The process of bidirectional compression of a powder titanium sponge in a pressing tool with a floating die is considered. The paper studies powder screenings of titanium sponge of TG-100 grade according to GOST 17746-96 with a fraction of -3 + 1 mm. A new design of the pressing tool is proposed to implement the process of bidirectional compression. The simultaneous movement of the upper and lower punches relative to the sectional die is achieved by placing the die between two rubber springs. The pressing tool provides an efficient compression due to the implementation of a synchronous vibration-free movement of the lower and upper punches relative to the sectional die, as well as a uniform compression unloading on all sides, which eliminates the occurrence of splitting cracks. Numerical simulation of the process was performed using a finite element analysis. In the simulation, it was assumed that the elements of the pressing tool have properties of an absolutely rigid body. The powder material is considered as a continuous compressed elastoplastic medium with initial isotropic properties. The powdered material yield condition is described by the Modified Drucker-Prager Cap yield model. The rate of plastic deformation is proportional to the voltage at the current moment, the stress state determines the instantaneous increments of plastic deformation components. The associated plastic flow rule is fulfilled. Mooney-Rivlin hyperelastic material model was used as a model of the material (SKU-7L rubber) of the spring elements. As a result of the simulation, the calculated density distribution in the cross-section of the compacted powder workpieces at different compression pressures was obtained. The dependence of the average relative density of the powder workpieces on the compression pressure was investigated. For the compacts obtained at different compression pressures (100 and 500 MPa), a micrographic study of the microstructure of the samples longitudinal sections surfaces was performed. The change in the shape and size of pores in the lower and upper parts of compacts was studied. In order to assess micromechanical properties of the obtained workpieces, kinetic microindentation of thin section surfaces of the longitudinal axial sections was carried out, which allowed determining the microhardness values, the creep characteristic, and the reduced modulus of elasticity. It is shown that the proposed design of the pressing tool allows obtaining workpieces with a more uniform density distribution in comparison with those manufactured using monodirectional compression.

The real experience of different structural elements shows that cyclic loading conditions and stress strain state are often quite different from laboratory test conditions such as axial tension-compression, bending or pure torsion. As a rule, the structural elements are subjected to complex (multiaxial) loading conditions during service, that is why multiaxial fatigue criteria should be used for durability estimation of such elements. A present multiaxial criterion allows us to estimate the number of cycles to fracture for specimens or structural element (fatigue life) with an influence of the orientation of the so-call critical plane of fatigue damage accumulation. Analytical solutions were obtained for the present fatigue criterion to determine the orientation of the critical plane of the fatigue damage development under cyclic loading for multiaxial stress states. Cyclic loading with arbitrary shifts of phases for the classical fatigue range (low-cycle and high-cycle fatigue) was considered. Several common cases of the three dimensional cyclic loading, i.e. tension-compression and bending-torsion, are studied. It is shown that at certain values of phase shifts the fatigue durability can be very low even under stress amplitudes that do not lead to fracture in the case of sine phase loading. The comparison with the experimental data and numerical calculations based on the other criterion is made. A disc of a low-pressure stage of a gas-turbine engine subjected to cyclic loading due to centrifugal forces was considered. By using a simplified stress distribution, as well as a stress distribution calculated by the finite element method, the areas of stress concentration and orientation of the critical plane in these zones are determine and the durability of the disk operating was estimated.

In practice, composite shells, plates and beams of complex shapes are widely used. Finite element calculations of three-dimensional composite bodies, taking into account their structure and complex shape are reduced to the construction of high dimensional discrete models. To reduce the discrete model dimension, multigrid finite elements (MgFE) are effectively used. When constructing m - grid finite element ( m gFE) m nested grids are used. The fine grid is generated by the base partitioning of m gFE, taking into account its heterogeneous structure and shape. On m - 1 coarse grids, the displacement functions used to reduce the dimension of the base partitioning are determined, which allows one to develop a small dimensional MgFE. The displacement functions and stress state in the MgFE described by the equations of the three-dimensional elasticity problems are represented in local rectangular coordinates. Characteristic properties of MgFE are as follows. When constructing MgFE (without increasing their dimension), arbitrarily small basic partitions can be used arbitrarily closely taking into account the complex inhomogeneous structure and shape of the MgFE, and arbitrarily closely describing the three-dimensional stress state in the MgFE. The present paper proposes a method of generating finite elements (FE) to construct complex-shaped three-dimensional composite multi-grid finite elements (MgFE) of two types. The principal of the generating FE method is as follows. The 1st type MgFE region is obtained by turning a given flat generating single-grid FE (complex shape) around a given axis by a given angle, the 2nd type MgFE region by a parallel moving the generated FE in a given direction to a specified distance. The 1st type MgFEs are used to calculate the composite rotational shells, the 2nd type MgFE are for composite cylindrical complex-shaped shells (with a variable radius of curvature), plates and beams. The advantages of the proposed MgFE are to take into account the complex heterogeneous and micro-heterogeneous body structure and shape, to give rise to small-dimensional discrete models and high accuracy solutions.

Multiple fracture surface investigations of real aviation industry products have proved that low-amplitude high-frequency oscillations can lead to an unexpected failure of aviation elements and other structures. High-frequency loading is the reason for this, as it produces a large number of loading cycles that often exceed an investigated area of a material fatigue behavior. This new fatigue failure mode (very-high-cycle fatigue) requires a special experimental study with the use of both experimental and mathematical modeling. This paper is focused on a numerical determination of stress intensity factors (SIF) in the specimen with the edge notch specimen loaded by harmonic high frequency displacements of small amplitudes. The numerical calculations were performed for the case of loading with frequency close to its natural frequency. A dimensionless adjusting function was determined for SIF that takes into account a change in modal characteristics of the resonance system (the specimen with rectilinear edge notch) due to crack propagation. The obtained equation was used to model the position of the curvilinear fatigue crack front. A general scheme of a piezoelectric fatigue testing machine is introduced with a technique of tensile-compression fatigue tests on the titanium crack growth specimen with an edge notch in the range of very high cycle fatigue. The analysis of the fracture surfaces with the identification of the front stop lines and mathematical modeling of the crack front evolution under high-frequency loading are carried out. The results of mathematical modeling are comparing with experimental data obtained during high-frequency fatigue tests on a piezoelectric fatigue testing machine. The numerical calculations have shown that this approach allows us to qualitatively and quantitatively simulate the evolution of the edge fatigue crack with a curvilinear front under very-high-cycle fatigue (high-frequency) loading mode.

Polymeric materials on the basis of epoxy resins are widely applied in production of various devices and structures. In real work electrical conductivity of epoxy matrixes modified by carbon nanotubes under continuous current in the course of their polymerization at a constant tension is experimentally investigated. The relevance of the research is bound to an adequate theoretical model of orientation ordering of carbon nanotubes for a liquid polymeric matrix for an electric field. The description of the pilot unit and measurement technique is provided. The paper presents the measurement results of volt-ampere characteristics of specimens of composite materials with various percentages (by weight) of carbon nanotubes, which prove that the conductivity has an ohmic character. Stabilization times of the current proceeding through the specimens after the beginning of polymerization at a constant tension are defined. According to established values of current it is shown that the conductivity of the specimens of epoxy matrixes through which current at polymerization proceeded is higher than the conductivity of specimens through which current didn't proceed. At the same time with an increase of nanotubes concentration, there comes an increase of difference of the specimens’ conductivity. The research of dependence of the specimen conductivity on temperature in a day after the beginning of polymerization of the composite material is conducted. It is established that when heating to 90 ͦ C, the conductivity of the specimen imposed with the current during polymerization decreases to values of the specimen conductivity without current. The research is aimed at studying how to make solidification technologies of composite materials faster for production of large parts in space applications. The received results can be also used for development of prospective manufacturing techniques of composite materials with the given electrophysical and mechanical characteristics using electric fields of the corresponding configuration in the course of their polymerization.

Experimental studies of deformation of laminated composite materials often show a complex dependence of stiffness and strength characteristics on the type of loading. The most obvious examples are the difference of elastic moduli in tension and compression, nonlinear shear diagrams. It is possible to take into account such effects in applications only with the use of nonlinear elasticity models. Such models should not contradict fundamental physical principles and, in addition, should not require too complex experiments for validation. In this paper, we consider and numerically implement a model of nonlinear elasticity based on the use of the triaxiality parameter to describe the type of the material stress state. For a numerical implementation, the finite element modelling software Abaqus with user-defined subroutines was used. As a demonstration example, the applied problem of compression of a thin-walled composite cylindrical shell supported by stiffeners is considered. During loading, the shell exhibits an unstable behavior and stress state in its various areas can change drastically. For example, a change from the prevailing tension to compression and vice versa. In this case, damage to the shell material is not observed until a complete structure failure due to the loss of stability of stiffeners, which allows considering only the elastic model for this problem. The use of linear elasticity theory to model such a critical behavior of the structure leads to inaccurate results even at the initial stage of loading, while the proposed model shows a good consistency of the loading diagram, as well as the shape and magnitude of the shell deflections with the experiment.

In this review, the traditional tasks of high-speed penetration are defined as tasks aimed at describing the movement of penetrators in monolithic barriers and determining integral characteristics of penetration, such as the depth of penetration into a semi-infinite shield or the ballistic limit when penetrating the barrier of finite thickness. Most of the papers on penetration mechanics dedicated to such problems are based on experimental and numerical methods; many of them are based on the use of analytical methods. Tasks that do not fall into this category will be referred to as non-traditional; this review is dedicated to them, with the main emphasis on tasks for the study of which the use of analytical methods or the potential and feasibility of using them has been characteristic. These are the tasks of penetration into non-monotonic barriers (multilayer layers with adjacent layers or with air gaps between them); the task of optimizing the shape of the strikers; the task of modeling and optimizing the "active" penetration when controlling the movement of the penetrator (the use of impactor with jet thruster to increase the penetration depth with retaining the integrity of the penetrator when getting soil samples from the surface of the planets or when delivering explosives to the object of destruction; the use of artillery for driving piles); the effectiveness analysis of segmented impactors (impactors with spaced elements); and others. An important feature of the review is the desire to highlight the characteristic methodological features of the implemented approaches, which are often hidden behind the list of research results. The material presented in the review covers promising areas of research and designed to facilitate orientation in the relevant topics, in particular, to select a revevant topic of the thesis, which is of both theoretical and practical interest.

The Bergström-Boyce hyper-viscoelasticity model, which is based on considerations of the microstructure of rubber-like materials and uses the multiplicative decomposition of the total strain gradient, is considered and analyzed. Special attention is paid to the choice of the single-valuedness condition, which determines the rotation of the intermediate (relaxed) configuration and ensures the uniqueness of the multiplicative decomposition of the gradient total strain to the gradient of elastic deformations and the gradient of viscous deformations. To verify the validity of the statement that this choice is not essential, we found a solution of the test problem of simple shear according to the Bergström-Boyce model is obtained for the three most frequently used single-valuedness conditions. The results of numerical calculations showed a significant discrepancy for dynamic stresses and a less significant discrepancy for total stresses. To separate the permissible single-valuedness conditions from the physically unacceptable single-valuedness conditions, it is proposed to use the principle of the material frame-indifference. For this purpose, of we studied the transformation of the elastic deformations and viscous deformations gradients when replacing the reference system, to which there is no single point of view in the scientific literature. For the most frequently proposed and used single-valuedness conditions, it is shown which of them do not depend on the reference system choice. Since the list of such kind of allowable ratios can be expanded many times, the choice a single-valuedness condition should be solved in the same way as it is done, e.g. for elastic potentials: a proper formulation and conducting experimental studies, or a theoretical study of the material microstructure. A phenomenological model of hyper-viscoelasticity is proposed, based on a one-dimensional Kelvin-Poynting model and limited to the case when the main axes of stresses and strains (full, elastic and viscous ones) coincide and do not change their orientation relative to the material lines (fibers). This ensures the uniqueness of the corresponding multiplicative decomposition. In order to expand the range of strain rates when describing experimental data, the dependence of the viscosity coefficient on the second invariant of the right Cauchy-Green viscous strain measure in the power law of the apparent viscosity of the Reiner-Rivlin model is taken into account, which generalizes the corresponding dependence of the Bergström-Boyce model. The developed mathematical model of hyper-viscoelasticity of rubber-like materials is intended for the stress-strain state calculation of highly elastic shells of rotation under symmetric loading.