Network weakest-link

This theory was based on the assumption that when the network is stressed, the links between the microstructures are more likely to be stressed than the microstructures themselves or the structures within them. This is in fact reminiscent of the old adage the strength of a chain lies in its weakest link —the weakest links here are the links between the microstructures. This theory is simply, and appropriately, called the weak-link theory. Figure 7.14 shows a schematic of a fat network under extension when the weak-link theory is applicable. 

There are a number of reasons for developing techniques for controlling network chain-length distributions one is to check the weakest-link theory for elastomer rupture, which states that the shortest chains are the culprits in causing rupture. Due to their limited extensibility, short chains supposedly break at relatively small deformations and then act as rupture nuclei. 

The theory of rubber elasticity (Section 9.7) assumes a monodisperse distribution of chain lengths. Earher, the weakest link theory of elastomer rupture postulated that a typical elastomeric network with a broad distribution of chain lengths would have the shortest chains break first, the cause of failure. This was attributed to the limited extensibility presumably associated with such chains, causing breakage at relatively small deformations. The flaw in the weakest link theory involves the implicit assumption that all parts of the network deform affinely (24), whereas chain deformation is markedly nonaffine see Section 9.10.6. Also, it is commonly observed that stress-strain experiments are nearly reversible right up to the point of rupture. 

In the case of such noncrystalUzable, unfilled elastomers, the mechanism for network rupture has been elucidated to a great extent by studies of model networks similar to those already described. For example, values of the modulus of bimodal networks formed by end-linking mixtures of very short and relatively long chains as illustrated in Fig. 6.4 were used to test the weakest-link theory [7] in which rupture was thought to be initiated by the shortest chains (because of their very limited extensibility). It was observed that increasing the number of very short chains did not significantly decrease the ultimate properties. The reason [85] is the very nonaffine... 

The weakest link issue having been resolved, it became of interest to see what would happen in the case of bimodal networks having such overwhelming numbers of short chains that they could not be ignored in the network s response. As described below, there is a synergistic effect leading to mechanical properties that are better than those obtainable from the usual unimodal distributions ... 

---