In this paper, the two state -integral is extended from macrofacture to nanodefect mechanics. The question as to why the -integral for a nanovoid or a soft nano-inclusion might be negative is clarified. It is concluded that the surface tension plays a dominant role in evaluating the -integral, whereas the surface Lamè constants yield much less influence than the surface tension. Their influence on the -integral for a nanovoid or a soft nano-inclusion could be neglected.
1.
Chen
, F. H. K.
, and Shield
, R. T.
, 1977, “Conservation Laws in Elasticity of the J-Integral Type
,” Z. Angew. Math. Phys.
0044-2275, 28
, pp. 1
–22
.2.
Yau
, J. F.
, Wang
, S. S.
, and Corten
, H. T.
, 1980, “A Mixed Mode Crack Analysis of Isotropic Solids Using Conservation Laws of Elasticity
,” ASME J. Appl. Mech.
0021-8936, 47
, pp. 335
–341
.3.
Choi
, N. Y.
, and Earmme
, Y. Y.
, 1992, “Evaluation of Stress Intensity Factors in a Circular Arc-Shaped Interfacial Crack Using L-Integral
,” Mech. Mater.
0167-6636, 14
, pp. 141
–153
.4.
Kfouri
, A. P.
, 1986, “Some Evaluations of Elastic T-Term Using Eshelby’s Method
,” Int. J. Fract.
0376-9429, 30
, pp. 301
–315
.5.
Matos
, P. P. L.
, McMeeking
, R. M.
, Charalambides
, P. G.
, and Drory
, M. D.
, 1989, “A Method for Calculating Stress Intensities in Bimaterial Fracture
,” Int. J. Fract.
0376-9429, 40
, pp. 235
–254
.6.
Im
, S.
, and Kim
, K. S.
, 2000, “An Application of Two-State M-Integral for Computing the Intensity of the Singular Near-Tip Field for a Generic Wedge
,” J. Mech. Phys. Solids
0022-5096, 48
, pp. 129
–151
.7.
Hui
, C. Y.
, and Riana
, A.
, 1995, “Why K? Higher Order Singularities and Small Scale Yielding
,” Int. J. Fract.
0376-9429, 72
, pp. 97
–120
.8.
Chen
, Y. H.
, and Hasebe
, N.
, 1997, “Explicit Formulations of J-Integral Considering Higher Order Singular Terms in Eigenfunction Expansion Form
,” Int. J. Fract.
0376-9429, 85
, pp. 11
–14
.9.
Jeon
, I.
, and Im
, S.
, 2001, “The Role of Higher Order Eigenfields in Elastic-Plastic Cracks
,” J. Mech. Phys. Solids
0022-5096, 49
, pp. 2789
–2818
.10.
Kim
, Y. J.
, Kim
, H. G.
, and Im
, S.
, 2001, “Mode Decomposition of Three-Dimensional Mixed-Mode Cracks Via Two-State Integrals
,” Int. J. Solids Struct.
0020-7683, 38
, pp. 6405
–6426
.11.
Hui
, T.
, and Chen
, Y. H.
, 2010, “The M-Integral Analysis for a Nano-Inclusion in Plane Elastic Materials Under Uni-Axial or Bi-Axial Loadings
,” ASME J. Appl. Mech.
0021-8936, 77
, p. 021019
.12.
Tian
, L.
, and Rajapakse
, R. K. N. D.
, 2007, “Analytical Solution for Size-Dependent Elastic Field of a Nanoscale Circular Inhomogeneity
,” ASME J. Appl. Mech.
0021-8936, 74
, pp. 568
–574
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