Modulus

Modulus

1. modulus intro

   • Resistance to deformation of the material
   • a result of how easily atoms move relative to each other
   • Depend on
     • stiffness of interatomic bonds in a crystalline material
     • entanglement (enredo) of chains in an amorphous material

2. type of bonds

   • primary or strong (ionic, covalent and metallic)
   • secondary or weaker (van der Waals and Hydrogen bonds)

3. theoretical modulus (equations)

   • stiffness
   • Stress = force per unit area
   • Strain = deformation per length
   • Young' s modulus = stiffness of one interatomic bond divided by atomic separation
     • higher stiffness<>higher YM

4. Moduli of materials (equations)

   • Elactic M (Young's Moduli E)
     • considers tension or compression thus loading along the specimen/object
   • Shear Moduli (G)
     • in torsion or shear loading
   • Bulk Modulus (K)
     • whole material is being compressed

5. Elastic deformation

   • Bonds within a material stretch and compress
     • tension in one direction leads to contraction in the perpendicular direction
     • compression in one direction leads to contraction in the perpendicular direction
     • Poisson's ratio (v)
       • depends on type metals
         • provides relationship between the 3 moduli
       • max value= 0.5 (no change in volume)
       • Isotropic materials (same properties in all directions) eq
         • single YM, shear mod and PR
       • Anisotropy (an=not) eq
         • 3 values for YM, shear modulus and PR

6. Polymers

   • loading polymers move the chains and does not stretch the backbone
   • loaded bonds arevan der Waals orces bw chains (weak forces)
   • have C-C chains in its backbone, covalently bonded (strong) HOWEVER its stiffness is low
   • types
     • non (or low) crosslinked
       • limited connection btw chains so can slide past each other
     • crosslinked are joined
       • more cross links > more covalent bonds> less movement
         • polymers backbone movement instead of chains moving relative with each other
       • increasing links> increase modulus (diamont)
   • tmp BIG INFLUENCE: rate deformation decrease<>increase tmp = softer and ductile