Exploring design with CES (use Level 2 unless otherwise indicated)

7.8 Exploring design with CES (use Level 2 unless otherwise indicated)

Exercise E7.11 Use the ‘Search’ facility in CES to search for materials that are used for springs. Report what you find.

Exercise E7.12 Use the ‘Search’ facility in CES to search for materials that are used for light springs. Report what you find.

Exercise E7.13 Make a property chart with σ y on one axis and E on the other. Use it to select materials for springs, using the index σ 2 y /E derived in the text. Which three metals emerge as the best metallic choices?

Exercise E7.14

A material is required for a spring that must be as light as possible. To be stiff enough it must also have a Young’s modulus E ⬎ 20 GPa. Make a bar chart

with the index σ 2 y /Eρ for selecting light springs derived in Exercise E7.10 (you will need to use the ‘Advanced’ facility in the axis-choice dialog box to do this). Add a ‘Limit’ stage to apply the constraint E ⬎ 20 GPa. Hence find the two materials that are the best choices for this application.

Exercise E7.15 Exercise E7.10 describes the requirements for valve springs for high-per- formance engines. Apply the index derived there, σ 2 y /ρE, by making an appropriate chart and plotting an appropriate selection line on it. Engines are hot: add a ‘Limit’ stage on maximum service temperature of 250°C. Hence select metals for this application.

Exercise E7.16 Abrasives have high hardness, H. Make a bar chart of hardness and identify the four materials with the highest values. They are prime choices for abra- sive wheels and pastes.

Exercise E7.17 The text showed that the power required to roll a metal is proportional to its yield strength. Make a bar chart of yield strength, σ y for metals. Open the record for low-carbon steel, find the range of its yield strength and take the average. Normalize all the yield strengths in the database by dividing them by this value, using the ‘Advanced’ option in the dialog box for selecting the axes, so that low-carbon steel now lies at the value 1 on the bar chart. Use the chart to read off how much less power is required to roll: (a) commer- cially pure zinc and (b) commercially pure lead at room temperature.

Exercise E7.18 Crash barriers, auto fenders and other protective structures rely on absorb- ing kinetic energy by plastic deformation. The energy W pl absorbed in deforming a material to fracture (the area under the stress–strain curve) can

be estimated approximately in CES as

1 W pl ⫽ ( σ y ⫹ σε )

2 ts f

162 Chapter 7 Bend and crush: strength-limited design

Make a chart with density on the x-axis and W pl on the y-axis by using the ‘Advanced’ facility in the axis-selection dialog box. Use a box selection to

find the three materials that absorb the most energy. Rank them by price, using a ‘Graph’ stage to plot price.

Exercise E7.19 If the crash barrier of the last exercise is part of a vehicle, fuel is saved if it is light. We then want the materials with the largest value of W pl /ρ, where ρ is the density. These are found by using a selection line of slope 1 on the chart made in the last exercise and selecting the materials above the line. In this application the materials must also have adequate stiffness so that they do not bend elastically too much, requiring a Young’s modulus of at least 2.5 GPa. Apply this requirement using a ‘Limit’ stage, return to the chart and move the selection line until only three materials remain. Comment on the choice.

Exercise E7.20 Now explore what Level 3 of the database can do. Leave all the selection lines and criteria in example E7.19. Go to File ⬎ Change Database ⬎ CES

Edu Level 3 ⬎ Open. A dialog box asks if you wish to apply this to your cur- rent project. Click on Yes. Then list the materials that now appear in the results window. Comment on the choice.

Chapter 8

Fracture and fracture

toughness

Chapter contents

8.1 Introduction and synopsis 164

8.2 Strength and toughness 164

8.3 The mechanics of fracture 166

8.4 Material property charts for toughness 172

8.5 Drilling down: the origins of toughness 174

8.6 Manipulating properties: the 178 strength–toughness trade-off

8.7 Summary and conclusions 181

8.8 Further reading 181

8.9 Exercises 182

8.10 Exploring design with CES 183

8.11 Exploring the science with CES Elements

164 Chapter 8 Fracture and fracture toughness