A synthesis of work in various research fields shows that (i) the microscopic damage processes in insulating materials under stress (electrical, mechanical, thermal or radiation) are not yet understood but are indisputably related to energy localization on defects. The nature of these defects is still debated but it is acquired that their annihilation is exothermic, (ii) by trapping of charges one localizes a mechanical energy which is relaxed after detrapping, (iii) the charge injection and the dielectrics characterization by electron beam techniques are particularly suited to the damage process study. In the scanning electron microscope chamber, an adapted sample holder measured separately the influence and conduction currents in order to study the charge dynamic during irradiation and discharge dynamic after irradiation of insulating materials. The studied materials are polycrystalline alpha-alumina and yttria stabilized zirconia, characterized by their grain sizes, respectively of 2.5 mu m and 300 nm, their mechanical fracture stress, respectively of 400 MPa and 96 MPa, their electric conductivity, respectively of 10(-14) S/m and 10(-8) S/m and their electrical breakdown field, respectively of 21.2 MV/m and 18.2 MV/m. Interestingly, it was observed that the charging and discharging dynamics of these two materials are quite different. At room temperature, the electrons are trapped in a very stable manner by alpha-alumina and are labile in yttria stabilized zirconia. This difference in stability can be (i) the result of electronic structure differences of both materials, and (ii) the internal stresses effect in the grain boundaries where the oxygen vacancies concentration greatly increases the Debye-Waller factor. This is consistent with the fact that the electron-phonon interactions are at the heart of the damage process. Studies are ongoing to develop characterization techniques to guide the materials manufacture by optimizing their internal stresses.