LECTURE 12.1LECTURE 12.1

LECTURE OUTLINELECTURE OUTLINE

Weekly DeadlinesWeekly DeadlinesAshby MapsAshby Maps

THE MATERIALS SCIENCE THE MATERIALS SCIENCE TETRAHEDRONTETRAHEDRON

THE HARDNESS OF BRONZESTHE HARDNESS OF BRONZES

HARDNESS AND SPECIFIC HARDNESS AND SPECIFIC GRAVITYGRAVITY

WEIGHT; WHERE LESS IS WEIGHT; WHERE LESS IS MOREMORE

A “PERFORMANCE INDEX”A “PERFORMANCE INDEX”

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

Specific Strength = HardnessSpecific Strength = Hardness

Specific GravitySpecific Gravity

SPECIFIC STRENGTH/SPECIFIC SPECIFIC STRENGTH/SPECIFIC STIFFNESSSTIFFNESS

Weight-Limited Design!Weight-Limited Design! Suppose that we have two materials, A and B, Suppose that we have two materials, A and B,

and that A has a yield strength of 200MPa and and that A has a yield strength of 200MPa and that B has a yield strength of 100MPa.that B has a yield strength of 100MPa.

Could I replace material A with material B for Could I replace material A with material B for e.g., the fuselage of a commercial aircraft? e.g., the fuselage of a commercial aircraft?

I would need “struts”of material B that were twice I would need “struts”of material B that were twice as thick as “struts” of material A. Is this a as thick as “struts” of material A. Is this a problem?problem?

SPECIFIC STRENGTH/SPECIFIC SPECIFIC STRENGTH/SPECIFIC STIFFNESS IISTIFFNESS II

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

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

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

SPECIFIC STRENGTH/SPECIFIC SPECIFIC STRENGTH/SPECIFIC STIFFNESS IIISTIFFNESS III

Conclusion:Conclusion: A more important parameter than “Strength” is A more important parameter than “Strength” is

‘Specific Strength” where‘Specific Strength” where Specific Strength is the strength/unit weight, or:Specific Strength is the strength/unit weight, or: Specific Strength = Yield StrengthSpecific Strength = Yield Strength

Specific GravitySpecific Gravity

Also:Also:

Specific Stiffness = Young’s ModulusSpecific Stiffness = Young’s Modulus

Specific GravitySpecific Gravity

SELECTED PROPERTIES OF SELECTED PROPERTIES OF SELECTED MATERIALSSELECTED MATERIALS

Table 36.1.

Selected Materials and Selected Physical/Mechanical Properties.

Material Specific Gravity Young's Modulus(GPa)

Approximate YieldStrength. (MNm-2).

Alloy Steel 7.8 200 1000Aluminum Alloys 2.7 69 500Titanium Alloys 4.5 120 1000Beryllium Alloys 1.9 300 250

Wood 0.6 12 40Polyurethane Foam 0.1 6 1

Concrete 2.5 47 25Alumina 3.9 390 400

GFRP* 2.0 40 200CFRP** 1.5 270 650

SELECTED PROPERTIES OF SELECTED PROPERTIES OF SELECTED MATERIALSSELECTED MATERIALS

SELECTED PROPERTIES OF SELECTED PROPERTIES OF SELECTED MATERIALSSELECTED MATERIALS

TOWARDS THE “ASHBY MAP”TOWARDS THE “ASHBY MAP”

E/E/ = q = q ““q” is a “number” which can be q” is a “number” which can be

used as a benchmark. used as a benchmark. Materials with a larger value of Materials with a larger value of “q”, will have a better “specific “q”, will have a better “specific stiffness” than our benchmark, stiffness” than our benchmark, whereas materials with a lower whereas materials with a lower value of “q” will be inferior.value of “q” will be inferior.

We can plot the straight line: We can plot the straight line: E = E = qq

Materials above this line are Materials above this line are superior: those below, are superior: those below, are inferior.inferior.

A “PROPERTY MAP”A “PROPERTY MAP”

TOWARDS THE “ASHBY MAP”TOWARDS THE “ASHBY MAP”

Reminder: E/Reminder: E/ = q = q When values of E/When values of E/vary vary

over orders of magnitude, over orders of magnitude, it is necessary to use a it is necessary to use a “log-log” plot, and:“log-log” plot, and:

logE = loglogE = log + logq + logq y = mx + Cy = mx + C

LINEAR AND LOG-LOG LINEAR AND LOG-LOG PERFORMANCE MAPSPERFORMANCE MAPS

AN “ASHBY MAP”AN “ASHBY MAP”