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# Designer Materials 4

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### Designer Materials 4

1. 1. Testing Materials Stress and Strain Graphs May 29, 2009
2. 2. To Review Homework... <ul><li>Calculations on Stress, Strain and Y.M. </li></ul><ul><li>1) Strain = Extension / Original Length </li></ul><ul><ul><li>= 25mm / 75mm = 0.33 </li></ul></ul><ul><li>2) mm / mm : Cancel Out </li></ul><ul><li>3) Stress = Force / Area </li></ul><ul><ul><li>Therefore Force = Stress x Area </li></ul></ul><ul><ul><li>=10 9 Nm -2 x 10 -8 m 2 = 10N </li></ul></ul>
3. 3. To Review Homework... <ul><li>Calculations on Stress, Strain and Y.M. </li></ul><ul><li>4) Stress = Force / Area </li></ul><ul><ul><li>so Area = Force / Stress = 15kN / 75MNm -2 </li></ul></ul><ul><ul><li>= 2 x 10 -4 m 2 </li></ul></ul><ul><ul><li>Area =  d 2 / 4 </li></ul></ul><ul><ul><li>therefore d =  4 x 2 x 10 -4 m 2 / 3.14 </li></ul></ul><ul><ul><li>d = 1.6 x 10 -2 m or 1.6 cm </li></ul></ul>
4. 4. To Review Homework... <ul><li>5) Stress = Force / Area </li></ul><ul><ul><li>Area =  d 2 / 4 </li></ul></ul><ul><ul><li>3.14 x (50 x 10 -3 m) 2 / 4 </li></ul></ul><ul><ul><li>= 1.96 x 10 -3 m 2 </li></ul></ul><ul><ul><li>Therefore Stress = 4kN / 1.96 x 10 -3 m 2 </li></ul></ul><ul><ul><li>= 2.0 x 10 6 Nm -2 or 2.0 MPa </li></ul></ul>
5. 5. To Review Homework... <ul><li>6) Stress = 2MPa </li></ul><ul><li>7) Stress is same for nylon and cable </li></ul><ul><ul><li>The Y.M for nylon is about 2 - 4GPa and 200 GPa for steel </li></ul></ul><ul><ul><li>Therefore Strain would be greater for nylon - it would extend more..! </li></ul></ul><ul><li>8) Y.M = Stress / Strain = </li></ul><ul><li>(Force / Area) / (Extension / Orig. Length) </li></ul><ul><ul><li>Therefore Extension = (F x OL)/(Area x Y.M.) </li></ul></ul><ul><ul><li>=2.5 x 10 -3 m </li></ul></ul>
6. 6. To Review Homework... <ul><li>Exam Question 10a </li></ul><ul><ul><li>Brittle - Shatters on impact / cracks propagate easily </li></ul></ul><ul><ul><li>Hard - Difficult to scratch or dent </li></ul></ul><ul><ul><li>Strong - Large breaking stress </li></ul></ul><ul><ul><li>Tough - Difficult to crack / large energy to break </li></ul></ul>
7. 7. To Review Homework... <ul><li>Exam Question 10 </li></ul><ul><li>bi) Steel is 4 times tougher </li></ul><ul><li>bii) Toughness is (energy) per new surface (area) </li></ul><ul><li>ci) B is best fit </li></ul><ul><ul><ul><li>Tougher than A, less tougher than C </li></ul></ul></ul>
8. 8. To Review Homework... <ul><li>Exam Question 1 </li></ul><ul><li>Car bodies e.g. steel - B - Strong and Tough </li></ul><ul><li>Weak material e.g. biscuit - C Weak and Brittle </li></ul><ul><li>Brittle Metal e.g. cast iron under tension - A - Strong but brittle </li></ul>
9. 9. To Review Homework... <ul><li>Exam Question 7 </li></ul><ul><li>a) Elastic and Tough </li></ul><ul><li>b) Area = Force / Stress = 550 / 2.0 x 10 9 = 2.8 x 10 -7 m 2 </li></ul><ul><li>ci) Elastic limit is past the elastic behaviour of material. Behaviour is plastic beyond this </li></ul><ul><li>cii) Y.M. = Stress / Strain 1.6 x 10 9 Nm -2 / 0.35m = 4.6 x 10 9 Pa </li></ul>
10. 10. Graphs of Young’s Modulus <ul><li>In pairs, summarise the key characteristics of the graphs you obtained from your practical results: </li></ul>
11. 12. Graphs for Different Characteristics <ul><li>Sketch graphs for the following different materials: </li></ul><ul><li>An elastic rubber band </li></ul><ul><li>A piece of steel under tension </li></ul><ul><li>A piece of cast iron under tension (more brittle than steel) </li></ul><ul><li>A glass fibre (brittle and stiff) </li></ul><ul><li>A plastic ruler </li></ul>
12. 13. Strain Stress
13. 14. Key Terms <ul><li>Elastic Limit - point at which elastic behavior is replaced by plastic deformation </li></ul><ul><li>Yield Point - Stress at which elastic limit is reached </li></ul><ul><li>Breaking Stress - the stress at which a material breaks </li></ul><ul><li>Plastic Region - Deformation of material is permanent (non-elastic). It can result in: </li></ul><ul><ul><li>Uniform extension along length of material </li></ul></ul><ul><ul><li>Necking at a point </li></ul></ul>
14. 15. Questions <ul><li>Answer questions 1 to 6 on page 91 </li></ul><ul><li>Show working out </li></ul>