Mode I cracking

The existence of a wedge-shaped cavitated or fibrillar deformation zone or craze, ahead of the crack-tip in mode I crack opening, has led to widespread use of models based on a planar cohesive zone in the crack plane [39, 40, 41, 42]. The applicability of such models to time-dependent failure in PE is the focus of considerable attention at present [43, 44, 45, 46, 47]. However, given the parallels with glassy polymers, a recent static model for craze breakdown developed for these latter, but which may to some extent be generalised to polyolefins [19, 48, 49], will first be introduced. This helps establish important links between microscopic quantities and macroscopic fracture, to be referred to later. 

Fig. 21 The critical stress intensity for mode I crack initiation at different temperatures as a function of test speed in a iPP with Mw of 248 kg mol1 and a polydispersity of 5.2 and a similar material containing approximately 80 wt% y3 phase. The arrows mark ductile-brittle transitions in the y3 modified specimens [24]...

The approach used to simulate Mode I cracking under monotonic loading is to define tractions [Pg.38]

Consider a sharp, Mode I crack in an elastic-power-law creeping solid (Eqn. (2)). The isotropic multiaxial generalization of Eqn. (2) is in terms of the Von Mises effective stress [Pg.337]

Concerning system C, little is known about the fracture toughness of the Si02 4.5 wt.% P. Considering a mode I crack opening (tensile), the fracture toughness parameter is estimated from the relation ... 

The scaling constant Ki for mode I crack opening, which occurs in these equations, is known as the stress intensity factor. It is proportional to the K of Eq. (9.7). The inclusion of the term is a result of the 1939 definition of Ki—logically it could be omitted. Both stress components given by Eq. (9.8) are zero along the crack surface, as required by the boundary... 

Figure 5.23 (a) Schematics of interlaminar and intralaminar fracture, (b) DCB and ENF specimens, (c) Relationship between mode I crack propagation rate and cyclic stress intensity range for a T300/914c laminate... 

Han Han, Y.-C., Yang, Y.-M., Li, B.-Y., Feng, Z.-L. Plastic zone in front of mode I crack in phe-nolphthalein polyether ketone. Angew. Makromol. Chem. 235 (1996) 47-55. 

Fig. 12.3 Three common mode I cracked-plate geometries (a) (CN) center-notched plate (b) (SEN) single-edge-notched plate and (c) (DEN) double-edge-notched plate.

The displacements ue and Ur around the mode I crack are also of interest for certain critical crack-tip environments. These are also readily obtainable for a linear elastic material, together with the local strains Srr, and Sre through the use of Hooke s law, and are (Williams 1984)... 

Fig. 12.8 (a) A mode I crack with a cohesive zone of length c over which the opening tractions at the two tips of the crack are limited to <7c. (b) The shape of a mode I crack with a cohesive zone of length c under a traction of compared with the shape of a mode I crack with a singular field (v is the half crack-flank displacement shown in (a) (from Williams (1984) courtesy of Wiley). 

Fig. 12.15 A comparison of three plastic-field solutions at the mode I crack tip the HRR solution the slip-line field solution, and the numerical FEM solution of McMeeking (1977).

Figure 3.487. Slowly opened mode I crack (in situ) in CF/PEEK (dashed circle marks the approximate size of the damage zone around the crack tip [1317],...

Figure 3.488. Very slowly opened mode I crack in CF/PEEK, giving evidence for significant deformation around the main crack.

In this case, cracks run along the interface between two materials due to interactions between the stress field in the adhesive layer and spatial variations in fracture properties. The cracks are not generally free to evolve as mode I cracks, as was the case for cohesive cracks, and mixed-mode fracture concepts (combinations of tension and shear) have to be considered. Mode II or shear components are induced, even in what appear to be nominally mode I loadings, due to differences in moduli about the interface. Again, if the presence of the adhesive layer is being ignored and the adherends are dissimilar, then a crack appears to be adhesive (i.e. an adhesion failure) on the macroscopic scale. 

---