PSI - Issue 6

Ekaterina L. Alekseeva et al. / Procedia Structural Integrity 6 (2017) 128–133 E.A. Alekseeva et al. / Structural Integrity Procedia 00 (2017) 000–000

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Fig. 4. Distributions of the Mises equivalent plastic strain on the surface of the specimen along the center line AB (see Fig.3.).

The direction of the localization bands of plastic deformations does not coincide with the direction of the maximum tangential stresses in the three-dimensional formulation.

4. Discussion

As can be seen from the presented graphs, the proposed model of a polycrystalline metal with inhomogeneity at the mesolevel allows us to describe the e ff ect of localization of plastic strains. This result was obtained using the simplest bilinear material model without the descending branch on the stress-strain curve and without using other sources of instability of uniform deformations, for example, stochastic di ff erential equations and random processes. As a result, it is possible to obtain an wavy picture of plastic strains under uniform tension of the strip, which can be treated as a ”chessboard” on the surface of the sample. A good qualitative agreement with the results of the experiment in Fig. 2 is observed. A new assumption was made in Kudinova (2016) on the influence of the forces of the surface tension of the grains of a metal on its yield strength. In view of this assumption, the scattering in yield stress values can be related to the natural scattering of the size and shape of the grains, which in some cases is directly measurable. Thus, the parameters of the plastic strain localization bands can be predicted by knowing the dispersion of the sizes of the multicrystalline grains. This agrees well with known experimental data. An empirical dependence of the average distance between the bands on the grain size was constructed in Zuev (2001), which is linear in a wide range of sizes from 10 µ m to 4 mm. The presence of a unique relationship between the mean values makes it possible to generalize the relationship between the grain size and its yield point at the mesolevel. Such relationship makes it possible to approximate the nonlinearity at the transition point to the plastic flow due to the scatter of grain parameters. The same dependence describes well the nonlinear portion of the stress-strain curve that is observed in most mate rials during the transition from elastic to plastic deformation. Thus, local plastic strains lead to the appearance of an inhomogeneous distribution of the acoustic anisotropy in the investigated structural element. This makes possible to apply the method of acoustic anisotropy to detect zones of localization of plastic deformation. There is a new diagnostic feature that allows by means of non-destructive testing methods to assess the proximity of metal to failure, to conduct technical diagnostics of structures and machine parts. A new mathematical model of a polycrystalline material is proposed, in which the deformation of each of the grains obeys a bilinear law with a normal distribution of the yield stress along grains, without involving more complex 5. Conclusions