Fragment statistics

Quack M 1981 Statistical mechanics and dynamics of molecular fragmentation Nuovo Cimento B 63 358-77... 

Theoretical efforts a step beyond simply fitting standard statistical curves to fragment size distribution data have involved applications of geometric statistical concepts, i.e., the random partitioning of lines, areas, or volumes into the most probable distribution of sizes. The one-dimensional problem is reasonably straightforward and has been discussed by numerous authors... 

Figure 8.20. Cumulative number distribution of fragments from four expanding ring experiments (10 fragments each) and comparison with one-dimensional theoretical distribution based on Poisson statistics.

The more common approach is the actual positioning of random lines on a surface to create a statistical distribution of fragment sizes. One example of this, suggested by Mott and Linfoot (1943), is a construction of randomly positioned and oriented infinite lines as illustrated in Fig. 8.23. If the random lines are restricted to horizontal or vertical orientation an analytic solution can be obtained for the cumulative fragment number (Mott and Linfoot,... 

The present statistical study has been motivated by a desire to better understand and interpret dynamic fragmentation in mechanical systems. Applications include the blasting of rock with explosives or the fragmentation caused by the impact of a high-velocity projectile. For the reasons noted earlier it is difficult to verify the present statistical theory with experiments. Recently, however, support for the theories have emerged from rather diverse sources. 

Strong support for the statistical theory has been provided by computational dynamic fragmentation experiments (Holian and Grady, 1988). In... 

Several further comparisons attest to the universal nature of the statistical fragmentation theory. In Fig. 8.28 the consequences of a nuclear fragmentation event brought about by the 70 MeV per nucleon collision of a carbon nucleus with a silver nucleus is shown (Greiner and Stocker, 1985). In this... 

Although progress in continuum and computer modeling of dynamic fracture and fragmentation is encouraging, it is apparent that further advancements are needed. Many of the emerging physical and statistical concepts, some of which have been discussed in the present chapter, are not yet included in these... 

Finally the concepts of fragment size, and fracture number or frequency statistics, need to be included within the framework of continuum and computational modeling of dynamic fracture and fragmentation. This challenging area of research has the potential for addressing many needs related to dynamic fragmentation. 

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