Research On Saint-Venant's Torsion Of Circular Cylinder Containing Cracks Incorporating Surface Elasticity

The key issue of this thesis is the Saint-Venant torsion problem of a circular containing cracks with surface elasticity.The surface elasticity is incorporated into the crack faces by employing the continuum-based surface/interface model of Gurtin-Murdoch which has been used extensively in numerous studies on fracture mechanics.In this thesis,by using the Green's function method.the Gauss-Chebyshev integration formula,the Chebyshev polynomials and the collocation methods,problems of surface effects,varied surface effects and surface strain gradient effects in the torsion of circular bars with cracks are addressed respectively.First,the Saint-Venant torsion problem of a circular cylinder containing a radial crack with surface elasticity is studied.Both an internal crack and an edge crack are considered.Due to the incorporation of the surface elasticity,the stresses exhibit the logarithmic singularity at the crack tips.The Saint-Venant torsion problem of circular cylinder containing two symmetric collinear radial cracks with surface elasticity is also solved.The strengths of the logarithm singularity and the size-dependent torsional rigidity are calculated.Second,the contribution of surface elasticity to the Saint-Venant torsion problem of a circular cylinder containing a non-radial crack is analytically investigated.Both internal and edge cracks are studied.The analysis indicates that in general the stresses at the crack tips exhibit both the weak logarithmic and the strong square root singularities.The jump in the warping function across the crack faces and size-dependent torsional rigidity are calculated.Third,the contribution of arbitrarily varied surface elasticity to the Saint-Venant torsion problem of a circular cylinder containing a radial crack is analytically investigated.The varied surface elasticity is incorporated by using a modified version of the continuum based surface/interface model of Gurtin and Murdoch.In this discussion,the shear modulus is assumed to be arbitrarily varied along the crack faces.The torsion problem of a cylinder containing two symmetric collinear radial cracks of equal length with symmetrically varied surface elasticity is also addressed.Numerical results indicate that the variation of the surface elasticity exerts a significant influence on the strengths of the logarithmic stress singularity,the torsional rigidity and the jump in warping function.Last,the contribution of surface strain gradient elasticity to the Saint-Venant torsion problem of a circular cylinder containing a radial crack is studied.The surface strain gradient elasticity is incorporated by using an enriched version of the continuum based surface/interface model of Gurtin and Murdoch accounting for the surface strain gradient effects.Due to the presence of surface strain gradient elasticity on the crack faces,the stresses are bounded at the crack tips.The torsion problem of a circular cylinder containing two symmetric collinear radial cracks of equal length with surface strain gradient elasticity is also solved.Numerical results indicate that the surface strain gradient effect exerts a significant influence on the torsional rigidity and the jump in warping function.In particular,the jump in warping function forms a cusp shape with zero enclosed angle at the crack tips.