Tensile Testing Machines

Back to Index

Brittle-Ductile Behavior of Amorphous Polymers

The intrinsic brittle-ductile behavior of polymers and blends is difficult to predict because it depends on many intrinsic and extrinsic factors. Important intrinsic factors of the crystal phase are crystal structure, crystal thickness, and degree of crystallinity, and those of the amorphous phase are free volume, entanglement density, and chain stiffness. Important extrinsic factors include temperature, rate of deformation, stress state, specimen geometry as well as number, size and shape of defects such as notches and cracks.

Because of their viscoelastic properties, the fracture behavior of polymeric materials varries considerably with the temperature. 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, molecular weight, and chain structure of the polymer.

The brittle-ductile transition is often described as a craze-yield transition. Fracture of brittle polymers is typically caused by cavitation and crazing. Cavitation is the formation of voids during deformation due to excessive stress which is often a precursor to crazing. The voids or cavities are often in the range of a few nanometers to several micrometers. They usually form inside the amorphous phase during deformation of the polymer. However, the formation of voids occurs only in tension whereas shear leads typically to the formation of shear bands. The voids usually form just before the material starts to craze, i.e. cavitation precedes crazing. The fracture of the amorphous phase through cavitation and crazing competes with plastic deformation. Plastic deformation before breaking is known as plasticity (in metals it is known as ductility). Ductile fracture involves a large degree of plastic deformation (high strain) and fracture not necessarily occurs at the highest stress.

The two most important chain parameters which control the brittle-ductile (craze-yield) behavior of a polymer are the entanglement density (νe) and the characteristic ratio (C∞). The later is a measure for the flexibility of the polymer backbone and the former describes the number of "knots" per unit volume. These two parameters are interrelated by following simple relation

νe = ρa / (3/2 · Mr · C∞2)

where Mr is the molecular weight of a repeat unit (vinyl monomer). A similar equation has been reported by Wu. et al. They postulated, that the equation is also applicable to more complex monomers if the molecular weight of a repeat unit is replaced by that of a statistical segment, Mv = Mr /2.1-3

Chain Parameters of some Amorphous Polymers1
Compound

Me
g/mol

 C∞

νe
mmol/cm3

ρa
g/cm3
PODMA 225000 20.6 0.004 0.942
PDMA 61000 13.4 0.016 0.95
PHMA 33500 12.2 0.030 1.01
PS 16600 10.3 0.064 1.06
PMMA 11300 8.1 0.101 1.15
PEMA 8600 8.0 0.130 1.12
PVC 4200 7.6 0.259 1.38
POM 2600 7.5 0.479 1.23
N66 2000 6.1 0.537 1.08
PET 1450 4.1 0.919 1.33
PC 1900 2.4 0.626 1.21
PSO 2300 2.2 0.535 1.24
1The parameters are the average of one or more experimental values

 

The intrinsic ductility, i.e. the propensity for yielding, increases as the characteristic ratio C∞ decreases. The maximum intrinsic ductility limit occurs when C∞ reaches its lowest value which equals a freely rotating chain with tetrahedral skeletal bonds, C∞  = 2.1 Two polymers with very low characterist ratio are polycarbonate (C∞  = 2.4) and polysulfone (C∞  = 2.2) which are some of the toughest polymers. These polymers also have a very high entanglement density. The entanglements behave like physical cross-links which increase both the resistance to void formation 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 also depend on the molecular weight (MW), temperature, and test speed. A lower MW and a higher temperature increases the mobility of the polymer chains due to the lower packing density4, which, in turn, increases the tendency of the polymer to yield under stress but it also decreases the mechanical strength. A higher strain rate has the same effect on the mechanical properties as a lower temperature (time-temperature equivalence). In other words, high strain rates (high velocity of impact) promote brittle fracture (crazing) and low strain rates ductile fracture (yielding).

References & Notes

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

  2. S. Wu, Poly. Engin. & Sci., Vol 30, No. 13 (1990)

  3. S . Wu & R. Beckerbauer, Polymer, 33, 509 (1992)

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

  • 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.

  • 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.

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

    •   Read More  

  •  

  • The two most important chain parameters which control the brittle-ductile (craze-yield) behavior of a polymer are the entanglement density (νe) and the characteristic ratio (C∞). The later is a measure for the flexibility of the polymer backbone and the former describes the number of entanglements per unit volume.

  • 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 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 ultimate (maximum) intrinsic ductility  occurs when C∞ reaches its lowest value which equals a freely rotating chain with tetrahedral skeletal bonds, C∞  = 2.

  •  

Chain PArameters
(Extended List)

       Table