Abstract
The strain gradient elasticity theory is applied to the solution of a mode III crack in an elastic layer sandwiched by two elastic layers of infinite thickness. The model includes volumetric and surface strain gradient characteristic length parameters. Both the near-tip asymptotic stresses and the crack displacement are obtained. Due to stain gradient effects, the magnitudes of the stress ahead of the crack tip are significantly higher than those in the classical linear elastic fracture mechanics. When the gradient parameters reduce to sufficiently small, all results reduce to the conventional linear elastic fracture mechanics results. In addition to the single crack in the finite layer, the solution and the results for two collinear cracks are also established and given.
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Chan, Y.S., Fannjiang, A.C., Glaucio, H.: Integral equations with hypersingular kernels—theory and applications to fracture mechanics. Int. J. Eng. Sci. 41, 683–720 (2003)
Chan, Y.S., Paulino, G.H., Fannjiang, A.C.: Gradient elasticity theory for mode III fracture in functionally graded materials-part II: crack parallel to the material gradation. J. Appl. Mech. 75, 061015 (2008)
Exadaktylos, G.: Gradient elasticity with surface energy: mode-I crack problem. Int. J. Solids Struct. 35, 421–456 (1998)
Exadaktylos, G., Vardoulakis, I., Aifantis, E.: Cracks in gradient elastic bodies with surface energy. Int. J. Fract. 79, 107–119 (1996)
Fang, T.H., Li, W.L., Tao, N.R., Lu, K.: Revealing extraordinary intrinsic tensile plasticity in gradient nano-grained copper. Science 331, 1587–1590 (2011)
Fannjiang, A.C., Paulino, G.H., Chan, Y.S.: Strain gradient elasticity for antiplane shear cracks: a hypersingular integrodifferential equation approach. SIAM J. Appl. Math. 62, 1066–1091 (2002)
Fleck, N.A., Muller, G.M., Ashby, M.F., Hutchinson, J.W.: Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42, 475–487 (1994)
Giannakopoulos, A., Stamoulis, K.: Structural analysis of gradient elastic components. Int. J. Solids Struct. 44, 3440–3451 (2007)
Joseph, R.P., Wang, B.L., Samali, B.: Strain gradient fracture in an anti-plane cracked material layer. Int. J. Solids Struct. 146, 214–223 (2018)
Karimipour, I., Fotuhi, A.R.: Anti-plane analysis of an infinite plane with multiple cracks based on strain gradient theory. Acta Mech. 228, 1793–1817 (2017)
Lam, D.C., Yang, F., Chong, A., Wang, J., Tong, P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51, 1477–1508 (2003)
Ma, Q., Clarke, D.R.: Size dependent hardness of silver single crystals. J. Mater. Res. 10, 853–863 (1995)
McElhaney, K.W., Vlassak, J.J., Nix, W.D.: Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments. J. Mater. Res. 5, 1300–1306 (1998)
McFarland, A.W., Colton, J.S.: Role of material microstructure in plate stiffness with relevance to microcantilever sensors. J. Micromech. Microeng. 15, 1060–1067 (2005)
Mousavi, S.M., Aifantis, E.: A note on dislocation-based mode III gradient elastic fracture mechanics. J. Mech. Behav. Mater. 24, 115–119 (2005)
Paulino, G., Fannjiang, A., Chan, Y.-S.: Gradient elasticity theory for mode III fracture in functionally graded materials—part I: crack perpendicular to the material gradation. J. Appl. Mech. 70, 531–542 (2003)
Piccolroaz, A., Mishuris, G., Radi, E.: Mode III interfacial crack in the presence of couple-stress elastic materials. Eng. Fract. Mech. 80, 60–71 (2012)
Poole, W.J., Ashby, M.F., Fleck, N.A.: Micro-hardness of annealed and work-hardened copper polycrystals. Scripta Mater. 34, 559–564 (1996)
Qiu, Y., Wu, H., Wang, J., Lou, J., Zhang, Z., Liu, A., Chai, G.: The enhanced piezoelectricity in compositionally graded ferroelectric thin films under electric field: a role of flexoelectric effect. J. Appl. Phys. 123, 084103 (2018)
Shi, M., Wu, H., Li, L., Chai, G.: Calculation of stress intensity factors for functionally graded materials by using the weight functions derived by the virtual crack extension technique. Int. J. Mech. Mater. Des. 10, 65–77 (2014)
Stolken, J.S.: The Role of Oxygen in Nickel–Sapphire Interface Fracture. Ph.D. Dissertation, University of California, Santa Barbara (1997)
Thevamaran, R., Lawal, O., Yazdi, S., Jeon, S., Lee, J.-H., Thomas, E.: Dynamic creation and evolution of gradient nanostructure in single-crystal metallic microcubes. Science 354, 312–316 (2016)
Vardoulakis, I., Exadaktylos, G., Aifantis, E.: Gradient elasticity with surface energy: mode-III crack problem. Int. J. Solids Struct. 33, 4531–4559 (1996)
Wei, Y.: A new finite element method for strain gradient theories and applications to fracture analyses. Eur. J. Mech. A. Solids 25, 897–913 (2006)
Wu, H., Li, L., Chai, G., Song, F., Kitamura, T.: Three-dimensional thermal weight function method for the interface crack problems in bimaterial structures under a transient thermal loading. J. Therm. Stress. 39, 371–385 (2016a)
Wu, H., Ma, X., Zhang, Z., Zhu, J., Wang, J., Chai, G.: Dielectric tunability of vertically aligned ferroelectric-metal oxide nanocomposite films controlled by out-of-plane misfit strain. J. Appl. Phys. 119, 154102 (2016b)
Zeng, Z., Li, X., Xu, D., Lu, L., Gao, H., Zhu, T.: Gradient plasticity in gradient nano-grained metals. Extreme Mech. Lett. 8, 213–219 (2016)
Zhang, L., Huang, Y., Chen, Y.J., Hwang, K.C.: The mode III full-field solution in elastic materials with strain gradient effects. Int. J. Fract. 92, 325–348 (1998)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Project Nos. 11502101, 11672084, 11372086), Research Innovation Foundation of Jinling Institute of Technology, China (Project No. jit-b-201515), and Research Innovation Fund of Shenzhen City of China (Project No. JCYJ20170413104256729).
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Appendix
Appendix
The following formulas (Chan et al. 2008; Fannjiang et al. 2002; Paulino et al. 2003) are used in deriving the hypersingular integral equations:
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Li, J., Wang, B. Fracture mechanics analysis of an anti-plane crack in gradient elastic sandwich composite structures. Int J Mech Mater Des 15, 507–519 (2019). https://doi.org/10.1007/s10999-018-9425-6
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DOI: https://doi.org/10.1007/s10999-018-9425-6