Fracture rate process

Molecular tl iy for fracture could be traced ba k to an application of the rate-process theory to fracture teiomena (65) and al the similar line of thou t Beuche (1) developed his theory for fracture in p<%mer. Zhurkov (66,67) derived independently the same equation to the Beuche s one the time to fracture. Based on this equation the activation energies for the fracture were estimated from the experimental results on the time to fracture under the unaxial load (20,68). Change of deformation potential in a stressed chain was discussed by Kausch (J9.20). Fracture developement has been discussed from the a >ects of micromori lr of polymers by Peterlin (J5, 69-71), Kausch (19,20) and DeVries(/7,61, 72). 

Thus, the conqilex water-flow behavior observed under laboratory and field conditions can represent the cumulative effect of the many degrees of fieedom involved in water flow. For the fracture flow process described by die K-S equation, we can reasonably hypodiesize that on a local scale, die linear relationship between the pressure head and the flow rate (i.e., Darcy s law) is invalid. 

Processes that are dependent on time are called kinetic processes or rate processes. Creep, the crystal growth, fatigue, fracture, friction, and wear progress in time are the examples of kinetic processes in solids. 

Hydraulic fracture stimulations are overseen continuously by operators and service companies to evaluate and document the events of the treatment process. Every aspect of the fracture stimulation process is carefully monitored, from the well head and downhole pressures to pumping rates and density of the fracturing fluid slurry. The monitors also track the volumes of each additive and the water used and ensure that equipment is functioning... 

Vapors from depressurization valves are typically routed to a pipe header and then to the flare to safely remove the vapors from the area and dispose of them without impact to the environment. A special concern when high levels of pressurized gases are released into a piping system is the possibihty of auto-refrigeration of the piping material that may cause a brittle fracture. A process engineer should verify which pipe materials and flow rates, specified for the depressurization system, are suitable for the pressures, flows, and gases under consideration. 

From a chemical viewpoint, bond scission under stress is a particular case of a un-imolecular dissociation reaction whose rate is enhanced by mechanical stress. As such, it could be treated with Eyring s transition-state theory [Eq. (37)], which permits one to bring the treatment of rate processes within the scope of thermodynamic arguments. By combining de Boer s thermodynamic formulation and the transition-state theory, Tobolsky and Eyring in 1943 developed the rate theory for thermally activated fracture of polymeric threads. When put into an Arrhenius-... 

Statistical, Continuum Mechanical, and Rate Process Theories of Fracture... 

In this chapter an overview of conceptually different fracture theories is presented which have in common that they do not make explicite reference to the characteristic properties of the molecular chains, their configurational and super-molecular order and their thermal and mechanical interaction. This will be seen to apply to the classical failure criteria and general continuum mechanical models. Rate process fracture theories take into consideration the viscoelastic behavior of polymeric materials but do not derive their fracture criteria from detailed morphological analysis. These basic theories are invaluable, however, to elucidate statistical, non-morphological, or continuum mechanical aspects of the fracture process. 

As opposed to the continuum mechanical theories, molecular rate process theories of fracture recognize the presence of discrete particles or elements forming the material body. Rate process theories intend to relate in a straightforward manner breakage, displacement, and reformation of these elements to deformation, defect development, and fracture of the structured material. 

In the following the characteristic aspects of these generalized, nonmorphological rate process fracture theories are to be discussed, i.e. the nature of the basic fracture events, their distribution in space and time, the law of the accumulation of these events, and resulting fracture criteria. 

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