5.1         Axial strain field distribution measurements

5.1.6        Finite element simulations

Fig. 5-12 Finite Element mesh used for the simulations

This experiment has also been simulated with the finite elements technique. The mesh definition and the calculations have been performed by Dr. Laurent Humbert (LMAF, EPFL). We present in Fig. 5-12 the defined mesh, where only one eighth of the sample has been considered due to the symmetry properties of the sample (adding limits conditions). The mesh density is increased near and inside the fiber region and near the notch region.

The linear behavior of the sample to axial stress loading allows defining a normalized strain distribution f(z) at the fiber core location

This normalized strain function is presented in Fig. 5-13 (top). From equation (5-9), we have the experimental axial strain distribution e_z,b(z) for z Î [-1.4 , 9.1]. In this range, the minimal strain e_z,b(z = 0) can be used with the normalized value at the origin f(z = 0) = 1.0476 to calculate the finite element simulation axial strain distributions for the different loading cases. These simulations are presented in Fig. 5-13 (bottom).

Fig. 5-13 Normalized strain distribution along the fiber (top) and axial strain distributions for the four loading cases (bottom)

The comparison with the experimental axial strain distributions is shown in Fig. 5-14. An overall agreement is observed but the position scale between experimental and calculated strains does not match well. This effect is not explained yet and further investigations on the finite element simulations are currently conducted.

Fig. 5-14 Left : axial strain distributions for different axial stress loading forces and right : difference with the axial strain value at z = L; the discrete points represent the experimental results from the OLCR measurements and the lines represent the calculated values obtained with the finite element method