metals Article Probability Assessment of the Mechanical and Low-Cycle Properties of Structural Steels and Aluminium Žilvinas Bazaras, Vaidas Lukoševiˇ cius *, Andrius Vilkauskas and Ram ¯ unas ˇ Cesnaviˇ cius   Citation: Bazaras, Ž.; Lukoševiˇ cius, V.; Vilkauskas, A.; ˇ Cesnaviˇ cius, R. Probability Assessment of the Mechanical and Low-Cycle Properties of Structural Steels and Aluminium. Metals 2021, 11, 918. https://doi.org/10.3390/ met11060918 Academic Editor: Filippo Berto Received: 21 May 2021 Accepted: 1 June 2021 Published: 4 June 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentu˛ Str. 56, 51424 Kaunas, Lithuania; zilvinas.bazaras@ktu.lt (Ž.B.); andrius.vilkauskas@ktu.lt (A.V.); ramunas.cesnavicius@ktu.lt (R. ˇ C.) * Correspondence: vaidas.lukosevicius@ktu.lt Abstract: Key mechanical properties used in low-cycle strength and durability calculations are the strength (proportional limit stress, σ pr ; relative yield strength, σ 0.2 ; and ultimate tensile stress, σ u ) and strain properties (proportional limit strain, e pr ; percent area reduction, ψ; and percent area reduction at failure, ψ u ). When selecting the key mechanical properties provided in the specifications, an error may be made due to the failure to account for a series of random factors that determine the distribution of properties. The majority of research papers dealing with statistical descriptions of the low-cycle strain properties do not look deeper into the distribution of mechanical properties and the diagram parameters of strain characteristics. This paper provides a description of the distribution patterns of mechanical properties, statistical parameters, and low-cycle fatigue curves. Log-normal distribution generated the lowest values for the coefficient of variation of one of the key statistical indicators, suggesting that log-normal distribution is superior to normal or Weibull distribution in this respect. The distribution of low-cycle strain parameters exceeded the distribution of mechanical properties considerably. Minimum coefficients of variation of the parameters were generated at normal distribution. The statistical analysis showed the lower distribution of the durability parameters compared to the distribution of parameters of the strain diagrams. The findings of the paper enable a revision of the durability and life of the structural elements of in-service facilities subject to elastoplastic loading by assessing the distribution of mechanical characteristics and low-cycle strain parameters as well as the permissible distribution limits. Keywords: probability; durability; low-cycle fatigue; normal distributions; log-normal distribution; Weibull distribution; coefficient of variation 1. Introduction Contemporary transport engineering facilities operate at high speeds, high produc- tivity, and high capacities to achieve the best performance. For aerospace and transport engineering, the equipment and facilities perform under high stress, which may result in elastic–plastic cyclic deformation. Overloading present particular dangers, as cyclically varying loads exceed the proportional limit of the material and cause plastic deformation and the formation of a hysteresis loop. As a result, the durability of the material decreases by hundreds or thousands of cycles. A wise range of fatigue life prediction methods and probabilistic approaches, as well as mechanical and low cycle properties have been investigated in recent years. A considerable contribution to the calculation of probabilistic methods for mechanical and low-cycle properties was made by a series of investigators. Daunys et al. [1–4] investigated the dependences of the low-cycle durability of mechanical properties for steels of welded joints used in nuclear power plants. Ellingwood et al. [5,6] investigated the applicability of existing statistical data for describing the resistance of steel and reinforced concrete used in nuclear power plants. Liu et al. [7] proposed calculating the equivalent initial flaw size (EIFS) distribution, which is very efficient for calculating the statistics of EIFS. Metals 2021, 11, 918. https://doi.org/10.3390/met11060918 https://www.mdpi.com/journal/metals