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The Theory of Critical Distances is a group of phenomenological methods for fracture prediction of materials subjected different loading conditions with accounting effect of stress concentration features. When estimating strength of components under dynamic loading by directly postprocessing the elastoplastic stress fields acting on the material in the notch tip the critical distance is a material parameter. Based on research of physical processes taking place at a micro/mesoscopic level near the notch tip the physical meaning of the parameters of theory of critical distances was investigated. The modeling of solids with defects behavior based on self-similar solutions for stress and defect density fields in one- and three-dimensional cases was carried out. Established link between critical distance and fundamental length of dissipative structure growing in a blow-up regime.

Development of the method for assessing the strength of engineering structures, considering the effects of the non-locality fracture in the area of stress concentrators, under different loading regime is one of the major scientific interests. In the present study the linear-elastic Theory of Critical Distances (TCD) is modificated for the case of elasto-plastic material behavior. The for plotting Johnson–Cook model was used for simulation of material behavior, and an elasto-plastic critical distance value was used in order to estimate the strength of the tested samples. The accuracy and reliability of the proposed design methodology was checked against experimental data: the cylindrical un-notched specimens and samples with stress concentrators of titanium alloy Grade2 were tested under tensile loading with different strain rate. Mechanical tests were carried out using a 300 kN electromechanical testing machine Shimadzu AG-X Plus and Gopkinson-Kolskiy's split bar. The obtained results showed that the use of the modification of the TCD based on elasto-plastic material behavior gives us estimates falling within an error up to 12% which means that the elasto-plastic TCD gives more accurate predictions than the linear elastic TCD solution (when using of elastic stress information the error interval is ± 15-20%).