Fracture process

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. 

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. 

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. 

There is considerable literature on material imperfections and their relation to the failure process. Typically, these theories are material dependent flaws are idealized as penny-shaped cracks, spherical pores, or other regular geometries, and their distribution in size, orientation, and spatial extent is specified. The tensile stress at which fracture initiates at a flaw depends on material properties and geometry of the flaw, and scales with the size of the flaw (Carroll and Holt, 1972a, b Curran et al., 1977 Davison et al., 1977). In thermally activated fracture processes, one or more specific mechanisms are considered, and the fracture activation rate at a specified tensile-stress level follows from the stress dependence of the Boltzmann factor (Zlatin and Ioffe, 1973). 

Assuming a complete transfer of the kinetic energy in (8.24) into energy dissipated during the spall fracture process in (8.25) provides an expression for the characteristic spall fragment size... 

In other fracture processes, the ideas presented here would be couched somewhat differently. For instance, if fracture occurred through a rate-controlled thermally activated process, such as might apply in the dynamic... 

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... 

Step 3. The set of fracture properties G(t) are related to the interfaee structure H(t) through suitable deformation mechanisms deduced from the micromechanics of fracture. This is the most difficult part of the problem but the analysis of the fracture process in situ can lead to valuable information on the microscopic deformation mechanisms. SEM, optical and XPS analysis of the fractured interface usually determine the mode of fracture (cohesive, adhesive or mixed) and details of the fracture micromechanics. However, considerable modeling may be required with entanglement and chain fracture mechanisms to realize useful solutions since most of the important events occur within the deformation zone before new fracture surfaces are created. We then obtain a solution to the problem. 

The stress-intensity factors are quite different from stress concentration factors. For the same circular hole, the stress concentration factor is 3 under uniaxial tension, 2 under biaxiai tension, and 4 under pure shear. Thus, the stress concentration factor, which is a single scalar parameter, cannot characterize the stress state, a second-order tensor. However, the stress-intensity factor exists in all stress components, so is a useful concept in stress-type fracture processes. For example. 

A. S. Tetelman, Fracture Processes in Fiber Composite Materials, in Composite Materials Testing and Design, Steven Yurenka (Chairman), New Orleans, Louisiana, 11-13 February 1969, ASTM STP 460, American Society for Testing and Materials, 1969, pp. 473-502. 

Whether the adsorbed hydrogen is produced from the gas phase or from aqueous solution, it appears that the presence of hydrogen atoms distorts the crystal structure of the metal surface, and this results in a surface solubility which is higher than that of the bulk. The depth of this distortion is not clear, but it seems possible that the distorted zone may play an important part in initiating brittle-fracture processes. 

In more recent work embrittlement in water vapour-saturated air and in various aqueous solutions has been systematically examined together with the influence of strain rate, alloy composition and loading mode, all in conjunction with various metallographic techniques. The general conclusion is that stress-corrosion crack propagation in aluminium alloys under open circuit conditions is mainly caused by hydrogen embrittlement, but that there is a component of the fracture process that is caused by dissolution. The relative importance of these two processes may well vary between alloys of different composition or even between specimens of an alloy that have been heat treated differently. 

Whereas ductile materials, such as iron and mild steel, are often considered not to crack when charged with hydrogen and subjected to a tensile stress below the yield stress, the position is different with high-strength ferrous alloys where, depending on the strength of the steel and the hydrogen content, failure may occur well below the yield stress. However, the fracture process is not instantaneous and there is a time delay before cracks are... 

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