Lengthwise Fracture Analysis of Inhomogeneous Viscoelastic Cantilever Beam Subjected to Sinusoidal Strains

Year 2024, Volume: 37 Issue: 1, 376 - 391, 01.03.2024

Victor Rizov

https://doi.org/10.35378/gujs.1062749

Abstract

This paper describes a research of lengthwise fracture in a viscoelastic inhomogeneous cantilever beam under strain that is a sinusoidal function of time. The beam mechanical behavior is investigated by a model having two linear springs and a linear dashpot. The beam material is continuously inhomogeneous along thickness. Therefore, the modules of elasticity of the springs and the coefficient of viscosity of the dashpot vary smoothly in the thickness direction. The compliance method is applied to derive the strain energy release rate (SERR) for the lengthwise crack in the beam structure. The integral J is applied for verification. The stress-strain-time dependence of the viscoelastic model is used for describing the behavior of the beam when obtaining solutions of the SERR and the J-integral. Solutions are derived for both positive and negative rotation angle of the lower crack arm end (when the angle is positive, the upper crack arm is load free, while at negative angle both crack arms are loaded). The effects of various factors including the sign of the angle of rotation on the SERR are analyzed.

Keywords

Inhomogeneous beam, Lengthwise crack, Sinusoidal strain, Analytical approach, Viscoelastic behavior

Supporting Institution

No.

Project Number

No.

Thanks

No.

References

• [1] Karacor, B., Özcanlı, M., “Examination of Fiber Reinforced Composite Materialsˮ, Gazi University Journal of Science, 36(1): 301-320, (2023).
• [2] Özdemir , A.O., Subaşı, M., Karataş, Ç., “Investigating the Effects of Forming Parameters on Molding Force and Springback in Deep Drawing Process of Thermoplastic Composite Laminatesˮ, Gazi University Journal of Science, 34(2): 506-515, (2021).
• [3] Hirai, T., Chen, L., “Recent and prospective development of functionally graded materials in Japanˮ, Mater Science Forum, 308-311(4): 509-514, (1999).
• [4] Butcher, R.J., Rousseau, C.E., Tippur, H.V., “A functionally graded particulate composite: Measurements and Failure Analysisˮ, Acta Materialia, 47(2): 259-268, (1999).
• [5] Markworth, A.J., Ramesh, K.S., Parks, Jr.W.P., “Review: modeling studies applied to functionally graded materialsˮ, Journal of Materials Science, 30(3): 2183-2193, (1995).
• [6] Nemat-Allal, M.M., Ata, M.H., Bayoumi, M.R., Khair-Eldeen, W., “Powder metallurgical fabrication and microstructural investigations of Aluminum/Steel functionally graded materialˮ, Materials Sciences and Applications, 2(5): 1708-1718, (2011).
• [7] Tımeslı, A., “Analytical Modeling of Buckling Behavior of Porous FGM Cylindrical Shell Embedded within an Elastic Foundationˮ, Gazi University Journal of Science, 35(1): 148-165, (2022).
• [8] Boğa, C., “Effect of Inhomogeneity Constant on Equivalent Stresses in Elastic Analysis of Hollow Cylinder Made from Functionally Graded Materialˮ, Gazi University Journal of Science, 33(1): 201-212, (2020).
• [9] Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A., Ford, R.G. “Functionally Graded Materials: Design, Processing and Applications”. Kluwer Academic Publishers: Dordrecht/London/Boston, (1999).
• [10] Mahamood, R.M., Akinlabi, E.T. “Functionally Graded Materials”. Springer, (2017).
• [11] Gasik, M.M., “Functionally graded materials: bulk processing techniquesˮ, International Journal of Materials and Product Technology, 39(1-2): 20-29, (2010).
• [12] Wu, X.L., Jiang, P., Chen, L., Zhang, J.F., Yuan, F.P., Zhu, Y.T., “Synergetic strengthening by gradient structureˮ, Materials Research Letters, 2(1): 185–191, (2014).
• [13] Shrikantha Rao, S., Gangadharan, K. V., “Functionally graded composite materials: an overviewˮ, Procedia Materials Science, 5(1): 1291-1299, (2014).
• [14] Tejaswini, N., Babu, R., Ram, S., “Functionally graded material: an overviewˮ, International Journal of Advance Engineering Science and Technololgy, 4: 183–188, (2013).
• [15] El-Galy, I.M., Saleh, B.I., Ahmed, M.H., “Functionally graded materials classifications and development trends from industrial point of viewˮ, SN Applied Sciences, 1: 1378-1389, (2019).
• [16] Nikbakht, S., Kamarian, S., Shakeri, M., “A review on optimization of composite structures Part II: Functionally graded materialsˮ, Composite Structures, 214: 83-102, (2019).
• [17] Zhang, Y., Ming-jie Sun, Zhang, D., “Designing functionally graded materials with superior load-bearing propertiesˮ, Acta Biomaterialia, 8: 1101-1108, (2012).
• [18] Uslu Uysal, M., Kremzer, M., “Buckling Behaviour of Short Cylindrical Functionally Gradient Polymeric Materialsˮ, Acta Physica Polonica, A127: 1355-1357, (2015).
• [19] Uslu Uysal, M., “Buckling behaviours of functionally graded polymeric thin-walled hemispherical shellsˮ, Steel and Composite Structures: An International Journal, 21(1): 849-862, (2016).
• [20] Uslu Uysal, M., Güven, U. “Buckling of Functional Graded Polymeric Sandwich Panel under Different Load Casesˮ, Composite Structures, 121: 182-196, (2015).
• [21] Uslu Uysal, M., Güven, U., “A Bonded Plate Having Orthotropic Inclusion in Adhesive Layer under In-Plane Shear Loadingˮ, The Journal of Adhesion, 92: 214-235, (2016).
• [22] Dolgov, N. A., “Effect of the elastic modulus of a coating on the serviceability of the substrate-coating system”, Strength of Materials, 37(2): 422-431, (2002).
• [23] Dolgov, N. A., “Determination of Stresses in a Two-Layer Coating”, Strength of Materials, 37(2): 422-431, (2005).
• [24] Dolgov, N. A., “Analytical Methods to Determine the Stress State in the Substrate–Coating System Under Mechanical Loads”, Strength of Materials, 48(1): 658-667, (2016).
• [25] Rizov, V.I., “Non-linear fracture in bi-directional graded shafts in torsionˮ, Multidiscipline Modeling in Materials and Structures, 15(1): 156-169, (2018).
• [26] Rizov, V.I., “Analysis of Two Lengthwise Cracks in a Viscoelastic Inhomogeneous Beam Structureˮ, Engineering Transactions, 68(4): 397–415, (2020).
• [27] Broek, D. “Elementary engineering fracture mechanics”. Springer, (1986).