Transcript Document 7405762
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”