Research On Bridged Nanocracks With Surface Elasticity

This paper studies the problem of bridged nanocracks with surface elasticity.The surface elasticity is incorporated into the crack faces by utilizing the continuum-based surface/interface model of Gurtin-Murdoch.The crack faces are assumed to be fully or partially bridged by fibers or ligaments with variable bridging stiffness.In this thesis,by using the Green's function method,the Chebyshev polynomials and the collocation methods,the problem is numerically solved and the effects of surface elasticity and crack bridging on nanocracks are analyzed in detail.First,the Saint-Venant torsion problem of a circular cylinder containing a radial nanocrack with surface elasticity is studied.Both an internal crack and an edge crack are considered.The stresses exhibit a weak logarithmic singularity rather than a strong square root singularity at the crack tips due to the surface effect.In addition,the crack bridging can have both toughening and stiffening effects on the crack.The strengths of the logarithmic singularity at the crack tips,the reduction in torsional rigidity and the jump in warping function across the crack faces are calculated.Second,the contribution of crack bridging and surface elasticity to the elastic interaction between a mode III finite crack and a screw dislocation is examined.Owing to the incorporation of surface elasticity,the stresses at the crack tips only exhibit the weak logarithmic singularity when the dislocation is located on the real axis where the crack is located,whereas in the case when the dislocation is not on the real axis,the stresses at the crack tips exhibit both the weak logarithmic and the strong square-root singularities.The two densities,the crack opening displacement across the crack faces and the image force acting on the screw dislocation are specifically calculated.The crack bridging only exerts an effect on the line dislocation density but has no influence on the line force density.In addition,both surface elasticity and crack bridging can reduce the strengths of the logarithmic stress singularity at the crack tips and the magnitude of the crack opening displacement across the crack faces.It is clearly shown that both crack bridging and surface elasticity exert a significant influence on the magnitude and direction of the image force acting on the screw dislocation.Third,the contribution of crack bridging and surface elasticity to the elastic interaction between a finite crack and an edge dislocation is examined.The residual surface tension is taken to be zero in our discussion.A general formula is derived for calculating the image force acting on the edge dislocation.Our analysis indicates that the stresses exhibit both the weak logarithmic and the strong square root singularities at the crack tips.We note that both crack bridging and surface elasticity influence the magnitude and direction of the image force acting on the edge dislocation.Particularly,the results show that the dislocation may have four stable and two unstable equilibrium positions due to the presence of surface elasticity.In addition,the number and location of the equilibrium positions depend on both surface elasticity and crack bridging.Last,the contribution of crack bridging and surface elasticity to fully or partially bridged mode-I and mode-II cracks is examined.The surface tension is taken into consideration in our discussion.Our analysis indicates that the stresses exhibit the weak logarithmic singularity rather than the classical strong square-root singularity at the crack tips due to the presence of surface elasticity.We also note that both crack bridging and surface elasticity can suppress the strengths of the logarithmic singularity at the crack tips,and thus toughen the solid.In addition,the magnitudes of the tangential and normal displacement jumps across the crack faces are reduced due to the stiffening effect of crack bridging.