LECTURE 12.1

LECTURE OUTLINE

 Weekly Deadlines  Ashby Maps

THE MATERIALS SCIENCE TETRAHEDRON

THE HARDNESS OF BRONZES

HARDNESS AND SPECIFIC GRAVITY

WEIGHT; WHERE LESS IS MORE

A “PERFORMANCE INDEX”

 Define a “Performance Index” as Strength (Hardness)/ Unit Weight, or  Specific Strength = Hardness Specific Gravity

SPECIFIC STRENGTH/SPECIFIC STIFFNESS

 Weight-Limited Design!

 Suppose that we have two materials, A and B, and that A has a yield strength of 200MPa and that B has a yield strength of 100MPa.

  Could I replace material A with material B for e.g., the fuselage of a commercial aircraft? I would need “struts”of material B that were twice as thick as “struts” of material A. Is this a problem?

SPECIFIC STRENGTH/SPECIFIC STIFFNESS II

 Answer: It depends on the specific gravity of the two materials!

 Case #1. Material B has a specific gravity ~ 0.33 x that of material A. Even though the struts must be twice as thick, they will still weigh less than the smaller struts of Material A.

 Case #2. Material B has the same specific gravity as Material A. The struts of Material B will now weigh twice that of Material A.



SPECIFIC STRENGTH/SPECIFIC STIFFNESS III

Conclusion:  A more important parameter than “Strength” is ‘Specific Strength” where  Specific Strength is the strength/unit weight, or:  Specific Strength = Yield Strength Specific Gravity Also: Specific Stiffness = Young’s Modulus Specific Gravity

SELECTED PROPERTIES OF SELECTED MATERIALS Table 36.1.

Selected Materials and Selected P hysical/Mechanical Properties.

Material

Alloy Steel Aluminum Alloys Titanium Alloys Beryllium Alloys Wood Polyurethane Foa m Concre te Alumina GFRP* CFRP** Specific Grav ity

7.8

2.7

4.5

1.9

0.6

0.1

2.5

3.9

2.0

1.5

Yo ung's Modulus (GPa)

200 69 120 300 12 6 47 390 40 270

Approx imate Yield Strength. (MNm -2 ).

1000 500 1000 250 40 1 25 400 200 650

SELECTED PROPERTIES OF SELECTED MATERIALS

SELECTED PROPERTIES OF SELECTED MATERIALS

TOWARDS THE “ASHBY MAP”

    E/ r = q “q” is a “number” which can be used as a benchmark. Materials with a larger value of “q”, will have a better “specific stiffness” than our benchmark, whereas materials with a lower value of “q” will be inferior.

We can plot the straight line: E = r q Materials above this line are superior: those below, are inferior.

A “PROPERTY MAP”

TOWARDS THE “ASHBY MAP”

   Reminder: E/ r = q When values of E/ r vary over orders of magnitude, it is necessary to use a “log-log” plot, and: logE = log r + logq  y = mx + C

LINEAR AND LOG-LOG PERFORMANCE MAPS

AN “ASHBY MAP”