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Yield-Craze Behavior of Amorphous Polymers

Molecular Criterion for Failure Mode

Many fractures of plastics are caused by cavitation and crazing or by yielding. Which mechanism dominates depends on the properties of the plastic and on the test conditions. Important plastic properties that affect the fracture behavior include free volume, entanglement density, molecular weight, as well as number, size and shape of defects (voids) in the plastic. The fracture is also affected by the test method and test conditions such as rate of deformation, stress state, temperature, age of sample, and specimen geometry. The effect of these extrinsic and intrinsic variables on the brittle-ductile behavior is as follows

Because of their viscoelastic properties, the fracture behavior of polymeric materials varries considerably with the temperature. At low temperatures and/or high strain rates, polymers tend to fail via cavitation and crazing whereas at high temperatures and/or low strain rates yielding is more likely to occur. Thus the two failure modes compete with each other.

The intrinsic ductility, i.e. the propensity for yielding, increases as the characteristic ratio (C) decreases. It has been postulated1 that the yield stress σy is directly proportional to C and the cohesive energy density (or square of solubility parameter), ecoh = δh2:

σyC δh2

Crazing, on the other hand, is initiated by chain scission, and thus the energy to initiate cavitation and crazing, Ecav, should be proportional to the entanglement density νe. Since the crazing or cavitation stress, σz, is proportional to ecav½, we find:(2,3)

σzνe1/2

Combining these two equation gives the molecular condition for the main failure mode of the craze-yield behavior:

σz / σyνe1/2 / C δh2

With

νe = ρa / (3 Mr C2)

the expression above can be rewritten as

σz / σy ≅ (ρa / 3Mr)1/2 / [C δh]2

or

σz / σy ≅ (3Mr / ρa)1/2 νe / δh2

The factor (ρa / 3Mr)1/2 is more or less constant for the majority of polymers, except for those with high packing density, ρa, and/or with very large repeat units, Mr2,3. Thus the competition between crazing and yielding is determined by the entanglement density νe (or characteristic ratio C) and by the cohesive energy ecoh or by the solubility parameter δh, respectively. Polymers having a low entanglement density νe (large characteristic ratio C) and/or high cohesive energy density ecoh have a low σz / σy ratio, and thus tend to craze whereas polymers with small C (high νe) and low ecoh have a high σz / σy ratio, and thus tend to yield rather than craze.6

References & Notes
  1. R. P. Kambour, Polymer Communications, 24 (1983) 292.

  2. Souheng Wu, Poly. Engineering & Science, Vol 30, No. 13 (1990)

  3. Souheng Wu, Polymer International, 29, 229-247 (1992)

  4. Shorter polymers have more end groups per unit volume which have more degrees of
    freedom, which increases the free volume and thus the chain mobility.

  5. The critcal entanglement weight Mc is about twice the weight of an entanglement strand,
    Mc ≈ 2Me

  6. Both the entanglement density and cohesive energy depend on the temperature. Thus,
    when the temperature changes, the ratio σz / σy changes as well. Since a decrease in
    cohesive energy density and packing density increases chain mobility, polymers tend to
    yield at higher temperatures.

  • Summary

    Fracture Of Polymers

    The intrinsic brittle-ductile behavior of polymers depends on intrinsic and extrinsic factors.

  • Important intrinsic factors  are crystal structure, crystal thickness, degree of crystallinity, molecular weight, chain structure and composition.

  • Important extrinsic factors include temperature, rate of deformation, stress state, specimen geometry and number, size and shape of defects.

  • 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.

  • Crazing in a glassy polymer can be easily observed because crazes have a different index of refraction than the undeformed phase.

  • 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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  • At low temperatures and/or high strain rates, crazing is the dominating failure mode, whereas at high temperatures and low strain rates yielding precedes fracture.

  • The two most important chain parameters which control the  craze-yield behavior of a polymer are the entanglement density and cohesive energy density.

  • Entanglements behave like physical cross-links and increase the resistance to void formation/growth and crack propagation. Thus, polymers with a low entanglement density tend to craze whereas polymers with high entanglement density tend to yield.

  • The intrinsic ductility, i.e. the propensity for yielding, increases as the characteristic ratio C decreases. The maximum intrinsic plasticity limit occurs when C reaches its lowest value which equals a freely rotating chain with tetrahedral skeletal bonds, C = 2.

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Chain PArameters
(C, Me, νe & ρa)

       Table