PSI - Issue 14

Sarthak S. Singh et al. / Procedia Structural Integrity 14 (2019) 915–921 Author name / Structural Integrity Procedia 00 (2018) 000–000

919

5

(1          (1 ) true engg pl pl true engg

engg

)

pl

(2)

pl

pl

The linear region of the curve is characterized by the elastic modulus and Poisson’s ratio. The corresponding values used in the simulations are, 3 GPa and 0.33, respectively. Plane stress four node elements CPS4R are used for meshing the geometry and the size of the elements is chosen based on the convergence study. The displacement boundary condition ( 2 mm/sec u 0.5   ) is applied at the top surface of the model where the simulation is allowed to run until the geometry is deformed by 50% under compression. Roller supports are applied at the bottom face to allow free deformation along the horizontal direction and the node at the mid-point of the bottom face is fixed to constrain the displacements in both 1 and 2 directions. In order to avoid non-uniform deformation of the side edges, multi-point constraints (MPC) are applied at the nodes on both side edges. This ensures zero relative motion amongst the nodes; thus allowing planar deformation at the side edges and preserving the material symmetry and continuity across it. The reaction forces at the top nodes are extracted and summed over all these nodes to get the total reaction force in the block. Since the block is of unit dimension, the total reaction force is the engineering stress developed due to the deformation. The average displacements at the top nodes are also retrieved to get the engineering strain values. This procedure to calculate engineering stress and strain values is adopted to analyze the mechanical behaviour of composites through the simulations. 5.1 Effect volume fraction of the fillers In this section, the effect of volume fraction ( f V ) of the fillers on the post yield regime of the stress vs. strain plot is discussed. The shape of the filler is chosen as circular which is analogous to the spherical particles. The arrangement of circular fillers in the matrix is illustrated in Fig. 4. The diameter of the circular fillers is estimated using the relationship described below.

4

f V

Volume of fillers

V

  d

 f

Volume of composite sample

N



(3) Here, ‘ N ’ and ‘d’ represent the number of fillers and its diameter in the composite sample, respectively. In the present case ‘ N ’ is fixed as 8. The f V is varied from 0 % to 15 % in a step of 5 %.

The fillers are assumed to be deforming elastically and their elastic modulus and Poisson’s ratio are taken as 72 GPa and 0.2, respectively. The epoxy matrix is modeled with elasto-plastic stress-strain behaviour of neat epoxy as discussed already in the previous section. All the boundary conditions which are used in simulating the neat epoxy case are also applied to filler reinforced composites. A finer mesh was made at the interface between the fillers and the matrix to capture the deformation process accurately. Plane stress four node elements CPS4R are used to mesh the fillers and matrix. Figure 4. RVE of circular filler reinforced epoxy composites