Utilization of viscoelatic models with non-linear springs and dashpots in delamination study of multilayered beams

Utilization of viscoelatic models with non-linear springs and dashpots in delamination study of multilayered beams

Автор: Rizov V.I.

Журнал: Вестник Пермского национального исследовательского политехнического университета. Механика @vestnik-pnrpu-mechanics

Статья в выпуске: 1, 2022 года.

Бесплатный доступ

This paper analyzes delamination of multilayered inhomogeneous beam structure by utilization a non-linear viscoelastic mechanical model. The non-linear time-dependent response is treated by a non-linear spring and a non-linear dashpot connected in series to a system of two linear springs and two linear dashpots. The model is under stress that is a linear function of time. The constitutive law of the model representing a non-linear dependence between stress, strain and time is derived. The main goal of the paper is to obtain a solution of the strain energy release rate for the delamination in the multilayered inhomogeneous beam by applying the non-linear viscoelastic model. Solutions are derived by using the complementary strain energy and by analyzing the balance of the energy with taking into account the non-linear viscoelastic behaviour. For this purpose, the constitutive law of the non-linear viscoelastic mechanical model is used. The solutions are applied to obtain results for multilayered beams with non-linear variation of material properties in longitudinal direction. The influence of different parameters on the time-dependent strain energy release rate is assessed. The study indicates the effectiveness of the viscoelastic mechanical models with non-linear springs and dashpots in time-dependent delamination analyses of multilayered inhomogeneous beam structures.

Еще

Inhomogeneous material, multilayered beam, non-linear springs and dashpots, delamination, non-linear viscoelastic behavio

Короткий адрес: https://sciup.org/146282438

IDR: 146282438

Список литературы Utilization of viscoelatic models with non-linear springs and dashpots in delamination study of multilayered beams

  • Li X.F., Peng X.L., Kang Y.A. Pressurized hollow spherical vessels with arbitrary radial nonhomogeneity. AIAA J., 2009, vol. 47, pp. 2262-2266.
  • Tanigawa Y. Some basic thermoelastic problems for nonhomogeneous structural materials. Appl. Mech. Rev., 1995, vol. 48, pp. 287-300.
  • Dai H.-L., Luo W.-F., Dai T. Multi-Field Coupling Static Bending of a Finite Length Inhomogeneous Double-Layered Structure With Inner Hollow Cylinder and Oute Shell. Appl. Math. Modell., 2016, vol. 40, pp. 6006-6025.
  • Suresh S. Graded materials for resistance to contact deformation and damage. Science, 2001, vol. 292, pp. 2447-2451.
  • Babushkin A.V., Sokolkin Y.V., Chekalkin A.A. Fatigue Resistance of Structurally Inhomogeneous Powdered Materials in a Complex Stress-Strain State. Mech Compos Mater, 2014, vol. 50, pp. 1-8.
  • Paimushin V.N., Ivanov V.A., Lukankin S.A. et al. Shear and Flexural Buckling Modes of a Spherical Sandwich Shell in a Centrosymmetric Temperature Field Inhomogeneous across the Thickness. Mechanics of Composite Materials, 2004, vol. 40, pp. 309-330.
  • Bochkareva S.A., Grishaeva N.Y., Lyukshin B.A. et al. A Unified Approach to Determining the Effective Physicomechanical Characteristics of Filled Polymer Composites Based on Variational Principles. Mech Compos Mater, 2019, vol. 54, pp. 775-788.
  • Sheshenin S.V., Yikun D. Homogenization of Rubber-Cord Layers at Moderately Large Deformations. Mech Compos Mater, 2021, vol. 57, pp. 275-286.
  • Malakhov A.V., Polilov A.N., Li D. Increasing the Bearing Capacity of Composite Plates in the Zone of Bolted Joints by Using Curvilinear Trajectories and a Variable Fiber Volume Fraction. Mech Compos Mater, 2021, vol. 57, pp. 287-300.
  • Zarubin V.S., Savelyeva I.Y., Sergeeva E.S. Estimates for the Thermoelastic Properties of a Composite with Ellipsoidal Anisotropic Inclusions. Mech Compos Mater, 2019, vol. 55, pp. 513-524.
  • Bakulin V.N., Boitsova D.A., Nedbai, A.Y. Parametric Resonance of a Three-Layered Cylindrical Composite Rib-Stiffened Shell. Mech Compos Mater, 2021, vol. 57, pp. 623-634.
  • Fedotov A.F. Hybrid Model for Homogenization of the Elastoplastic Properties of Isotropic Matrix Composites. Mech Compos Mater, 2017, vol. 53, pp. 361-372.
  • Zhang X., Hasebe N. Elasticity Solution for a Radially Nonhomogeneous Hollow Circular Cylinder. ASME J. Appl. Mech, 1999, vol. 66, pp. 598-606.
  • Ter-Mkrtich'ian L.N. Some Problems in the Theory of Elasticity of Nonhomogeneous Elastic Media. J. Appl. Math. Mech, 1961, vol. 25, pp. 1667-1675.
  • Plevako V.P. On the Theory of Elasticity of Inho-mogeneous Media. Journal of Applied Mathematics and Mechanics, 1971, vol. 35, pp. 806-813.
  • Groves J., Wadley H. Fabrication of Functionally graded materials synthesis via low vacuum directed vapor deposition. Composites Part B: Engineering, 1997, vol. 28, pp. 57-69.
  • Mortensen A,. Suresh S. Functionally graded metals and metal-ceramic composites: Part 1 Processing. International Materials Reviews, 1995, vol. 40, pp. 239-265.
  • Robert C., Wetherhold Steven Seelman, Jianzhong Wang. The use of functionally graded materials to eliminate or control thermal deformation. Composites Science and Technology, 1996, vol. 56, pp. 1099-1104.
  • Lee W. Y., Stinton D.P., Berndt C.C., Erdogan F., Yi-Der Lee, Mutasim Z. Concept of Functionally Graded Materials for Advanced Thermal Barrier Coating Applications. Journal of the American Ceramic Society, 1996, vol. 79, pp. 3003-3012.
  • Pei Y.T., De Hosson J.Th.M Functionally graded materials produced by laser cladding. Acta Materialia, 2000, vol. 48, pp. 2617-2624.
  • Aizikovich S.M., Vasil'ev A.S., Krenev L.I. et al. Contact problems for functionally graded materials of complicated structure. Mech Compos Mater, 2011, vol. 47, pp. 539-548.
  • Bochkarev S.A., Lekomtsev S.V. Stability of Functionally Graded Circular Cylindrical Shells under Combined Loading. Mech Compos Mater, 2019, vol. 55, pp. 349-362.
  • Bochkarev S.A., Lekomtsev S.V., Matveenko V.P. Hydro-thermoelastic Stability of Functionally Graded Circular Cylindrical Shells Containing a Fluid. Mech Compos Mater, 2016, vol. 52, pp. 507-520.
  • Kieback B., Neubrand A., Riedel H. Processing techniques for functionally graded materials. Materials Science and Engineering: A, 2003, vol. 362 pp. 81-106.
  • Chen Y., Lin X. Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials. Computational Materials Science, 2008, vol. 44, pp. 581-581.
  • Dias C.M.R., Savastano Jr.H., John V.M. Exploring the potential of functionally graded materials concept for the development of fiber cement. Construction and Building Materials, 2010, vol. 24, pp. 140-146.
  • Gandra J., Miranda R., Vila^a P., Velhinho A., Teixeira J.P. Functionally graded materials produced by friction stir processing. Journal of Materials Processing Technology, 2011, vol. 211, pp. 1659-1668.
  • Zhang Y., Ming-jie Sun, Zhang D. Designing functionally graded materials with superior load-bearing properties. Acta Biomaterialia 2012, vol. 8, pp. 1101-1108.
  • Tejaswini N., Babu R., Ram S. Functionally graded material: an overview. Int J Adv Eng Sci Technol 2013, vol. 4, pp. 183-188.
  • Sola A., Bellucci D., Cannillo V. Functionally graded materials for orthopedic applications - an update on design and manufacturing. Biotechnology Advances, 2016, vol. 34, pp. 504-531.
  • Minoo Naebe, Kamyar Shirvanimoghaddam. Functionally graded materials: A review of fabrication and properties. Applied materials today, 2016, vol. 5, pp. 223-245.
  • Toudehdehghan J., Lim W., Foo1 K.E., Ma'arof M.I.N., Mathews J. A brief review of functionally graded materials. MATEC Web of Conferences, 2017, vol. 131, 03010.
  • Nikbakht S., Kamarian S., Shakeri M. A review on optimization of composite structures Part II: Functionally graded materials. Composite Structures, 2019, vol. 214, pp. 83-102.
  • El-Galy I.M., Saleh B.I., Ahmed M.H. Functionally graded materials classifications and development trends from industrial point of view. SN Appl. Sci., 2019, vol. 1, pp. 1378-1389.
  • Rzhanitsyn A.R. Built-up Bars and Plates. Moscow, Stroyiizdat, 1986.
  • Drory M., Thouless M., Evans A. On the decohesion of residually stressed thin films. Acta Metall, 1988, vol. 36, pp. 2019-2028.
  • Townsend P., Barnet D., Brunner T. Elastic relationships in layered composite media with approximation for the case of thin films on a thick substrate. J Appl Phys, 1987, vol. 62, pp. 4438-4446.
  • Freund L.B. The stress distribution and curvature of a general compositionally graded semiconductor layer. J. Cryst. Growth, 1995, vol. 132, pp. 341-344.
  • Finot M., Suresh S. Small and large deformation of thick and thin-film multilayers: effect of layer geometry and compositonal gradients. J Mech Phys Solids, 1996, vol. 44, pp. 683-721.
  • Kim J.S., Paik K.W., Oh S.H. The Multilayer-Modified Stoney's Formula for Laminated Polymer Composites on a Silicon Substrate. J. Appl. Phys., 1999, vol. 86, pp. 5474-5479.
  • Yu J.-H, Guo S., Gillard, D.A. Bimaterial curvature measurements for CTE of adhesives: optimization and modelling. Journal of Adhesion Science and Technology, 2003, vol. 17, pp. 149-164.
  • Markov I., Dinev D., Theoretical and experimental investigation of a beam strengthened by bonded composite strip. Reports of International Scientific Conference VSU'2005, 2005, pp. 123-131.
  • Ivanov Ya., Stoyanov V. High Technologies and New Construction Materials in Civil Engineering. In: Education, Science, Innovations (Proc. 1st Int. Conf. of the European Polytechnical University, June 9-10, 2011, Pernik), 2011, pp. 161-169.
  • Tahar H.D., Abderezak R., Rabia B. Flexural performance of wooden beams strengthened by composite plate. Structural Monitoring and Maintenance: An International Journal, 2020, vol. 7, pp. 233-259.
  • Dolgov N.A. Determination of Stresses in a Two-Layer Coating. Strength of Materials, 2005, vol. 37, pp. 422-431.
  • Dolgov N.A. Analytical Methods to Determine the Stress State in the Substrate-Coating System Under Mechanical Loads. Strength of Materials, 2016, vol. 48, pp. 658-667.
  • Yang W., Shih C.F. Fracture along an interlayer. Int. J. Solids Structures, 1994, vol. 31, pp. 985-1002.
  • Dowling N.E. Mechanical behaviour of materials. Person, 2013.
  • Rizov V.I. Analysis of Two Lengthwise Cracks in a Viscoelastic Inhomogeneous Beam Structure. Engineering Transactions, 2020, vol. 68, pp. 397-415.
  • Rizov V.I. Delamination analysis of multilayered beams exhibiting creep under torsion. Coupled Systems Mechanics, 2021, vol. 10, pp. 317-331.
  • Lukash P. Fundamentals of non-linear structural mechanics. Moscow, Stroiizdat, 1978.
Еще
Статья научная
QR-код для установки приложения SciUp Наведите камеру и скачайте бесплатное приложение SciUp