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

PHY States of matter

PHY Phase transformations

PHY solids amorphous ordered crystalline

PHY 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)

PHY 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).

PHY 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

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

PHY 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.

PHY The Shear Modulus xx

PHY 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

PHY Bulk Modulus Compressibility: 1/(Bulk modulus)

PHY 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 !!!

PHY Some typical elastic moduli

PHY Density

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

PHY 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).