Surface stress and surface elasticity are related to the organization of surface morphology, surface patterns, and surface atomic structures. As the size of the structure approaches the nanometer level, the surface-to-volume ratio increases. Generally the surface energy in deformable solids depends on the surface strain. The surface stress and elasticity influence the distribution of bulk stress near the surface. Interface stress and elasticity also exist at material interfaces and determine the interface properties. In the present study, the singular stress at a wedge corner in an anisotropic two-dimensional joint under tensile loading is analyzed using the molecular dynamic (MD) method and the anisotropic elasticity theory using a boundary condition with interface stress and interface elasticity. Not only the interface stress but also surface stress on the free surface are considered as a special case of an interface. The interface stress and interface elasticity are obtained through the MD analysis. In the case of a two-dimensional joint, the interface stress and elasticity depend on the distance from the wedge corner. In the analysis of anisotropic elasticity, the eigenequation used to determine the order of the stress singularity is newly derived using a boundary condition that considers the interface stress and interface elasticity. The order of the stress singularity varies with distance from the wedge corner. The stress distribution near the wedge corner can be expressed by the relation between the order of the stress singularity and the distance from the wedge corner.

References

References
1.
Ibach
,
H.
,
1997
, “
The Role of Surface Stress in Reconstruction, Epitaxial Growth and Stabilization of Mesoscopic Structures
,”
Surf. Sci. Rep.
,
29
(5-6), pp.
195
263
.10.1016/S0167-5729(97)00010-1
2.
Muller
,
P.
, and
Saul
,
A.
,
2004
, “
Elastic Effects on Surface Physics
,”
Surf. Sci. Rep.
,
54
(5-8), pp.
157
258
.10.1016/j.surfrep.2004.05.001
3.
Koguchi
,
H.
,
2007
, “
Effects of Surface Stresses on Elastic Fields Near Surface and Interface
,”
J. Solid Mech. Mater. Eng.
,
1
(
2
), pp.
152
168
.10.1299/jmmp.1.152
4.
Hanbucken
,
M.
,
Muller
,
P.
, and
Wehrspohn
,
R. B.
,
2011
,
Mechanical Stress on the Nanoscale
,
Wiley
,
Berlin
.
5.
Gurtin
,
M. E.
, and
Murdoch
,
A. I.
,
1975
, “
A Continuum Theory of Elastic Material Surfaces
,”
Arch. Rat. Mech. Anal.
,
57
(4), pp.
291
323
.10.1007/BF00261375
6.
Gurtin
,
M. E.
, and
Murdoch
,
A. I.
,
1978
, “
Surface Stress in Solids
,”
Int. J. Solids Struct.
,
14
(6), pp.
431
440
.10.1016/0020-7683(78)90008-2
7.
Thomson
,
R.
,
Chuang
,
T.-J.
, and
Lin
,
I.-H.
,
1986
, “
The Role of Surface Stress in Fracture
,”
Acta Metall.
,
34
(
6
), pp.
1133
1143
.10.1016/0001-6160(86)90223-3
8.
Koguchi
,
H.
,
1992
, “
Stress Analysis for Nano-Scale Elastic Materials (1st Report, Formulation of Boundary Condition for Interface with Surface Stress)
,”
Trans. Jpn. Soc. Mech. Eng.
,
58
(
555
), pp.
2132
2137
.10.1299/kikaia.58.2132
9.
Koguchi
,
H.
,
1994
, “
Stress Analysis for Nano-Scale Elastic Materials: Elastic Contact Problems Considering Surface Stresses
,”
JSME Int. J.
,
39
(
3
), pp.
337
345
.
10.
Koguchi
,
H.
,
2003
, “
Surface Deformation Induced by a Variation in Surface Stresses in Anisotropic Half-Regions
,”
Philos. Mag.
,
83
(
10
), pp.
1205
1226
.10.1080/0141861031000071971
11.
Koguchi
,
H.
,
1997
, “
Fundamental Solution for a Prismatic Dislocation Loop in a Two-Phase Transversely Isotropic Elastic Material Considering Interfacial Energy
,”
Trans. Jpn. Soc. Mech. Eng.
,
63
(
615
), pp.
2417
2423
.10.1299/kikaia.63.2417
12.
Koguchi
,
H.
,
2000
, “
Characteristics of Surface Wave Propagation at Nanometer Range of Wave Length
,”
Trans. Jpn. Soc. Mech. Eng.
,
66
(
645
), pp.
1030
1038
.10.1299/kikaia.66.1030
13.
Koguchi
,
H.
,
2004
, “
Contact and Adhesion Analysis Considering a Variation of Surface Stresses: 1st Report, A Comparison of Fundamental Theory and Hertz Theory
,”
Trans. Jpn. Soc. Mech. Eng.
,
70
(
690
), pp.
289
297
.10.1299/kikaia.70.289
14.
Koguchi
,
H.
,
2004
, “
Contact and Adhesion Analysis Considering a Variation of Surface Stresses: 2nd Report, A Comparison of The Present Theory and JKR Theory
,”
Trans. Jpn. Soc. Mech. Eng.
,
70
(
697
), pp.
1332
1340
.10.1299/kikaia.70.1332
15.
Koguchi
,
H.
, and
Nishi
,
N.
,
2010
, “
Contact Analysis Using Surface Green's Functions for Isotropic Materials With Surface Stress and Surface Elasticity
,”
ASME
Paper No. IMECE2010-37814.10.1115/IMECE2010-37814
16.
Koguchi
,
H.
,
2008
, “
Surface Green Function With Surface Stresses and Surface Elasticity Using Stroh's Formalism
,”
ASME J. Appl. Mech.
,
75
(
6
), pp.
104
115
.10.1115/1.2967893
17.
Miller
,
R. E.
, and
Shenoy
,
V. B.
,
2000
, “
Size-Dependent Elastic Properties of Nanosized Structural Elements
,”
Nanotechnology
,
11
(3), pp.
139
147
.10.1088/0957-4484/11/3/301
18.
Shenoy
,
V. B.
,
2002
, “
Size-Dependent Rigidities of Nanosized Torsional Elements
,”
Int. J. Solids Struct.
,
39
(15), pp.
4039
4052
.10.1016/S0020-7683(02)00261-5
19.
Duan
,
H. L.
,
Wang
,
J.
,
Huang
,
Z. P.
, and
Karihaloo
,
B. L.
,
2005
, “
Size-Dependent Effective Elastic Constants of Solids Containing Nano-Inhomogeneities With Interface Stress
,”
J. Mech. Phys. Solids
,
53
(7), pp.
1574
1596
.10.1016/j.jmps.2005.02.009
20.
Duan
,
H. L.
,
Wang
,
J.
,
Huang
,
Z. P.
, and
Karihaloo
,
B. L.
,
2005
, “
Eshelby Formalism for Nano-Inhomogeneities
,”
Proc. R. Soc. London Ser. A
,
461
(2062), pp.
3335
3353
.10.1098/rspa.2005.1520
21.
Kim
,
C. I.
,
Schiavone
,
P.
, and
Ru
,
C.-Q.
,
2009
, “
The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution
,”
ASME J. Appl. Mech.
,
77
(2), p. 021011.10.1115/1.3177000
22.
Kim
,
C. I.
,
Ru
,
C.-Q.
, and
Schiavone
,
P.
,
2010
, “
Analysis of Plane-Strain Crack Problems (Mode-I & Mode-II) in the Presence of Surface Elasticity
,”
J. Elast.
,
104
(1-2), pp.
397
420
.10.1007/s10659-010-9287-0
23.
Nan
,
H.
, and
Wang
,
B.
,
2012
, “
Effect of Residual Surface Stress on the Fracture of Nanoscale Materials
,”
Mech. Res. Commun.
,
44
, pp.
30
34
.10.1016/j.mechrescom.2012.05.006
24.
Kim
,
C. I.
,
Schiavone
,
P.
, and
Ru
,
C.-Q.
,
2011
, “
Effects of Surface Elasticity on an Interface Crack in Plane Deformations
,”
Proc. R. Soc. London Ser. A
,
467
(2136), pp.
3530
3549
.10.1098/rspa.2011.0311
25.
Ladan
,
P.
, and
Hossein
,
M. S.
,
2010
, “
Surface and Interface Effects on Torsion of Eccentrically Two-Phase fcc Circular Nanorods: Determination of the Surface/Interface Elastic Properties Via an Atomistic Approach
,”
ASME J. Appl. Mech.
,
78
(1), p. 011011.10.1115/1.4002211
26.
Kouris
,
D.
, and
Mi
,
C.
,
2007
, “
Surface Strain Due to Embedded Epitaxial Islands
,”
Surf. Sci.
,
601
(3), pp.
757
762
.10.1016/j.susc.2006.11.003
27.
Albina
,
J.-M.
,
Elsasser
,
C.
,
Weissmuller
,
J.
,
Gumbsch
,
P.
, and
Umeno
,
Y.
,
2012
, “
Ab Initio Investigation of Surface Stress Response to Charging of Transition and Noble Metals
,”
Phys. Rev. B
,
85
, p.
125118
.10.1103/PhysRevB.85.125118
28.
Fang
,
X. Q.
,
Yang
,
Q.
,
Liu
,
J. X.
, and
Feng
,
W. J.
,
2012
, “
Surface/Interface Effect Around a Piezoelectric Nano-Particle in a Polymer Matrix Under Compressional Waves
,”
Appl. Phys. Lett.
,
100
, p.
151602
.10.1063/1.3702780
29.
Khoei
,
A. R.
,
Ghahremani
,
P.
, and
DorMohammadi
,
H.
,
2014
, “
Multi-Scale Modeling of Surface Effects in Nano-Materials With Temperature-Related Cauchy-Barn Hypothesis via the Modified Boundary Cauchy-Born Model
,”
Int. J. Numer. Methods Eng.
,
97
(2), pp.
79
110
.10.1002/nme.4579
30.
Williams
,
M. L.
,
1952
. “
Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension
,”
J. Appl. Mech.
,
19
, pp.
526
528
.
31.
Chen
,
D. H.
,
1995
, “
Stress Intensity Factors for V-Notched Strip Under Tension or In-Plane Bending
,”
Int. J. Fracture
,
70
(1), pp.
81
97
.10.1007/BF00018137
32.
Bogy
,
D. B.
,
1970
, “
On the Problem of Edge-Bonded Elastic Quarter-Planes Loaded at the Boundary
,”
Int. J. Solids Struct.
,
6
(9), pp.
1287
1313
.10.1016/0020-7683(70)90104-6
33.
Bogy
,
D. B.
,
1971
, “
Two Edge-Bonded Elastic Wedges of Different Materials and Wedge Angles Under Surface Tractions
,”
J. Appl. Mech.
,
38
(2), pp.
377
386
.10.1115/1.3408786
34.
Hein
, V
. L.
, and
Erdogan
,
F.
,
1971
, “
Stress Singularities in a Two Material Wedge
,”
Int. J. Fracture Mech.
,
7
(3), pp.
317
330
.10.1007/BF00184307
35.
Dempsey
,
J. P.
, and
Sinclair
,
G. B.
,
1979
, “
On the Stress Singularities in the Plane Elasticity of the Composite Wedge
,”
J. Elast.
,
9
(4), pp.
373
391
.10.1007/BF00044615
36.
Reedy
,
E. D.
, Jr.
,
1993
, “
Asymptotic Interface-Corner Solutions for Butt Tensile Joints
,”
Int. J. Solids Struct.
,
30
(6), pp.
767
777
.10.1016/0020-7683(93)90039-A
37.
Yang
,
Y. Y.
, and
Munz
,
D.
,
1997
, “
Stress Singularities in a Dissimilar Materials Joint With Edge Tractions Under Mechanical and Thermal Loadings
,”
Int. J. Solids Struct.
,
34
(
10
), pp.
1199
1216
.10.1016/S0020-7683(96)00097-2
38.
Chen
,
D. H.
,
1997
, “
Condition for Occurrence of Logarithmic Stress Singularity
,”
JSME Int. J.
,
40
(
3
), pp.
298
305
.10.1299/jsmea.40.298
39.
Koguchi
,
H.
,
Inoue
,
T.
, and
Yada
,
T.
,
1996
, “
Stress Singularity in Three-Phase Bonded Structure
,”
ASME J. Appl. Mech.
,
63
(
2
), pp.
252
258
.10.1115/1.2788857
40.
Labossiere
,
P. E. W.
,
Dunn
,
M. L.
, and
Cunningham
,
S. J.
,
2002
, “
Application of Bilateral Interface Corner Failure Mechanics to Silicon/Glass Anodic Bonds
,”
J. Mech. Phys. Solids
,
50
(3), pp.
405
433
.10.1016/S0022-5096(01)00087-4
41.
Suo
,
Z.
,
1990
, “
Singularities, Interfaces and Cracks in Dissimilar Anisotropic Media
,”
Proc. R. Soc. London Ser. A
,
427
(1873), pp.
331
358
.10.1098/rspa.1990.0016
42.
Labossiere
,
P. E. W.
, and
Dunn
,
M. L.
,
1999
, “
Stress Intensities at Interface Corners in Anisotropic Bimaterials
,”
Eng. Fracture Mech.
,
62
(6), pp.
555
575
.10.1016/S0013-7944(99)00005-3
43.
Hwu
,
C.
,
Omiya
,
M.
, and
Kishimoto
,
K.
,
2003
, “
A Key Matrix N for the Stress Singularity of the Anisotropic Elastic Composite Wedges
,”
JSME Int. J. Ser. A
,
46
(
1
), pp.
40
50
.10.1299/jsmea.46.40
44.
Hwu
,
C.
, and
Kuo
,
T. L.
,
2007
, “
A Unified Definition for Stress Intensity Factors of Interface Corners and Cracks
,”
Int. J. Solids Struct.
,
44
(18-19), pp.
6340
6359
.10.1016/j.ijsolstr.2007.02.031
45.
Horiike
,
K.
,
Ikeda
,
T.
,
Matsumoto
,
R.
, and
Miyazaki
,
N.
,
2010
, “
Stress Singularity Analysis at an Interfacial Corner Between Dissimilar Crystals and Evaluation of Mixed Modes Fracture Criteria Using Molecular Statics
,”
J. Soc. Mater. Sci. Jpn.
,
59
(
12
), pp.
908
915
.10.2472/jsms.59.908
46.
Wadley
,
H. N. G.
,
Zhou
,
X.
,
Johnson
,
R. A.
, and
Neurock
,
M.
,
2001
, “
Mechanisms, Models and Methods of Vapor Deposition
,”
Progress Mater. Sci.
,
46
(3-4), pp.
329
377
.10.1016/S0079-6425(00)00009-8
47.
Ting
,
T. C. T.
,
1996
,
Anisotropic Elasticity—Theory and Application
,
Oxford University Press
,
New York
.
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