Crazing growth

Xiao, F. and Curtin, W.A., Numerical investigation of polymer craze growth and fracture. Macromolecules, 28, 1654-1660 (1995). 

Usually, the molecular strands are coiled in the glassy polymer. They become stretched when a crack arrives and starts to build up the deformation zone. Presumably, strain softened polymer molecules from the bulk material are drawn into the deformation zone. This microscopic surface drawing mechanism may be considered to be analogous to that observed in lateral craze growth or in necking of thermoplastics. Chan, Donald and Kramer [87] observed by transmission electron microscopy how polymer chains were drawn into the fibrils at the craze-matrix-interface in PS films [92]. One explanation, the hypothesis of devitrification by Gent and Thomas [89] was set forth as early as 1972. 

Lauterwasser BD, Kramer EJ (1979) Microscopic mechanisms and mechanics of craze growth and fracture. Philos Mag A Phys Condens Matter Struct Defects Mech Prop 39 469 95... 

The craze thickening, associated with the craze growth, implies an increase of fibril length. This is achieved by pulling out polymer chains from the craze-bulk interface, according to a behaviour analogous to plastic flow within the active layer (5-10 nm thick), as shown in Fig. 5b [21]. 

FIG. 13.81 Continuous craze growth and formation of a crack, which cannot support load, as shown in the stress distribution. 

Marshall GP, Culver LE, Williams JG (1970) Craze growth in poly(methyl methacrylate) a fracture mechanics approach. Proc R Soc Lond A Math Phys Eng Sci 319(1537) 165-187... 

Williams JG, Marshall GP (1975) Environmental crack and craze growth phenomena in polymers. Proc R Soc Lond Ser A 342(1628) 55-57... 

Wyzgoski MG, Novak GE (1987) Stress cracking of nylon polymers in aqueous salt solutions. Part 3 Craze-growth kinetics. J Mater Sci 22(7) 2615-2623... 

Figure 14 shows the craze growth resistance curves for the above loading rates together with that for Ki = 30 MPa /m/s from the isothermal analysis in Fig. 11 (Ki = 900Kj°) [22] for which isothermal conditions prevail. As the loading rate increases, Kf remains constant. Toughening caused by temperature effects is not observed, even when the local temperature increases at the highest loading rates.

Figure 6. Diagrams of planar shape and thickness profile of full grown craze and shear zone beyond root of notch in BPA polycarbonate specimen. Shear bands initiate from positions of maximum shear stress at root. Arrows indicate craze growth directions.

There are two important questions about craze growth, namely what are the mechanisms of craze tip advance (expansion of the craze periphery generating more fibrils) and craze thickening (normal separation of craze surfaces lengthening the craze fibrils). Unlike the cloudy experimental situation regarding craze nucleation, that regarding craze growth now seems quite clear. 

It is observed that the normal craze fibril structure can be observed just behind the craze tip where the craze is as thin as 5—lOnm . This observation was difficult to reconcile with early models of craze tip advance which postulated that this occurred by repeated nucleation and expansion of isolated voids in advance of the tip. One problem was to explain how the void phase became interconnected while the craze was still so thin. Another was that the predicted kinetics of craze growth appeared to be incorrectly predicted indeed since this mechanism almost involves the same steps as the original craze nucleation, it is hard to understand how craze growth could be so much faster than craze nucleation as observed experimentally. 

The dislocation method of stress analysis is also useful for determining craze stress fields in anisotropic (e.g., oriented) polymers . All one needs here is the stress field of a single dislocation in a single crystal with the same symmetry as the oriented polymer (the text by Hirth and Lothe provides a number of simple cases plus copious references to more complete treatments in the literature) the craze stress field can be generated by superposition of the stress fields of an array of these dislocations of density a(x). Dislocations may also be used to represent the self-stress fields of curvilinear crazes (produced by craze growth in a non-homogeneous stress field for example). Such a method has been developed by Mills... 

J/m. In turn these values of F produce substantial predicted differences in craze growth kinetics. Substituting these values into Eq. (7) the craze tip velocity at constant S, = 100 MPa is predicted to decrease by a factor of 10 from PTBS to PC (values for h of 10 nm and for n, the power law exponent, of 17 are assumed for both) or equivalently the value of Sj to give the same craze tip growth rate increases by a factor of 2.8. Since the measured stress S at the craze tip in PTBS is 27 MPa, the craze tip stress in PC is predicted to be 74 MPa, well above its... 

Craze growth occurs in a lateral direction by advance of a thin finger-like craze tip by the meniscus instability mechanism. Crazes increase in thickness by a surface drawing mechanism in which more polymer is drawn into the craze fibrils at essentially constant extension ratio X from the craze-bulk polymer interface. 

In this Section the kinetics of craze growth at crack tips in air will be considered in some detail. We shall not be concerned with the initiation phase and any micro mechanism (e.g. leading to craze initiation. 

Fig. 20. Craze growth at a stationary crack tip in PMMA in methanol...

In all papers mentioned above the characterization of the craze growth has been performed by measuring the craze length. By application of the optical interference method the essential information on the growth of craze width is awiilable. Figure 22 shows the interference fringe patterns and measured craze zone sizes at a stationary crack tip in PMMA loaded in a creep test at a constant K,-value at loading times of 150 s and 2 1(F s... 

Craze growth at the crack tip has been qualitatively interpreted as a cooperative effect between the inhomogeneous stress field at the crack tip and the viscoelastic material behavior of PMMA, the latter leading to a decrease of creep modulus and yield stress with loading time. If a constant stress on the whole craze is assumed then time dependent material parameters can be derived by the aid of the Dugdale model. An averaged curve of the creep modulus E(t) is shown in Fig. 13 as a function of time, whilst the craze stress is shown in Fig. 24. 

---