ENSC1004 - Lecture 12

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ENSC1004 - Lecture 11
Strength & Ductility 5 - Slides

Structure and Deformation of Polymers

• Due to wide variation in polymer structure, they can have different mechanical properties
• They are classified into 3 stress-strain behaviour types:
  • Brittle behaviour
  • Plastic behaviour
  • Rubber elasticity

Brittle Behaviour:

• Deforms to fracture with little plastic deformation
• Observed in highly crosslinked and networked polymers
• Relative high stiffness, high strength, low ductility
  • Inability of molecular chains to slide past each other

Plastic Behaviour:

• Observed in linear and branched chain molecules with semicrystalline microstructure
• Similar deformation behaviour to metals
  • Elastic → plastic deformation

Rubber Elasticity:

• Completely elastic, large recoverable strains at low stress
  • Elasticity is non-linear, unlike ceramics and metals
• Crosslinked molecular structure
  • In unstressed state, chains are highly twisted and coiled
    
  • Upon stretching, chains are uncoiled but cannot slip past each other due to crosslinks
    
  • When load is removed, chains are pulled back to their unstressed state

Density and Mechanical Properties of Materials

• Density of materials are determined by mass of their atoms and how these atoms are packed together

Metals → high density
Ceramics → lower density
Polymers → lowest density

• Metals are heavy and have packed structures with no free space
• Ceramics have a mix of metal and light elements
  • No free spaces like metals
• Polymers made of light elements
  • Packing is much less dense, more free space

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Mechanical Failure 1 - Slides

Failure by Plastic Yielding

• Yielding marks onset of plastic deformation
• In many engineering designs, this is not permitted
  • Thus, yield strength is used over ultimate tensile strength as design criterion
• In design against plastic yielding, we apply safety factor $N$
  • Thus ${\sigma }_w=\frac{{\sigma }_y}{N}$, typically $N$ falls between 1.2 to 4

Failure by Fracture

• Fail by a sudden, spontaneous fracture
  • Fracture is often propagative
  • Can occur before plastic deformation
• Brittle fracture occurs in load bearing and pressurized structures
  e.g. bridges and trucks, pressure vessels and gas pipelines
  • Fracture can occur due to ductile-to-brittle metal transition
• Fracture occurs when the energy stored in the system surpasses the energy criterion of fracture
  • Typically, fractures occur due to tensile stress

Energy Criterion of Fracture

• For a fracture to take place, the stored energy must be greater than the energy criterion of fracture
  $E_{stored}\ge E_f\to \text{fracture}$
  Graph Example:
• Yellow area $-$ dissipated energy
  • Energy cannot be used to do work
• Blue area $-$ elastic energy (stored)
  • Energy can be released to do work
    e.g. fracture the material

Modes of Fracture

• Brittle fracture $-$ little to no plastic deformation
  • Ceramics, high strength steels and brass
• Ductile fracture $-$ excessive plastic deformation
  • Most polymers and pure and soft metals
• Mixed fracture $-$ mix of both
  • Carbon steels and other alloy

Brittle Fracture

• Low energy absorbed by fracture
• No ‘necking’
• Flat fracture surface morphology $-$ cleavage fracture

Stress is uniform at low applied load, when the applied stress is high enough, cracks form and propagate through the material

• Propagation occurs when stress at crack tip $=$ fracture strength ${\sigma }_m={\sigma }_f$
  Ductile Fracture:
• High energy absorbed by fracture
• ‘Necking’ gives early warning signs of fracture
• ‘Cup-and-cone’ fracture surface morphology

Ductile materials fail at the yield strength which is lower than fracture strength

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ENSC1004 - Lecture 13