Threshold toughness

The above-mentioned models differ in the relation that is derived between the rate of pull-out of the individual chain and the crack velocity. These models also differ in their interpretation of the threshold stress and the threshold toughness (Go). Also, V is expected to be dependent on the configuration of the connector chain at the interface. The value of v when connector chain crosses the interface just once is higher than the value when the chain forms multiple stitches, even though Go is not altered. When the chain forms multiple stitches, the block and tackle effect ensures that the viscous processes dominate even at lower velocities, and V is reduced by a factor of N from the value obtained from the single crossing case. These models are discussed by Brown and coworkers [45,46]. 

The most recent model of de Gennes and coworkers [100,101], the threshold toughness is related to the extra surface and elastic energy of the individual chains as they are pulled out. The threshold toughness and the critical crack propagation speed are given by... 

Fig. 11. The variation of the threshold toughness Gy with S when an end-reactive PDMS chain was coupled into a PDMS network (H.R. Brown, W. Hu, J. Koberstein, unpublished work).

Flowever, in order to probe the fracture toughness of thin films or small volumes using ultra low load indentation, it is necessary to use special indenters with cracking thresholds lower than those observed with the Vickers or Berkovich indenters (for Vickers and Berkovich indenters, cracking... 

A threshold of interfacial adhesion between both phases is needed to (a) promote the cavitation mechanism and (b) activate the crack-bridging mechanism. For rubbery particles, the former contributes much more than the latter to the total fracture energy. Adhesion is achieved by the use of functionalized rubbers that become covalently bonded to the matrix. Higher toughness values have been reported by the use of functionalized rubbers (Kinloch, 1989 Huang et al., 1993b). However, these experimental results also reflect the effect of other changes (particle size distribution,... 

It seems intuitively obvious that threshold doses exist for all chemicals, but there is considerable debate among toxicologists on this issue. Unfortunately the debate is a tough one to resolve because its resolution requires something like the proof of a negative, which is scientifically impossible. It will be worthwhile to explore this problem in a little detail. 

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