Brittle-Ductile Transition
Shear-Yielding and Crazing

Polymeric materials can break immediately or they can undergo (considerable) plastic deformation before breaking which is known as plasticity (in metals it is known as ductility). Brittle failure is characterized by low strain and fracture at the highest stress whereas ductile fracture involves a large degree of plastic deformation and fracture not necessarily occurs at the highest stress.

Because of their viscoelastic properties, the fracture behavior of polymeric materials varries considerably with temperature and strain rate (frequency). Below the brittle-ductile transition temperature, polymers fail via crazing wheras above this temperature yielding dominates. The brittle-ductile transition temperature itself strongly depends on the morphology and the chain structure of the polymer.

The two most important chain parameters which control the brittle-ductile (craze-yield) behavior of a polymer are its entanglement density (ν) and the characteristic ratio (C). The later is a measure for the flexibility of the polymer backbone. The intrinsic ductility, i.e. the tendency for yielding, increases as the characteristic ratio C decreases. The maximum intrinsic plasticity limit occurs when Creaches its lowest value which equals a freely rotating chain with tetrahedral skeletal bonds, C = 2. Two polymers with very low characterist ratio are polycarbonate (C = 2.4) and polysulfone (C = 2.2) which are some of the toughest polymers. Entanglements behave like physical cross-links and increase the resistance to void formation/growth and crack propagation. Thus, (high molecular weight) polymers with a low entanglement density and a large characteristic ratio tend to craze whereas polymers with high entanglement density and small characteristic ratio tend to yield.

The mechanical properties of a polymer strongly depend on its molecular weight (MW). Lowering the molecular weight greatly increases the mobility of the polymer chains. Thus, a lower MW polymer has a greater tendency to yield than a higher MW polymer, i.e. with decreasing MW, the brittle-ductile transition shifts to higher temperatures.   

The prevailing view is that materials below their glass transition are brittle. However, this is only the case for polymers with large bulky side groups such as polystyrene or polyphenyl methacrylate. In this case, the the brittle-ductile transition coincides with the α-transtion,

Tb = Tα = Tg

For the majority of polymers the ductile-brittle transition occurs at a much lower temperature. For most amorphous polymers, vitrification or glassification coincides with the β-transtion,

Tb = Tβ  

and for very tough polymers such as polycarbonate and polysulfone and many semic-crystalline polymers the brittle-ductile transition temperature corresponds with the γ-transtion,

Tb = Tγ  

A number of relationships have been proposed to relate the β-transition temperature to the glass transition temperature. For example, Boyer1 suggested Tb / Tg ≈ 0.75. However, no such simple relationships exist. As has been shown by Wu, the brittle-to-ductile transition temperature is a function of the intrinsic chain stiffness or flexibility. Wu2 found following relation:

{Tβ} / {Tα} = Tb / Tg = 0.135 + 0.082 C

which is only applicable to polymers with Tb < Tg , i.e. polymers without bulky side groups. This is the case for polymers with  C ≤ 10.5.

 

Brittle-Ductile Transition of some Polymers,
TB / TG versus C (1 Hz)

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With the Tb - Tg data from several sources for both amorhpous and semi-crystalline polymers we find a similar relationship:

 Tb / Tg = 0.208 + 0.069 C

Thus, the ratio Tb / Tg is indeed a function of the chain stiffness (C) (see Figure above).

References
  1. R. F. Boyer, Polymer 17, 996 (1976).

  2. Souheng Wu, J. Appl. Poly. Sci., Vol. 45, 619 - 624 (1992)

  • Summary

    Fracture Of Ppolymers

    At low temperature and/or high strain rates, brittle failure is the dominating failure mode in plastics, whereas at high temperatures and strain rates plastic deformation precedes fracture.

  • The two competing failure modes are crazing and yielding. Below the brittle-ductile transition temperature, many polymers fail via crazing wheras above this temperature shear yielding is the dominating failure mode.

  • Crazing

    A craze is defined as a microvoid which develops similar to a crack normal to the main stress/strain axis, usually via chain scission. Crazes can sustain stress due to the formation of fibrills of oriented chains that span from one face of the microvoid to the other.

  • Shear-Yielding

    Shear-yielding is caused by chain slippage, usually at an angle of 45° to the applied load. It is usually observed right after the material yields. Further deformation causes chain hardening due to orientation / allignment of the polymer chains.

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