Failure of fibrous materials

Fibrous solids or fiber reinforced composites have very special rupture properties. With Ferenc Kun and Stefano Zapperi we studied in particular the Continuous Damage Model describing systems in which a single fibre can have several failures and solved for it analytically as presented in our paper published in E.Phys.J. B Vol.17, 269-279 (2000).

With Raul Cruz and again Ferenc Kun we studied the statistics of bursts in this continuous damage model as you can see in our paper published in Phys. Rev. E Vol. 64, 066122 (2001) and generalized the fibre rupture model to viscoelastic fibres as described in the paper published in Phys. Rev. E. Vol. 65, 032502 (2002).

In the above team together with Yamir Moreno we studied a fibre model interpolating between local and global load sharing by introducing a power law dependence of load sharing with distance and changing the exponent. We found a transition between the global and local behaviour at an exponent value of two. All this is presented in our paper published in Phys. Rev. E Vol. 65, p. 046148 (2002). A further extension of this work is given in the paper published in Phys. Rev. E, Vol. 68, 026116 (2003). In a paper published in Physica A, Vol.347, p.402-410 (2005) we extended this model to viscoelastic creep of the fibres at failure.

Another interesting application of the fibre model resulted from the inversion of tension to compression and from softening to hardening. This gave a model for the change of the force network in a granular medium under uniaxial stress which gave very good agreement with experimental data on acoustic emission signals. The experiment was conducted in a cylindrical cell filled with glass beads and eight acoustic sensors

The histogram of the acoustic emission signals is shown in the plot together with the theoretical prediction. In the inset one sees an example of the time series of the acoustic emission. For more details see our paper published in Physical Review Letters, Vol. 89, 205501 (2002). More details were presented in the proceedings of the Varenna school.

Within the PhD thesis of Frank Raischel we studied a model for fracture under shear and plasticity .

In order to model the failure of asphalt in Brasil tests under cyclic load we introduced recently a fiber model that includes damaging and healing. In the figure we see an example of such a damaged disk and the corresponding experimental setup from the pavement laboratory of the UFC in Fortaleza, Brazil.

This model could be solved analytically to a certain degree and shows astonishingly good agreement with the expeimental results. One of them is the strain as function of time seen in the plot which diverges at the failure time. More can be seen in the preprint .

In a long review article we presented an overview of our work on fibres. You can also download a talk that I gave in several occasions on the subject.

In a recent work with Ferenc Kun, Humbert Carmona and Jose Soares Andrade we were able to elucidate the microscopic origin of the Basquin law for fatigue. This was published in Physical Review Letter Vol.100, 094301 (2008) and became a Focus and was commented in Brazilian news .