Epoxy annulus

The Spherical-Material Model. The finite-element model used for the spherical-material model is a single rubber sphere surrounded by an annulus of epoxy resin. The complete cell can be represented by axisymmetric elements in an analogous manner to the cylindrical model, as shown in Figure 2. The same number and types of elements were used for this model. Analyses were also undertaken assuming a hole instead of the rubber particle the grid then consisted of the epoxy annulus alone. 

Figure 7. Stress profiles through the epoxy annulus for an applied pure hydrostatic tension of 100 MPa. The volume fraction of the rubber phase is 20%, ana the rubber properties are as follows E = 1 MPa, v = 0.49992, and K = 2.083 GPa.

The stress distributions for the different properties of the rubber sphere, for this pure hydrostatic applied stress, have been found to be unique functions of the bulk modulus, K, of the rubber (27). In other words, for a given volume fraction, the values of maximum stress for the different rubber properties fall on single curves when plotted as functions of the bulk modulus of the rubber. The relationships are shown for a 20% volume fraction of rubber in Figure 8 the values plotted are the hydrostatic stress in the rubber particle and the maximum von Mises stress in the epoxy, occurring at the interface. The results shown in Figure 8 demonstrate that the hydrostatic stress in the rubber sphere increases steadily with increasing values of K of the rubber, although the rate of increase is lower as the value of K rises. When the value of K of the rubber equals that of the epoxy annulus (i.e., 3.333 GPa), the model responds as an isotropic sphere and the stress state is pure hydrostatic tension. The maximum von Mises stress in the epoxy annulus decreases relatively... 

Figure 12. Predicted elastic-plastic, stress-strain curves for the epoxy annulus. The volume fraction of voids is 20%.

Encycl) with a binder (such as epoxy-polyamide, expoxy-anhydride, and polyurethane resins) and loading the resulting mixture into the annulus between the inner and outer parts of a cylindrical mold. After curing for 24hr, this cylindrical part of cartridge was attached to a noncombustible base(metallic or plastic), which served as an obturator... 

As just described, the deformed shape of the rubber sphere surrounded by an annulus of epoxy must be a perfect ellipsoid because the overall material is isotropic. As shown by equations 1 and 2, the deformed shape BC is defined from the Poisson ratio, and Youngs modulus can be calculated from summing the reactions. However, for the toughened material, the value of the Poisson ratio is not known only a relationship between E and v is known, as defined by K. Thus, the analysis of unidirectional loading for the spherical cell must be carried out using an iterative procedure. The method has been described in detail elsewhere (15). The results of the iteration can be verified by checking the reduction of the x reactions-to-earth to zero this verification was used for all the results presented here. 

Analyses have been carried out assuming a cavitated particle, that is, the particle is replaced by a void (see the section Cavitation of the Rubber Particles ). The analysis is applied to an annulus of epoxy resin. The volume fraction of the void is 20%. The elastic material properties used for the epoxy matrix are shown in Table I. The elastic-plastic material properties used are shown in Figure 4. Nonlinear geometric effects were included to take account of large deformations. Final failure of the cell was defined (23) to be the applied strain required for the maximum linear tensile strain in the resin to attain the value of 20%. 

The second type of system is marketed as encapsulated packs of polyester or epoxy resin within which there is a thin skin to keep the two eomponents separated. The capsules are placed in the hole and are fractured when the bolt or bar is inserted and turned (Fig. 7.4). In all such systems it is essential that the fixing is mechanically rotated in the hole to ensure correct mixing of the resin components. The requirements for drilling and cleaning the hole are similar to the poured grout systems but the hole size should be strictly in accordance with the manufacturer s instructions. This is to ensure that the pre-measured volume of resin in the pack completely fills the annulus between the bolt and the hole. 

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