The product and free product of fuzzy subgroups

Authors

  • Bassma Auhida Ali Abdulsamad Faculty of Education, Sirte University, Sirte, Libya. Corresponding

DOI:

https://doi.org/10.37375/foej.v3i2.2866

Keywords:

Fracture surface roughness, microhardness, surface waviness, Optical properties, Tin alloy

Abstract

Because of their expanding importance in evaluating surface properties, optical non-destructive technologies for 3D surface metrology have gained importance in research and engineering in recent years. In this study, optical 3D Infinite Focus measurement (IFM) system based on the technology of focus-variation was used for qualitative and quantitative evaluation of alloy Tin (Sn). The capabilities of the system on a series of applications ranging from surface roughness, waviness, bearing ratio, determining of depth and diameter of Sn-0.7Cu solder was demonstrated. Samples used in this study were subject zato micro-hardness tests conduct on a soft material (alloyed Sn) using micro hardness indeed. Sample differences in surface morphology were caused by variations in the load and application that the samples were subjected to during the indentation test. Plotting the soft material's surface roughness, waviness, and bearing ratio required the use of indentation testing under load, as determined by the micro hardness tool (Sn-0.7Cu). Results from two measurements were used to determine the diameter, depth, surface roughness, waviness and bearing ratio of the alloyed Sn (Sn-0.7Cu) using waviness, roughness and bearing ratio analysis. In order to construct their 3D profile and analyze their surface roughness and waviness of the dented soft material, samples were further examined based on their surface parameter. Results also showed that the unreformed materials processed elastic properties when subjected to some amount of force under the influence of load.

References

- Molodets, A.M. & Nabatov, S.S. (2000) Thermodynamic potentials, diagram of state, and phase transitions of Tin on shock compression. High Temperature, 38, 715–721

Kubinova, L., Janacek, J., Guilak, F. & Opatrny, Z. (1999) Comparison of several digital and stereological methods for estimating surface area and volume of cells studied by confocal microscopy. Cytometry, 36, 85–95. DOI: 10.1002/(sici)1097-0320(19990601)

- Russ, J.C. (1990). Computer Microscopy: The Measurement and Analysis of Images. Plenum Press: New York, USA.

- Pawley (1995). Handbook of Biological Confocal Microscopy, 2nd end. Plenum Press: New York, USA.

- Rigaut, J.P., Carvajal-Gonzales, S. & Vassy, J. (1992) 3-D image Cytometry. In: Kriete, A(Ed) Visualization in Biomedical Microscopies, VCH, Wenham New York.

- Singh, R., Melkote, S.N. & Hashimoto, F. (2005) Frictional response of precision finished surface in pure sliding. Wear, 258, 1500–1509.

- Barrekette, E.S. & Christensen, R.L. (2002) on plane blazed gratings. IBM Journal of Research and Development, 9, 108–117.

- Bello, D.O. & Walton, S. (1987) Surface topography and lubrication in sheet metal forming. Tribology International, 20, 59–65.

- El-Daly, A.A., Fawzy, A., Mohamed, A.Z. & Ei-El-Taher, A.M. (2011) Microstructural evolution and tensile properties of Sn-5Sb solder alloy containing small amount of Ag and Cu. Journal of Alloys and Compounds, 509, 4574–4582.

- Ţǎlu, Ş. (2015) Micro and nanoscale characterization of three-dimensional surfaces: Basics and applications. Napoca Star.

- Ţălu, Ş., Bramowicz, M., Kulesza, S., Dalouji, V., Solaymani, S. & Valedbagi, S. (2016) Fractal features of carbon-nickel composite thin films. Microscopy Research and Technique, 79, 1208–1213.

- Kaspar, P., Sobola, D., Dallaev, R., Ramazanov, S., Nebojsa, A., Rezaee, S. & Grmela, L. (2019) Characterization of Fe2O3 thin film on highly oriented pyrolytic graphite by AFM, Ellipsometry and XPS. Applied Surface Science, 493, 673–678.

- Knápek, A., Sýkora, J., Chlumská, J. & Sobola, D. (2017) Programmable set-up for electrochemical preparation of STM tips and ultra-sharp field emission cathodes. Microelectronic Engineering, 173, 42–47.

- Stach, S., Sapota, W., Ţălu, Ş., Ahmadpourian, A., Luna, C., Ghobadi, N., Arman, A. & Ganji, M. (2017) 3-D surface stereometry studies of sputtered TiN thin films obtained at different substrate temperatures. Journal of Materials Science: Materials in Electronics, 28, 2113–2122.

- Arman, A., Ţălu, Ş., Luna, C., Ahmadpourian, A., Naseri, M. & Molamohammadi, M. (2015) Micromorphology characterization of copper thin films by AFM and fractal analysis. Journal of Materials Science: Materials in Electronics, 26, 9630–9639.

- Ţălu, Ş., Bramowicz, M., Kulesza, S., Dalouji, V., Solaymani, S. & Valedbagi, S. (2016) Fractal features of carbon-nickel composite thin films. Microscopy Research and Technique, 79, 1208–1213.

- Yadav, R.P., Kumar, M., Mittal, A.K. & Pandey, A.C. (2015) Fractal and multifractal characteristics of swift heavy ion induced self-affine nanostructured BaF2 thin film surfaces. Chaos, 25, 083115.

- Shikhgasan, R., Stefan, Ţ., Dinar, S., Sebastian, S. & Guseyn, R. (2015) Epitaxy of silicon carbide on silicon: Micromorphological analysis of growth surface evolution. Superlattices and Microstructures, 86, 395–402.

- Weibel, E.R. (1979) Stereological methods, Vol. I. Practical Methods for Biological Morphometry. Academic Press: London.

- Serra, J. (1982). Image Analysis and Mathematical Morphology. Academic Press: London.

- Meyer, F. (1992) Mathematical morphology; from two dimensions to three dimensions. Journal of Microscopy, 165, 5–28.

- Chen, C.Y., Chang, M.C., Ke, M.D., Lin, C.C. & Chen, Y.M. (2008) A novel high brightness parallax barrier stereoscopy technology using a reflective crown grating. Microwave and Optical Technology Letters, 50, 1610–1616.

- Campos, I., Rosas, R., Figueroa, U., VillaVelázquez, C., Meneses, A. & Guevara, A. (2008) Fracture toughness evaluation using Palmqvist crack models on AISI 1045 boride steels. Materials Science and Engineering, 488, 562–568.

- Chen, J. & Bull, S.J. (2007) Indentation fracture and toughness assessment for thin optical coatings on glass. Journal of Physics D, 40, 5401–5417.

Published

2024-07-02

How to Cite

Bassma Auhida Ali Abdulsamad. (2024). The product and free product of fuzzy subgroups. Faculty of Education Scientific Journal, 3(2), 392–381. https://doi.org/10.37375/foej.v3i2.2866