Evaluation of the length scale parameters of metals based on fatigue tests data for samples with surface defects

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Abstract

A method for identifying the scale parameter of the gradient theory of elasticity is proposed based on known experimental data on the effect of the size of surface corrosion defects on the fatigue resistance parameters of steels and aluminum alloys. The possibility of a natural description of a decrease in the stress concentration coefficient near small-sized corrosion defects, which in this work are modeled as semi-ellipsoidal surface cavities, is shown. The identified values of the scale parameters are in the range of 20–230 microns.

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About the authors

Y. O. Solyaev

Institute of Applied Mechanics of the Russian Academy of Sciences; Moscow Aviation Institute (National Research University)

Author for correspondence.
Email: yos@iam.ras.ru
Russian Federation, Moscow; Moscow

S. S. Sherbakov

Belarusian State University

Email: sherbakovss@mail.ru
Belarus, Minsk

K. S. Golubkin

Moscow Aviation Institute (National Research University)

Email: golubkink@mail.ru
Russian Federation, Moscow

P. O. Polyakov

Moscow Aviation Institute (National Research University)

Email: p.o.polyakov@yandex.ru
Russian Federation, Moscow

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Supplementary files

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2. Fig. 1. A model of a semi–ellipsoidal surface defect, a - geometry of the model and an example of a finite element grid. The purple color shows the surface of the cavity, b is an example of the calculation results for the concentration of maximum principal stresses tI /t under uniaxial tension conditions.

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3. Fig. 2. Calculation examples, (a) – the change in stress concentration along the contour of a hemispheroidal cavity (a = b = 2h) for different h/l ratios, (b) – the dependence of the stress concentration coefficient on the h/l ratio for different geometry of the cavity (b/h = 2).

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4. Fig. 3. Estimation of the accuracy of the boundary conditions by the absence of rib forces (si) on the sharp edge (edge) of the surface cavity.

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5. Fig. 4. Distribution of the concentration of maximum main stresses (a) and equivalent stresses according to Mises (b) along the contour of cavities of different depths in steel X65 in the classical solution (markers without filling) and in the GTU solution with a scale parameter value of l = 0.24 mm (markers with filling). The horizontal dotted line shows the concentration level corresponding to the yield point.

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6. Fig. 5. The dependence of the stress concentration coefficient on the depth of the defect h [microns] in steel samples X20Cr13. The points are the nominal values of Kt, corresponding to experimental data. The lines are the solution of the GTU (l = 20 microns – solid, l = 5 microns – dashed, l = 50 microns – dotted). The blue color is h/a = 0.62, the yellow color is h/a = 1.24.

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7. 6. Estimation of the size of the plastic deformation zone in the classical elastic solution (a, equivalent stresses, MPa) and in the elastoplastic solution (b, plastic deformations, %) for Al 2024-T3 alloy samples with a surface cavity with dimensions a = b = 250 microns, h = 375 microns under tensile load 206 MPa.

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8. 7. Dependence of the stress concentration on the depth of the surface cavity in a sample of Al 2024-T3 alloy for different diameter to depth ratios (a/h). The points are experimental data, the lines are the solution of the GTU with a scale parameter l = 100 microns, h [microns].

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9. 8. Processing of experimental data for 7075-T6 alloy samples containing defects of various sizes (according to Table 4). (a) Dependence of stress concentration in the solution of the GTU on the scale parameter. (b) Fatigue curves. The points are experimental data (in hours) [15], the lines are an approximation based on the calculated stress concentration values in the solution of the GTU, l [microns], N is the number of cycles before failure.

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