LECTURE 12.2

LECTURE OUTLINE Lesson 12 Quiz Feedback Lesson 12 Quiz Feedback Ashby Maps Ashby Maps

Q1. Table 1 shows some of the materials that were listed as Table 3.4 in the book. Use this information to answer the following question. The object is to design a scratch resistant countertop for the kitchen. Which material would be employed for maximum scratch resistance? Soda-Lime Glass HDPE Tungsten Alumina Mullite

Q2. Table 1 presents some property measurements for a series of materials, while Figure 1 plots the Young's moduli of these materials as a function of their specific gravities. The line P passes through the datum point for our benchmark material: aluminum. The datum point marked A on Figure 1 corresponds to _______. alumina tungsten copper mullite nylon

Q3. Table 2 presents atomic numbers (At #), melting points (MP), specific gravities (SG), and Mohs Hardness values (H) for a series of metals and their corresponding oxides. The specific gravity of a metal oxide increases as the specific gravity of the metal increases. Always true Sometimes false

Q4. Table 2 presents some properties of a variety of materials. Corundum is a ________. metal ceramic polymer composite Corundum is a compound; it is non-metallic and inorganic; it is an oxide-ceramic.

Q5. Table 2 presents some properties of a variety of materials. Corundum is an ore for which metal? Magnesium Aluminum Manganese Iron Copper

Q6. Figure 2 shows the variation in the specific strengths of a series of composites (also see Chapter 27) as a function of the percent of glass fiber in the composite. In order to attain a specific strength of approximately 105 MPa, the % fiber should be about _______

Q7. Table 3 presents the specific gravities, Young's moduli, and yield strengths for a series of materials. The specific modulus of an alloy steel is approximately _______. 26 MPa 13 GPa 128 GPa 260 GPa 1280 GPa

Q8. Table 3 presents some property measurements for a series of materials, while Figure 3 plots the yield strengths of these materials as a function of their specific gravities. The line P passes through the datum point for our benchmark material: aluminum. The datum point marked A on Figure 3 corresponds to ______. CFRP titanium alloys alloy steel alumina GFRP

Q10. The semiconductor gallium arsenide (GaAs) has a specific gravity of about 5.5 and a Young's modulus of approximately 100 GPa. Is gallium arsenide a better or worse choice than aluminum (our benchmark material) for an aircraft wing—based on specific stiffness alone? Better Worse

Q11. Table 1 presents some property measurements for a series of materials, while Figure 1 plots the Young's moduli of these materials as a function of their specific gravities. The line P passes through the datum point for our benchmark material: aluminum. Which of the following materials would have a superior performance index for application as an aircraft wing, for which a high value of Young's modulus and a low value of specific gravity are desirable? Alumina Tungsten Nylon Copper

PERFORMANCE Ashby Maps Ashby Maps

THE MATERIALS SCIENCE TETRAHEDRON

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

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 200 MPa and B has a yield strength of 100 MPa. Suppose that we have two materials, A and B, and that A has a yield strength of 200 MPa and B has a yield strength of 100 MPa. Could I replace material A with material B for something such as the fuselage of a commercial aircraft? Could I replace material A with material B for something such as 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?

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.

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

SELECTED PROPERTIES OF SELECTED MATERIALS

TOWARD THE ASHBY MAP” E /  = q E /  = q “q” is a “number” that 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” that 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.

A “PROPERTY MAP”

TOWARD 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  + log q logE = log  + log q y = mx + C y = mx + C

LINEAR AND LOG-LOG PERFORMANCE MAPS

AN ASHBY MAP