DYNAMIC BIAXIAL STRESS ANALYSIS OF FLAT LAYERED CERAMIC COMPOSITES
Keywords:
layered ceramic composites, Kirchhoff theory of plates, biaxial stress, principal stresses
Abstract
We study theoretically the biaxial bending of symmetric, flat layered ceramic composites (laminates) due to external loading. We focus on three-layered alumina/zirconia laminates. We compare the principal stresses in the samples in the case of static and harmonic dynamic loading. The dynamic equation within the Kirchhoff theory for thin homogeneous plates is first generalized to the case of multilayered plates. It is solved numerically with the relaxation method, which we have developed for this purpose.
References
1 F. F. Lange, Transformation Toughening: Parts 1–5, Journal of Material Science 17 (1982) 5–6, 225–262
2 M. Rühle, N. Claussen, A. H. Heuer, Transformation and Microcrack Toughening as Complementary Processes in ZrO2-Toughened Al2O3, Journal of the American Ceramic Society, 69 (1986) 3, 195–197
3 H. E. Lutz, N. Claussen, Duplex ceramics, Parts 1–2, Journal of the European Ceramic Society, 7 (1991) 209–226
4 S. Deville, J. Chevalie, G. Fantozzi, J. F. Bartolome, J. Requena, J. S. Moya et al., Development of advanced zirconia-toughened alumina nanocomposites for orthopaedic applications, Key Engineering Materials, 264–268 (2004) 2012–2016
5 N. Mandal, B. Doloi, B. Mondal, R. Das, Optimization of flank wear using Zirconia Toughened Alumina (ZTA) cutting tool: Taguchi method and Regression analysis, Measurement, 44 (2011) 2149–2155
6 F. Sommer, R. Landfried, F. Kern, R. Gadov, Mechanical properties of zirconia toughened alumina with 10–24 vol. % 1Y–TZP reinforcement, Journal of the European Ceramic Society, 32 (2012) 4177–4184
7 A. V. Virkar, J. F. Jue, J. J. Hansen, and R. A. Cutler, Measurement of Residual Stresses in Oxide-ZrO2 Three-Layer Composites, Journal of the American Ceramic Society, 71 (1988) 3, C-148–151
8 D. J. Green, P. Z. Cai, and G. L. Messing, Residual Stresses in Alumina–Zirconia Laminates, Journal of the European Ceramic Society, 19 (1999) 2511–2517
9 C. H. Hsueh, Modeling of Elastic Deformation of Multilayers due to Residual Stresses and External Bending, Journal of Applied Physics, 91 (2002) 12, 9652–9656
10 D. D. Barnett-Ritcey, and P. S. Nicholson, Failure Prediction Maps for a Model Al2O3c-ZrO2/Al2O3Al2O3 Brittle Polycrystalline Trilayer Composite, Journal of the American Ceramic Society, 86 (2003) 1, 121–128
11 M. Ambrožič, T. Kosmač, Optimization of the Bend Strength of Flat-Layered Alumina–Zirconia Composites, Journal of the American Ceramic Society, 90 (2007) 5, 1545–1550
12 R. Bermejo, J. Pascual, T. Lube, R. Danzer, Optimal strength and toughness of Al2O3–ZrO2 laminates designed with external or internal compressive layers, Journal of the European Ceramic Society, 28 (2008) 1575–1583
13 E. Carrera, A. Ciuffreda, Bending of composites and sandwich plates subjected to localized lateral loadings: a comparison of various theories, Composite Structures, 68 (2005) 185–202
14 K. F. Graff, Wave Motion in Elastic Solids (2012), Courier Corporation
15 P. Lee, N. Chang, Harmonic in Elastic Sandwich Plates, Journal of Elasticity 9 (1979) 51–69
16 J. Kaplunov, D. A. Prikazchikov, L. A. Prikazchikova, Dispersion of Elastic Waves in a Strongly Inhomogeneous Three-Layered Plate, International Journal of Solids and Structures 113–114 (2017) 169–179, doi:10.1016/j.ijsolstr.2017.01.042
17 Z. J. Ai, C. J. Xu, G. P. Ren, Vibration of a pre-stressed plate on a transversely isotropic multilayered half-plane due to a moving load, Applied Mathematical Modeling, 59 (2018) 728–738, doi:10.1016/ j.apm.2018.02.027
18 M. Shariyat, M. Roshanfar, A new analytical solution and novel energy formulations for non-linear eccentric impact analysis of composite multi-layer/sandwich plates resting on point supports, Thin-Walled Structures, 127 (2018) 157–168, doi:10.1016/j.tws. 2018.02.001
19 S. Zhang, J. Yin, H. W. Zhang, B. S. Chen, A two-level method for static and dynamic analysis of multilayered composite beam and plate, Finite Elements in Analysis and Design, 111 (2016) 1–18, doi:10.1016/j.finel.2015.12.001
20 T. Ye, G. Yin, Z. Su, Three-dimensional vibrational analysis of sandwich and multilayered plates with general ply stacking sequences by a spectral sampling surface method, Composite Structures, 176 (2017) 1124–1142, doi:10.1016/j.compstruct.2017.06.008
21 W. Lacarbonara, M. Pasquali, A geometrically exact formulation for thin multi-layered laminated composite plates: Theory and experiment, Composite Structures, 93 (2011) 1649–1663, doi:10.1016/ j.compstruct.2010.12.005
22 L. V. Tran, S.-E. Kim, Static and free vibration analysis of multilayered plates by a higher-order shear and normal deformation theory and isogeometric analysis, Thin-Walled Structures, 130 (2018) 622–640, doi:10.1016/j.tws.2018.06.013
23 Y. Wang, Z. Li, W. Chen, C. Zhang, J. Zhu, Free vibration and active control of pre-streched multilayered electroactive plates, International Journal of Solids and Structures, 180–181 (2019) 108–124, doi:10.1016/j. ijsolstr.2019.07.010
24 P. Zhang, C. Qi, H. Fang, C. Ma, Y. Huang, Semi-analytical analysis of static and dynamic responses for laminated magneto-electro-elastic plates, Composite Structures, 222 (2019) 110933, doi:10.1016/j.compstruct.2019.110933
25 B. Erbaş, J. Kaplunov, E. Nolde, M. Palsü, Composite wave models for elastic plates, Preceedings of Royal Society A, 474 (2018) 20180103, doi:10.1098/j.rspa.2018.0103
26 L. D. Landau, E. M. Lifshitz, Theory of Elasticity, Course of Theoretical Physics, Vol. 7, Butterworth–Heinemann (1986)
27 V. V. Vasiliev, Modern Conceptions of Plate Theory, Composite Structures, 48 (2000), 93–84.
28 N. I. Robinson, Augmented Lévi–Michell equations for flexural plates, International Journal of Solids and Structures, 191–192 (2020) 497–508, doi:10.1016/j. ijsolstr.2019.12.021
2 M. Rühle, N. Claussen, A. H. Heuer, Transformation and Microcrack Toughening as Complementary Processes in ZrO2-Toughened Al2O3, Journal of the American Ceramic Society, 69 (1986) 3, 195–197
3 H. E. Lutz, N. Claussen, Duplex ceramics, Parts 1–2, Journal of the European Ceramic Society, 7 (1991) 209–226
4 S. Deville, J. Chevalie, G. Fantozzi, J. F. Bartolome, J. Requena, J. S. Moya et al., Development of advanced zirconia-toughened alumina nanocomposites for orthopaedic applications, Key Engineering Materials, 264–268 (2004) 2012–2016
5 N. Mandal, B. Doloi, B. Mondal, R. Das, Optimization of flank wear using Zirconia Toughened Alumina (ZTA) cutting tool: Taguchi method and Regression analysis, Measurement, 44 (2011) 2149–2155
6 F. Sommer, R. Landfried, F. Kern, R. Gadov, Mechanical properties of zirconia toughened alumina with 10–24 vol. % 1Y–TZP reinforcement, Journal of the European Ceramic Society, 32 (2012) 4177–4184
7 A. V. Virkar, J. F. Jue, J. J. Hansen, and R. A. Cutler, Measurement of Residual Stresses in Oxide-ZrO2 Three-Layer Composites, Journal of the American Ceramic Society, 71 (1988) 3, C-148–151
8 D. J. Green, P. Z. Cai, and G. L. Messing, Residual Stresses in Alumina–Zirconia Laminates, Journal of the European Ceramic Society, 19 (1999) 2511–2517
9 C. H. Hsueh, Modeling of Elastic Deformation of Multilayers due to Residual Stresses and External Bending, Journal of Applied Physics, 91 (2002) 12, 9652–9656
10 D. D. Barnett-Ritcey, and P. S. Nicholson, Failure Prediction Maps for a Model Al2O3c-ZrO2/Al2O3Al2O3 Brittle Polycrystalline Trilayer Composite, Journal of the American Ceramic Society, 86 (2003) 1, 121–128
11 M. Ambrožič, T. Kosmač, Optimization of the Bend Strength of Flat-Layered Alumina–Zirconia Composites, Journal of the American Ceramic Society, 90 (2007) 5, 1545–1550
12 R. Bermejo, J. Pascual, T. Lube, R. Danzer, Optimal strength and toughness of Al2O3–ZrO2 laminates designed with external or internal compressive layers, Journal of the European Ceramic Society, 28 (2008) 1575–1583
13 E. Carrera, A. Ciuffreda, Bending of composites and sandwich plates subjected to localized lateral loadings: a comparison of various theories, Composite Structures, 68 (2005) 185–202
14 K. F. Graff, Wave Motion in Elastic Solids (2012), Courier Corporation
15 P. Lee, N. Chang, Harmonic in Elastic Sandwich Plates, Journal of Elasticity 9 (1979) 51–69
16 J. Kaplunov, D. A. Prikazchikov, L. A. Prikazchikova, Dispersion of Elastic Waves in a Strongly Inhomogeneous Three-Layered Plate, International Journal of Solids and Structures 113–114 (2017) 169–179, doi:10.1016/j.ijsolstr.2017.01.042
17 Z. J. Ai, C. J. Xu, G. P. Ren, Vibration of a pre-stressed plate on a transversely isotropic multilayered half-plane due to a moving load, Applied Mathematical Modeling, 59 (2018) 728–738, doi:10.1016/ j.apm.2018.02.027
18 M. Shariyat, M. Roshanfar, A new analytical solution and novel energy formulations for non-linear eccentric impact analysis of composite multi-layer/sandwich plates resting on point supports, Thin-Walled Structures, 127 (2018) 157–168, doi:10.1016/j.tws. 2018.02.001
19 S. Zhang, J. Yin, H. W. Zhang, B. S. Chen, A two-level method for static and dynamic analysis of multilayered composite beam and plate, Finite Elements in Analysis and Design, 111 (2016) 1–18, doi:10.1016/j.finel.2015.12.001
20 T. Ye, G. Yin, Z. Su, Three-dimensional vibrational analysis of sandwich and multilayered plates with general ply stacking sequences by a spectral sampling surface method, Composite Structures, 176 (2017) 1124–1142, doi:10.1016/j.compstruct.2017.06.008
21 W. Lacarbonara, M. Pasquali, A geometrically exact formulation for thin multi-layered laminated composite plates: Theory and experiment, Composite Structures, 93 (2011) 1649–1663, doi:10.1016/ j.compstruct.2010.12.005
22 L. V. Tran, S.-E. Kim, Static and free vibration analysis of multilayered plates by a higher-order shear and normal deformation theory and isogeometric analysis, Thin-Walled Structures, 130 (2018) 622–640, doi:10.1016/j.tws.2018.06.013
23 Y. Wang, Z. Li, W. Chen, C. Zhang, J. Zhu, Free vibration and active control of pre-streched multilayered electroactive plates, International Journal of Solids and Structures, 180–181 (2019) 108–124, doi:10.1016/j. ijsolstr.2019.07.010
24 P. Zhang, C. Qi, H. Fang, C. Ma, Y. Huang, Semi-analytical analysis of static and dynamic responses for laminated magneto-electro-elastic plates, Composite Structures, 222 (2019) 110933, doi:10.1016/j.compstruct.2019.110933
25 B. Erbaş, J. Kaplunov, E. Nolde, M. Palsü, Composite wave models for elastic plates, Preceedings of Royal Society A, 474 (2018) 20180103, doi:10.1098/j.rspa.2018.0103
26 L. D. Landau, E. M. Lifshitz, Theory of Elasticity, Course of Theoretical Physics, Vol. 7, Butterworth–Heinemann (1986)
27 V. V. Vasiliev, Modern Conceptions of Plate Theory, Composite Structures, 48 (2000), 93–84.
28 N. I. Robinson, Augmented Lévi–Michell equations for flexural plates, International Journal of Solids and Structures, 191–192 (2020) 497–508, doi:10.1016/j. ijsolstr.2019.12.021
Published
2021-04-15
How to Cite
1.
Ambrožič M, Nikonov A. DYNAMIC BIAXIAL STRESS ANALYSIS OF FLAT LAYERED CERAMIC COMPOSITES. MatTech [Internet]. 2021Apr.15 [cited 2025Jul.13];55(2):195-00. Available from: https://mater-tehnol.si/index.php/MatTech/article/view/118
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