Micromechanical modelling of strain path dependency in FCC metals

The analysis of the formability of metals is a traditional topic in mechanical engineering, which is still characterised by many open issues. In spite of many decades of research, this field continues to trigger new challenges, especially promoted by industrial progress. The growing need for more precision in forming processes and the exploitation of more complex manufacturing processes, necessitates a better understanding of the relevant micromechanical processes and the development of more sophisticated engineering tools. The physical origins of the complex deformation behaviour observed for metals, reside, among others, in the textural anisotropy of the material and the anisotropy of the dislocation structures accompanying the plastic deformation. The microscopic deformation mechanisms, associated with the presence and development of these microstructural entities, affect the macroscopical behaviour of a metal, altering its formability. This thesis addresses two major aspects of the formability analysis of metals, both based on the underlying evolving microstructure: (1) the prediction of forming limits and (2) the prediction of strain path change effects. The following sections shortly highlight the challenges in these fields, from which the research scope of the thesis has been derive

Strain path dependency in metal plasticity

A change in strain path has a significant effect on the mechanical response of metals. Strain path change effects physically originate from a complex microstructure evolution. This paper deals with the contribution of cell structure evolution to the strain path change effect. The material with cells is modelled to behave like composite consisting of a periodic 2D array of two types of elements: the hard cell walls and the soft cell interiors. For the scalar internal variables figuring in the model, the cell size, the wall thickness and the dislocation density inside the walls, evolution equations are proposed to describe the cell development and the cell dissolution. The validation of the model is performed by comparing the results with experimental data on the deformation behaviour of copper which was subjected to a sequence of two uniaxial tensile tests performed in different directions. The model is concluded to be capable to describe the material behaviour for monotonic deformation and complex deformation with a strain path change up to 45 . The model predicts the strain path change, its dependency on the amount of prestrain and on the amplitude of the strain change that are in good agreement with experimental data. The slip anisotropy should be taken into account to improve the model for an adequate prediction of the deformation behaviour after strong strain path changes

Calculation of isotope shifts and King plot nonlinearities in Ca+^+

Many-body perturbation theory is implemented in order to calculate the isotope shifts of $4s$, $4p_{1/2}$, $4p_{3/2}$, $3d_{3/2}$, and $3d_{5/2}$ energy levels of Ca$^+$, for even isotopes $A=$40, 42, 44, 46, 48. The results are presented for mass shift and field shift, as well as for higher-order field shifts, quadratic mass shift, nuclear polarization correction, and the cross term between field and mass shifts. Additionally, we examine King-plot nonlinearities introduced by the higher-order isotope-shift corrections to the combinations of $3d_{3/2}\rightarrow 4s$, $3d_{5/2}\rightarrow 4s$, and $4p_{1/2}\rightarrow 4s$ transitions. For these transitions, second-order mass shift and nuclear polarization correction are identified as the dominant sources of King plot nonlinearity.Comment: 13 pages, 1 figur

GDP modelling: assessment of methodologies and peculiarities of its usage in Ukraine

GDP is one of the main indicators determining the level of economic growth in countries and regions across the globe, therefore, its calculation should be based on the advanced methodology. In the present context, the existing methods of the GDP calculation do not fully meet the fineness criterion subject to certain objective and subjective reasons. Hence, the development of more perfect methodology that takes into account the disadvantages of the existing techniques and is based on economic and mathematical modeling is an urgent national task for Ukraine. The purpose of the article is to assess the GDP calculation methodology used in Ukraine. To achieve this purpose, the relevant methods of GDP calculation, which are valid in Ukraine, have been analyzed, their specifics, certain drawbacks, problems of use and application scenarios have been also revealed. According to the analysis results, an advanced methodology based on an economic and mathematical model with the use of dynamic programming is proposed. The developed methodology for calculating the GDP takes into account the peculiarities of social development in Ukraine and the tendencies of world economic processes and contributes to obtaining more reliable GDP values. It will be useful for experts in financial institutions, including international ones, and scholars working in the macroeconomic modeling area