Steady crack growth

The third example of time effects in elastic fracture concerns accelerated crack growth. Up to the early 80 s it has been assumed that a unique relation exists between the stress intensity factor K and the rate of crack growth da/dt. This contention had been confirmed in many steady crack growth experiments. Using three point bending specimens Chan and Williams [33] obtained for HDPE in water the following relation between da/dt, and the acting stress intensity factor Kc ... 

The analysis presented in this paper will focus only on the toughening due to domain switching during the steady crack growth conditions described above. Under steady growth conditions, all increments of field quantities can be related to derivatives with respect to the x coordinate direction by... 

Here, is any scalar field quantity such as a Cartesian component of stress or strain, and d is the increment of crack advance in the xi direction. Finally, Hutchinson (1974) derived the following path-independent integral that can be use to determine the crack tip energy release rate Gtip during steady crack growth. 

Figure 5. The toughness enhancement, G /Go, during steady crack growth in a ferroelastic material as a function of the saturation strain level, ScElao, for a range of initial hardening values, Ho/cto.

In summary, results from numerical computations of the stress and strain fields and the toughness enhancement during steady crack growth in ferroelastic materials have been presented. The computations illustrate a few interesting features and confirm some intuitive hypotheses about the solution. First, the near tip stresses appear to recover a 1/v r singular form, however the radial dependence of these stresses is not the same as those for an isotropic elastic material. It was also shown that the distributions of remanent strain are not trivial and do reorient as the crack tip passes. Lastly, as would be expected, the steady state toughness of the material increases as the relative saturation strain increases, and decreases as the hardness of the material increases. 

Dean, R.H. and Hutchinson, J.W., 1980, Quasi static steady crack growth in small scale yielding. In Fracture Mechanics, ASTM STP 700, 383 405. 

Blackburn, W.S. (1971) Steady crack growth in a linear viscoelastic material. Int. J. Fract. Mech. 7, 354-356... 

Y.e. Gao and K.G. Hwang, Elastic plastic fields in steady crack growth in a strain hardening material, in Proceedings of Fifth Int. Conf on Fracture, Garmes, France, 1981, pp. 669-682. 

In the steady-state regime, the crack growth rate is described by... 

Typical results with such crack growth measurements are shown in Figure 3. In this example a notched specimen was used, with the first gold strip located immediately below the notch, and the phE recorded. The voltage is steady between... 

Fig. 10.5 (a-f) Normalized crack growth velocity A a/K] l versus normalized crack extension A = ball for transient SSC crack growth under constant / loading based on a model for crack growth by grain boundary cavitation (taken from Ref. 45). The parameters K, r A0, and Ass are normalized values of, respectively, the stress intensity factor (which is held constant), the crack growth initiation time, the initial crack velocity, and the steady-state crack velocity. 

A. Saxena, Creep Crack Growth under Non-Steady-State Conditions, in Fracture Mechanics Seventeenth Volume, eds. J. H. Underwood, R. Chait, C. W. Smith, D. P. Wilhem, W. A. Andrews, and J. C. Newman, ASTM STP 905, American Society for Testing and Materials, Philadelphia, PA,... 

Recent experiments and theory of truly steady state crack growth indicate that there is a threshold K and V and that the exponent m., changes to become nearly infinite just above the threshold. These complications are ignored in this treatment... 

Figure 16 shows a typical evolution of fringe pattern for the case of a crack that grows into an immobile craze. This kind of experiment allows a clean observation of crack growth. However, it has not been used at all, because a steady-state growing crack-craze system will be more efficient from a practical point of view, as shown in Sect. 3). Nevertheless, it will be encountered again in the case of an oscillating crack-craze system described below. 

Here the assumption that G = Gc as crack growth criterion is examined. This criterion is valid if the crack grows in an approximate steady state. 

In [3], it was noticed that DCB specimens with a higher bending stiffness required a longer crack extension before the steady-state crack growth resistance was attained. In [ I], the concept of a bridging law was introduced to characterise the f -curve for DCB specimens. 

The small slope of the stage II section of the crack-growth rate versus K curve is attributed to corrosion-related, diffusion-controlled processes in the crack. Steady-state diffusion mechanisms are required to account for the fact that the crack growth rate is essentially constant... 

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

Companion data on steady-state creep, over the same temperature range, are shown in Figs. 6.5-6.S and are in good agreement with those of crack growth. The direct linkage between creep and creep-controlled crack growth is summarized in the next sections. 

The foregoing experimental observations strongly suggested the connection between creep deformation at or near the crack tip and crack growth. For steady-state crack growth, the cooperative deformation at various positions ahead of the crack tip is required. The material at these positions experiences different levels of plastic strain and is subject to different flow stresses. The observed K dependence, therefore, represents the integrated effect and would have to be determined... 

By combining Eqns. (6.6) and (6.12), the rate of steady-state creep crack growth is related to the steady-state creep rate and other measurable properties of the material namely [3],... 

For temperatures well below the homologous temperature, the steady-state creep rate is well represented by Eqn. (6.3). By substituting Eqn. (6.3) into Eqn. (6.13), the steady-state creep crack growth rate becomes ... 

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. 

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