Fractures dilation

The second noteworthy morphological feature is presented in Fig. 12b. This micrograph depicts the pre-crack front of 15-1500-70F, which had a value significantly above that of the control, as shown in Fig. 11 a. The holes may be examples of the dilatation effect observed in CTBN-modified epoxies l9,22> in which rubber particles dilate in mutually perpendicular directions under the application of a triaxial stress and then collapse into spherical cavities following fracture. Dilatation requires a mismatch in coefficients of thermal expansion of resin and rubber 11. This effect will therefore be most striking when the elastomeric phase is homogeneous, as is apparently the case here. 

Fig. 6. Fracture dilation versus shear displacement CSFT result.

The second mechanism is dilation/contraction induced permeability change during shear (Figure 1 (b)). Fractures dilate when fracture failure occurs under high differential stresses. This mechanism can play a major role in the flow field since the dilated fracture tend to have much higher transmissivity than the fracture under elastic deformation. 

The increase of permeability is due to the increased apertures from fracture dilation. For this study, k=2.45 is the starting point of shear failure of fractures inclined at about 33 degrees from the horizontal plane. As horizontal boundary stress increases, the range of possible failure orientation angle also becomes larger and this gives increased permeability. The increase of permeability seems to stabilize after a certain k ratio because the dilation does not continue after the critical shear displacement. 

Figure 8 shows some examples of the channelling flow effect due to the fracture dilation. Note that all models have the same reference legend. One line indicates the flowrate of lO mvsec and the flowrates smaller than this value are not drawn in Figure 8. 

Properties of newly created fractures are found to be important parameters controlling the degree of rock failure. Many uncertainties still exist on these properties. Additional study on fracture stiffness and the fracture dilation angle of new fractures is needed to gain more reliable models of rock failure. 

As it was already mentioned, the above model contains the unknown values of shear dilation angles 0, , which can be predicted for the specified rock by analysing the effect of shears displacement of the syntactic fracture on the fracture dilation. This can be made with analytic-experimental method (it couples the analytical algorithm for fracture mathematical modelling and experimental data for the natural fracture... 

Fracture dilation is more pronounced for the fractal surfaces with lower fractal dimension Dj. As soon as the variation of the fracture dilation (which is measured geometrically) due to shear offset is computed, the shear dilation angle ( ), can be obtained as a mean angle between the shear dilation plot tangent and horizontal axis. This value is higher for the surfaces with lower fractal dimension. 

When a craze occurs around a rubber droplet the droplet is stressed not only in a direction parallel to the applied stress but also in the plane of the craze perpendicular to the applied stress (see Figure 3.9). Such a triaxial stress leading to dilation of the particle would be resisted by the high bulk modulus of the rubber, which would thus become load bearing. The fracture initiation stress of a polyblend should not therefore be substantially different from that of a glass. 

A shortening in relaxation time in the critically strained region makes some materials tough. The shift of relaxation time is attributed to strain-induced dilatation and can reach as much as five decades. Thermal history, on the other hand, dictates the initial state from which this dilatation starts and may be expressed in terms of excess entropy and enthalpy. The excess enthalpy at Tg is measurable by differential scanning calorimetry. Brittle to ductile transition behavior is determined by the strain-induced reduction in relaxation time, the initial amount of excess entropy, and the maximum elastic strain that the material can undergo without fracturing or crazing. 

Consider now a polymer sample of current volume V responding by craze plasticity to an imposed current elongational strain rate e, developing a tensile (dilatational) flow resistance until a final fracture strain is achieved as shown in Fig. 1. The specific toughness W or the total deformational energy absorbed per unit volume for this polymer is the area under the stress strain curve, or... 

We note from the outset that crazing, which is a form of cavitational localization of deformation, can be viewed as a form of transformation plasticity made possible by the long chain molecular nature of the material and the natural molecular entanglements that give rise to well-defined cavitational transformation strains. Therefore, we have called craze plasticity also dilatational plasticity. Thus, if well managed to avoid fracture in the fibrilated craze matter, crazing can be an attractive mechanism of inelastic deformation and a source of toughness. 

The total strain developed in all of these materials is essentially entirely from crazing and therefore at all points prior to fracture the imposed strain rate of the experiment must be matched by the specimen through its dilatational strain rate 6 which is a product of three terms... 

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