Abstract
This work presents an experimental—analytical study of the possibility of applying the method of the greatest probability to evaluate the sensitive thresholds of the bottom (N0) and top (Nk) of the statistical distribution of the mechanical structural characteristics. For the structural materials alloyed steel 15Cr2MoVA, steel C45 and aluminium alloy D16T1, the statistical distribution of proportional limit, yield strength, ultimate tensile strength, reduction in area, cyclic stress was estimated, as well as the following statistical parameters: mathematical mean, average square deviation, dispersion, asymmetry, variation coefficient, and excess. Purpose: to determine whether the limits of the sensitivity of the statistical distribution of the mechanical characteristics have been computed using the maximum likelihood method. Value: there is a certain upward and downward flattening of the probability curves in the statistical distribution curves of the fatigue test results. This implies that the chosen law of the distribution of random variables has an effect on the appearance of errors. These errors are unacceptable given the importance of accurately determining the reliability and durability of transport means, shipbuilding, machinery, and other important structures. Our results could potentially explain why sensitive limits cannot be applied to the statistical distribution of the mechanical characteristics of structural materials.
Highlights
Development of new machines and structures with high operational capabilities and specific capacities, as well as the necessity to reduce their metal consumption while increasing strength and durability is an urgent and challenging task, especially considering the high cost and uniqueness of a number of machines and structures
Lower N0 and upper Nk sensitivity thresholds have been determined (Table 4) for statistical distribution under the calculation methodology discussed in the above paragraph
Resulting from the statistical investigation of mechanical properties of the structural materials including the application of the maximum likelihood method to the identification of the sensitivity thresholds N0 and Nk for the statistical distribution, the following conclusions could be drawn: 1. Analysis of the graphical representation of the distribution in the probabilistic plot shows that the distribution curves for the random variable X” are more skewed due to the higher variance
Summary
Development of new machines and structures with high operational capabilities and specific capacities, as well as the necessity to reduce their metal consumption while increasing strength and durability is an urgent and challenging task, especially considering the high cost and uniqueness of a number of machines and structures (transport means, steam and gas turbine bodies and rotors, nuclear reactors and steam generators, pipelines, critical elements of welded and detachable joints, etc.). Matvienko et al [23] present a method to assess the probability of fracture of structural components of technical systems subjected to monotonic and cyclic loading, which allows the scattering of mechanical properties of materials to be taken into account. Bazaras [32] and Daunys et al [33] have investigated the probabilistic low cycle fatigue life and the dependence of low-cycle durability on the mechanical properties of the WWER nuclear power plant reactor of 15Cr2MoVA steel and structural steel C45. The references provide only minor information on the application of the threshold sensitivity measures to a statistical assessment of low-cycle durability test results and refrain from analysing the following questions:. Can threshold sensitivity measures for the statistical distribution be applied successfully to processing of the results of the tests of mechanical properties of materials?. Based on the topics discussed above, the main outcomes of this paper are as follows: (i) the attempt to analyse whether the application of the maximum likelihood method allows for determining the threshold sensitivity values N0 (bottom) and Nk (top) for statistical distribution of mechanical properties, (ii) generation of the statistical distribution curves for mechanical parameters, and (iii) verification of the influence of the statistical distribution curves on the statistical distribution parameters of mechanical properties of a structural materials
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