Finite-element model, rubber particles

A finite-element model for rubber particles in a polymeric matrix has been proposed that is based on a collection of spheres, each consisting of a sphere of rubber surrounded by an annulus of matrix. 

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. 

In view of these difficulties, we have taken the second of the options just discussed. Namely, we assume that the particles have cavitated, which is in agreement with experimental observations, and then we base our finite-element modeling studies on examining an already voided epoxy matrix. This approach avoids the necessity of defining the value of the bulk modulus of the rubber with a high degree of accuracy (see the section Material Properties,). 

Figure 6. Comparison of experimental and predicted values of Youngs modulus of epoxy resin toughened with rubber particles. Finite-element predicted values were calculated using two values of the Poisson ratio of the rubber phase and the predicted bounds using the Ishai and Cohen model (26).

Preliminary Value of Predicted Gc. The fracture model and the finite-element analysis lead to a predicted value of Gc of 5.5 kj/m2 for a rubber-toughened epoxy with a volume fraction of rubbery particles of 20%. In previous experimental studies (8), a rubber-toughened epoxy possessing the microstructure and mechanical properties of the epoxy matrix modeled in the present work was prepared, and Gc was measured. The measured value was 5.9 kj/m2 (8). The predicted value is in good agreement with the experimental value. 

There has been the question why the TPV materials with ductile thermoplastic matrix display rubber elasticity. Several models have been suggested to answer this question (41 7). Inoue group first analyzed the origin of mbber elasticity in TPVs (43). They constructed a two-dimensional model with four EPDM mbber inclusions in ductile PP matrix and carried out the elastic-plastic analysis on the deformation mechanism of the two-phase system by finite-element method (FEM). The FEM analysis revealed that, even at highly deformed states at which almost the whole matrix has been yielded by the stress concentration, the ligament matrix between mbber inclusions in the stretching direction is locally preserved within an elastic limit and it acts as an in-situ formed adhesive for interconnecting mbber particles. 

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