Materials- Material Indices

Question 1

Formula for performance metric

Answer 1

P=f(F,G,M)
Means performance metric is function of functional requirement (e.g load force), geometry parameter (e.g size/shape), material properties.

Question 2

Definition of performance

Answer 2

A structural material’s efficiency in performing the function it was designed for

Question 3

Material index defined

Answer 3

The property or property-group that maximises performance for a given design.

Question 4

What do ties, beams, shafts, columns do?

Answer 4

Ties: carry tensile loads
Beams: carry bending moments
Shafts: carry torques
Columns: carry compressive axial loads

Question 5

Equations for minimising mass while being able to support a certain load

Answer 5

m=ALρ, σf<=F/A
Eliminate A so m>=FL(ρ/σf)
ρ and σf are material properties
F is functional requirement, L is geometric parameter 
σf is failure stress.

Question 6

Convention for expressing material index

Answer 6

So that maximum value is required

Question 7

See slides for examples of combining property equations

Answer 7

Quite a few

Question 8

Example of material indices for different functions and constraints see slides

Answer 8

Slide 52

Question 9

Can you have multiple material indices?

Answer 9

Yes. For different properties

Question 10

How to construct an iso-line on an Ashby diagram

Answer 10

Get equation for the material index it is for (e.g M=E^0.5/ρ). Rearrange to make what’s on y axis the subject. Take logs of both sides (due to log axes). Equation is of form y=mx+c. In this example, gradient is 2 and y-intercept is 2log(M). Plot straight line on Ashby diagram. Gradient 2 would be up times 100 across times 10.

Question 11

What can be said about materials that lay along an iso-line?

Answer 11

They perform equally well according to the material index it is for

Question 12

What can be said for materials above the iso-line?

Answer 12

They perform better than those below the line for that material index because the line they correspond to will have a greater y-intercept.

Question 13

How to find search region on Ashby diagram using iso-line and constraints

Answer 13

Plot iso-line for required value of material index which will specify y intercept. Plot vertical or horizontal line for other constraints for properties on the same Ashby diagram. Search region is above iso-line and above or to right of vertical or horizontal line.

Question 14

If there are two material indices, what do you do after finding search region for one?

Answer 14

Include the materials in this search region on a new Ashby diagram for the other material index. Then do normal thing with contraints horizontal and vertical lines.