Page 286 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C006.fm Page 266 Monday, May 23, 2005 5:50 PM

266 Fracture Mechanics: Fundamentals and Applications

Shear yielding in polymers resembles plastic flow in metals, at least from a continuum mechan-
ics viewpoint. Molecules slide with respect to one another when subjected to a critical shear stress.
Shear-yielding criteria can either be based on the maximum shear stress or the octahedral shear
stress [11, 12]:
τ τ µ = σ − (6.15a)
max o s m
or
τ oct τ o µ = s σ − m (6.15b)

where σ is the hydrostatic stress and µ is a material constant that characterizes the sensitivity of
m
s
the yield behavior to σ . When µ = 0, Equation (6.15a) and Equation (6.15b) reduce to the Tresca
s
m
and von Mises yield criteria, respectively.
Glassy polymers subject to tensile loading often yield by crazing, which is a highly localized
deformation that leads to cavitation (void formation) and strains on the order of 100% [13, 14].
On the macroscopic level, crazing appears as a stress-whitened region, due to a low refractive index.
The craze zone usually forms perpendicular to the maximum principal normal stress.
Figure 6.7 illustrates the mechanism for crazing in homogeneous glassy polymers. At suffi-
ciently high strains, molecular chains form aligned packets called fibrils. Microvoids form between
the fibrils due to an incompatibility of strains in neighboring fibrils. The aligned structure enables
the fibrils to carry very high stresses relative to the undeformed amorphous state because covalent
bonds are much stronger and stiffer than the secondary bonds. The fibrils elongate by incorporating
additional material, as Figure 6.7 illustrates. Figure 6.8 shows an SEM fractograph of a craze zone.
Oxborough and Bowden [15] proposed the following craze criterion:

tT
β tT γ(, ) (, )
ε = + (6.16)
1 E 3 σ m

where ε is the maximum principal normal strain, and β and γ are parameters that are time and
1
temperature dependent. According to this model, the critical strain for crazing decreases with
increasing modulus and hydrostatic stress.

FIGURE 6.7 Craze formation in glassy polymers. Voids form between fibrils, which are bundles of aligned
molecular chains. The craze zone grows by drawing additional material into the fibrils.