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Finite elements analysis of the side grooved I-beam specimen for mode II fatigue crack growth rates determination

Lenkovskiy T. M., Kulyk V. V., Duriagina Z. A., Dzyubyk L. V., Vira V. V., Dzyubyk A. R., Tepla T. L.

Journal of Achievements in Materials and Manufacturing Engineering

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2018

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Vol. 86, nr 2

70--77

EN

Purpose: Carefully investigate the stress-strain state of the side grooved I-beam specimen with edge crack and determine the effect of crack length and crack faces friction on stress intensity factor at transverse shear. Design/methodology/approach: The finite element method was used to estimate the stress-strain state of I-beam specimen at transverse shear. For this purpose, a fullscale, three-dimensional model of the specimen was created, which precisely reproduces its geometry and fatigue crack faces contact. For the correct reproduction of the stress singularity at the crack tip, a special sub-model was used, which has been tested earlier in solving similar problems of fracture mechanics. In order to improve the accuracy of the calculations, for crack plane and cross-section of the specimen on the crack extension modeling, an algorithm for changing the crack length without changing the total number of elements in the model was developed and applied. Young's modulus and Poisson's ratio of structural steels were specified for the model material. The static loading of the model was realized assuming small scale yielding condition. The stress intensity factor was found through the displacement of nodes in the prismatic elements adjacent to the plane and the front of the crack. Findings: Mathematical dependences, which show an increase of stress intensity factor in the I-beam specimen with an increase in the crack length, and its decrease with an increase of crack faces friction factor at transverse shear, were established. The results are compared with the partial cases known from the literature and their good convergence was shown. Research limitations/implications: By analyzing the obtained graphical dependences, it is established that for relative crack lengths less than 0.4 there is a significant influence of the initial notch on the stress-strain state of the specimen, and for the lengths greater than 0.9 an influence of constrained gripping part took place. For this reason, all subsequent calculations were carried out in the range of relative crack length from 0.4 to 0.9, which represents the applicability range of the final calculation formula. Increasing of the crack faces friction factor from 0 to 1 monotonically reduces the stress at the crack tip. For a short crack, this effect is 1.5 times greater than for a long one, which is reflected by the calculation formula. Practical implications: Using the proposed calculation formula, one can calculate the stress intensity factor in the I-beam specimen, and to determine the crack growth resistance characteristics of structural steels at transverse shear. Originality/value: A new, easy-to-use in engineering calculations formula is proposed for stress intensity factor determination in the I-beam specimen at transverse shear. The formula takes into account crack faces friction for various crack lengths.

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Relationships between the fatigue crack growth resistance characteristics of a steel and the tread surface damage of railway wheel

Ostash O. P., Kulyk V. V., Lenkovskiy T. M., Duriagina Z. A., Vira V. V., Tepla T. L.

Archives of Materials Science and Engineering

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2018

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Vol. 90, nr 2

49--55

EN

Purpose: The aim of the proposed research is to establish experimentally the relation between damaging of the tread surface of model wheels and the characteristics of fatigue crack growth resistance of wheel steels AKh th AKh th AKh fc AKh fc), depending on its microstructure. Design/methodology/approach: Characteristics of the fatigue crack growth resistance have been determined on the specimens cut out from the hot rolled plate of thickness 10 mm of the steel which is an analogue of railway wheel steels. To obtain different steel microstructures and its strength level, test specimens were quenched (820°C, in oil) and then tempered at 400°C, 500°C, and 600°C for 2 h. The characteristics of Mode I fatigue crack growth resistance of steel were determined on the basis of fatigue macrocrack growth rate diagrams da/dN-AK, obtained by the standard method on compact specimens with the thickness of 10 mm at a frequency of 10-15 Hz and the stress ratio R = 0.1 of the loading cycle. The characteristics of Mode II fatigue crack growth resistance were determined on the basis of da/dN-AKH diagrams, obtained by authors method on edge notched specimens with the thickness 3.2 mm at a frequency of 10-15 Hz and R = –1 taking account of the crack face friction. The hardness was measured with a TK-2 hardness meter. Zeiss-EVO40XVP scanning electron microscope was used for microstructural investigations. Rolling contact fatigue testing was carried out on the model specimens of a wheel of thickness 8 mm and diameter 40 mm in contact with a rail of length 220 mm, width 8 mm and height 16 mm. Wheels were manufactured form the above-described steel after different treatment modes. Rails were cut out from a head the full-scale rail of hardness 46 HRC. The damaging was assessed by a ratio of the area with gaps formed by pitting and spalling to the general area of the wheel tread surface using a special stand. Findings: The growth of the damage of the tread surface of the model wheels correlates uniquely with the decrease of the cyclic fracture toughness of the wheel steel AKh fc and AKh fc, determined at Mode I and Mode II fracture mechanisms. These characteristics of the wheel steel can be considered as the determining parameter of this process, in contrast to the fatigue thresholds AKh th and AKh th. Research limitations/implications: Investigations were conducted on model wheels that simulate the damage of real railway wheels tread surface. Practical implications: A relationship between the damage of tread surface of railway wheels and the strength level of wheel steels is determined. Originality/value: The damage of the tread surface of the model wheels during the rolling contact fatigue of the pair wheel-rail increases with the growth of the strength (hardness) of the wheel steel, which corresponds to the statistical data of the operation of the real railway wheels. Research limitations/implications: Investigations were; conducted on model wheels that simulate the damage of real railway wheels tread surface. Practical implications: A relationship between the damage of tread surface of railway wheels and the strength level of wheel steels is determined. Originality/value: The damage of the tread surface of the model wheels during the rolling) contact fatigue; of the pair wheel-rail increases with the growth of the strength (hardness) of the wheel steel, which corresponds to the statistical data of the operation of the real railway wheels.

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Mode I and mode II fatigue crack growth resistance characteristics of high tempered 65G steel

Lenkovskiy T. M., Kulyk V. V., Duriagina Z. A., Kovalchuk R. A., Topilnytskyy V. H., Vira V. V., Tepla T. L.

Archives of Materials Science and Engineering

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2017

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Vol. 84, nr 1

34--41

EN

Purpose: To investigate the fatigue crack growth at normal tension and transverse shear of 65G steel with the high tempered martensite microstructure and to build an appropriate fatigue crack growth rate curves. To determine the main and auxiliary fatigue crack growth resistance characteristics, which are necessary for machine parts life-time estimation at rolling contact fatigue conditions. Design/methodology/approach: For determination of fatigue crack growth resistance at normal tension a standard compact specimens with edge crack were tested using a hydraulic testing machine and fatigue testing at transverse shear were performed on the I-beam specimens with the edge longitudinal crack using the original testing setup. For crack growth measurement an optical cathetometer B-630 was used. The crack growth rate V was calculated as crack length increment during loading cycles. The stress intensity factor range K was determined by dependence "K = (1 – R)Kmax accordingly to the standard test methods. To establish crack faces friction factor at transverse shear fragments of fractured beam specimen containing crack faces were cut out and tested as a friction pair according to Amontons Coulomb's law. On the base of test results the fatigue crack growth rate curves in logarithmic coordinates "K vs. V were built. These graphical dependencies for normal tension and transverse shear were used for determination of fatigue crack growth resistance characteristics: fatigue threshold "Kth, fracture toughness "Kfc, "K1-2 and "K2-3 which indicates the beginning and the end of middle-amplitude region of curve, "K*, parameters C and n of Paris’s equation. Metallographic and fractographic analyses were performed on the scanning electronic microscope Zeiss EVO 40XVP. Findings: Empirical dependences of the stress intensity factor range on fatigue crack growth rate at normal tension and transverse shear of 65G steel with the high tempered martensite microstructure are obtained. Based on these graphical dependencies the fatigue thresholds and fracture toughness as well as the parameters of Paris’s equation are determined. Research limitations/implications: The fatigue crack growth on 65G steel under low-, medium- and high-amplitude cyclic loading at normal tension and transverse shear was investigated. The fatigue crack growth rate values for a wide range of stress intensity factor are estimated. On the base of fractographical analysis the features of fracture of high tempered martensite in 65G steel at transverse shear are studied. It is shown that the transverse shear crack faces friction factor for high tempered martensite structure is less than for low tempered martensite. Practical implications: Using the fatigue crack growth resistance characteristics of 65G steel at normal tension and transverse shear and related fatigue crack growth rate curves it is possible to predict the life-time of machine parts made of steels with high tempered martensite structure, working at rolling contact fatigue conditions. Originality/value: Complete fatigue crack growth rate curves of 65G steel with tempered martensite structure at normal tension and transverse shear are built and the fatigue crack growth resistance characteristics for both modes of fracture are determined for the first time.

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An effective crack tip region finite element sub-model for fracture mechanics analysis

Lenkovskiy T. M., Kulyk V. V., Duriagina Z. A., Kovalchuk R. A., Topilnytskyy V. G, Vira V. V., Tepla T. L., Bilash O. V., Lishchynska K. I.

Archives of Materials Science and Engineering

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2017

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Vol. 87, nr 2

56--65

EN

Purpose: To create an effective in engineering strength calculation three-dimensional submodel of the near crack tip region in solids for hi-fidelity analysis of their stress-strain state by the finite element method. Design/methodology/approach: To create a volume near the crack tip, regular threedimensional 20-node prismatic isoparametric elements and 15-node special elements with edge length of 12.5 μm with shifted nodes in order to simulate the singularity of stress at the crack tip were used. Using these two types of elements, a cylindrical fragment of diameter of 100 μm was built. In its base is a 16-vertex polygon, and its axis is the crack front line. In the radial direction the size of the elements was smoothly enlarged by creating of 5 circular layers of elements, and in the axial direction 8 layers were created. For convenience of the sub-model usage, the cylindrical fragment was completed by regular elements to a cubic form with edge size 400 μm. For the sub-model approbation, the full-scale three-dimensional models of standard specimens with cracks were built. The stress intensity factor K at normal tension was calculated assuming small scale yielding conditions in a plane between 4th and 5th layers of special elements on the basis of analysis of displacement fields near the crack tip. Findings: An effective three-dimensional sub-model of the near crack tip region is proposed. The sub-model was used to obtain the dependence of the stress intensity factor on the relative crack length at normal tension for four types of standard specimens. The obtained dependences show excellent correlation with known analytical solutions. Research limitations/implications: The concept of finite element meshing at threedimensional modelling of the near crack tip region for high-fidelity stress-strain state analysis was generalized. A sub-model of the near crack tip region was created and used to determine the stress intensity factor at normal tension of four types of standard specimens. It is shown that the proposed methodology is effective for precise analysis of the stressstrain state of solids with cracks within the framework of linear fracture mechanics. Practical implications: By applying the generalized approach and the proposed threedimensional sub-model of the near crack tip region, one can determine the stress-strain state of structure elements and machine parts when analysing their workability by the finite element method. Originality/value: An effective finite-element sub-model for the stress-strain state analysis in the vicinity of the crack tip within the framework of the linear fracture mechanics is proposed.

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Influence of 65G steel microstructure on crack faces friction factor under mode II fatigue fracture

Ivanytskyj Y. L., Lenkovskiy T. M., Molkov Y. V., Kulyk V. V., Duriagina Z. A.

Archives of Materials Science and Engineering

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2016

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Vol. 82, nr 2

49--56

EN

Purpose: The aim of the paper is to evaluate the dependence of microstructure parameters, strength and plasticity of steel on crack faces friction factor. Design/methodology/approach: The specimens for the investigation were cut out from the 10 mm thick hot-rolled plate of 65G steel used as a model material for fatigue and durability testing of whole-rolled railway wheels. The mechanical characteristics of the steel were determined according to the state standard using cylindrical specimens of diameter 5 mm and effective length 50 mm. The specimens were heat-treated at the mentioned conditions. Fatigue testing under mode II loading was carried out on a special rigid loading machine in the standard laboratory conditions at symmetric sinusoidal cycle with a frequency of 12 Hz in the range of fatigue crack growth rates da/dN = 5∙10⁻⁸…5∙10⁻⁷ m/cycle until its reaches relative length l/b ≥ 0.8. The obtained microsections were investigated using the optical metallographic microscope Neophot 9 equipped with a digital camera Nikon D50 and electronic scanning microscope Zeiss EVO 40XVP. Hardness of the specimens with different microstructure was determined using durometer TK-2. The crack faces friction factor was determined using original device for fractured surfaces sliding under certain compression force realization. Findings: The dependences of microstructure parameters, strength and plasticity of steel on crack faces friction factor are obtained. Research limitations/implications: The investigation of the influence of microstructure parameters, strength and plasticity of real wheel steels on crack faces friction factor at the mode II fatigue crack growth will be carried out. Practical implications: The value of crack faces friction factor have strong impact on stress intensity at the crack tip and must be taken into account at crack growth rates curves plotting. Originality/value: Mode II fatigue crack faces friction factor of steel is firstly experimentally determined.