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

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2

1. Introduction We discuss changes in microstructure of austenitic metastable steels under conditions of low-cycle fatigue. More specifically, of interest is the density of microcracks that affects the effective elastic properties and hence the wave speeds. The latter are also affected by the nucleation of the martensitic phase that has elastic properties different from the ones of austenite. Monitoring of the microcrack damage requires, therefore, separation of the mentioned two factors affecting the elastic properties. These challenges require very high precision of acoustic monitoring, as discussed by Mishakin and coauthors (see the work of Mishakin et al. (2021)) where the acoustic techniques were also described. In particular, the effective Poisson ratio was evaluated via the ratio of the longitudinal , l V , and shear, V  , wave speeds as follows

2

2

2

2

2 V V 

2

t

t



l

l









  2 





2

2

2

2

V V 

2 2

t

t



l



l



where l t and t  are the corresponding times of their propagation across the thickness. One of the motivations for using this ratio was that it does not depend on the specimen thickness (that may not be precisely known). The wave speeds entering the formulas above are expressed in terms of the effective elastic properties of the composite material consisting of the austenite matrix and martensite inhomogeneities. This gives rise to a number of issues related to the effective media theories, the complicating factors being that the martensite particles have complex and largely unknown shapes and that microcracks in the austenite phase have complex (e.g., zigzags) shapes as well (see works of Anisimova et al. (2020), Barthélémy et al. (2021), Doan et al. (2020), Du et al. (2020), Kanaun (2021), Kolpakov and Kolpakov (2020), Kushch (2020), Martynyuk and Kachanov (2020), Sevostianov and Kushch (2020), Xu et al. (2021) for discussions of the mentioned issues). In particular, we note that, as far as strongly oblate, crack-like pores are concerned, their effect on the effective elastic properties – and hence on wave speeds – is determined by the crack density parameter (and not by porosity). In order to focus on microcracking, the effects on the elastic properties of the two factors – microcracking and the nucleation of the martensitic phase – need to be separated. More specifically, the effect of the martensitic phase needs to be evaluated separately. The experimental data available for this evaluation is given by the eddy-current technique (see, for example, Butusova et al (2020)), that yields the volume fraction of the martensitic phase. Generally, this information is insufficient, since the mentioned effect also depends on shapes of the martensitic particles. However, in cases when the elastic contrast between the two phases is moderate (up to the factor of two), the effect of shapes can be neglected so that that the volume fraction information is sufficient (see the work of Kachanov (in print)). In the text to follow, we show how this approach yields a methodology of monitoring the microcrack density changes based on combination of the acoustic and eddy current data. 2. On the effective elastic properties of materials with moderate contrast between the constituents’ properties We consider the mixture of the austenite and martensite phases as a composite material. To this end, we mention that, for a composite material that consists of two isotropic phases, with 1 K , 1 G and 2 K , 2 G being their bulk and shear moduli, and that is isotropic overall, the classical Voigt-Reuss-Hill bounds (see the works of Voigt (1889), Reuss (1929), and Hill (1963)) for the effective bulk and shear moduli have the form