Delamination of Two-Dimensional Functionally Graded Multilayered Non-Linear Elastic Beam - an Analytical Approach
محورهای موضوعی : Engineering
V Rizov
1
(Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, Bulgaria)
کلید واژه: Delamination, Two-dimensional functionally graded material, Multilayered structure, Material non-linearity, Analytical approach,
چکیده مقاله :
Delamination fracture of a two-dimensional functionally graded multilayered four-point bending beam that exhibits non-linear behaviour of the material is analyzed. The fracture is studied analytically in terms of the strain energy release rate. The beam under consideration has an arbitrary number of layers. Each layer has individual thickness and material properties. A delamination crack is located arbitrary between layers. The material is two-dimensional functionally graded in the cross-section of each layer. The beam mechanical behaviour is described by a power-law stress-strain relation. The fracture is analyzed also by applying the J-integral approach in order to verify the solution derived for the strain energy release rate. The effects of crack location, material gradient and non-linear behaviour of material on the delamination fracture are evaluated. It is found that the material non-linearity leads to increase of the strain energy release rate. Therefore, the material non-linearity should be taken into account in fracture mechanics based safety design of two-dimensional functionally graded multilayered structural members. It is found also that the delamination behaviour can be effectively regulated by using appropriate material gradients in the design stage of functionally graded multilayered structural members and components.
[1] Koizumi M., 1993, The concept of FGM ceramic trans, Functionally Gradient Materials 34(2): 3-10.
[2] Suresh S., Mortensen A., 1998, Fundamentals of Functionally Graded Materials, IOM Communications Ltd, London.
[3] Levashov E.A., Larikin D.V., Shtansky D.V., Rogachev A.S., Grigorian H.E., Moore J.J., 2002, Self-propagating high-temperature synthesis of functionally graded PVD targets with a ceramic working layer of TiB-TiN or TiSi-Tin, Journal of Materials Synthesis and Processing 10(2): 319.
[4] Tokova L., Yasinskyy A., Ma C. C., 2016, Effect of the layer inhomogeneity on the distribution of stresses and displacements in an elastic multilayer cylinder, Acta Mechanica 228: 2865-2877.
[5] Tokovyy Y., Ma C. C., 2013, Three-dimensional temperature and thermal stress analysis of an inhomogeneous layer, Journal of Thermal Stresses 36: 790- 808.
[6] Tokovyy Y., Ma C. C., 2016, Axisymmetric stresses in an elastic radially inhomogeneous cylinder under length-varying loadings, ASME Journal of Applied Mechanics 83: 111007-111013.
[7] Uslu Uysal M., Kremzer M., 2015, Buckling behaviour of short cylindrical functionally gradient polymeric materials, Acta Physica Polonica A 127: 1355-1357.
[8] Uslu Uysal M., 2016, Buckling behaviours of functionally graded polymeric thin-walled hemispherical shells, Steel and Composite Structures, An International Journal 21: 849-862.
[9] Szekrenyes A., 2010, Fracture analysis in the modified split-cantilever beam using the classical theories of strength of materials, Journal of Physics: Conference Series 240(4): 012030.
[10] Szekrenyes A., 2016, Semi-layerwise analysis of laminated plates with nonsingular delamination - the theorem of autocontinuity, Applied Mathematical Modelling 40(2): 1344-1371.
[11] Paulino G.C., 2002, Fracture in functionally graded materials, Engineering Fracture Mechanics 69(2): 1519-1530.
[12] Tilbrook M.T., Moon R.J., Hoffman M., 2005, Crack propagation in graded composites, Composite Science and Technology 65(2): 201-220.
[13] Carpinteri A., Pugno N., 2006, Cracks in re-entrant corners in functionally graded materials, Engineering Fracture Mechanics 73(4): 1279-1291.
[14] Upadhyay A.K., Simha K.R.Y., 2007, Equivalent homogeneous variable depth beams for cracked FGM beams; compliance approach, International Journal of Fracture 144(4): 209-213.
[15] Zhang H., Li X.F., Tang G.J., Shen Z.B., 2013, Stress intensity factors of double cantilever nanobeams via gradient elasticity theory, Engineering Fracture Mechanics 105(4): 58-64.
[16] Uslu Uysal M., Güven U., 2016, A bonded plate having orthotropic inclusion in adhesive layer under in-plane shear loading, The Journal of Adhesion 92(2): 214-235.
[17] Dahan I., Admon U., Sarei J., Yahav B., Amar M., Frage N., Dariel M. P., 1999, Functionally graded Ti-TiC multilayers: the effect of a graded profile on adhesion to substrate, Materials Science Forum 308-311(3): 923-929.
[18] Bora Y., Suphi Y., Suat K., 2008, Material coatings under thermal loading, Journal of Applied Mechanics 75(4): 051106.
[19] Sung Ryul Ch., Hutchinson J.W., Evans A.G., 1999, Delamination of multilayer thermal barrier coatings, Mechanics of Materials 31(3): 431-447.
[20] Szekrenyes A., 2016, Nonsingular crack modelling in orthotropic plates by four equivalent single layers, European Journal of Mechanics – A/Solids 55: 73-99.
[21] Petrov V.V., 2014, Non-Linear Incremental Structural Mechanics, Infra-Injeneria.
[22] Lubliner J., 2006, Plasticity Theory, University of California, Berkeley.
[23] Dowling N., 2007, Mechanical Behavior of Materials, Pearson.
[24] Hutchinson W., Suo Z., 1992, Mixed mode cracking in layered materials, Advances in Applied Mechanics 64(3): 804-810.
[25] Broek D., 1986, Elementary Engineering Fracture Mechanics, Springer.
