Computational Methods for Debonding in Composites

15 Numerical Simulation of Fiber Orientation and Resulting Thermo-Elastic Behavior 301
Table 15.1 Parameters used in Eqs. 15.15, 15.18 and 15.19
Fig. 15.6 Sensors on the plate symmetry plan
τs
8.18 10 −2 MPa
η0 (Tref) 270 Pa.s
α 0.55
m 0.4
Tref 549 K
β 7,764 K
k 0.3 W/m.K
Cp 1,766 J/Kg.K
ρ 1,522 Kg/m3 Table 15.2 Computation time for discontinuous and continuous approaches
Assembly time Resolution time Computation time
Continuous approach 2 days, 12 hours, 15 hours, 3 days, 3 hours
42 minutes 17 minutes
Discontinuous approach 8 hours, 3 days, 5 hours, 3 days, 13 hours,
29 minutes 15 minutes 44 minutes
The experimental measurements [42] of the orientation gives, for example, the
distribution of the first component, a11, of the orientation tensor on three sensors
(see Figs. 15.5 and 15.6).
In what concerns simulation data, orientation is supposed isotropic at the cavity
inlet. The orientation problem is solved after the thermal and the mechanical problems.
All computations are carried out on an anisotropic mesh of 165,000 nodes
and 902,000 elements. Computations were launched on 12 processors; each one has
2.4 GHz frequency and 2 GB RAM, with a time step equal to 10 −4 s. Resolution,
assembly and computation times are shown in Table 15.2. In this case, continuous
versus discontinuous approaches are compared.
If a discontinuous approximation of the orientation tensor is considered [36], the
orientation tensor is approximated per element P0, whereas in the continuous case
P1 (nodal) approximation is used. The number of nodes is 5.5 times lower than the
number of elements for a three-dimensional mesh, and thus the memory space is
then less important with the second approach.