Fragment Size Predictions in Dynamic Fragmentation

In the present section, attention will focus on the size of fragments created in a violent fragmentation event. The objective will be to explore some theoretical ideas which appear important to the dynamic fragmentation process. The two underlying phenomena that have dominated theoretical efforts in this area of dynamic fracture mechanics are the presence of an inherent flaw structure, and energy balance in the fracture process. 

On one hand, inherent flaws or perturbations in a fracturing body, which are the sites of internal fracture nucleation, have been recognized as important in determining characteristic fracture spacing and, consequently, the nominal fragment size in a fracture event. Theoretical work based on a physical description of these material imperfections has been actively pursued (Curran et al., 1977 Grady and Kipp, 1980). 

Each approach emphasizes different physical features observed in the fracture process. Either approach, under certain sets of conditions, may provide a satisfactory theory of fragmentation, although neither is apparently complete. 

An acceptable reconciliation of inherent flaw and fracture energy concepts has not been achieved and provides an area of current study. The two theoretical concepts will be discussed, and several applications in fragment-size prediction will be described. We will make comparisons between the two fragmentation approaches and attempt to identify some conditions which determine when one or the other method applies. 

The importance of inherent flaws as sites of weakness for the nucleation of internal fracture seems almost intuitive. There is no need to dwell on theories of the strength of solids to recognize that material tensile strengths are orders of magnitude below theoretical limits. The Griffith theory of fracture in brittle material (Griflfith, 1920) is now a well-accepted part of linear-elastic fracture mechanics, and these concepts are readily extended to other material response laws. 

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