The R-curve effect

It is clear that if a material shows the R-curve effect, its behavior at fiacture can no longer be defined by a sole parameter (Kj. or Gj. for example), but requires investigation of the resistance curve for crack extension. Such a cmve is obtained from controlled (or stable) cracking tests. This type of test is difficult to conduct on ceramics which are materials that are both rigid and brittle furthermore, the curve obtained is sensitive to the nature of tests conducted and dimensions of the test specimen. 

The analysis of a resistance curve to the extension of a crack may basically be made in three different manners. 

The observations are defined in terms of shielding factor or resistance (known as SSC for stress shielding coefficient) and we then elaborate  

Approach through distribution of stresses near the crack face 

We use the formalism introduced by Dugdale [DUG 60] and Barenblatt [BAR 32] for interpreting the phenomenon in terms of the closing forces  

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Figure 8.6. Zones where different mechanisms at the origin of the R-curve effect occur [SAK 87]...

The R-curve effect is largely responsible for the dispersion of Kj values and the influence of the size of test specimens on the results. Nevertheless, acicular grain ceramics or fiber composites partly owe their attraction to this same effect. This property is in fact put to good use now in the inspection logic of microstmctures for making the architecture of materials less brittle and therefore more attractive to the constructor [MIY 95]. Figure 8.7 is a collection of some examples of microstructures favorable to the appearance of the R-curve effect. Furthermore, it is noted that the materials for which this effect is pronoimced have a Weibull modulus higher than when the resistance curve is flat... 

Plots of the functions R R vs. for Ka =10 are shown in Fig.4. A point on the R curve corresponds to H2-He collisions on the Morse potential surface. One can see that the attractive enhancement of the VR cross section under consideration comes roughly evenly from resonance and potential effects. 

If the solvent system can be changed, or the reaction run at higher concentrations exceeding the solubility of R, R can be crystallized as the reaction proceeds. The selectivity can thus increase, as shown by a decrease in S in Fig. 1 l-5b. Note that although the amount of R as shown in Fig. 1 l-5b appears to decrease under these conditions, the R curves are for solution concentration and do not include the amount of R that has crystallized. This effect on yield/selectivity is also shown in Fig. 11-6. 

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