# Interval method for bonded joints characterization and prognosis (Méthode par Intervalles pour la Caractérisation et le Pronostic des Assemblages Collés)

## Summary:

Adhesives and sealants are widely used in many industrial applications, such as in aerospace, automotive and electrical industries. The characterisation, evaluation of their properties and diagnosis is a key-point for the use of these multi- materials: if the usual characterisation techniques allow a good description of the adhesives in the bulk, or their practical adhesion at model interfaces, reliable parameters of thick interphases between the substrates and the adhesives are missing. Then, dielectric spectroscopy is an extremely effective method for characterising the molecular dynamics over a large range of time scales, and a very promising method to study these complex multi-materials. Unfortunately, the resulting curves are very difficult to analyse as many phenomena take place at the same time (or frequency): dipole relaxations, sample conductivity, electrodes polarisation; Then, some modeling has to be done, and the real and imaginary parts of the permittivity have to be simultaneously modelled, which is really rarely done now. As classical tools for the dielectric spectroscopy data fitting are not satisfactory, we will develop new mathematical and simulation tools.

The interval analysis method we want to use takes into account the experimental error of each data point in the measured dielectric spectrum in order to find the suitable number of relaxations, and give a confidence interval for every parameter of the dielectric function implemented in the software (Set Inversion Via Interval Analysis applied to DiElectric Spectroscopy). The found result is guaranteed which means that the used algorithm is able to validate or nullify a mathematical model. Then, the number of relaxations in the system characterised, their position and intensity will be determined and guaranteed. On the one hand, this new approach of the polymer and interphase study will lead to a better comprehension of the bonded systems, their ageing and to the determination of their Remaining Useful Life (diagnosis). Of course, this fundamental research in molecular dynamic will be coupled with a strong experimental work in practical adhesion and interphases study. On the other hand, the interval analysis and the developed software will be put into a general use (all kind of fit and peak deconvolution): for example the fit of dynamical mechanical analysis data, or deconvolution of X-Ray diffraction, infra-red spectroscopy, Raman spectroscopy, X-ray photoelectron spectroscopy. Using the interval analysis, it will be possible to guarantee the number of Gauss or Lorentz type peaks hidden under a common peak. Just let us remind that the power of the interval analysis is not to use another deconvolution or fitting tool but to guarantee (taking into account the experimental error) the exact number of elementary peaks (relaxations) drawing the experimental curve.

## Partners:

**Ahmed Touhami**was recruited as a post-doc, expert on interval analysis and mathematical developments.

**Mickaël Pomes-Hadda**will arrive in september 2012 and will work as a PhD student on the MICPAC project.

- CIRIMAT:
- Maëlenn Aufray
- Alain Lamure
- Nadine Pébère
- David Grossin

- LAAS:
- Louise Travé-Massuyès
- Carine Jauberthie
- Renaud Pons

- LAPLACE:
- Sombel Diaham

Last update : June 2012