Kinetic crack growth

Lawn, B.R. (1975) An atomistic model of kinetic crack growth in brittle solids. J. Mater. Sci., 10 469-480. 

Typical experimental data on the crack growth rate vs stress intensity factor in LMIE conditions are shown in Figure 7.91. Large cracks are at the top portion (>2mm) and small cracks (<2 mm) are located at the bottom of the figure and reflect the kinetics of growth of cracks. The micromechanism of crack growth is different in the upper and lower regions. 

The kinetics of crack growth under SMIE conditions may be given by 5... 

Fig. 2 presents the analysis based on OIT data and the linear extrapolation of these data to longer times. The time to reach depletion of the antioxidant system can thus be predicted even after relatively short testing times (see insert figure in Fig. 2). Data by Hassinen et al. (//) for the antioxidant concentration profiles taken from high-density polyethylene pipes exposed to chlorinated water (3 ppm chlorine) at different temperatures between 25 and 105°C followed the Arrhenius equation with an activation energy of 85 kJ mol (0-0.1 mm beneath inner wall surface) and 80 kJ mol (0.35-0.45 mm beneath the inner wall surface). It is thus possible to make predictions about the time for antioxidant depletion at service temperatures (20-40°C) by extrapolation of high temperature data. However, there is currently not a sufficient set of data to reveal the kinetics of polymer degradation and crack growth that would allow reliable extrapolation to room temperature.

Crack Stability. At low test speeds, stable crack growth with an extended stress-whitened plastic zone and crack blunting occur by the same mechanisms as those involved in the kinetics of the plastic zone, namely, rubber cavitation followed by shear deformation of the matrix. The ability of the matrix to shear is controlled by its relaxation behavior, which therefore determines its plasticity and the deformation imposed on rubbery particles distant from the notch. 

Thus, the reliability of the design in general is determined not only by the conditions that start the cracks, but also the kinetics of growth. 

Figure 6.3. Steady-state crack growth kinetics for AISI 4340 steel in dehumidified argon [2].

Equation 6.14 provides a formal connection between creep crack growth and the kinetics of creep deformation in that the steady-state crack growth rates can be predicted from the data on uniaxial creep deformation. Such a comparison was made by Yin et al. [3] and is reconstructed here to correct for the previously described discrepancies in the location of the crack-tip coordinates (from dr/2 to dr) with respect to the microstructural features, and in the fracture and crack growth models. Steady-state creep deformation and crack growth rate data on an AlSl 4340 steel (tempered at 477 K), obtained by Landes and Wei [2] at 297, 353, and 413 K, were used. (AU of these temperatures were below the homologous temperature of about 450 K.) The sensitivity of the model to ys, N, and cr is assessed. 

The occurrence of creep-controlled crack growth, in an inert environment, has been demonstrated. It can occur even at modest temperatures, and has been linked to localized creep deformation and rupture of ligaments isolated by the growth of inclusion-nucleated voids ahead of the crack tip. Landes and Wei [2] and Yin et al. [3] have made a formal connection between the two processes, and provided a modeling framework and experimental data to link the kinetics of creep to creep-controlled crack growth. Further work is needed to develop, validate, and extend this understanding. In particular, its extension to high-temperature applications needs to be explored. 

Figure 7.4. Typical kinetics of sustained-load crack growth for a Ti-5Al-2.5Sn in gaseous hydrogen at 0.9 atm and temperatures from 223 to 344 K (-70 to 74C) [5].

Figure 7.5. Typical kinetics of sustained-load crack growth for an AISI 4340 steel in 0.6 N NaCl solution at temperatures from 276 to 358 K [6].

Figure 7.8. Typical fatigue crack growth kinetic data for a mill-annealed Ti-6A1-4V alloy (a) as a function of AK, and (b) as a function of [4].

Material Response - For simplicity, the kinetics of fatigue crack growth will be assumed to be describable by a single equation over the entire range of interest ... 

It has been shown that fatigue life is influenced by the fatigue crack growth kinetics and is reflected through changes in A and n in the power-law representation, for... 

If the rate of transport of gases along the crack were sufficiently fast, then crack growth would be controlled (rate limited) by the rate of surface reactions with the newly created crack surface. Assuming, for simplicity, that the reactions follow first-order kinetics, the rate of increase in the fractional surface coverage 6 is given by Eqn. (8.15) ... 

Figure 8.18. Influence of anion on sustained-load crack growth kinetics for AISI 4130 steel at room temperature [8].

Figure 8.20. Influence of anion (CO3 - HCO3) concentration on snstained-load crack growth kinetics [8].

By assuming that the rate of crack growth is controlled by the rate of tetragonal-to-monochnic phase transformation, a kinetic model was proposed as an analogue to that for martensitic transformation. Only the final form of the model is given here specific details of its formulation may be found in [9]. In this model, the rate... 

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