Flaws inherent

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). 

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. 

In many materials, the inherent flaws are easily recognized. Brittle polycrystalline materials, for example, contain microcracks, voids, and other imperfections that can be identified in micrographs, and are expected to provide sites for internal fracture activation. Artificial flaws introduced into a hollow metal shell by uniform scoring can be expected, under rapid expansion, to fracture the shell along the paths of scoring. 

In other cases, the inherent flaws or perturbations responsible for fracture are less easily recognized. The internal spalling of glass or the cavitation of a rapidly expanding liquid are examples although even here, some form of imperfection such as impurities, dislocations, or thermal fluctuations are expected to play an important role in nucleating the fracture process. 

An eminently practical, if less physical, approach to inherent flaw-dependent fracture was proposed by Weibull (1939) in which specific characteristics of the flaws were left unspecified. Fractures activate at flaws distributed randomly throughout the body according to a Poisson point process, and the statistical mean number of active flaws n in a unit volume was assumed to increase with tensile stress a through some empirical relations such as a two-parameter power law... 

Although accurate characterization of the inherent flaw structure appears to be important, there are clear indications that such characterization alone is... 

Comparison of Inherent Flaws and Energy Concepts in Dynamic Fragmentation... 

Even in the loading regime in which inherent flaw effects dominate the fracture process, further clarification of the fracture activation and growth process is needed. For example, dynamic crack branching leading to multiple fracturing is expected to constitute an important part of the breakage process. Such a cooperative and collective fracture process does not fit well within a... 

The low tensile strength of cement paste is, as we have seen, a result of low fracture toughness (0.3 MPa m ) and a distribution of large inherent flaws. The scale of the flaws can be greatly reduced by four steps ... 

The second approach to fracture is different in that it treats the material as a continuum rather than as an assembly of molecules. In this case it is recognised that failure initiates at microscopic defects and the strength predictions are then made on the basis of the stress system and the energy release processes around developing cracks. From the measured strength values it is possible to estimate the size of the inherent flaws which would have caused failure at this stress level. In some cases the flaw size prediction is unrealistically large but in many cases the predicted value agrees well with the size of the defects observed, or suspected to exist in the material. 

Historically, risk reduction strategies have been focused on the exposure side of the risk equation and in many cases have been very successful. However, there are inherent flaws in focusing primarily on controlling exposure that will be identified here. 

Manufacturing aspects of materials improper metal working, welding, heat treatment or casting results in inherent flaws... 

Consider next ancient slaveiy. Marx believes that this system was inherently flawed by the low productivity of labour. In Capital t he cites as a characteristic feature of capitalism the avoidance of waste of raw mater ials, instruments and labour. He then adds that ... 

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