Vol 52, No 4 (2017)

We study static and dynamic stability problems for a thin flexible rod subjected to axial compression with the geometric nonlinearity explicitly taken into account. In the case of static action of a force, the critical load and the bending shapes of the rod were determined by Euler. Lavrent’ev and Ishlinsky discovered that, in the case of rod dynamic loading significantly greater than the Euler static critical load, there arise buckling modes with a large number of waves in the longitudinal direction. Lavrent’ev and Ishlinsky referred to the first loading threshold discovered by Euler as the static threshold, and the subsequent ones were called dynamic thresholds; they can be attained under impact loading if the pulse growth time is less than the system relaxation time. Later, the buckling mechanism in this case and the arising parametric resonance were studied in detail by Academician Morozov and his colleagues.

In this paper, we complete and develop the approach to studying dynamic rod systems suggested by Morozov; in particular, we construct exact and approximate analytic solutions by using a system of special functions generalizing the Jacobi elliptic functions. We obtain approximate analytic solutions of the nonlinear dynamic problem of flexible rod deformation under longitudinal loading with regard to the boundary conditions and show that the analytic solution of static rod system stability problems in a geometrically nonlinear statement permits exactly determining all possible shapes of the bent rod and the complete system of buckling thresholds. The study of approximate analytic solutions of dynamic problems of nonlinear vibrations of rod systems loaded by lumped forces after buckling in the deformed state allows one to determine the vibration frequencies and then the parametric resonance thresholds.

A nondestructive method for monitoring the crack state in reinforced concrete structures based on the recoding of wave processes in these structures under shock actions is proposed. The essence of the method and its possibilities are demonstrated by an example of the study of the behavior of a reinforced concrete beam with a crack at various stages of crack development and repair. Numerical simulation was used to study variations in the wave front characteristics in the crack area. A quantitative criterion was formulated, which permits estimating the concrete integrity or the existence of crack in it and monitoring the variations in the crack state in the process of loading the structure and the crack repair. The criterion is determined as the ratio of the amplitudes of the first half-waves of the acceleration wave front registered in regions on the opposite shores of the crack. The criterion value is independent of the amplitude of the shock action and the beam fixation conditions and is solely determined by the mechanical state of the material used to repair the crack. The criterion adequacy was demonstrated by comparing the results of numerical simulation with experimental data. A cycle of numerical experiments were carried out, which, for each duration of the shock action, permits determining the optimal values of the distance between the pulse application point and the acceleration recording points at which the criterion is most sensitive to the crack state.

A model of material of complex crystalline structure consisting of two lattices coupled by nonlinear interaction forces that ensure several stable equilibrium configurations is considered. The continuum model is compared with the discrete model whose analysis reveals the effect, which has been observed in high-speed deformation experiments, of decrease in the initial pulse under nonstationary actions.

Measurement results for the shock wave compression profiles of 12Cr19Ni10Ti steel and its dynamic strength in the strain rate range 10⁵–10⁶ s⁻¹ are presented. The protracted viscous character of the spall fracture is revealed. With the previously obtained data taken into account, the measurement results are described by a polynomial relation, which can be used to construct the fracture kinetics. On the lower boundary of the range, the resistance to spall fracture is close to the value of the true strength of the material under standard low-rate strain conditions; on the upper boundary, the spall strength is more than twice greater than this quantity. An increase in the temperature results in a decrease in both the dynamic limit of elasticity and the spall fracture strength of steel. The most interesting result is the anomaly in the dependence of the spall fracture strength on the duration of the shock wave compression pulse, which is related to the formation of deformation martensite near the growing discontinuities.

Several general laws of deformation of an inhomogeneous elastic layered structure under the action of an indentor and the force–indentation dependence during the loading of cracked specimens are studied, and relations for the critical values of the parameters at which separation is possible are constructed.

The axisymmetric contact problem of interaction between a two-layer foundation and a rigid annular punch is considered under the assumption that the surface nonuniformity of the upper layer and the shape of the punch base are described by rapidly varying functions. The integral equation of the problem containing two rapidly varying functions is derived, and two versions of the problem are considered. Their solutions were first constructed by the generalized projection method. As an illustration, the model problem is analyzed numerically to demonstrate the high efficiency of the method.

The cold gas dynamic spray (CGDS) method used to form composite Ni+B₄C coatings from mechanical powder mixture with various content of abrasive components is investigated, and the surface and microstructure of these coatings are considered. An experimental dependence of the deposition coefficient on the abrasive content in the mechanical powder mixture is obtained. The coatings are studied by interference profilometry, optical microscopy, and microindentation methods. The dependence of the bulk and mass B₄C content in the sprayed material on the abrasive content in the sprayed powder mixture is obtained. The bulk B₄C content in the coating c_V ≈ 0.27 is attained. The dependence of the microhardness of composite CGDS coatings on the boron carbide content in them is investigated. The results of this paper demonstrate that the powder mixture composition significantly affects the CGDS coating growth and the properties of these coatings and can be used to control the properties of the CGDS cermet materials.