1. PHY 231 1 PHYSICS 231 Lecture 21: Some material science Remco Zegers Walk-in hour: Thursday 11:30-13:30 am Helproom gas liquidsolid

2. PHY 231 2 States of matter

3. PHY 231 3 Phase transformations

4. PHY 231 4 solids amorphous ordered crystalline

5. PHY 231 5 The deformation of solids Stress: Tells something about the force causing the deformation Strain: Measure of the degree of deformation For small stress, strain and stress are linearly correlated. Strain = Constant*Stress Constant: elastic modulus The elastic modulus depends on: Material that is deformed Type of deformation (a different modulus is defined for different types of deformations)

6. PHY 231 6 The Young’s modulus Beyond the elastic limit an object is permanently deformed (it does not return to its original shape if the stress is removed).

7. PHY 231 7 example An architect wants to design a 5m high circular pillar with a radius of 0.5 m that holds a bronze statue that weighs 1.0E+04 kg. He chooses concrete for the material of the pillar (Y=1.0E+10 Pa). How much does the pillar compress? 5m R=0.5 m L 0 =5m Y=1.0E+10 Pa M=1.0E+04 kg  L=6.2E-05 m

8. PHY 231 8 Ultimate strength Ultimate strength: maximum force per unit area a material can withstand before it breaks or fractures. Different for compression and tension.

9. PHY 231 9 example A builder is stacking 1 m 3 cubic concrete blocks. Each blocks weighs 5E+03 kg. The ultimate strength of concrete for compression is 2E+07 Pa. How many blocks can he stack before the lowest block is crushed? The force on the low end of the lowest block is: F=Nm block g. N: total number of blocks m block =mass of one block g=9.81 m/s 2 Ultimate strength: 2E+07=F/A =Nm block g/1 N=408 blocks.

10. PHY 231 10 The Shear Modulus xx

11. PHY 231 11 Moving earth crust 30 m 100 m A tectonic plate in the lower crust (100 m deep) of the earth is shifted during an earthquake by 30m. What is the shear stress involved, if the upper layer of the earth does not move? (S=1.5E+10 Pa) F/A=4.5E+09 Pa

12. PHY 231 12 Bulk Modulus Compressibility: 1/(Bulk modulus)

13. PHY 231 13 example What force per unit area needs to be applied to compress 1 m 3 water by 1%? (B=0.21E+10 Pa)  V/V 0 =0.01 so,  F/A=2.1E+07 Pa !!!

14. PHY 231 14 Some typical elastic moduli

15. PHY 231 15 Density

16. PHY 231 16 Pressure Pressure=F/A (N/m 2 =Pa) Same Force, different pressure

17. PHY 231 17 example A nail is driven into a piece of wood with a force of 700N. What is the pressure on the wood if A nail =1 mm 2 ? A person (weighing 700 N) is lying on a bed of such nails (his body covers 1000 nails). What is the pressure exerted by each of the nails? P nail =F/A nail =700N/1E-06m 2 =7E+08 Pa P person =F/(1000A nail )=700/1E-03= 7E+05 Pa (about 7 times the atmospheric pressure).