The Choice of Spacing in Measuring Displacements for the Evaluation of Strains by the Method of Optical-Digital Image Co
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THE CHOICE OF SPACING IN MEASURING DISPLACEMENTS FOR THE EVALUATION OF STRAINS BY THE METHOD OF OPTICAL-DIGITAL IMAGE CORRELATION Ya. L. Ivanyts’kyi,1 P. S. Kun’,1,2 T. М. Lenkovs’kyi,1 Yu. V. Mol’kov,1 and S. Т. Shtayura1 We analyze the influence of the size of spacing for measuring the displacements of the surface points on the corresponding macrostrains. We propose an algorithm for the determination of this size in inhomogeneous strain fields. For a specimen of 20 steel stretched by a specified force, we determine the optimal size of spacing, its relationship with the size of structural elements, and correlation with the known characteristics of the material. Keywords: spacing of measurements, microstructure of the material, displacements, macrostrains, optical-digital correlation.
To extend the service life of equipment, it is necessary to establish its actual stress-strain state with regard for the presence of defects in the material appearing after long-term operation. This is especially important if we observe the formation of the zones of elastoplastic strains in the material, which can be found by monitoring the structural elements with the help of the method of optical-digital correlation [1, 2]. For the detailed investigation of the strained state of the surfaces of structural elements in the course of their operation, it is necessary to choose the optimal size of spacing for measuring surface displacements in view of the changes in external loads, environmental conditions, and creep. The theoretical models and numerical analyses of the distributions of stress and strain fields in deformed solids are, as a rule, based on the assumption of their homogeneity. This enables one to use well-developed classical and contemporary mathematical methods with limit transitions to infinitely small or infinitely large quantities. However, in the process of deformation, the materials of actual structures may satisfy the condition of homogeneity only approximately and only on the macrolevel because they are strongly inhomogeneous on the microlevel due to their crystalline (granular) microstructure. Therefore, in finding the values of strains at points of the analyzed surfaces, it is incorrect to deal with small sizes of spacing used for measuring the displacements, comparable with the sizes of structural elements of the material. By the theoretical definition, for a homogeneous body subjected to the action of a system of external force ! factors (Fig. 1), the level of linear strains at a point A(x, y) in the direction n for the spacing b is given by the formula
b* − b . b→0 b
ε n! = lim
(1)
Under the conditions of plane deformation, at any point of the surface, the displacements and strains have their components along two coordinate axes. In this case, the theoretical Cauchy formulas, in particular, for 1 2
Karpenko Physicomechanical Institute, Ukrainian National Academy of Sciences, Lviv, Ukraine. Corresponding author; e-mail: [email protected].
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 53, No. 6,
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