Abstract
On the physical nature, most crack tips are not ideally sharp but have a small curvature radius. Both surface energy and crack-root curvature affect the stress and displacement fields in the vicinity of the crack tip. In the present paper, a numerical method, which incorporates the effect of surface elasticity into the finite element method, is employed to study the surface effects on the mode-II crack tip fields. It is found that when the curvature radius of the crack root decreases to micro-/nanometers, surface elasticity has a significant influence on the stresses near the crack tip. For a mode-II crack, surface effects alter both the magnitude and position of the maximum stresses, as is different from a mode-I crack, in which case only the stress magnitude is influence by surface stresses.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chen T, Dvorak GJ, Yu CC (2007) Size-dependent elastic properties of unidirectional nano-composites with interface stresses. Acta Mech 188(1): 39–54 doi:10.1007/s00707-006-0371-2
Creager M, Paris PC (1967) Elastic field equations for blunt cracks with reference to stress corrosion cracking. Int J Fract Mech 2: 247–252
Dingreville R, Qu JM, Cherkaoui M (2005) Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films. J Mech Phys Solids 53: 1827–1854 doi:10.1016/j.jmps.2005.02.012
Dini D, Hills DA (2004) Asymptotic characterization of nearly-sharp notch root stress fields. Int J Fract 130(3): 651–666 doi:10.1007/s10704-004-2510-x
Duan HL, Wang J, Huang ZP, Karihaloo BL (2005) Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J Mech Phys Solids 53: 1574–1596 doi:10.1016/j.jmps.2005.02.009
Fu SY, Feng SY, Mai YW, Lauke B (2008) Effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate polymer composites. Compos Part B Eng 39: 933–961 doi:10.1016/j.compositesb.2008.01.002
Gao W, Yu SW, Huang GY (2006) Finite element characterization of the size-dependent mechanical behaviour in nanosystems. Nanotechnology 17: 1118–1122 doi:10.1088/0957-4484/17/4/045
Gurtin ME, Murdoch AI (1975) A continuum theory of elastic material surfaces. Arch Ration Mech Anal 57: 291–323 doi:10.1007/BF00261375
Gurtin ME, Weissmüller J, Larche F (1998) A general theory of curved deformable interfaces in solids at equilibrium. Philos Mag A 78: 1093–1109
He J, Lilley CM (2008) Surface effect on the elastic behavior of static bending nanowires. Nano Lett 8: 1798–1802 doi:10.1021/nl0733233
He LH, Lim CW, Wu BS (2004) A continuum model for size-dependent deformation of elastic films of nano-scale thickness. Int J Solids Struct 41(3): 847–857 doi:10.1016/j.ijsolstr.2003.10.001
Miller RE, Shenoy VB (2000) Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11: 139–147 doi:10.1088/0957-4484/11/3/301
Sharma P, Ganti S, Bhate N (2003) Effect of surfaces on the size-dependent elastic state of nanoinhomogeneities. Appl Phys Lett 82: 535–537 doi:10.1063/1.1539929
Tian L, Rajapakse RKND (2007) Finite element modelling of nanoscale inhomogeneities in an elastic matrix. Comput Mater Sci 41: 44–53 doi:10.1016/j.commatsci.2007.02.013
Wang GF, Feng XQ (2006) Effects of surface stresses on contact problems at nanoscale. J Appl Phys 101: 013510 doi:10.1063/1.2405127
Wang GF, Feng XQ (2007) Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Appl Phys Lett 90: 231904 doi:10.1063/1.2746950
Wang GF, Feng XQ, Wang TJ, Gao W (2008) Surface effects on the near-tip stresses for Mode-I and Mode-III cracks. J Appl Mech 75: 011001 doi:10.1115/1.2712233
Wang JS, Feng XQ, Wang GF, Yu SW (2008) Twisting of nanowires induced by anisotropic surface stresses. Appl Phys Lett 92: 191901 doi:10.1063/1.2928221
Wu CH (1999) The effect of surface stress on the configurational equilibrium of voids and cracks. J Mech Phys Solids 47: 2469–2492 doi:10.1016/S0022-5096(99)00021-6
Zappalorto M, Lazzarin P (2007) Analytical study of the elastic-plastic stress fields ahead of parabolic notches under antiplane shear loading. Int J Fract 48: 139–154 doi:10.1007/s10704-008-9185-7
Zhang TY, Luo M, Chen WK (2008) Size-dependent surface stress, surface stiffness, and Young’s modulus of hexagonal prism [111] beta-SiC nanowires. J Appl Phys 103: 104308 doi:10.1063/1.2927453
Zhou LG, Huang HC (2004) Are surfaces elastically softer or stiffer. Appl Phys Lett 84: 1940–1942 doi:10.1063/1.1682698
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fu, X.L., Wang, G.F. & Feng, X.Q. Surface effects on the near-tip stress fields of a mode-II crack. Int J Fract 151, 95–106 (2008). https://doi.org/10.1007/s10704-008-9245-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-008-9245-z