Yury O. Solyaev

Bending problems in the theory of elastic materials with voids and surface effects

In the present study, a comparison of pure, three-point, four-point and cantilever beam bending problems in the frame of the theory of elastic materials with voids (micro-dilatational elasticity) has been provided via analytical modelling and three-dimensional finite-element analysis. We consider the extended variant of the theory with surface effects using a variational approach. At first, we compare the known approximate semi-inverse analytical solution of the pure bending problem with a corresponding three-dimensional finite-element solution in the frame of micro-dilatational theory. It is demonstrated that in the numerical solution – unlike the analytical one – all boundary conditions are satisfied accurately, and there exist distortions of the cross-sections and lateral faces of the beam. The generalized analytical solution of the beam pure bending problem with surface effects is also established and compared with numerical simulations. The effective elastic properties of the beam with micro-dilatations are introduced by comparing its displacements and corresponding classical beam displacements. The influence of scale, coupling and surface parameters on the effective elastic moduli in different bending and simple tension tests is studied. It is shown that all considered types of bending experiments provide the determination of close values of the effective flexural modulus of the beams with different thickness. This means that it is possible to use any bending test with beams of different thickness for reliable identification of the material constants of the theory. It is also possible to use the simple analytical expression for an effective flexural modulus that follows from the analytical solution of the pure bending problem. It is also shown that stiffness of the beam with micro-dilatation in any bending tests should always be higher as compared with the stiffness of such a beam in simple tension. For thin beams, there are no scale effects, and its effective flexural modulus is equal to the material’s Young’s modulus without micro-dilatation. Possible rise of the negative size effects in the model with surface effects is also discussed.

Mechanical behavior of porous Si 3 N 4 ceramics manufactured with 3D printing technology

The paper focuses on experimental measurement and analytical and numerical modeling of the elastic moduli of porous Si3N4 ceramics obtained by 3D printing and pressureless sintering. The pores in such a material have complex irregular shape and porosity varies over a wide range (up to 50%), depending on the technological parameters used. For analytical modeling, we use effective field methods (Mori–Tanaka–Benveniste and Maxwell homogenization schemes) recently developed for pores of superspherical shape. For FEM simulation, we used microstructures generated by overlapping solid spheres and overlapping spherical pores. It is shown that elastic properties of ceramics are largely determined by the granular structure and the concave pore shape, which have been observed in the ceramics microstructure after sintering of the 3D-printed powder green bodies.

Fabrication of porous silicon nitride ceramics using binder jetting technology

This paper presents the results of the binder jetting technology application for the processing of the Si3N4-based ceramics. The difference of the developed technology from analogues used for additive manufacturing of silicon nitride ceramics is a method of the separate deposition of the mineral powder and binder without direct injection of suspensions/slurries. It is assumed that such approach allows reducing the technology complexity and simplifying the process of the feedstock preparation, including the simplification of the composite materials production. The binders based on methyl ester of acrylic acid with polyurethane and modified starch were studied. At this stage of the investigations, the technology of green bodys fabrication is implemented using a standard HP cartridge mounted on the robotic arm. For the coordinated operation of the cartridge and robot the specially developed software was used. Obtained green bodies of silicon powder were used to produce the ceramic samples via reaction sintering. The results of study of ceramics samples microstructure and composition are presented. Sintered ceramics are characterized by fibrous α-Si3N4 structure and porosity up to 70%.

Intermediate layer formation between inclusion and matrix during synthesis of unidirectional fibrous composite

The problem of transient layer formation in given composition between inclusions and matrix can be solved using mathematical modeling. This paper suggests a suitable model taking into account multi staging of chemical conversion. Numerical realization of this model allows studying the dynamics of transient layer formation at varying temperature and pressure. As a result, the phase structure and thickness of a transient zone depending on synthesis conditions are obtained.

Binder Jetting of Si3N4 Ceramics with Different Porosity

This article presents the results of the binder jetting technology application for the silicon nitride ceramics production. A modified version of the Plan-B 3D printer with an epoxy-based binder was used for silicon green bodies preforming. Silicon powder was pre-coated with epoxy resin, and the curing agent was added during 3-D printing of green bodies using a standard cartridge. Curing and removal of organics was carried out during the high-temperature vacuum drying of the printed preforms. Reaction-bonded silicon nitride was obtained by using pressureless sintering. An additional compaction of green bodies is proposed to reduce the porosity of green bodies and sintered ceramics. It is shown that the proposed methods allows to improve the mechanical properties of sintered specimens.

Semi-Inverse Solution of a Pure Beam Bending Problem in Gradient Elasticity Theory: The Absence of Scale Effects

The semi-inverse solutions of pure beam bending problems within the three-dimensional formulation of gradient elasticity theory as exact tests for the problem of estimating the efficient bending stiffness of so-called scale-dependent thin beams and plates due to the necessity of modeling sensing devices are presented. It is shown that the solutions within the gradient elasticity theory give classic beam bending stiffnesses and demonstrate the invalidity of the widespread results and estimates obtained in the past 15 years during study of scale effects within the gradient beam theories, according to which the relative bending stiffness grows by a hyperbolic law with decreasing thickness.

Optimal Damping Behavior of a Composite Sandwich Beam Reinforced with Coated Fibers

In the present paper, the effective damping properties of a symmetric foam-core sandwich beam with composite face plates reinforced with coated fibers is studied. A glass fiber-epoxy composite with additional rubber-toughened epoxy coatings on the fibers is considered as the material of the face plates. A micromechanical analysis of the effective properties of the unidirectional lamina is conducted based on the generalized self-consistent method and the viscoelastic correspondence principle. The effective complex moduli of composite face plates with a symmetric angle-ply structure are evaluated based on classical lamination theory. A modified Mead-Markus model is utilized to evaluate the fundamental modal loss factor of a simply supported sandwich beam with a polyurethane core. The viscoelastic frequency-dependent behaviors of the core and face plate materials are both considered. The properties of the face plates are evaluated based on a micromechanical analysis and found to implicitly depend on frequency; thus, an iterative procedure is applied to find the natural frequencies of the lateral vibrations of the beam. The optimal values of the coating thickness, lamination angle and core thickness for the best multi-scale damping behavior of the beam are found.