Critical energy release rates

Fig. 7. Adhesion (critical energy release rate, Fc) of zinc coatings to steel substrates effect of steel surface roughness (after Ye et al. [68]).

The cohesive stress ac is assumed to be constant (Dugdale model) as in Eq. (7.5). Chan, Donald and Kramer [87] found a good agreement between the critical energy release rate GIC, as estimated by the Dugdale model and G)C as computed from the actual stress and displacement profiles in their experiments. 

T, To Energy release rate, maximum, threshold Tc Critical energy release rate... 

In contrast to the impact tests, these can be analysed toughness is reported as the critical energy release rate (7, or the stress concentration factor K Values may tange from 5000 J. nr for a tough nylon or polycarbonate down to 350. J/m lor buttle unmodified polystyrene. The values can be sensitive to rale and temprature... 

In a first testing series, the fracture behavior of the neat, fully crosslinked epoxy network was studied. A fully unstable crack propagation behavior was observed and the critical stress intensity factor, Kj (0.82 MPaxm ), and the critical energy release rate, Gj (0.28 kj/m ), were determined [87]. These are typical values for highly crosslinked epoxy networks prepared with DGEBPA and aromatic or cycloaliphatic diamines. 

Figure 12.12 Critical stress intensity factor (K C) and critical energy release rate (G C) at 25°C as a function of DGEBD percentage. (Reprinted with permission of SPE from Urbaczewski-Espuche et al., 1991.)...

Lange (1970) gives a quantitative description of the critical energy release rate supplied by this mechanism ... 

The critical energy release rate, Gic,[ll] was also determined experimentally by using the relation ... 

In order to obtain the total energy release rate, which can be compared to the critical energy release rate Gc, the same finite element model is used, where the energy release rate is calculated according to [7] ... 

The question rise whether the behaviour described can be evaluated on a fracture mechanics basis. The critical energy release rate associated with the formation of a transverse crack is technically difficult to measure. As a first approximation, it is possible to use the critical energy release rate obtained from a double cantilever beam fracture mechanics test (DCB). This test concerns the growth of a delamination between two layers (mostly oriented ai 0°) in opening mode I. Tests performed on the same carbon-polyetherimide at 0°/0° interface as in this study were reported recently [9] and gave a value of 1200 J/m. ... 

An other approximation is to use the energy release rate evaluated on basis of the experimental as the critical energy release rate, since it is hardly dependant on the level of residual stress (see Table 6 as well as Fig, 7). This would give a critical energy release rate of about 650 J/m, Worth adding is that this value is only valid in mode I, and not in mixed... 

The results based on a fracture mechanics analysis show that the experiments were able to give an (expensive) approximation of the critical energy release rate for transverse cracking in carbon-polyetherimide under mode I. Limitation is that the choice of an initial crack length is critical. This should be of less importance when considering multiple transverse cracking. 

The important parameter obtained from an adhesion experiment is the critical energy release rate, Qc, which is the energy necessary to grow a crack by a unit... 

A reliable mechanical test to measure the adhesion of the interface is required. The standard method to quantify adhesion is to drive a crack at the interface between the two bulk materials and measure the critical energy release rate, (jc, to propagate such a crack. The implicit assumption made in most measurements of Qc is that the external work is dissipated in the plastic deformation of a small volume close to the crack tip. 

To provide a means for comparison of the dynamic data to static DCB results. Fig. 14 shows only the peaks of the dynamic DCB results for the bonded 12 ply adherends, which may or may not represent the actual critical energy release rates. The peaks in energy release rate may or may not have been captured because the data collection was limited to 2000 ames/s by the imaging system. These results could be verified by using a higher speed imaging system to capture more data points per test. 

The test results were also used to construct a preliminary failure envelope, which is shown in Fig. 16. The data points represent the average critical energy release rates obtained for the mode II and mixed-mode dynamic testing and the peak values previously presented for the dynamic DCB testing. A rough failure curve was drawn through the data points to illustrate the general... 

This balance between interfacial propagation and bulk deformation has been described for linear elastic materials [56] and results from the competition between two mechanisms the velocity of propagation of an interfacial crack, which is controlled by the critical energy release rate Gc, and the bulk deformation, which is controlled by the cavitation stress and hence essentially by the elastic modulus E or G. In the hnear elastic model, the key parameter is the ratio GJE, which represents the distance over which an elastic layer needs to be deformed before being fuUy detached from the hard surface. This model has been verified experimentally for elastic gels [57]. 

Gc, G critical energy release rate and energy release rate, respectively (the additional... 

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