Dilation process

Two mechanisms of yielding may be distinguished in polymers diear yielding, which occurs essentially at constant volume, and crazing, which is a dilatation process. There are important differences between the two mechanisms, both in their dependence upon stress and temperature, and in their effects on fracture behaviour. 

There is a conceptual difference between tube dilation and constraint release. The motion of the tube in constraint release does not affect singlechain modes inside the tube (reptation and tube length fluctuation). The tube diameter for these single chains in a tube processes is, on average, constant. In contrast, the tube diameter increases with time in the tube dilation process and dramatically affects the chain motion within the tube. 

Sanding processes are accompanied by strong non-linearities. Cohesion loss takes place early in the dilation process because stresses are high and shear distortion occurs. Permeability changes from 0.5 - 5 Darcy to very high values, and properties such as matrix compressibility change from -0.50x10 kPa to infinite when the system is liquefied. Initial fabric eventually is fully destroyed by these plasticity processes. 

All these measures are applicable to monitor the development of the properties of the rock during loading and deformation. The development of the dilatancy can be divided very roughly into three phases. Phase I characterizes a decrease of the volume attributed to elastic compression of the rock salt, a decrease of permeability and an increase of seismic velocity. The volume becomes nearly constant at the end of Phase I. It can be assumed that elastic compression processes and dilatancy processes balance at this point. Dilatant microcracking generates only weak AE activity. 

The phase saturations related to the capillary pressure are subsequendy determined by dilating the eroded pore space and evaluating the corresponding occupied volume tractions of the pore space. Details of the erosion and dilation process related to mathematical morphology can be found in Hilpert and Miller. The erosion-dilation process is repeated with the next larger spherical element corresponding to varying capillary pressures. 

Within the fi-ameworks of the cluster model [55] it has been assumed, that the segment joined to cluster means fluctuation fi-ee volume microvoid shrinkage and vice versa. In this case the microvoids number AA/j, forming in polymer dilation process, should be approximately equal to segments number AN subjected to partial melting process. These parameters can be estimated by following methods. The value AN is equal to [51] ... 

Dreger DS, Tkalcic H, Johnston M (2000) Dilational processes accompanying earthquakes in the Long Valley caldera. Science 288 122-125 Dreger D, Ford SR, Walter WR (2008) Source analysis of the Crandall Canyon, Utah mine collapse. Science 321 217... 

Watanabe, H., Matsumiya, Y, Osaki, K. Tube dilation process in star-branched cis-polyisoprenes. /. Polym. Sci. (2000) 38, pp. 1024-1036... 

Where p is the density of dilated microsphere, Mq is the velocity of the charged jet at r = R is the maximal radius of the microsphere, u j is the minimal velocity. Higher voltage means higher value of the jet speed ( Mq ) at r = and a more drastic electrospiiming-dilation process happens, resulting in a lower density (P) of dilated microsphere, smaller size (R) of the microsphere and smaller pores as well [77-78]. 

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