Theoretical Analysis On Surface Nano-defects At The Plane Boundary Of An Elastic Half-space

Stress concentration near geometric defects is an important factor affecting the bearing capacity of engineering structure.For macroscopic structures,the surface atom ratio and specific surface area are extremely small.It is commonly accepreatd that the stress concentration factor at the boundary of macroscopic defects is independent of surface/interface parameters.The surface atom ratio and specific surface area of nanostructures are so large that the mechanical behavior of these structures strongly depends on the mechanical response of surfaces.When the structure size is on the nanometer scale,the surface atom ratio and specific surface area increase sharply with the decrease of the structural characteristic dimension.Therefore,the stress concentration factor at the nanoscopic defects boundary exhibits a strong dependence on defect size.In this thesis,the mechanical response of an elastic half-space with surface nano-defects is studied.Frist,considering the uncertainty of the shape of surface defects,general expressions of the displacement and stress field in orthogonal curvilinear coordinates were deduced.These expressions are important to the basic governing equations of the displacement potential function method and the Gurtin-Murdoch surface/interface mechanic model.Furthermore,general expressions for vector gradient,vector divergence,tensor gradient and tensor divergence in orthogonal curving coordinates were developed.Second,a micromechanical model that couples Gurtin and Murdoch’s model of surface mechanics with the classical theory of elasticity was developed to analyze a soft half-space with a nanoscopic semisphere surface pit.The stress concentration,displacement and stress distributions resulting from a family of statically equivalent shear tractions applied on the pit surface were explicitly evaluated.It is found that two intrinsic dimensionless parameters govern the highly localized elastic field.These two dimensionless parameters were constructed from the characteristic length,the residues surface stress and the surface shear moduls.Both the magnitude and sign of these parameters are of great importance.Negative values tend to increase stress concentrations,whereas positive ones have the opposite effect.The consequences of our analysis were further highlighted by comparing a number of shear tractions that correspond to the same torque.The comparison provides the means of evaluating the degree of difference in elastic fields in the immediate vicinity of statically equivalent force distributions.Finally,the principle of minimum potential energy was used to solve the stress concentration factor,displacement and stress field of a metallic half-space with surface nanodefects subjected to far-field biaxial tension.Given the fact that the effects of surface residual stress to local elastic field is much more significant than surface lame parameters,only surface residual stress was considered in the analyze of meatic substrates.Semianalyiz results suggest that both the values and signs of the surface residual stress significantly affect the stress concentration factor at the nano-pit surface.The difference between the stress concentration factor at the hemispherical nano-pit boundary and its classical counterpart is proportional to the absolute value of the surface residual stress.A positive residual surface stress tends to decrease the stress concentration factor at the nano-pit boundary,while a negative surface residual stress has the opposite effect.The effect of the residual surface stress on stress field is limited to the extent of several pit radii measured from the pit surface.The influence of residual surface stress can be neglected when the distance from the nano-pit surface is further than five times of the radius of hemispherical pit.The impact of residual surface stress on the elastic field depends on the radius of nano-pit.The residual surface stress is negligible for voids larger than 100nm,but becomes dominant when the void size decreases down to the order of 10nm.To summarize,the displacement field,stress field and stress concentration factor of an elastic half-space with a hemispheral nanopit are subjected to either statically equivalent shear tractions or far-field biaxial tensions were explicitly derived.The obtained results are able to extend the field of research on elastic hale-spaces emiedded with micro and nanoscle defects,and are very important to the understanding of failure of nanostructured caused by stress concentrations.