Steady-state cracking

The ubiquity of this power-law behaviour in SCG tests on PE has been the subject of considerable discussion, usually based on the assumption of a fibril creep failure mechanism [43, 45, 46, 47, 76, 79]. At high and intermediate K, after a certain induction period, steady-state crack advance is generally observed to occur by a stick-slip mechanism all or part of the fibrillar zone breaks down rapidly after an incubation time during which fibril creep takes place. The crack-tip then advances rapidly over a short distance and a new fibrillar zone stabilises, as sketched in Fig. 12. 

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. 

The brittle film cracking with plastic deformation of the ductile substrate at the interface has been described by using the shear lag model. " This model, which was proposed in the analysis of the fragmentation of fiber composites," " develops a relation for the critical stress producing the steady-state cracking of the film. It assumes that the interfacial shear stress, on the one hand, is activated at each crack tip along the characteristic slip length r, and, on the... 

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... 

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 corresponding 7 -curves are presented in Figs. 6 and 7. It is seen that the results obi ained by the recommended analytical formula and the area method are rather close. The initial alue of the fracture toughness is 0.3 kJ/m, and the fracture toughness during the steady-state crack... 

Most of the experimental results presented above were obtained for the case of a steady-state crack propagating around 1-5 pm/s. The crack velocity in the DCB experiment performed with a wedge is controlled by the velocity at which the wedge is pushed to separate the sample. It is therefore possible in principle to do tests over a range of velocities. However, a few studies have been reported where the velocity of crack propagation has been investigated in a systematic way. The trend in these studies, illustrated by Fig. 30 in the case of a PS/PVP interface reinforced with a dPS-PVP 800-870 diblock copolymer, is however always one of increasing Qc with crack velocity [60]. 

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

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... 

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. 

Figure 7.2. Manifestations of non-steady-state (transient) and steady-state crack growth response in terms of crack length versus time (a) and dajdt versus Ki under constant load (where K increases with crack growth) (b) [3].

Figure 7.6. Typical sustained-load (stress corrosion) cracking response in terms of steady-state crack growth rates (left) and time (right) [3].

Transient and steady state crack growth kinetics for SCC ofcold worked 316 stainless steel... 

Z. Lu, T. Shoji, Y. Takeda, Y. Ito, A. Kai, S. Yamazaki, Transient and steady state crack growth kinetics for stress corrosion cracking of a cold worked 316L stainless steel in oxygenated pure water at different temperatures, Corros. Sci. 50 (2008) 561—575. 

The parameter R provides a measure of the resistance to crack propagation, such that 1/R is proportional to the steady state crack velocity. The R values obtained from the intercept at. y = 0 indicate that the steady state crack velocity is independent of stress intensity. 

The puqjose of generalized fracture mechanics (GFM) is to overcome some of the problems raised above. Specifically, GFM addresses (1) nonlinear and inelastic materials, (2) steady-state crack propagation, and (3) the expression of critical fracture parameters in terms of the physical properties of the material(s) involved. 

K. Ravi-Chandar and W. G. Knauss, An experimental investigation into dynamic fracture III. On steady-state crack propagation and crack branching, Int. J. Fract. 26, 141-154 (1984). 

A quantitative basis for these ideas has been provided by Beuth (1992) for the case of steady-state advance of a surface crack in an isotropic elastic film bonded to an isotropic elastic substrate. Under circumstances of steady-state crack propagation, the conditions on system parameters that are necessary for growth can be expressed in terms of the states of plane strain deformation which exist far ahead of and far behind the advancing crack segment see Figure 4.37. The four material parameters i f, E, Vs>... 

Suo, Z. and Hutchinson, J. W. (1989), Steady-state cracking in brittle substrates beneath adherent films. International Journal of Solids and Structures 25,... 

It was noted in Section 2.3.2 that most of the current interfacial fracture mechanics methodologies describe steady-state crack propagation, but not the initiation of interfacial cracks. A recent approach to the prediction of initiation is based on the calculation of the singular stress field at the free edge of a bimaterial system loaded on the top layer [59,60]. Because the crack is assumed not to exist initially in this analysis, a very different singular field is predicted, and the results can be used to predict initiation of cracks in residually stressed coatings. Because the predictions of this theory sometimes contradict the predictions of the Suo and Hutchinson approach, we shall briefly review it as a final note. 

Ravi-Chandar, K. and Kjiauss, W.G., An investigation into dynamic fracture. Ill - On steady-state crack propagation and branching. Int. J. Fract., 26, 141-154 (1984), Ravi-Chandar, K. and Knauss, W.G., An investigation into dynamic fracture. IV - On the interaction of stress wave with propagating cracks. Int. J. Fract., 26, 189-200 (1984). Pocius, A., Verbal communication, 1998. 

THEORE-nCAL STEADY-STATE CRACK PROPAGATION RATE (mm s )... 

AG Varias, JL Feng, Simulation of hydride induced steady-state crack growth in metals - Part I Growth near hydrogen chemical equilibrium. Computational Mechanics, 2004, 34, 339-356. 

The mode I fracture resistance of adhesive joints is most commonly determined using the double cantilever beam (DCB) test. This test was initially described in the ASTM standard (ASTM 1990) and has been developed more recently in the British standard (BSI2001) and the international standard (ISO 2009). The original ASTM test standard specified metallic substrates and the critical strain energy release rate in mode I, Gic, was determined for repeated crack initiations using a version of simple, shear corrected beam theory. The later standards additionally accommodate nonmetaUic substrates and employ corrected beam theory to determine values of Qc 4t both crack initiation and during steady-state crack propagation. 

Figure 4.19 (a) Griffith crack (b) steady-state crack (after Li et al. [44]). 

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