PSI - Issue 42

Mark Kachanov et al. / Procedia Structural Integrity 42 (2022) 96–101 M.Kachanov, V.Mishakin, Y.Pronina / Structural Integrity Procedia 00 (2019) 000–000 (A) We used the data on porosity  and, assuming that microcrack openings had the spheroidal shape, of aspect ratio  , we applied the differential scheme to the prediction of   and identified the value of  that provided the best fit of the data. This methodology yielded the following results: the value of  was in the range 0.008–0.040 (thus indicating that pores had strongly oblate, crack-like shapes, so that the proper parameter of their concentration was, indeed, the crack density  (and not the crack porosity). Using thus obtained value of  , in combination with the data on porosity  , we estimated crack density  . Note that the described methodology is not non-destructive since the determination of porosity (density change) requires cutting the specimen. The density of the steel was determined on material fragments cut from the strained domain of the specimens (see works of Mishakin et al. (2021) and Kachanov et al. (2021) for details). (B) Due to low values of the observed crack density (not exceeding 0.1), their effect on the overall elastic properties can be considered in the framework of the non-interaction approximation (NIA) using the classic results of Bristow. Solving Bristow’s formulas (corrected for a misprint noted by Sevostianov and Kachanov (2009)) for     yields         0 0 2 0 0 0 2 45 16 1 10 3               In this general formula, 0  refers to the virgin material and  to the microcracked one. In our context, 0       . This formula allows direct determination of crack density that corresponds to data on .   Importantly, this methodology is non-destructive since it does not require the determination of porosity. The main observations are as follows: 1. The evolution of microcrack density  with growth  of the martensite phase (Fig. 1) under loading is described by curves of approximately similar shapes at different strain ranges (although the length of the curves increases with the range). 2. The critical value *  of microcrack density at the fracture point (defined as formation of a macrocrack, of the length 1 mm ) is, roughly, proportional to the accumulated value *  of the martensite volume at this point. 3. The value of *  tends to increase with increasing strain range. The above observations appear to have clear physical interpretation. In particular, growth of the martensite phase generates compressive stresses that impede propagation and coalescence of microcracks and thus postpone the formation of a macrocrack to later stages of loading. Smaller strain ranges produce smaller amounts of martensite and thus weaker compressive stresses; this facilitates the formation of dangerous microcrack clusters leading to the nucleation of a macrocrack; therefore, the formation of the latter becomes possible at smaller overall microcrack density. 99 4