ИСТИНА

This presentation consists of two parts. The first part deals with the behaviour of rigid plastic solutions in the vicinity of frictional interfaces at large strains. Several widely used material models are considered including rigid perfectly plastic material, the double shearing model and a viscoplastic model with a saturation stress. It is demonstrated that the solutions at maximum friction surfaces are singular. In particular, the quadratic invariant of the strain rate tensor approaches infinity in the vicinity of such surfaces. Asymptotic analysis shows that this invariant follows an inverse square root rule. This theoretical finding can be used for developing an approach for predicting the generation of fine grain layers near frictional interfaces in material processing including processing of composite materials. The second part of the presentation deals with the behaviour of elastic plastic solutions of damage mechanics in the vicinity of frictional interfaces at small strains. The constitutive equations comprise Hooke’s law, a yield criterion, its associated flow rule, and a damage evolution equation. The damage parameter affects the yield stress and elastic moduli but the associated flow rule is not altered by the damage parameter. A widely used fracture criterion postulates that the damage parameter attains a critical value at the instant of fracture initiation. The behavior of solution in the pull-out test is studied. It is assumed that the regime of sticking occurs at the friction surface. The general solution to the boundary value problem is found. As the loading parameter increases, the shear stress at the friction surface increases. It is shown that there is such a value of the loading parameter that the general solution breaks down but the fracture criterion is not satisfied. This means that no solution to the boundary value problem exists.