Unstable crack propagation

In a first testing series, the fracture behavior of the neat, fully crosslinked epoxy network was studied. A fully unstable crack propagation behavior was observed and the critical stress intensity factor, Kj (0.82 MPaxm ), and the critical energy release rate, Gj (0.28 kj/m ), were determined [87]. These are typical values for highly crosslinked epoxy networks prepared with DGEBPA and aromatic or cycloaliphatic diamines. 

Various types of crack propagation, namely unstable, partially stable, and fully stable can be observed during SENB tests [85,131]. Solvent-modified epoxy networks prepared via CIPS with 13-16 wt % and 22 wt % cyclohexane show unstable crack propagation. For solvent-concentrations of 18 wt % and 20 wt % cyclohexane, a partially stable crack propagation is observed. The amount of energy consumption upon crack propagation is only 10% and 14% respectively for these two compositions. The change in the fracture behavior indicates that the... 

As a representative example, three of the failure modes of internally pressurized polyethylene pipes are indicated in Fig. 8 in the plot of circumferential stress <7f versus time to failure ff. (Not shown is the regime of brittle fracture by unstable crack propagation, since it only occurs at much lower temperatures and frequently requires a special crack initiation procedure). 

Fig. 17 Contact mechanics analysis of Herztian cracks within brittle materials.a Schematic description of a Hertzian cone crack induced under normal indentation by a rigid sphere, b Reduced plot of JC-field as function of cone crack length and for increasing loads pf < p// < pm during sphere-on-flat normal indentation of brittle materials. Arrowed segments denote stage of stable ring crack extension from Cf to cc (initiation), then unstable to ci at P = P,n (cone-crack pop-in) (From [67]). Branches (1) and (3) correspond to unstable crack propagation (dK/dc > 0), branches (2) and (4) to stable crack propagation (dK/dc < 0)...

The observation that an increase in temperature or a decrease in rate both result in the same fracture response points toward a viscoelastic influence on thermoset fracture behavior, especially crack initiation. This characteristic behavior of epoxies has been explained qualitatively by consideration of the temperature and strain rate effects on the plasticity of the material at the crack tip . In effect, test conditions which promote the formation of a so-called crack tip plastic zone, or blunt the crack by a ductile process, promote unstable crack propagation. This aspect of unstable fracture is subsequently discussed in more detail. 

When the polymer is more ductile, several steps of stable and unstable crack propagation can successively occur during the fracture process of the sample. Figure 27.2 illustrates the observed fracture surface of such fracture behavior. 

It is noteworthy that this variation is similar to that of Gc for unstable crack propagation observed in polypropylene [24]. The sharp increase in Gx might be due to a blunting effect at the crack tip, induced by localized adiabatic heating. Figure 27.11 shows the variation of Ta with loading rate for these temperatures. In this case, like the effect of temperature, Ta also tends to vary inversely with G. Plots of G[ as a function of Ta are shown in Figure 27.12. It can be observed that the correlation between these parameters is also linear. 

While restricted here to glassy polymers, such configuration test may be extended to other polymeric materials such as polymer blends and could help in determining the mechanism involved before unstable crack propagation. 

The LEFM approach have been conceived for brittle materials exhibiting unstable crack propagation. The obtained K-values are considered to be intrinsic properties when [4,5] ... 

Keff is always higher than Kimax- In the ductile range, Kjmax/Keff 0.70 0.03 for both grades whatever the test conditions. In case of unstable crack propagation, Kimax Ketr The values of Ken(iPP/EPR-l)/KeH(iPP/EPR-2) for given test conditions are close to those of Kimax(iPP/EPR-l)/Kimax(iPP/EPR-2) when both grades exhibit the same macroscopic behaviour. In other words, Kimax is a semi-quantitative toughness parameter, whereas Kefr provides a quantitative description of the fracture resistance. 

By analogy with what have been done with the conventional LEFM approach, the first solution seems to be the most appropriate. This point is, however, ambiguous two values of rp and therefore of Ketr could not have been determined with certainty those in the transition zone at 0.4 and 0.7 m/s as direct consequence of the unstable-stable transition occurring in each series. We have indeed noticed that for an a/W, where both macroscopic behaviours have been observed, the values of Fmax were 5 to 10% higher under unstable crack propagation than for stable fracture growth. Table 6 shows the different values of rp and Ketr obtained ... 

Fig. 3. Craze-crack resistance curves for isothermal conditions with = 30 MPav /s and temperature dependent stress-displacement fields for ki = 300 MPa- /m/s and Ki = 3000 MPa- /m/s. The triangle indicates the initiation of crazing while the square corresponds to the onset of unstable crack propagation, defining...

At higher concentrations of fibres or at intermediate concentrations when a few fibres around the crack tip are orientated perpendicular to the notch plane, the loading curve increases linearly up to a maximum load Pi as the load is transferred onto the fibres at the crack front and a process zone develops. Fracture of the fibres lying normal to the notch plane results in unstable crack propagation until it is arrested by a packet of fibres favourably orientated then the applied load must be increased to create a new frontal process zone. Tlierefore the successive unstable crack extensions result in a saw-tooth like loading curve behaviour (types 3 and 3 loading curves in Table II, associated with Figures I OB and lOE, I OF respectively). 

KEYWORDS Z-Fiber , Acoustic Emission (AE), delamination, unstable crack propagation, crack arrest, Z-pin blocks, IM7/977-2... 

Figure 8. 2 L45 tested at 0.1 m/s (a) SEM fractographic observation of the intermediate region between stable and unstable crack propagation and (b) direction of the main and secondary cracks, indicated by arrows, according to the three regions (see text) containing parabolic marks.

Wells, A. A., Unstable Crack Propagation in Metals-Cleavage and Fast Fracture, Proc. Crack Propagation Symposium, Cranfield (1961), 210-230. 

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