Vol 222, No 2 (2017)

We formulate a mathematical model for the investigation of the processes of propagation of creepfatigue cracks in plates under block loading. The influence of the shape of loading blocks on the durability of structural elements is investigated and the the subcritical growth of creep-fatigue cracks in thin-walled structural elements is analyzed.

We model contact interaction of two elastic semiinfinite bodies in the presence of a real gas in the interface gaps formed by a periodic array of grooves on the surface of one of the bodies. The state of the gas is described by the van der Waals equation, which enables us to consider the phase transition from the gas into the liquid phase. The posed contact problem is reduced to a singular integral equation with Hilbert kernel for the height of the gap. This equation is transformed into a singular integral equation with Cauchy kernel and is solved analytically. To determine the length of the gap and gas pressure, we derive a system of transcendental equations from the condition of boundedness of the solution of this singular integral equation and from the van der Waals equation. The dependences of the gap length, gas pressure, contact approach, and contact compliance of the bodies on the applied load are analyzed.

A continual model of deformation of piezoelectric materials weakened by a system of microcracks dispersed over the bulk of the material is constructed with use of the energy method. This method is based on the assumption of equivalence of the strain energy of the cracked electroelastic medium and the strain energy of a continuum modeling the indicated medium. A generalization of the Eshelby principle is used to determine the strain energy of microinhomogeneous media with inclusions.

Under conditions of plane deformation, by using the Wiener–Hopf method, we compute a small-scale contact zone near the tip of an interface crack under the condition of formation of the lateral process zone in its vicinity. It is assumed that the dry friction of the faces according to the Coulomb law is realized in the contact zone. We determine the sizes of the contact zone and deduce an expression for the contact stresses and an equation for the determination of the index of singularity of stresses near the crack tip. The influence of the load, friction coefficient, and elastic characteristics of the joined materials on the sizes of the contact zone is investigated. It is shown that, in the presence of the process zone, the length of the contact zone begins to depend not only on the configuration of the external load but also on its value.