1. LECTURE 12.1

2. LECTURE OUTLINE Weekly Deadlines Weekly Deadlines Ashby Maps Ashby Maps

4. THE MATERIALS SCIENCE TETRAHEDRON

5. THE HARDNESS OF BRONZES

6. HARDNESS AND SPECIFIC GRAVITY

7. WEIGHT; WHERE LESS IS MORE

8. A “PERFORMANCE INDEX” Define a “Performance Index” as Strength (Hardness)/ Unit Weight, or Define a “Performance Index” as Strength (Hardness)/ Unit Weight, or Specific Strength = Hardness Specific Strength = Hardness Specific Gravity

9. SPECIFIC STRENGTH/SPECIFIC STIFFNESS Weight-Limited Design! 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. 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? 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? I would need “struts”of material B that were twice as thick as “struts” of material A. Is this a problem?

10. SPECIFIC STRENGTH/SPECIFIC STIFFNESS II Answer: It depends on the specific gravity of the two materials! 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 #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. 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.

11. SPECIFIC STRENGTH/SPECIFIC STIFFNESS III Conclusion: Conclusion: A more important parameter than “Strength” is ‘Specific Strength” where A more important parameter than “Strength” is ‘Specific Strength” where Specific Strength is the strength/unit weight, or: Specific Strength is the strength/unit weight, or: Specific Strength = Yield Strength Specific Strength = Yield Strength Specific Gravity Specific GravityAlso: Specific Stiffness = Young’s Modulus Specific Gravity Specific Gravity

12. SELECTED PROPERTIES OF SELECTED MATERIALS

15. TOWARDS THE “ASHBY MAP” E/  = q E/  = 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. “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 =  q We can plot the straight line: E =  q Materials above this line are superior: those below, are inferior. Materials above this line are superior: those below, are inferior.

16. A “PROPERTY MAP”

17. TOWARDS THE “ASHBY MAP” Reminder: E/  = q Reminder: E/  = q When values of E/  vary over orders of magnitude, it is necessary to use a “log-log” plot, and: When values of E/  vary over orders of magnitude, it is necessary to use a “log-log” plot, and: logE = log  + logq logE = log  + logq y = mx + C y = mx + C

18. LINEAR AND LOG-LOG PERFORMANCE MAPS

19. AN “ASHBY MAP”