Issue 50

V. Kytopoulos et alii, Frattura ed Integrità Strutturale, 50 (2019) 414-422; DOI: 10.3221/IGF-ESIS.50.35 416 simple, first-order approximation model the distribution function φ (ρz) of X-rays generation can be described by a single exponential decrease [23]:   z z e       (1) where σ is a material-instrument set-up constant and ρ the mass density of material. At the same time the attenuation (absorption) processes is given by Beer’s law as exp[-μ z ], where z is the X-Ray travelling depth. Thereafter the emitted and detected X-ray intensity can be described, at first, as: em I e e dz      x Z  ρz μz 0 (2) where the mass density ρ is assumed in a first approximation to remain constant along the X-ray generation path z . Nevertheless, the presence of crack-like micro-defects, i.e., volumetric damage in the material, imposes a related local variation of the mass density ρ . As such, the above integration should be made with respect to the “effective” variable, ρz , called mass-depth. Therefore the above integral takes the final form:   x Z z z em I  K e e d z           0 (2a) where /     is the so-called mass absorption (attenuation) coefficient, which is a very important material constant for the non-destructive testing given that it is independent of the physical and/or chemical state of the material [22-24]. The constant K σ takes into account the atomic mass and number as well as fluorescence effects [23] while Z x is the maximum effective depth of X-rays generation. Integration with respect to (ρ z ) yields:   x  Z em K I    e                1 (3) Furthermore, it is valid that maximum mass-depth ρz x is almost constant under the same experimental set-up conditions [23]. On the basis of this fact, one may similarly assume that the effective mass-volume M x of X-rays generation, sampled by the electron beam, remains almost constant. Hence, one may write: x x x M V   z  const      3 (3a) where V x ≈z x 3 is the associated effective maximum volume of X-rays generation. Using now Eq.(3a) and substituting z x =( const / ρ 1/3 ) into Eq.(3) one arrives at the final-general form of emitted x-Ray signal intensity: a  em I A e                 2 3 1 (4) Constants A, α take into account all constants of Eq.(3). As such, the basic Eq.(4) implies that the emitted and detected signal intensity should increase (decrease) monotonically with increasing (decreasing) local mass density ρ. Since damage can be assumed to be (in a first approximation) inversely proportional to the local mass density it means that the measured damage degree should monotonically increase (decrease) with decreasing (increasing) signal emission intensity, given by Eq.(4). E XPERIMENTAL DETAILS Methods he X-rays used are generated and emitted from a specimen bombarded with a focused electron beam of the Scanning Electron Microscope. The X-ray generation and emission is a result of complex electron beam-specimen interactions, which describe the mechanisms for both characteristic and continuum X-ray production. In this study T