AML 883 Properties and selection of engineering materials

Transcription

1 AML 883 Properties and selection of engineering materials LECTURE 3. Density and moduli M P Gururajan guru.courses@gmail.com Room No. MS 207/A 3 Phone: 1340 Homepage:

2 Density Modulus chart

3 Density Mass per unit volume How to measure it?

4 Archimedes principle! Buoyancy A body, when immersed in a liquid, feels an upward force equal to the weight of liquid it displaces Image courtesy: wiki

5 Double weighing method Measure the mass m1 of the sample of unknown volume Measure the mass m 2 of the sample when it is fully immersed in a fluid of known density fl Density of the sample is = fl m 1 / m 1 m 2

6 What determines density? Mainly, the atomic weight. Why? Atoms differe greatly in weigth but little in size Largest atoms (Cesium) is 2.5 times larger than the smallest, beryllium Heaviest stable atoms (Uranium) is about 35 times heavier than the lightest (lithium); yet when packed to form slids, they are almost of the same diameter (0.32 nm)

7 What determines density? Atomic size and packing lesser role Metals made up of heavy atoms and crystalline dense Polymers made up of carbon and hydrogen and amorphous or semi crystalline light Ceramics lower than metals since they contain light Si, O, N, or C atoms Even lightest atoms, packed in a solid will give 3 densities equivalent to water 1 kg/ m

8 Atomic packing in metals Atoms often behave as if they are hard spheres!

9 FCC unit cell Face centered cubic Image courtesy: wiki

10 BCC Unit cell Body centered cubic cell Image courtesy: wiki

11 Hexagonal unit cell Hexagonal unit cell Image courtesy: wiki

12 Close packing: HCP and FCC Image courtesy: wiki

13 Non close packing: BCC

14 FCC: cannonball packing! An usual site in the bazaars! Image courtesy: wiki

15 HCP: cannonball packing May be not very usual but still not unknown either Image courtesy: wiki

16 Atomic packing in metals Atoms often behave as if they are hard spheres! FCC (face centered cubic) and HCP (hexagonal close packing) FCC...ABCABC... HCP...ABABAB... Packing fraction of FCC and HCP = 0.74 BCC (Body centered cubic) Not close packed (packing fraction of 0.68)

17 Atom packing in glasses Silica glass atomic structure Amorphous Image courtesy: wiki

18 Silicon carbide Ceramics Ball and stick model of silicon carbide Image courtesy: wiki

19 Polymers Single chains of a polymer image obtained using Atomic Force Microscopy Image courtesy: wiki

20 Amorphous polymers Both in molten and solid state the same type of internal structure Image courtesy (this and the next third): Zeus white paper on crystallanity in polymers

21 Crystalline polymer

22 Cross linking An example of cross linking Vulcanisation of rubber Image courtesy: wiki

23 Spherulites Equivalent of grains in polymers Several bundles of crystalline polymers

24 Stress Tensile/compressive/shear/hydrostatic Force per unit area is stress

25 Strain Tensile/compressive/shear/volume Response of the material to stress Change in dimensions/size/shape with respect to the original dimensions/size/shape

26 Stress strain curves and moduli Slope of the elastic region gives the moduli Image courtesy: wiki

27 Moduli and their relationships Tensile stress to tensile strain: Young's modulus (E) Shear stress to shear strain: Shear modulus (G) Pressure to volume strain: Bulk modulus Poisson's ratio: of transverse to axial strain Isotropic material G=E / 2 1 ; K =E /3 1 2

28 Who is this? Image courtesy: wiki

29 A hint! A statue in his honour! Image courtesy: wiki

30 Sergey Bubka 35 times men's pole vaulting record was broken by him! Well what does it to do with us?

31 Pole vaulting sequence Step 1

32 Pole vaulting sequence Step 2

33 Pole vaulting sequence Step 3

34 Pole vaulting sequence Step 4

35 Pole vaulting sequence Step 5

36 Pole vaulting sequence Step 6

37 What is happening? The vaulting pole is a very advanced piece of equipment. It is constructed from carbon fiber and fiberglass composite materials in several layers. The pole must be able to absorb all of the vaulter's energy while bending, and then return all of that energy as it straightens out. These advanced composite materials waste very little energy when they bend, and have a good strength to weight ratio. How stuff works site

38 Elastic energy Area under the stress strain curve elastic energy per unit volume W = (½) 2 /E

39 Measurement of Young's modulus How is it done?

40 Measurement of Young's modulus Not by stress strain measurement Values obtained using such experiments are off by a factor of 2 or more Accurate moduli measurement are done dynamically: using natural vibrations or by meauring the velocity of sound waves

41 Stress free strain Magneto striction Piezo electric materials Thermal expansion Phase transformations Though these strains are not due to stresses, they do give rise to stresses themselves.

42 Isotropy and anisotropy Glasses, polymers isotropic Metals and ceramics polycrystallinity makes them isotropic Composites not isotropic

43 LT and LN shear moduli Woods for fanblades our case study Tensile tests should be carried out to calculate two strengths, for example! LT and LN Longitudinal transverse and Longitudinal Normal

44 Cohesive energy and elastic moduli From PJM Monteiro's lecture notes (U C Berkeley) This figure and the next two The forces between two atoms as a function of separation

45 Cohesive energy and elastic moduli The picture in terms of the potential

46 Cohesive energy and elastic moduli

47 Bond stiffness and moduli Covalent, metallic, ionic, Hydrogen and Van der Waals bonds Stiffness: , 15 75, 8 24, 3 6, N/m Modulus: ,60 300,32 96,2 12,1 4 Carbon carbon, metals, NaCl, Polythene, Waxes Table 4.1 of the book!

48 Elastomers are different Poisson's ratio 0f 0.5 instead of 0.33 Easy to stretch in tension, but loaded hydrostatically (or when constrained to retain shape), is very stiff Above glass transition, the hydrogen bonds are molten No stiffness at all Below glass transition, the hydrogen bonds resist stretching and try to take it back to its original shape However, when stretched, there is some ordering associated with stretching

49 Elastomers are different Strain induced ordering Corss links in the elastomer try to resist deformation On heating, this strain induced ordering is disrupted Explains the low modulus as well as the increase in the same with temperature (unlike a treu solid)

50 Manipulating density and modulus Now that we know the atomic origins of modulus and density for different types of materials, how do we go about manipulating them?