Steady-state crack propagation

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]. 

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>... 

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 )... 

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. 

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 work done in the deformation zone can be estimated assuming the deformation zone propagates together with the crack and maintains its steady state displacement profile [86]... 

Experiment shows that when the hydrogen concentration is enough to cause embrittlement, the permeation current builds up with time and then instead of stabilizing to a steady state as it normally does in the absence of a crack-initiation and propagation process, it drops down and only then becomes steady (Fig. 12.83). Thus, the fall in permeation current occurs at the onset of crack propagation and embrittlement. 

In the previous sections properties of crack tip crazes in thermoplastics within two different regimes of damage behavior have been described, that of stationary and slowly propagating cracks. During steady state slow crack propagation, as described above, at a particular crack speed the crack tip is preceded by a craze zone of constant size, indicating an equilibrium between fibril formation and fibril failure as demonstrated exemplarily in Fig. 3.27 a by two interference micrographs of the... 

In the case of a steady-state propagating crack tip, replacing Tq and V in equation 1 (Sect. 3.1.1), the craze length yields ... 

Whereas in Sect. 2 the use of optical interferometry to study qualitatively the morphology of the running crack-tip craze has been shown, this section shows several quantitative craze material models adapted to the experimental results obtained from optical interferometry in the case of a running crack-tip. As mentioned in Sect. 1, the lack of information about the inner craze structure confines the choice to models not sensitive to details in the craze structure. The proposed mechanisms are the following in the case of a steady-state propagating crack-craze system, with breakage in the craze midrib, the fibril breaks at the oldest part. The drawing... 

When the shear waves propagate through the elastic layer, or the elastic plate and reach the steady state, the type of the wave, SH wave for example, and it s dispersion relation are determined by the boundary conditions at the plate surfaces [7]. We have assumed that the sound waves modulate the stress fields at the tip of the crack, and then solved the wave equations with the boundary conditions at the surfaces of the crack and the plate. If the analysis is extended to derive the higher order fields and the dispersion relation of the wave is then obtained, such a wave do exist in the steady state. In this case we could confirm the existence of such "new wave" associated with the crack. Much algebra is required to obtain the higher order fields, however, it is not difficult to see the structure of the fields with the boundary condition at the plate surfaces. We find the boundary conditions at the plate surfaces for the second order stress fields are satisfied by the factor, cos /5 z, in the similar manner to Eq. 

The crack, semi-infinite in length, is assumed to propagate along the interface of two linearly elastic half spaces with a steady state velocity of a under small-scale yielding conditions, which implies that the region of pullout is small compared with typical specimen dimension. The interfaces are reinforced by chains which obey the pullout laws stated above. The steady state condition implies that all quantities are independent of time with respect to an observer moving with the crack tip. 

The quasi-steady hypothesis is used when short-lived intermediates are formed as part of a relatively slow overall reaction. The short-lived molecules are hypothesized to achieve an approximate steady state in which they are created at nearly the same rate that they are consumed. Their concentration in this quasi-steady state is necessarily small. A typical use of the quasi-steady hypothesis is in chain reactions propagated by free radicals. Free radicals are molecules or atoms having an unpaired electron. Many common organic reactions such as thermal cracking and vinyl polymerization occur by free-radical processes. There are three steps to a typical free-radical reaction initiation, propagation, and termination. 

ISO 13477 1997 Thermoplastics pipes for the conveyance of fluids - Determination of resistance to rapid crack propagation (RCP) - Small-scale steady-state test (S4 test). 

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