Abstract
This paper considers solutions that can determine the nature of the stress singularity in the vicinity of a singular point for two-dimensional and three-dimensional closed composite wedges. A comparative analysis of stress singularity exponents is carried out for closed composite wedges with perfectly bonded interfaces and homogeneous wedges with stress-free edges. Using analysis results, it is possible to evaluate a change in the nature of the stress singularity near the crack tip when the crack cavity is filled with a certain material. Results were obtained for different ratios of the wedge component’s opening angles, different values of elastic moduli, and different Poisson ratios of the wedge’s constituent materials. The anomalous nature of changes in singular solutions for a composite closed wedge is established for Poisson’s ratios of the wedge part corresponding to a weakly compressible or incompressible material. In the context of the model and applied problems, it is shown that the use of eigensolutions for composite wedges makes it possible to find material characteristics that ensure maximum reduction in the stress concentration near the crack tip in the case of the crack cavity being filled with a certain material. The dependence of these solutions on the Poisson ratio demonstrates a significant reduction in stress concentration at sufficiently large crack opening angles and at low rigidity of the material.
Similar content being viewed by others
References
Baladi, A., Arezoodar, A.: Dissimilar materials joint and effect of angle junction on stress distribution at interface. Int. J. Mech. Aerosp. Ind. Mechatron. Manuf. Eng. 5(7), 1184–1187 (2011)
Baryakh, A.A., Lobanov, S.Y., Lomakin, I.S.: Analysis of time-to-time variation of load on interchamber pillars in mines of the upper kama potash salt deposit. J. Min. Sci. 51(4), 696–706 (2015). https://doi.org/10.1134/S1062739115040064
Becker, E.B., Dunham, R.S., Stern, M.: Some stress intensity calculations using finite elements. In: Pulmans V.A., Kabaila A.P. (eds.) Finite Element Methods in Engineering, Proceedings of the 1974 International Conference on Finite Element Methods in Engineering. The School of Civil Engineering, pp. 117–138. The University of New South Wales, Unisearch Ltd., Kensington (1974)
Bogy, D., Wang, K.: Stress singularities at interface corners in bonded dissimilar isotropic elastic materials. Int. J. Solids Struct. 7(8), 993–1005 (1971). https://doi.org/10.1016/0020-7683(71)90077-1
Bogy, D.B.: Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading. ASME J. Appl. Mech. 35(3), 460–466 (1968). https://doi.org/10.1115/1.3601236
Carpinteri, A., Paggi, M.: Asymptotic analysis in linear elasticity: from the pioneering studies by wieghardt and irwin until today. Eng. Fract. Mech. 76(12), 1771–1784 (2009). https://doi.org/10.1016/j.engfracmech.2009.03.012
Chen, D.H., Nisitani, H.: Singular stress field near the corner of jointed dissimilar materials. ASME J. Appl. Mech. 60(3), 607–613 (1993). https://doi.org/10.1115/1.2900847
Chobanyan, K.: Stress State in Compound Elastic Bodies. Armenian Academy of Sciences Press, Yerevan (1987)
Dempsey, J.P., Sinclair, G.B.: On the singular behavior at the vertex of a bi-material wedge. J. Elast. 11(3), 317–327 (1981). https://doi.org/10.1007/BF00041942
Dundurs, J.: Discussion: edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading (Bogy, D. B., 1968, ASME J. Appl. Mech., 35, pp. 460–466). ASME J. Appl. Mech. 36(3), 650–652 (1969). https://doi.org/10.1115/1.3564739
Fedorov, A.Y., Matveenko, V.P.: Optimization of geometry and mechanical characteristics of elastic bodies in the vicinity of singular points. Acta Mech. 229(2), 645–658 (2018). https://doi.org/10.1007/s00707-017-1990-5
Fedorov, A.Y., Matveenko, V.P., Shardakov, I.N.: Numerical analysis of stresses in the vicinity of internal singular points in polymer composite materials. Int. J. Civil Engi. Technol. (IJCIET) 9(8), 1062–1075 (2018). https://www.iaeme.com/MasterAdmin/Journal_uploads/IJCIET/VOLUME_9_ISSUE_8/IJCIET_09_08_107.pdf
Goldstein, R.V., Gorodtsov, V.A., Lisovenko, D.S.: Auxetic mechanics of crystalline materials. Mech. Solids 45(4), 529–545 (2010). https://doi.org/10.3103/S0025654410040047
Huang, C., Leissa, A.: Stress singularities in bimaterial bodies of revolution. Compos. Struct. 82(4), 488–498 (2008). https://doi.org/10.1016/j.compstruct.2007.01.026
Kondrat’ev, V.: Boundary value problems for elliptic equations in domains with conical or angular points. Trans. Mosc. Math. Soc. 16, 227–313 (1967)
Lang, T., Mallick, P.: Effect of spew geometry on stresses in single lap adhesive joints. Int. J. Adhes. Adhes. 18(1), 167–177 (1998). https://doi.org/10.1016/S0143-7496(97)00056-0
Leguillon, D., Sanchez-Palencia, E.: Computation of Singular Solutions in Elliptic Problems and Elasticity. John Wiley & Sons Inc., New York (1987)
Mihailov, S.: Stress singularity in the vicinity of an angle edge in an anisotropic composite and some applications to fibrous composites. Izv. Acad. Sci. USSR. Mechanica Twerdogo Tela 5, 103–110 (1979)
Paggi, M., Carpinteri, A.: On the stress singularities at multimaterial interfaces and related analogies with fluid dynamics and diffusion. ASME Appl. Mech. Rev. 61(2), 020801 (2008). https://doi.org/10.1115/1.2885134
Parton, V., Perlin, P.: Methods of Mathematical Theory of Elasticity. Nauka, Moscow (1981)
Pook, L.P.: A 50-year retrospective review of three-dimensional effects at cracks and sharp notches. Fatigue Fract. Eng. Mate. Struct. 36(8), 699–723 (2013). https://doi.org/10.1111/ffe.12074
Raju, I., Crews, J.H.: Interlaminar stress singularities at a straight free edge in composite laminates. Comput. Struct. 14(1), 21–28 (1981). https://doi.org/10.1016/0045-7949(81)90079-1
Sinclair, G.: Stress singularities in classical elasticity-ii: asymptotic identification. ASME Appl. Mech. Rev. 57(5), 385–439 (2004). https://doi.org/10.1115/1.1767846
Theocaris, P.S.: The order of singularity at a multi-wedge corner of a composite plate. Int. J. Eng. Sci. 12(2), 107–120 (1974). https://doi.org/10.1016/0020-7225(74)90011-1
Theocaris, P.S., Gdoutos, E.E., Thireos, C.G.: Stress singularities in a biwedge under various boundary conditions. Acta Mech. 29(1), 55–73 (1978). https://doi.org/10.1007/BF01176627
Tsai, M., Morton, J.: The effect of a spew fillet on adhesive stress distributions in laminated composite single-lap joints. Compos. Struct. 32(1–4), 123–131 (1995). https://doi.org/10.1016/0263-8223(95)00059-3
Wang, P., Xu, L.: Convex interfacial joints with least stress singularities in dissimilar materials. Mech. Mater. 38(11), 1001–1011 (2006). https://doi.org/10.1016/j.mechmat.2005.10.002
Williams, M.: Stress singularities resulting from various boundary conditions in angular corners of plates in extension. ASME J. Appl. Mech. 19(4), 526–528 (1952)
Wu, Z.: Design free of stress singularities for bi-material components. Compos. Struct. 65(3–4), 339–345 (2004). https://doi.org/10.1016/j.compstruct.2003.11.009
Xu, L., Kuai, H., Sengupta, S.: Dissimilar material joints with and without free-edge stress singularities: part i. a biologically inspired design. Exp. Mech. 44(6), 608–615 (2004). https://doi.org/10.1007/BF02428250
Xu, L.R., Sengupta, S.: Dissimilar material joints with and without free-edge stress singularities: part ii. an integrated numerical analysis. Exp. Mech. 44(6), 616–621 (2004). https://doi.org/10.1007/BF02428251
Zheng, Q.S., Chen, T.: New perspective on poisson’s ratios of elastic solids. Acta Mech. 150(3), 191–195 (2001). https://doi.org/10.1007/BF01181811
Zhigalkin, V.M., Usol’tseva, O.M., Semenov, V.N., Tsoi, P.A., Asanov, V.A., Baryakh, A.A., Pan’kov, I.L., Toksarov, V.N.: Deformation of quasi-plastic salt rocks under different conditions of loading. report i: deformation of salt rocks under uniaxial compression. J. Min. Sci. 41(6), 507–515 (2005). https://doi.org/10.1007/s10913-006-0013-z
Acknowledgements
This study was funded by the Russian Science Foundation (Project 19-77-30008).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Fedorov, A.Y., Matveenko, V.P. Numerical and applied results of the analysis of singular solutions for a closed wedge consisting of two dissimilar materials. Acta Mech 231, 2711–2721 (2020). https://doi.org/10.1007/s00707-020-02668-w
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-020-02668-w