THE EFFECT OF MECHANICAL AND GEOMETRIC CHARACTERISTICS OF INHOMOGENEOUS REGIONS ON THE INTENSITY OF CRACK FORMATION DURING THE GRINDING OF PARTS MADE OF FUNCTIONALLY-GRADIENT MATERIALS

Authors

DOI:

https://doi.org/10.20998/2078-7405.2026.104.06

Keywords:

functionally graded materials, inhomogeneities, grinding, crack formation

Abstract

The lack of research on the specifics of the initiation of grinding cracks and their development into main cracks depending on the design, technological, and structural inhomogeneities of the material of the products does not allow for the unambiguous application of existing recommendations for eliminating the defects in question. This work is devoted to investigating the influence of inherent inhomogeneities in the surface layer, their geometry, and mechanical characteristics in products made of functionally graded materials on the selection of technological conditions for defect-free machining of parts. It has been established that the magnitude of the stress intensity factors for inherent inhomogeneities formed in the surface layer of products made of functionally graded materials is influenced by the size and orientation of these defects, their depth of occurrence and mutual arrangement, and the magnitude of the heat flux during grinding. The geometry and properties of inclusions formed by previous operations in the surface layer can create conditions for both the inhibition and the development of grinding cracks. If the heat flux is directed parallel to the inclusion axis and a straight, thermally isolated crack, then when the linear thermal expansion coefficient of the inclusion is greater than that of the matrix, an increase in the stiffness of the inclusion leads to an increase in the stress intensity factors K_I (K_II=0) for various ratios of the thermal conductivity coefficients of the material components. This leads to the propagation of microcracks. Conversely, if the thermal expansion coefficient of the inclusion is lower than that of the matrix, a decrease in the stiffness of the inclusion leads to a decrease in the stress intensity factors K_I (K_II=0) for the same ratios of thermal conductivity coefficients, i.e., conditions favorable for the non-propagation of microcracks are present. Therefore, when determining defect-free grinding parameters, it is necessary, first and foremost, to establish the maximum permissible cutting depths. In doing so, it is also important to have information not only on the thermophysical and mechanical properties of the material and the presence of inhomogeneities in the surface layer, but also on its processing conditions.

Author Biographies

Usov Anatoliy, National University "Odessa Polytechnic", Odesa, Ukraine

Doctor of Technical Sciences, Professor, Head of the Department of Higher Mathematics and Modeling of Systems, National University "Odessa Polytechnic", Odesa, Ukraine

Kunitsyn Maksym, National University "Odessa Polytechnic", Odesa, Ukraine

Candidate of Technical Sciences, Associate Professor of the Department of Integrated Management Technologies, Deputy Director of the Institute of Integrated Management Technologies, National University "Odessa Polytechnic", Odesa, Ukraine

Sikirash Yuliia , National University "Odessa Polytechnic", Odesa, Ukraine

Senior Lecturer at the Department of Higher Mathematics and Systems Modeling, Odesа Polytechnic National University, Odesa, Ukraine

Davydiuk Valerii, National University "Odessa Polytechnic", Odesa, Ukraine

Deputy Postgraduate student of the Department of Higher Mathematics and Systems Modeling, Odesa Polytechnic National University, Odesa, Ukraine

References

A. A. Ferreira, ‘Effects of Processing Parameters on Functionally Graded Materials for Industrial Components Repair’, MCMS, vol. 4, no. 2, Sep. 2021, doi: 10.33552/MCMS.2021.04.000585.

А. Usov, M. Kunitsyn, D. Klymenko, and V. Davydiuk, ‘Modeling the effect of stochastic defects formed in products during machining on the loss of their functional dependencies’, Pratsi OPU, vol. 1, no. 65, pp. 16–29, 2022, doi: 10.15276/opu.1.65.2022.02.

F. Wöste, J. Kimm, J. A. Bergmann, W. Theisen, and P. Wiederkehr, ‘Investigation of the effect of residual stresses in the subsurface on process forces for consecutive orthogonal cuts’, Production Engineering, vol. 15, no. 6, pp. 873–883, Dec. 2021, doi: 10.1007/S11740-021-01058-Y.

L. Jakubovičová, M. Vaško, and F. Synák, ‘Evaluation of Load-Bearing Performance and Cost Efficiency in Steel-Welded and Modular Aluminum Rack Structures’, Machines, vol. 13, no. 6, Jun. 2025, doi: 10.3390/MACHINES13060506.

A. S. Kairov, V. Y. Oshovsky, and V. A. Kairov, ‘INVESTIGATION OF THE EFFECT OF NANOCOATINGS ON THE WEAR-RESISTANCE OF SOCKET CARBIDE MILLS’, Problems of computational mechanics and structural strength (in Ukrainian), no. 35, pp. 104–114, Dec. 2022, doi: 10.15421/4222220.

V. Greshta, A. Yershov, V. Hrabovskyi, V. Vinichenko, and S. Seidametov, ‘PHYSICAL-MECHANICAL CHARACTERISTICS AND THERMAL STRESS OF PLASMA COVERING’, New Materials and Technologies in Metallurgy and Mechanical Engineering, no. 3, pp. 27–33, Oct. 2023, doi: 10.15588/1607-6885-2023-3-4.

K. Osička, Z. Fišerová, J. Otoupalík, and J. Chladil, ‘Tension of the Surface Layer in Machining Hardened Steels’, Manufacturing Technology, vol. 17, no. 1, pp. 22–23, 2017, doi: 10.21062/UJEP/X.2017/A/1213-2489/MT/17/1/72.

A. Salenko et al., ‘Forming a defective surface layer when cutting parts made from Carbon-carbon and carbon-polymeric composites’, Eastern-European Journal of Enterprise Technologies, vol. 4, no. 1–94, pp. 61–72, 2018, doi: 10.15587/1729-4061.2018.139556.

G. Sun and Z. Ding, ‘Effects of Heating Rate and Strain Rate on Phase Transformation in Micro-Grinding’, EPJ Web of Conferences, vol. 224, pp. 05003–05003, 2019, doi: 10.1051/EPJCONF/201922405003.

S. J. Eder et al., ‘Experimentally validated atomistic simulation of the effect of relevant grinding parameters on work piece topography, internal stresses, and microstructure’, Friction, vol. 10, no. 4, pp. 608–629, Apr. 2022, doi: 10.1007/S40544-021-0523-3.

A. Rajaei, B. Hallstedt, C. Broeckmann, S. Barth, D. Trauth, and T. Bergs, ‘Numerical Prediction of the Microstructure and Stress Evolution During Surface Grinding of AISI 52100 (DIN 100Cr6)’, Integr Mater Manuf Innov, vol. 7, no. 4, pp. 202–213, Dec. 2018, doi: 10.1007/s40192-018-0122-y.

E. Sauter, E. Sarikaya, M. Winter, and K. Wegener, ‘In-process detection of grinding burn using machine learning’, International Journal of Advanced Manufacturing Technology, vol. 115, no. 7–8, pp. 2281–2297, Aug. 2021, doi: 10.1007/S00170-021-06896-9.

I. Pavlenko et al., ‘Parameter identification of cutting forces in crankshaft grinding using artificial neural networks’, Materials, vol. 13, no. 23, pp. 1–12, Dec. 2020, doi: 10.3390/MA13235357.

P. Krajnik, K. Wegener, T. Bergs, and A. J. Shih, ‘Advances in modeling of fixed-abrasive processes’, CIRP Annals, vol. 73, no. 2, pp. 589–614, Jan. 2024, doi: 10.1016/J.CIRP.2024.05.001.

R. Strunk, F. Borchers, B. Clausen, and C. Heinzel, ‘Influence of subsequently applied mechanical and thermal loads on surfaces ground with mechanical main impact’, Materials, vol. 14, no. 9, May 2021, doi: 10.3390/MA14092386.

V. Stupnytskyy, E. Dragašius, S. Baskutis, and S. Xianning, ‘Modeling and simulation of machined surface layer microgeometry parameters’, Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 8, no. 1, pp. 1–11, 2022, doi: 10.23939/UJMEMS2022.01.001.

L. Urgoiti, D. Barrenetxea, J. A. Sánchez, and J. L. Lanzagorta, ‘Detailed thermo-kinematic analysis of face grinding operations with straight wheels’, Metals, vol. 10, no. 4, Apr. 2020, doi: 10.3390/MET10040524.

A. A. Dyakonov and L. V. Shipulin, ‘Geometric Model of the Interaction of the Grinding Wheel and Workpiece during Surface Grinding with the Periphery of a Straight Wheel’, Applied Mechanics and Materials, vol. 756, pp. 41–46, Apr. 2015, doi: 10.4028/WWW.SCIENTIFIC.NET/AMM.756.41.

W. Graham and A. T. Abdullahi, ‘The nature of wheel-workpiece contact in surface grinding’, International Journal of Machine Tool Design and Research, vol. 15, no. 3, pp. 153–160, 1975, doi: 10.1016/0020-7357(75)90017-7.

C. F. Tiffany and J. N. Masters, ‘APPLIED FRACTURE MECHANICS’, ASTM Special Technical Publication, vol. STP 381, pp. 249–277, 1965, doi: 10.1520/STP26592S.

G. I. Barenblatt, ‘The Mathematical Theory of Equilibrium Cracks in Brittle Fracture’, in Advances in Applied Mechanics, vol. 7, H. L. Dryden, Th. von Kármán, G. Kuerti, F. H. van den Dungen, and L. Howarth, Eds, Elsevier, 1962, pp. 55–129. doi: 10.1016/S0065-2156(08)70121-2.

B. Skjetne and A. Hansen, ‘Implications of realistic fracture criteria on crack morphology’, Frontiers in Physics, vol. 7, no. APR, 2019, doi: 10.3389/FPHY.2019.00050.

‘Fracture mechanics criteria and applications’, Choice Reviews Online, vol. 29, no. 03, pp. 29–1536, Nov. 1991, doi: 10.5860/CHOICE.29-1536.

P. Cornetti, N. Pugno, A. Carpinteri, and D. Taylor, ‘Finite fracture mechanics: A coupled stress and energy failure criterion’, Engineering Fracture Mechanics, vol. 73, no. 14, pp. 2021–2033, Sep. 2006, doi: 10.1016/J.ENGFRACMECH.2006.03.010.

M. Kunitsyn, A. Usov, and Y. Zaychyk, ‘The Influence of Cutting Forces on Cracks Formation During the Grinding of Products from Materials Prone to Defect Formation’, in Advances in Design, Simulation and Manufacturing VII, V. Ivanov, J. Trojanowska, I. Pavlenko, E. Rauch, and J. Piteľ, Eds, in Lecture Notes in Mechanical Engineering. , Cham: Springer Nature Switzerland, 2024, pp. 240–250. doi: 10.1007/978-3-031-61797-3_20.

Q. H. Qin, ‘Trefftz finite element method and its applications’, Applied Mechanics Reviews, vol. 58, no. 1–6, pp. 316–337, 2005, doi: 10.1115/1.1995716.

F. L. de Silva Bussamra, E. L. Neto, and M. A. C. Rodrigues, ‘Simulation of stress concentration problems in laminated plates by quasi-Trefftz finite element models’, Latin American Journal of Solids and Structures, vol. 13, no. 9, pp. 1677–1694, 2016, doi: 10.1590/1679-78252698.

A. Mioduchowski and Z. Płochocki, ‘Thermal stresses in a coating layer. I. General theoretical scheme’, Acta Mech, vol. 215, no. 1–4, pp. 319–333, Dec. 2010, doi: 10.1007/s00707-010-0345-2.

W. T. Ang, ‘A boundary integral equation for deformations of an elastic body with an arc crack’, Quarterly of Applied Mathematics, vol. 45, no. 1, pp. 131–139, Apr. 1987, doi: 10.1090/QAM/885175.

O. Maksymovych and A. Podhorecki, ‘Determination of Stresses in Composite Plates with Holes and Cracks Based on Singular Integral Equations’, Dynamical Systems Theory, Mar. 2020, doi: 10.5772/INTECHOPEN.87718.

P. S. Theocaris and G. A. Papadopoulos, ‘Crack-propagation trajectories under biaxial loading, based on fracture criteria’, Journal of the Franklin Institute, vol. 319, no. 4, pp. 443–456, 1985, doi: 10.1016/0016-0032(85)90013-4.

D. Leguillon, E. Martin, O. Sevecek, and R. Bermejo, ‘What is the tensile strength of a ceramic to be used in numerical models for predicting crack initiation?’, Int J Fract, vol. 212, no. 1, pp. 89–103, Jul. 2018, doi: 10.1007/s10704-018-0294-7.

H. F. Li, P. Zhang, B. Wang, and Z. F. Zhang, ‘Predictive fatigue crack growth law of high-strength steels’, Journal of Materials Science & Technology, vol. 100, pp. 46–50, Feb. 2022, doi: 10.1016/j.jmst.2021.04.042.

F. Erdogan, ‘Fracture problems in composite materials’, Engineering Fracture Mechanics, vol. 4, no. 4, pp. 811–840, 1972, doi: 10.1016/0013-7944(72)90018-5.

F. Erdogan, G. D. Gupta, and M. Ratwani, ‘Interaction between a circular inclusion and an arbitrarily oriented crack’, Journal of Applied Mechanics, Transactions ASME, vol. 41, no. 4, pp. 1007–1013, 1974, doi: 10.1115/1.3423424.

H. Shen, P. Schiavone, C. Q. Ru, and A. Mioduchowski, ‘Interfacial thermal stress analysis of an elliptic inclusion with a compliant interphase layer in plane elasticity’, International Journal of Solids and Structures, vol. 38, no. 42–43, pp. 7587–7606, Sep. 2001, doi: 10.1016/S0020-7683(01)00033-6.

J. Lee, S. Oh, and A. Mal, ‘Calculation of interfacial stresses in composites containing elliptical inclusions of various types’, European Journal of Mechanics, A/Solids, vol. 44, pp. 17–40, 2014, doi: 10.1016/J.EUROMECHSOL.2013.09.008.

B. Gao, W. Bao, T. Jin, C. Chen, M. Qu, and A. Lu, ‘Variation of wheel-work contact geometry and temperature responses: Thermal modeling of cup wheel grinding’, International Journal of Mechanical Sciences, vol. 196, Apr. 2021, doi: 10.1016/J.IJMECSCI.2021.106305.

V. N. Burlayenko, H. Altenbach, T. Sadowski, S. D. Dimitrova, and A. Bhaskar, ‘Modelling functionally graded materials in heat transfer and thermal stress analysis by means of graded finite elements’, Applied Mathematical Modelling, vol. 45, pp. 422–438, May 2017, doi: 10.1016/j.apm.2017.01.005.

K. Topczewska and P. Zamojski, ‘Effect of Pressure Fluctuations on the Temperature during Braking’, Acta Mechanica et Automatica, vol. 14, no. 2, pp. 103–107, Jun. 2020, doi: 10.2478/AMA-2020-0015.

P. Oza, K. Agarwal, and J. Tyagi, ‘Fundamental solutions: a brief review’, Differential Equations & Applications, no. 1, pp. 39–70, 2024, doi: 10.7153/DEA-2024-16-03.

X. Xu, G. Li, Y. Zhao, and T. Liu, ‘Analytical solutions for heat conduction problems with three kinds of periodic boundary conditions and their applications’, Applied Mathematics and Computation, vol. 442, Apr. 2023, doi: 10.1016/J.AMC.2022.127735.

A. A. Snarskii and I. V. Bezsudnov, ‘Rotating thermoelectric device in periodic steady state’, Energy Conversion and Management, vol. 94, pp. 103–111, 2015, doi: 10.1016/J.ENCONMAN.2015.01.058.

M. Bayram, T. Partal, and G. Orucova Buyukoz, ‘Numerical methods for simulation of stochastic differential equations’, Adv Differ Equ, vol. 2018, no. 1, p. 17, Dec. 2018, doi: 10.1186/s13662-018-1466-5.

S. C. Gupta, ‘Temperature and moving boundary in two-phase freezing due to an axisymmetric cold spot’, Quarterly of Applied Mathematics, vol. 45, no. 2, pp. 205–222, Jul. 1987, doi: 10.1090/QAM/895094.

J. J. Shu and K. K. Shastri, ‘Basic Properties of Incomplete Macdonald Function with Applications’, Journal of Function Spaces, vol. 2020, 2020, doi: 10.1155/2020/6548298.

J. L. González-Santander, ‘Analytic solution for maximum temperature during cut in and cut out in surface dry grinding’, Applied Mathematical Modelling, vol. 40, no. 3, pp. 2356–2367, Feb. 2016, doi: 10.1016/J.APM.2015.09.031.

C. Salame and A. Malakizadi, ‘An enhanced semi-analytical estimation of tool-chip interface temperature in metal cutting’, Journal of Manufacturing Processes, vol. 105, pp. 407–430, Nov. 2023, doi: 10.1016/J.JMAPRO.2023.09.015.

G. Anlas, M. H. Santare, and J. Lambros, ‘Numerical Calculation of Stress Intensity Factors in Functionally Graded Materials’, International Journal of Fracture, vol. 104, no. 2, pp. 131–143, Jul. 2000, doi: 10.1023/A:1007652711735.

A. Fesenko, F. Yevsiukova, and O. Naboka, ‘Development of a tool module for external intermittent grinding with the activation of the cutting fluid’, Mechanics and Advanced Technologies, vol. 5, no. 2, Dec. 2021, doi: 10.20535/2521-1943.2021.5.2.234543.

J. Pérez et al., ‘Heat transfer analysis of intermittent grinding processes’, International Journal of Heat and Mass Transfer, vol. 51, no. 15–16, pp. 4132–4138, Jul. 2008, doi: 10.1016/J.IJHEATMASSTRANSFER.2007.11.043.

E. Asadi, S. Fariborz, and M. Ayatollahi, ‘Analysis of multiple axisymmetric annular cracks’, Journal of Mechanics of Materials and Structures, vol. 4, no. 1, pp. 1–11, Jan. 2009, doi: 10.2140/JOMMS.2009.4.1.

J. Tweed, S. C. Das, D. P. Rooke, and D. P. Rooke, ‘The stress intensity factors of a radial crack in a finite elastic disc’, International Journal of Engineering Science, vol. 10, no. 3, pp. 323–335, 1972, doi: 10.1016/0020-7225(72)90047-X.

Downloads

Published

2026-05-15

Issue

Section

Mechanical processing of materials, the theory of cutting materials, mathematical and computer simulation of machining p