Basic fracture zones

The experimental results described above can be explained within the basic fracture mechanism map after detailed consideration of the processes necessary to generate a craze at the interface. The criterion lfb > ocmze is a necessary condition for the formation of stable craze fibrils. However, it is not sufficient for the formation of a craze at an interface. Craze initiation is believed to occur by a meniscus instability process that happens within a yield zone (an active zone) at a... 

The basic assumptions of fracture mechanics are (1) that the material behaves as a linear elastic isotropic continuum and (2) the crack tip inelastic zone size is small with respect to all other dimensions. Here we will consider the limitations of using the term K = YOpos Ttato describe the mechanical driving force for crack extension of small cracks at values of stress that are high with respect to the elastic limit. 

In its basic form, bioremediation of the vadose zone involves introduction of nutrients and electron acceptors necessary to stimulate the indigenous bacteria and provide for removal of waste products generated by the reactions. This sometimes takes the form of a series of injections of a soup of nutrients and electron acceptors into the vadose zone through wells, or infiltration galleries. Other sites may require pressure fracturing of the soil before the stimulant blend can be injected. 

Before discussing specific aspects of micro deformation and fracture in bulk polyolefins, some basic notions of microdeformation and the micromechanics of fracture mediated by generation and breakdown of cavitated or fibrillar deformation zones or crazes are introduced. SCG in PE and rate-depen-dent fracture in iPP are then considered in more detail. 

When building a model to predict the mechanical behavior of heterogeneous materials based on polypropylene, the basic principle of fracture mechanics should be considered that fracture is induced in a material when an energy threshold on the weakest zones is reached. It is also well accepted that such energy threshold consists of at least two components necessary energy to initiate a craze and the necessary energy to propagate it. 

Williams (49), Ward (79), and Jancar et al. (89) proposed an approximate model of mixed mode of fracture to account for the effect of finite specimen dimensions for Kc and G, respectively. The basic idea in both theories is a substitution of the actual distribution of fracture toughness across the cross-section by a simple bimodal distribution, assuming plane strain value in the center and plane stress value at the surface area of the specimen. Size of the plastic zone IR relative to the specimen width B gives the contribution of plane stress regions and is a measure of the displacement of the state of stress at the crack tip from the plane strain conditions. Note that this approach can be used only if the mode of failure does not change with the test conditions or material composition (i.e., it attains its brittle character). 

Permeability modification also is applicable to fractured systems and to reservoirs with areal heterogeneities, although the latter case is more difficult to address. Basically, the process requires application of suitable chemical systems and techniques to place these systems selectively in the reservoir rock. Calculations show that some gel solution will flow into the low-permeability zone unless provision is made to isolate the different zones mechanically during treatment. This must he considered in the design. Calculations of the type described also indicate the desirability of conducting permeability modifications that extend a considerable distance into the reservoir from the treated wells. 

One of the purposes of this paper is to differentiate between surface free energy and fracture surface energy. Thus, several basic principles of fracture mechanics are discussed with reference to the Griffith s energy-b J nce concept and the Irwin-Orowan s plastic-zone concept. We also define several frequently misused terms, e.g., effective fracture surface energy, fracture energy and fracture toughness. Actual values of related parameters are presented to illustrate the applicability of fracture mechanics to the selection of polymers for structural materials. 

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