Similarity of Stress-Singularity Problems for Materials with Linear and Bilinear Behaviors

An analogy is established between the solutions of the problems of singularities of stresses in linear and bilinear elastic isotropic media. It is shown that the distributions of stresses and displacements in the vicinity of singular points on the boundary of the body (characterized by the singularities of stresses) are described, in both cases, by the same functional dependences on the space coordinates but with different characteristics of the material. We deduce expressions for the effective moduli of elasticity and Poisson's ratio of the bielastic medium including the parameter of hardening of the material. The solution of the problem of singularities of stresses in bilinear materials is obtained from the solution of the corresponding problem for the linear elastic medium by replacing the elastic constants with the corresponding effective values depending on the parameter of hardening of the material. The cases of wedge-shaped notches (for various boundary conditions imposed on their edges), two-component wedges, plane wedge-shaped cracks, and circular conic notches or rigid inclusions in the bielastic space are studied in detail.     

Torsion of an elastic space with a crack on the surface of revolution

Numerical methods for solving integral equations of an axisymmetric problem of torsion of an elastic space with cracks on the surface of revolution are suggested for the cases of cracks crossing the axis of symmetry and cracks that have no common points with this axis. We also present relations for calculating the stress intensity factors at crack tips. Numerical results are obtained for a conic or paraboloidal simply connected crack and for a doubly connected crack lying on a surface formed by the revolution of an arbitrarily oriented straight segment or a parabolic arc. The crack faces are either subjected to a constant load or free of any forces; the body is subjected to torsion at infinity.Karpenko Physico-Mechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 29, No. 6, pp. 87–93, November–December, 1993.     

Two-Dimensional Periodic Problem of the Theory of Elasticity for an Isotropic Plane with Curvilinear Holes and Edge Cracks

Materials Science - By the method of singular integral equations, we solve a two-dimensional periodic problem of the theory of elasticity for an isotropic plane with infinitely many curvilinear...     

Antiplane deformation of a cracked composite strip

We obtain the analytic solution of an antiplane problem of the theory of elasticity for a cracked layer made of a composite material whose cross section is formed by a periodic array of repeated rectangular elements. Each element, in turn, contains four rectangular cells of different types. A crack is located on one of the interfaces of materials of these cells. The distributions of displacements on the outer surfaces of the layer are regarded as given. The numerical analyses are performed for the stress intensity factors depending on the mechanical properties of materials and the sizes of the cells.