Computational Methods for Debonding in Composites

236 J.A. Oliveira et al.
Fig. 11.10 Representation
of the components of the
constitutive material matrix
D h calculated with tetrahedra
(T) and hexahedra (H)
finite element meshes, for an
aluminium matrix composite
material reinforced with
boron continuous cylindrical
fibres (47% vol.)
Table 11.2 Numerical (N), analytical (A) and experimental (E) elastic properties of an aluminium
matrix composite material reinforced with boron fibres (47% vol.)
Results E11 [GPa] E22 [GPa] G12 [GPa] G23 [GPa] ν12 [-] ν23 [-]
N – AEH 214.6 144.5 54.7 46.2 0.19 0.25
N – Xia et al. 214 143 54.2 45.7 0.195 0.253
N – Sun and Vaidya 215 144 57.2 45.9 0.19 0.29
A – Sun and Chen 214 135 51.1 – 0.19 –
A – Chamis 214 156 62.6 43.6 0.20 0.31
A – Whitney and Riley 215 123 53.9 – 0.19 –
E – Kenaga et al. 216 140 52 – 0.29 –
use of these finite element meshes are represented in Fig. 11.10, where, according
to Eq. (11.25), the tetragonal character of the composite material is observed. The
manipulation of the homogenised flexibility matrix components associated to the
numerical analysis using the tetrahedral finite element mesh allows the calculation
of the elastic properties of the composite material. These properties are shown in
Table 11.2, along with results taken from numerical (N) and analytical (A) predictions,
and experimental results (E) [12]. In what concerns the numerical prediction
results, Xia et al. [24] presented values achieved through a combination of the finite
element method with explicit periodicity conditions based on the micromechanical
models developed by Suquet [20]. Sun and Vaidya [19] presented numerical results
based on the conjugation of principles of equivalent deformation energy with the
finite element method. The analytical prediction results of Whitney and Riley [23]
are based on energy weighting methods derived from the classical theory of elasticity.
The analytical prediction results presented by Sun and Chen [18] and Chamis [4]
are based on micromechanical models involving continuity and load equilibrium
conditions. The numerical values were obtained by the inversion of the elasticity