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By dimensional analysis, it is confirmed that a cumulative local size xy for one-dimentional irreversible submonolayergrowth of point islands [J. G. Amar and M. N. Popescu, Surf. Sci. 419, 239 (2001)] is expressed bya function of scaled gap length Y and dimensionless deposition time R1/3θ, where R is the ratio of the monomerdiffusion rate to the deposition rate and θ is coverage. Using asymptotic analysis for xy as the limit R Ishow that xy/sav I = 1/B ∫ 1 ϕY uα tanh (YBu−α) du, where B is a certain monotonically decreasing function ofthe variable R1/3θ, α is dynamical exponent of nucleation length and sav is average size. At both of the numericalresult of xy/sav and the approximate analytical evaluation for the integral I with Taylor expansion in YB for theintegrand, correction term for Y Y−3( or limit of xy/sav as is shown to be proportional to (R1/3θ)−3/4,and the analytical evaluation is in good agreement with the numerical result in R1/3θ 400. Finally, I findanother evaluation for I with the expansion in α to improve the deviation in 100 R1/3θ < 400.

金沢大学理工研究域環境デザイン学系, A new fracture criterion of the shear failure for the geomaterials is presented which enables to predict a straight extension of a crack in the elastic plastic materials under the compressive loads. It is an application of the Coulomb fracture criterion to a crack extension criterion called "The maximum frictional shear stress criterion". We examine the criterion by using both the singular and the constant terms in the asymptotic expansion of the crack tip stress fields for a linear hardening Drucker-Prager elastic plastic material. As a result, we find that the confining pressure, the frictional coefficient of the crack surface, the small hardening parameter, and the dilatancy effect is the lowering of the extensive hoop stress causing the crack kink, which contribute the frictional shear stress extending a crack straight to maximum. © 2008 The Society of Materials Science.

金沢大学理工研究域環境デザイン学系, In the geomechanical studies the mechanism of the shear failure for the Mode II crack extension is still an open problem. As the basic research, the purpose of this paper is, therefore, to obtain the Mode II singular fields near a crack tip. The geomaterials, in general, have a pressure sensitive yield function to yield a dilatant effect. Thus, assuming a proportional loading, we obtain the asymptotic stress and displacement fields for the Mode II crack in the linear hardening Drucker-Prager elastic-plastic material. For the Mode II crack of the Drucker-Prager material, the boundary conditions can not be given on the extension of the crack surface, since the informations of the boundary are unknown : This is due to the loss of symmetry or asymmetry of the displacements and the stresses because of the existence of a parameter of the dilatant effect. Then the boundary conditions for the Mode II crack are given on the crack surfaces ; that is, the jumps of the normal displacement, the normal stress, and the shear stress vanish. As a result, a very small normal stress appears on the crack surfaces. We finally examine the angular distribution of the displacement and stress fields which depend on the hardening parameter and the pressure sensitivity parameter.

A new fracture criterion of the shear failure for the geomaterials is presented which predicts a straight extension of a crack in an elastic plastic material under compressive loads called “The maximum frictional shear stress criterion”. Weexamine the criterion by using both the singular and the constant terms in the asymptotic expansion of the crack tip stress fields for a non-associate linear hardening Drucker-Prager elastic-plastic material. As a result, we find that the confining pressure, the friction along the crack surfaces, the internal material friction, and the dilatancy effect are the lowering of the extensive hoop stress: Then they cause the maximum frictional shear stress to extend a crack straight