Vibrations in engineering and technology

Yaroshenko Leonid – candidate of technical sciences, associate professor of the department of electric power engineering, electrical engineering and electromechanics of Vinnitsa national agrarian university, Service address: Vinnitsa, st. Sonyachna 3, VNAU 21008, e-mail: volvinlv@gmail.com,  https://orcid.org/0000- 0002-0261-006X   

Kolisnyk Mykola – Assistant Professor, Department of Electric Power Engineering, Electrical Engineering and Electromechanics, Vinnitsa National Agrarian University (3, Solnechna str., Vinnitsa, 21008, Ukraine, email: kolisnik30@gmail.com, https://orcid.org/0000-0001-5502-6556).

Andrii Shtuts – Assistant Professor, Department of Electric Power Engineering, Electrical Engineering and Electromechanics, Vinnitsa National Agrarian University (3, Solnechna str., Vinnitsa, 21008, Ukraine, email: shtuts1989@gmail.com, https://orcid.org/0000-0002-4242-2100). 

Yurii Prysiazhniuk – postgraduate in specialty 133 «Sectoral Mechanical Engineering» of Vinnytsia National Agrarian University (3, Sonychna St., Vinnytsia, 21008, Ukraine, +380964117015, prisaznuku13@gmail.com, https://orcid.org/0000-0002-3351-3676).

In this scientific article, two deformation models for analyzing the accumulation of material damage during upsetting and direct extrusion using the die forming method are investigated. Both models include an analytical representation of the deformation trajectory, approximation of the boundary deformation curve, and a damage accumulation model. A three-parameter representation of the boundary deformation curve is applied, utilizing a power-law model and a linear damage accumulation model.

The process of direct extrusion is examined by constructing parametric equations for the deformation trajectory. The functional dependence for the stress state indicator involves three constants, while a non-elementary function with a single constant is used for the accumulated deformation, determined using the theory of limit functions. Considering the complexity of trajectories, the use of a power-law accumulation model with a fixed nonlinearity indicator value is justified. The methodology for determining this indicator confirms its positive values less than one for the investigated trajectories, affirming its applicability. Numerical experiments demonstrate an increasing dependence of the limiting deformation with the increase of this indicator, indicating the effectiveness of the model.

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