Slant edge cracked effect considering the inherent relation between surface energy and mixed-mode crack propagations on the free transverse vibrations of nanobeams with surface effect is investigated. First, the slant edge cracked effect, which considers residual surface stress effect on the crack tip fields of a mode-I and mode-II surface edge crack, is developed and the corresponding stress intensity factors (SIFs) and local flexibility coefficients are derived. Moreover, a refined continuum model of slant cracked nanobeams is established by considering both slant edge cracked effect and surface effect. The effects of fracture angles, crack depth, surface elasticity, surface stress, and surface density on the local flexibility and free transverse vibration characteristics of cracked nanobeams are, respectively, analyzed. The results show that the flexibility coefficients distribute symmetrically about residual surface stress. Fracture angles have a profound influence on both the symmetries of the mode shapes and the natural frequencies of nanobeams, and the influence becomes more pronounced as crack depth ratios increase. Furthermore, the natural frequencies will first decrease and then increase with fracture angles when the slant edge cracked effect is considered. The results demonstrate that the inherent relation between surface energy and crack propagations should be considered for both the stress distributions at the crack tip and the dynamic behavior of cracked nanobeams.
Issue Section:
Research Papers
References
1.
Abdi
, H.
, Nayeb-Hashemi
, H.
, Hamouda
, A.
, and Vaziri
, A.
, 2014
, “Torsional Dynamic Response of a Shaft With Longitudinal and Circumferential Cracks
,” ASME J. Vib. Acoust.
, 136
(6
), p. 061011
.2.
Chatterjee
, A.
, 2011
, “Nonlinear Dynamics and Damage Assessment of a Cantilever Beam With Breathing Edge Crack
,” ASME J. Vib. Acoust.
, 133
(5
), p. 051004
.3.
Lin
, Y.
, and Chu
, F.
, 2010
, “The Dynamic Behavior of a Rotor System With a Slant Crack on the Shaft
,” Mech. Syst. Signal Process.
, 24
(2
), pp. 522
–545
.4.
Lin
, H.-P.
, Chang
, S.-C.
, and Wu
, J.-D.
, 2002
, “Beam Vibrations With an Arbitrary Number of Cracks
,” J. Sound Vib.
, 258
(5
), pp. 987
–999
.5.
Carneiro
, S. H.
, and Inman
, D. J.
, 2002
, “Continuous Model for the Transverse Vibration of Cracked Timoshenko Beams
,” ASME J. Vib. Acoust.
, 124
(2
), pp. 310
–320
.6.
Chondros
, T.
, and Dimarogonas
, A.
, 1998
, “Vibration of a Cracked Cantilever Beam
,” ASME J. Vib. Acoust.
, 120
(3
), pp. 742
–746
.7.
Feng
, X.-Q.
, Wang
, T.-J.
, and Gao
, W.
, 2008
, “Surface Effects on the Near-Tip Stresses for Mode-I and Mode-III Cracks
,” ASME J. Appl. Mech.
, 75
(1
), p. 011001
.8.
Fu
, X.
, Wang
, G.
, and Feng
, X.
, 2008
, “Surface Effects on the Near-Tip Stress Fields of a Mode-II Crack
,” Int. J. Fract.
, 151
(2
), pp. 95
–106
.9.
Fu
, X.
, Wang
, G.
, and Feng
, X.
, 2010
, “Surface Effects on Mode-I Crack Tip Fields: A Numerical Study
,” Eng. Fract. Mech.
, 77
(7
), pp. 1048
–1057
.10.
Belytschko
, T.
, Xiao
, S.
, Schatz
, G.
, and Ruoff
, R.
, 2002
, “Atomistic Simulations of Nanotube Fracture
,” Phys. Rev. B
, 65
(23
), p. 235430
.11.
Dewapriya
, M.
, and Rajapakse
, R.
, 2014
, “Molecular Dynamics Simulations and Continuum Modeling of Temperature and Strain Rate Dependent Fracture Strength of Graphene With Vacancy Defects
,” ASME J. Appl. Mech.
, 81
(8
), p. 081010
.12.
Joshi
, A. Y.
, Sharma
, S. C.
, and Harsha
, S.
, 2010
, “Analysis of Crack Propagation in Fixed-Free Single-Walled Carbon Nanotube Under Tensile Loading Using XFEM
,” ASME J. Nanotechnol. Eng. Med.
, 1
(4
), p. 041008
.13.
Tsai
, J.-L.
, Tzeng
, S.-H.
, and Tzou
, Y.-J.
, 2010
, “Characterizing the Fracture Parameters of a Graphene Sheet Using Atomistic Simulation and Continuum Mechanics
,” Int. J. Solids Struct.
, 47
(3
), pp. 503
–509
.14.
He
, L.
, Lim
, C.
, and Wu
, B.
, 2004
, “A Continuum Model for Size-Dependent Deformation of Elastic Films of Nano-Scale Thickness
,” Int. J. Solids Struct.
, 41
(3
), pp. 847
–857
.15.
Kim
, C.
, Schiavone
, P.
, and Ru
, C.-Q.
, 2010
, “The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution
,” ASME J. Appl. Mech.
, 77
(2
), p. 021011
.16.
Kim
, C.
, Schiavone
, P.
, and Ru
, C.-Q.
, 2011
, “The Effect of Surface Elasticity on a Mode-III Interface Crack
,” Arch. Mech.
, 63
(3
), pp. 267
–286
.17.
Nan
, H.
, and Wang
, B.
, 2013
, “Effect of Crack Face Residual Surface Stress on Nanoscale Fracture of Piezoelectric Materials
,” Eng. Fract. Mech.
, 110
(1
), pp. 68
–80
.18.
Nan
, H.
, and Wang
, B.
, 2012
, “Effect of Residual Surface Stress on the Fracture of Nanoscale Materials
,” Mech. Res. Commun.
, 44
(1
), pp. 30
–34
.19.
Nan
, H.
, and Wang
, B.
, 2014
, “Effect of Interface Stress on the Fracture Behavior of a Nanoscale Linear Inclusion Along the Interface of Bimaterials
,” Int. J. Solids Struct.
, 51
(23
), pp. 4094
–4100
.20.
Hasheminejad
, B. S. M.
, Gheshlaghi
, B.
, Mirzaei
, Y.
, and Abbasion
, S.
, 2011
, “Free Transverse Vibrations of Cracked Nanobeams With Surface Effects
,” Thin Solid Films
, 519
(8
), pp. 2477
–2482
.21.
Wang
, G.-F.
, and Feng
, X.-Q.
, 2009
, “Surface Effects on Buckling of Nanowires Under Uniaxial Compression
,” Appl. Phys. Lett.
, 94
(14
), p. 141913
.22.
Wang
, K.
, and Wang
, B.
, 2013
, “Timoshenko Beam Model for the Vibration Analysis of a Cracked Nanobeam With Surface Energy
,” J. Vib. Control
, 21
(12
), pp. 2452
–2464
.23.
Hosseini-Hashemi
, S.
, Fakher
, M.
, Nazemnezhad
, R.
, and Sotoude Haghighi
, M. H.
, 2014
, “Dynamic Behavior of Thin and Thick Cracked Nanobeams Incorporating Surface Effects
,” Composites, Part B
, 61
(1
), pp. 66
–72
.24.
Lu
, P.
, He
, L.
, Lee
, H.
, and Lu
, C.
, 2006
, “Thin Plate Theory Including Surface Effects
,” Int. J. Solids Struct.
, 43
(16
), pp. 4631
–4647
.25.
Loya
, J.
, López-Puente
, J.
, Zaera
, R.
, and Fernández-Sáez
, J.
, 2009
, “Free Transverse Vibrations of Cracked Nanobeams Using a Nonlocal Elasticity Model
,” J. Appl. Phys.
, 105
(4
), p. 044309
.26.
Torabi
, K.
, and Nafar Dastgerdi
, J.
, 2012
, “An Analytical Method for Free Vibration Analysis of Timoshenko Beam Theory Applied to Cracked Nanobeams Using a Nonlocal Elasticity Model
,” Thin Solid Films
, 520
(21
), pp. 6595
–6602
.27.
Hsu
, J.-C.
, Lee
, H.-L.
, and Chang
, W.-J.
, 2011
, “Longitudinal Vibration of Cracked Nanobeams Using Nonlocal Elasticity Theory
,” Curr. Appl. Phys.
, 11
(6
), pp. 1384
–1388
.28.
Loya
, J.
, Aranda-Ruiz
, J.
, and Fernández-Sáez
, J.
, 2014
, “Torsion of Cracked Nanorods Using a Nonlocal Elasticity Model
,” J. Phys. D: Appl. Phys.
, 47
(11
), p. 115304
.29.
Roostai
, H.
, and Haghpanahi
, M.
, 2014
, “Vibration of Nanobeams of Different Boundary Conditions With Multiple Cracks Based on Nonlocal Elasticity Theory
,” Appl. Math. Modell.
, 38
(3
), pp. 1159
–1169
.30.
Liu
, C.
, and Rajapakse
, R.
, 2010
, “Continuum Models Incorporating Surface Energy for Static and Dynamic Response of Nanoscale Beams
,” IEEE Trans. Nanotechnol.
, 9
(4
), pp. 422
–431
.31.
Gurtin
, M. E.
, and Murdoch
, A. I.
, 1975
, “A Continuum Theory of Elastic Material Surfaces
,” Arch. Ration. Mech. Anal.
, 57
(4
), pp. 291
–323
.32.
He
, J.
, and Lilley
, C. M.
, 2008
, “Surface Effect on the Elastic Behavior of Static Bending Nanowires
,” Nano Lett.
, 8
(7
), pp. 1798
–1802
.33.
Park
, H. S.
, Klein
, P. A.
, and Wagner
, G. J.
, 2006
, “A Surface Cauchy–Born Model for Nanoscale Materials
,” Int. J. Numer. Methods Eng.
, 68
(10
), pp. 1072
–1095
.34.
Shenoy
, V. B.
, 2005
, “Atomistic Calculations of Elastic Properties of Metallic FCC Crystal Surfaces
,” Phys. Rev. B
, 71
(9
), p. 094104
.35.
De Pasquale
, G.
, and Soma
, A.
, 2011
, “MEMS Mechanical Fatigue: Effect of Mean Stress on Gold Microbeams
,” J. Microelectromech. Syst.
, 20
(4
), pp. 1054
–1063
.36.
Kisa
, M.
, and Brandon
, J.
, 2000
, “The Effects of Closure of Cracks on the Dynamics of a Cracked Cantilever Beam
,” J. Sound Vib.
, 238
(1
), pp. 1
–18
.37.
Ou
, Z.
, Wang
, G.
, and Wang
, T.
, 2008
, “Effect of Residual Surface Tension on the Stress Concentration Around a Nanosized Spheroidal Cavity
,” Int. J. Eng. Sci.
, 46
(5
), pp. 475
–485
.38.
Wang
, G.
, and Wang
, T.
, 2006
, “Deformation Around a Nanosized Elliptical Hole With Surface Effect
,” Appl. Phys. Lett.
, 89
(16
), p. 161901
.39.
Wang
, B.
, Han
, J.
, and Du
, S.
, 2000
, “Cracks Problem for Non-Homogeneous Composite Material Subjected to Dynamic Loading
,” Int. J. Solids Struct.
, 37
(9
), pp. 1251
–1274
.40.
Rubio
, L.
, and Fernández-Sáez
, J.
, 2010
, “A Note on the Use of Approximate Solutions for the Bending Vibrations of Simply Supported Cracked Beams
,” ASME J. Vib. Acoust.
, 132
(2
), p. 024504
.41.
Timoshenko
, S.
, and Goodier
, J.
, 1970
, Theory of Elasticity
, McGraw-Hill
, New York
.42.
Rao
, S. S.
, 2007
, Vibration of Continuous Systems
, Wiley
, Hoboken, NJ
.43.
Aydin
, K.
, 2007
, “Vibratory Characteristics of Axially-Loaded Timoshenko Beams With Arbitrary Number of Cracks
,” ASME J. Vib. Acoust.
, 129
(3
), pp. 341
–354
.44.
Miller
, R. E.
, and Shenoy
, V. B.
, 2000
, “Size-Dependent Elastic Properties of Nanosized Structural Elements
,” Nanotechnology
, 11
(3
), pp. 139
–147.Copyright © 2016 by ASME
You do not currently have access to this content.
