Crack speed

The question of the actual form of the relation between toughness and crack speed is still rather unclear. It is tempting to relate 4> V) to the imaginary part of the elastic modulus, but the size parameter required to relate V to a time or... 

The implication of Eq. (6.21) is that the criterion is dependent mainly on the ratio of the energies for longitudinal splitting and transverse cracking, and is relatively insensitive to crack length and the elastic modulus. It is also noted from experimental study that crack speed has a pronounced effect on the toughness ratio, Rl/Ri, and thus the crack deflection phenomenon. 

Many studies [40-43] have been performed on the fracture behaviour of PMMA as a function of temperature or cross-head speed. As an illustration, Fig. 30 shows the critical stress intensity factor, K c, in a log-log plot as a function of temperature for various crack speeds [40]. The temperature range is limited to + 80 °C in order to avoid ductile tearing. In the stable crack growth regime of interest here, whatever the crack speed, K c decreases with increasing temperature. 

At each temperature, K c increases with crack speed and a linear log-log dependence is observed. However, when considering the slopes, two regimes clearly appear, depending on temperature, with a transition between - 20 °C and 0 °C. In the low temperature range a lower sensitivity to crack speed is... 

Fig. 30 Fracture toughness, iCic, as a function of crack speed at various temperatures for stable crack growth (From [40])...

A convenient technique for studying the crack tip craze propagation in amorphous polymers deals with optical interferometry. It has been applied to the examination of PMMA behaviour at various temperatures and crack speeds under conditions of stable propagation [44,45]. 

Besides, the lower sensitivity of K c to the crack speed, observed in Fig. 30 at temperatures below - 20 °C, has to be related to the occurrence of the multiple craze mechanism (it does not require any slippage time, but only a time for fibrillation) and, so, to the isolated ft transition motions, as described above. 

Figure 19.3 Crack speed in fatigue of sPS as a function of the amplitude of the stress intensity factor for different molecular weights...

Derived Material Parameters as Functions of Crack Speed and Time 121... 

Fig. 10. Fracture toughness K, as function of crack speed a in PMMA at room temperature as reported by different authors...

All thermoplastics are known as viscoelastic materials and hence exhibit time dependent properties. It is known that during crack propagation the influence of time is also involved such that slow crack speeds correspond to long times and high crack speeds to short times. In the following we will be concerned with this problem in more detail. 

Another aspect of viscoelastic behavior is the influence of temperature and in the slow crack propagation region is has also been well documented. Marshall et al. observed that in PMMA the crack speed curves are shifted to lower Kpvalues with increasing temperature and that also Ki decreases in the temperature range from -60 Cto 80 C. 

Fig. It a and b. Variation with crack speed of the dimensions of the craze zone at the tip of a propagating crack in PMMA a maximum craze width 2Vj b craze length s...

Figure 11 a shows the maximum craze width 2v as a function of crack speed d and Fig. lib the corresponding craze length s. Initially the results were interpreted as... 

Attempts have been made to correlate crack speed a with time t. An analysis of the fracture behavior of thermoplastics shows that it is essentially determined by craze formation and stretching the fibrils up to fracture. Therefore, the time involved in this process is considered to be the relevant time t which may be calculated by ... 

Thus in Fig. 12 a, b the crack speed axis can be converted into a time scale ranging from about 10 to 10 seconds. On this basis a comparison has been made... 

At the lower end of the crack speed range the craze dimensions increase the slowlier the crack moves. This is to be seen as a reflection of the time dependence of craze growth discussed in Sect. 3.2.2 (slower speeds = longer times). At the other end of the speed range, at speeds rising to the transition speed ( 10 mm/s), the increasing build-up of heat in and around the craze leads to a rise in temperature. For example, using the data for PMMA (1) in Fig. 15, it can be estimated that there... 

---