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Fracture Properties of Surface Modification Layers Via a Modified Bi-Layer Beam Model

  • H. T. Liu (a1), M. H. Zhao (a1) (a2) and J. W. Zhang (a1)


A modified bi-layer beam model is proposed to study the fracture-dominated scratch process of the brittle material with surface modification layer considering residual stress. The nonlinear analytical solution of the energy release rate is derived considering the graded distribution of the elastic modulus and residual stress. Finite element analysis is also conducted. Both analytical and numerical results show that the graded distribution of the material properties and residual stress plays an important role in the fracture process. Based on the inverse analysis, the proposed model could provide a convenient way to determine the energy release rate of materials possessing a surface modification layer.


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1.Podgornika, B., Sedlaceka, M. and Cekadab, M., “Impact of Fracture Toughness on Surface Properties of PVD Coated Cold Work Tool Steel,” Surface & Coatings Technology, 277, pp. 144150 (2015).
2.Ju, H. B. et al., “The Enhancement of Fracture Toughness and Tribological Properties of the Fitanium Nitride Films by Droping Yttrium,” Surface & Coatings Technology, 321, pp. 5763 (2017).
3.Chen, L. H., Huang, K. C. and Chen, Y. C., “Acoustic Emission at Wedge Indentation Fracture in Quasi-Brittle Materials,” Journal of Mechanics, 25, pp. 213223 (2009).
4.Huang, B., Zhao, M. H. and Zhang, T. Y., “Indentation Fracture and Indentation Delamination in ZnO Film/Si Substrate Systems,” Philosophical Magazine, 84, pp. 12331256 (2004).
5.Prasad, A., Dao, M. and Suresh, S., “Steady-State Frictional Sliding Contact on Surfaces of Plastically Graded Materials,” Acta Materialia, 57, pp. 511524 (2009).
6.Zhang, F. Y., Duan, C. Z. and Wang, M. J., “Research Status of the Machined Surface Metamorphic Layer,” Machinery Design & Manufacture, 10, pp. 265268 (2014).
7.Zhu, Z. Y. and Zhang, J. L., “The Study on Mechanical Property of the Metamorphic Layer after Electron Discharge Machining for Die Steels,” Materials for Mechanical Engineering, 68, pp. 4852 (1988).
8.Ma, F. B. and Chen, S. F., “Study of Surface Modification Layer has Been Processed,” Coal Mine Machinery, 34, pp. 113114 (2013).
9.Cao, H. Y., “Analysis and Calculation of EDM Mold Surface Deterioration Layer,” Mechanical Engineer, 4, pp. 5859 (2010).
10.Lida, K. and Tosha, K., “Behavior of Surface Residual Stress Induced by Shot Peening (II),” Advances in Surface Treatments, 52, pp. 139144 (1987).
11.Gee, M. G., “Low Load Multiple Pass Scratch Testing for Ceramics and Hardmetals,” Wear, 250, pp. 264281 (2001).
12.Jiang, H., Zhang, J. W., Yang, Z. R., Jiang, C. K. and Kang, G. Z., “Modeling of Competition between Shear Yielding and Crazing in Amorphous Polymers’ Scratch,” International Journal of Solids and Structures, 124, pp. 215228 (2017).
13.Akono, A. T., Reis, P. M. and Ulm, F. J., “Scratching as a Fracture Process: From Butter to Steel,” Physical Review Letters, 106, pp. 204302 (2011).
14.Akono, A. T. and Ulm, F. J., “Scratch Test Model for the Determination of Fracture Toughness,” Engineering Fracture Mechanics, 78, pp. 334342 (2011).
15.Lin, J. S. and Zhou, Y. N., “Can Scratch Tests Give Fracture Toughness?Engineering Fracture Mechanics, 109, pp. 161168 (2013).
16.Lin, J. S. and Zhou, Y. N., “Rebuttal: Shallow Wide Groove Scratch Tests Do Not Give Fracture Toughness,” Engineering Fracture Mechanics, 133, pp. 117124 (2014).
17.Le, J. L. and Detournay, E., “Discussion on the “Fracture Mechanics Interpretation of the Scratch Test” by Akono et al.,” Engineering Fracture Mechanics, 168, pp. 4650 (2016).
18.Zhou, Y. N., “Discussion on the Interpretation of Scratch Tests with Size Effect Law,” Engineering Fracture Mechanics, 169, pp. 178183 (2017).
19.Akono, A. T. and Ulm, F. J., “An Improved Technique for Characterizing the Fracture Toughness via Scratch Test Experiments,” Wear, 313, pp. 117124 (2014).
20.Akono, A. T. and Gregory, A. B., “Rebuttal: Shallow and Deep Scratch Tests as Powerful Alternatives to Assess the Fracture Properties of Quasi-Brittle Materials,” Engineering Fracture Mechanics, 158, pp. 2338 (2016).
21.Blackman, B. R. K., Hoult, T., Patel, Y., Steininger, H. and Williams, J. G., “Steady-State Scratch Testing of Polymers,” Polymer Testing, 49, pp. 3845 (2016).
22.Suo, Z. G. and Hutchinson, J. W., “Interface Crack between Two Elastic Layers,” International Journal of Fracture, 25, pp. 13371353 (1989).
23.Zhang, T. Y. and Xie, T., “Effect of Electrostatic Tractions on the Fracture Behavior of a Dielectric Material under Mechanical and/or Electric Loading,” Science China: Technological Sciences, 55, pp. 23912403 (2012).
24.Xie, T., Fan, C. Y., Liu, H. T., Zhao, M. H. and Zhang, T. Y., “Effect of Electrostatic Trations on the Fracture Behavior of a Piezoelectric Material under Mechanical and/or Electric Loading,” Theoretical Applied Fracture Mechanics, 69, pp. 616 (2014).
25.Zhao, M. H., Liu, H. T., Fan, C. Y., Pan, E. and Zhang, T. Y., “A Nonlinear Bilayer Beam Model for an Interfacial Crack in Dielectric Bimaterials under Mechanical/Electrical Loading,” International Journal of Fracture, 188, pp. 4758 (2014).
26.Zhao, M. H., Liu, H. T., Xu, G. T. and Fan, C. Y., “Effects of Electrostatic Tractions on the Interfacial Fracture Behavior of Two-Phase Piezoelectric Materials”, Engineering Fracture Mechanics, 153, pp. 289301 (2016).
27.Goutianos, S. and Sorensen, B. F., “The Application of J Integral to Measure Cohesive Laws under Large-Scale Yielding,” Engineering Fracture Mechanics, 155, pp. 145165 (2016).
28.Luo, Q. H., Li, C. Z., Luo, Y. Z. and Zhao, Z. Y., “Grinding Process Effect on Surface Modificative Layer Microstructure, Property and Fatigue Behavior of Carburized M50NiL Steel,” Acta Metallurgica Sinica, 48, pp. 194198 (2012).
29.Yang, D., Liu, Z. Q., Ren, X. P. and Zhuang, P., “Hybrid Modeling with Finite Element and Statistical Methods for Residual Stress Prediction in Peripheral Milling of Titanium Alloy Ti-6Al-4V,” International Journal of Mechanical Science, 108, pp. 2938 (2016).
30.Jin, Z. and Batra, R. C., “Some Basic Fracture Mechanics Concept in Functionally Graded Materials,” Journal of the Mechanics and Physics of Solids, 44, pp. 12211235 (1996).
31.Simha, N. K., Fischer, F. D., Kolednik, O. and Chen, C.R., “Inhomogeneity Effects on the Crack Driving Force in Elastic and Elastic-Plastic Materials,” Journal of Mechanics and Physics of Solids, 51, pp. 334342 (2003).
32.Shang, Y. B., Shi, H. J., Wang, Z. X. and Zhang, G. D., “A Crack Tip Driving Force Model for Mode I Crack Propagation Along Linear Strength Gradient: Comparison with the Sharp Strength Gradient Case,” Acta Mechanica, 227, pp. 26832702 (2016).
33.Zhang, T. Y., Zhao, M. H. and Qian, C. F., “Effect of Substrate Deformation on the Microcantilever Beam-Bending Test,” Journal of Materials Research, 15, pp. 18681871 (2000).
34.Fan, C. Y., Zhao, M. H., Zhu, Y. J., Liu, H. T. and Zhang, T. Y., “Analysis of Micro/Nanobridge Test Based on Nonlocal Elasticity,” International Journal of Solids and Structures, 49, pp. 21682176 (2012).


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Fracture Properties of Surface Modification Layers Via a Modified Bi-Layer Beam Model

  • H. T. Liu (a1), M. H. Zhao (a1) (a2) and J. W. Zhang (a1)


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