A Crack with Interfacial Bonds in an Isotropic Medium Strengthened with a Regular System of Stringers

An isotropic medium containing a system of foreign transverse rectilinear inclusions is considered. Such a medium can be interpreted as an infinite plate strengthened with a regular system of ribs (stringers) whose cross section is a very narrow rectangle. The medium is weakened by a rectilinear crack. The action of the stringers is replaced with unknown equivalent concentrated forces at the points of their connection with the medium. A model of a crack with areas where its faces interact with each other is investigated. This interaction is modeled by introducing bonds (adhesion forces) between faces in the crack tip zone. The boundary-value problem on equilibrium of the crack under the action of external tensile forces is reduced to a nonlinear singular integral equation, from the solution of which the tractions in the bonds are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 773–782, November–December, 2005.     

Modeling of partial closure of cracks in a perforated isotropic medium reinforced by a regular system of stringers

A mathematical model of partial closure of a crack in a perforated isotropic medium with a system of rectilinear foreign inclusions is constructed. Such a medium can be interpreted as an unbounded plate reinforced by a regular system of ribs whose cross sections are shaped as narrow rectangles. The medium is assumed to be attenuated by a periodic system of circular holes and straight-line cracks. Determination of unknown contact stresses and contact zone sizes is reduced to solving a singular integral equation, which is transformed by an algebraization procedure to a system of nonlinear algebraic equations solved by the method of consecutive approximations.     

Interaction of cracks with bonds between their faces in an isotropic medium reinforced by a regular system of stringers

A problem of an elastic isotropic medium with a system of foreign (transverse with respect to crack alignment) rectilinear inclusions is considered. The medium is assumed to be attenuated by a periodic system of rectilinear cracks with zones where the crack faces interact with each other. These zones are assumed to be adjacent to the crack tips, and their sizes can be commensurable with the crack size. Interaction between the crack faces in the tip zone is modeled by introducing bonds (adhesion forces) between the cracks with a specified strain diagram. The boundary-value problem of the equilibrium of a periodic system of cracks with bonds between their faces under the action of external tensile loads and forces in the bonds is reduced to a nonlinear singular integrodifferential equation with a kernel of the Cauchy kernel type. The condition of critical equilibrium of the cracks with the tip zones is formulated with allowance for the criterion of critical tension of the bonds. A case of a stress state of the medium containing zones where the crack faces interact with each other is considered.     

Fracture of an isotropic medium strengthened with a regular system of stringers

An isotropic medium containing a system of foreign transverse rectilinear inclusions is considered. Such a medium can be interpreted as an infinite plate strengthened with a regular system of ribs (stringers) whose cross section is a very narrow rectangle. The medium is weakened by a periodic system of rectilinear cracks. The action of the stringers is re placed by unknown equivalent concentrated forces at the points of their connection with the medium. The boundary-value problem on equilibrium of the periodic system of cracks under the action of external tensile forces is reduced to a singular integral equation, from the solution of which the stress in tensity factors are found. The condition of limiting state of equilibrium of the cracks is formulated based on a criterion of brittle fracture. The stress state in the case where crack faces come into a partial contact is also considered. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 59–72, January–February, 2007.