard CD (“Jewel case”) cracks easily and, if broken can scratch the CD. Jewel cases are made of injection moulded polystyrene, chosen because it is transparent, cheap and easy to mould. A material is sought that does not crack so easily. The case must still be transparent, able to be injection moulded and compete with polystyrene in cost.

Answer 3

Function

CD Jewel case

Constraints

Transparent

Able to be injection moulded

Compete with polystyrene in cost

Objectives

Free variables

Choice of material

Candidate material

Acrylonitrile butadiene styrene (ABS)

Polycarbonate (PC)

Polypropylene (PP)

### Q4

A storage heater captures heat over a period of time, then releases it, usually to an air stream when required. Those for domestic heating store solar energy or energy from cheap off-peak electricity and release it slowly during the cold part of the day. What is a good material for the core of a compact storage material capable of temperatures up to 120oC?

### Answer 4

Function

Material for the core of Compact Storage

Constraints

Capable of temperature up to 120oC

Objectives

Maximum thermal captivity

Free variables

Choice of material

Candid material

### Q5

Aperture grills for cathode ray tubes

Two types of cathode ray tube (CRT) dominate the computer monitor and television marketplace. In the older technology, colour separation is achieved by using a shadow mask: a thin metal plate with a grid of holes that can allow only the correct beam to strike a red, green or blue phosphor. A shadow mask can heat up and distort at high brightness levels (“doming”), causing the beams to miss their targets and giving a blotchy image. To avoid this, the newest shadow masks are made of Invar, a nickel alloy with near zero expansion coefficient. It is a consequence of shadow-mask technology that the glass screen of the CRT curves inwards on all four edges, increasing the probability of reflected glare.

Sony`s Trinitron technology overcomes this problem by replacing the shadow mask with an aperture grill of fine vertical wires, each about 200 μm thickness, that allows the intended beam to strike either the red, the green or the blue phosphor to create the image. The glass face of the Trinitron tube is curved in one plane only reducing glare.

The wires of the aperture grill are tightly stretched, so that they remain taut (the wires must not sag) even when hot – it is the tension that allows the greater brightness. Derive the material index that guides the choice of material to make them.

### Table below summarises the requirements:

Function

Aperture grill for CRT

Constraints

Wire thickness and spacing specified

Must carry pre-tension without failure

Electrically conducting to prevent charging

Able to be drawn to wire

Objectives:

Maximize permitted temperature rise without loss of tension

Free Variables

Choice of Material

### Q6

Material Index for a light strong beam ( 2)

In stiffness limited applications, it is elastic deflection that is the active constraint: it limits performance. In strength limited applications, deflection is acceptable as long as the component does not fail: strength is the active constraint.

Derive the material index for selecting materials for a beam of length L, specified strength and minimum weight. For simplicity assume the beam to have a solid square cross-section t x t.

The failure load Ff is given by:

Where

ym is the distance between the neutral element of a beam and its outer filament

I is the second moment of area of the cross section =

Design Requirements

Function

Beam

Constraints

Length L is specified

Beam to support a bending load F without yield or fracture

Objectives:

Minimize mass of beam

Free Variables

Cross section area A

Choice of material

### Q7

Indices for stiff plates and shells ( Q3)

Aircraft and space industries make use of plates and shells. The material index depends on the configuration. Here you are asked to derive the materials index for:

(a) A circular plate of radius a carrying a central load W with a prescribed stiffness S = W/δ and of minimum mass, as shown in Q3.

(b) A spherical shell of radius a carrying a central load W with a prescribed stiffness S = W/δ and of minimum mass, as shown in Q3.

Use the two equations below for the mid-point deflection δ of a plate or spherical shell under a load W applied over a small central circular area

Circular plate:

Hemispherical shell:

In which A ≈ 0.35 is a constant. Here E is the Elastic Modulus, t is the thickness of the plate or shell and υ is Poissons ratio. Poissons ratio is almost the same for all structural materials and can be treated as a constant. The table summarises the requirements.

Function

Stiff circular plate, or Stiff hemispherical shell

Constraints

Stiffness S under central load W is specified

Radius a of plate or shell is specified

Objectives:

Minimise mass of plate or shell

Free Variables

Plate or Shell thickness t

Choice of Material

### Q8

Fin for a rocket ( Q4)

A tube launched rocket has stabilizing fins at its rear. During launch the fins experience hot gas at Tg = 1700oC for a time of 0.3 s. It is important that the fins survive launch without surface melting.

Suggest a suitable materials index for the fins

The table summarises the requirements:

Function

High heat transfer rocket fins

Constraints

All dimensions specified

Must not suffer surface melting during exposure to gas at 1700oC for 0.3 s

Objectives:

Maximising the melting point of the material

Minimise the surface temperature rise during firing

Free Variables

Choice of Material

This is tricky!

Heat enters the surface of the fin by transfer from the gas. If the heat transfer coefficient is h, the heat flux per unit area is:

(1)

Where Ts is the surface temperature of the fin – the critical quantity we wish to minimize.

Heat diffuses into the fin surface by thermal conduction

If the heating time is small then the surface temperature adjust itself so that the heat entering from the gas is equal to that diffusing inwards by conduction. Thus:

(2)

Where

λ is the thermal conductivity

Ti is the temperature of the cold interior of the fin

x is a characteristic heat diffusion length

(3)

Where

α is the thermal diffusivity

(4)

Substituting (3) and (4) into (2) gives

(5)

Where

ρ is the density

Cp is the specific heat capacity of the material of the fin

To proceed

Derive a material index that will minimise Ts

Materials selection is made based on the materials index and that of a material with a high melting point