Assessment of the residual strength of composite structural elements that can be subjected to low-velocity impact during operation is still a vital engineering problem. Its solution requires not only the understanding of the basic mechanisms of energy dissipation in composites but, the study of factors affecting the impact resistance of the material. The thickness is one of the main parameters that affects the mechanical behaviour of the composite at low-velocity impacts and, as a consequence, its residual strength. This paper presents the experimental study of the material thickness and impact energy influence on the residual flexural strength of woven glass fibre-reinforced plastic specimens. At the first stage of the study, low-velocity impact tests with different impact energies on GFRP plate specimens with the thickness of 2 mm, 4 mm, and 6 mm were carried out. At the second stage, the beam specimens were cut out from the plate specimens with impact damages, and three-point bending tests were carried out. The dependencies of the residual flexural strength were obtained at various impact energies for all specimen thicknesses. The sensitivity of the Flexure-After-Impact test protocol to the delamination and fibre damages in the composite specimens were assessed.

The paper deals with the elastic deformation of a composite consisting of plates connected with an adhesive layer on the basis of the interaction layer concept. The layer thickness is taken as a linear parameter. Under loading by the normal separation in the case of plane deformation, the triaxial stress state of the adhesive layer is taken into account. From the general variational setting, by using the hypothesis of flat sections, the problem is formulated in a differential form. Within the framework of a simplified formulation, an analytical solution is found that agrees with the numerical solution obtained by the finite element method. It is shown that Poisson's ratio of the adhesive layer significantly affects its stress state, in which there is a coincidence of the two principal stresses. For weakly compressible adhesion layers, a stress state close to hydrostatic tension is realized. In order to analyze the stress state of the adhesion layer, which is singular at extremely small values of the linear parameter, it is proposed to use the energy product (EP), local stresses (LS) and local deformations (LD). EP is determined as the product of the specific free energy of the layer and the linear parameter, and LS (LD) is determined as the product of stresses (deformations) and the square root of the linear parameter. It is shown that these characteristics are not singular with respect to small layer thicknesses and do not depend on the linear parameter. It was found that the value to which the EP converges at a fixed external load and the linear parameter tends to zero does not depend on the mechanical properties of the adhesive, and the LS (LD) values depend on the properties of the adhesive. At the critical load of crack initiation in the adhesive, the LD in the direction of the separation is significantly (by several orders of magnitude) higher than the LD in the orthogonal direction. In this case, the LS and LD of separation make the main contribution to the formation of the EP. A method is proposed for determining the critical value of the EP corresponding to crack initiation in the adhesive based on the use of the maximum external load from the experimental R-curves.

We investigated an unsteady elastic diffusion vibration of a simply supported rectangular isotropic Kirchhoff-Love plate. The plate is under the action of a distributed transverse load. A model that describes coupled elastic diffusion processes in a multicomponent continuum is used for the mathematical problem formulation. The model is taking into account the diffusion fluxes relaxation. The transverse vibration equations of a rectangular isotropic Kirchhoff-Love plate with diffusion were obtained from the model using the d'Alembert variational principle. The initial-boundary value problem of a freely supported isotropic rectangular plate bending is formulated on the basis of the obtained equations. The plate is under the action of elastic diffusion perturbations distributed over the surface. The problem solution of an unsteady elastic diffusion plate vibration is sought in an integral form. The surface Green's functions are the kernels of the integral representations. To find the Green's functions, we used the Laplace transform in time and the expansion into double trigonometric Fourier series in spatial coordinates. Green's functions in the image domain are represented in the form of rational functions and depend on the Laplace transform parameter. The transition to the original domain is done analytically through residues and tables of operational calculus. The surface Green's function analytical expressions are obtained. As a calculation example, we considered a freely supported elastodiffusive plate under the action of suddenly applied unsteady bending moments distributed over the plate surface. By using a three-component continuum, a numerical study of interactions between unsteady mechanical and diffusion fieldsis done for an isotropic plate. The influence of relaxation effects on the kinetics of mass transfer is investigated. The solution is presented in the analytical form, as well as in the graphs of the displacement fields and concentration increments on time and coordinates. At the end of the publication, the main conclusions are given about the fields coupling effect and the relaxation of diffusion fluxes on the stress-strain state and mass transfer in the plate.

The paper studies effective elastic properties of foam or cellular materials modeled by a set of Gibson-Ashby open cells with regular or irregular structures. Currently, there are many papers that present results of studying cellular materials using theoretical, numerical and experimental methods. However, these papers consider either regular lattices, or a single cell, or representative volume models based not on the Gibson-Ashby models. In this paper, in addition to the regular lattice, irregular structures were numerically studied. A mathematical formulation of the homogenization problem based on the energy equivalence of a foam-like material and on a homogeneous comparison medium is described. Formulations of six boundary value problems are presented. The solutions of these problems allow us to determine a complete set of effective stiffness modules for foams with different types of physical and geometric anisotropies. All stages of the numerical study were implemented in the ANSYS finite element package. Two algorithms for forming solid-state and finite-element models of irregular Gibson-Ashby lattices with small and large porosity are described in detail. As an example, numerical calculations are carried out for polycarbonate foams. The values of the effective elastic modules for regular and irregular lattices and for the Gibson-Ashby analytical model are compared. The results of numerical experiments showed that the Gibson-Ashby model describes the behavior of highly porous materials quite well (for porosity more than 75%), but this model gives a less satisfactory prediction in case of lower porosity. It is noted that for a large number of cells, regular and irregular lattices statistically give similar results for effective modules. However, for individual structures of irregular lattices, especially with strongly differing cells in individual directions, the effective moduli can have significantly different values, and the effective homogeneous medium can have pronounced anisotropic properties. These effects are due to geometric anisotropy and stress concentration in long connecting beams and at the joints of beams of various sizes in highly irregular Gibson-Ashby lattices. Examples of such lattices are given. We analyze the scatter of value for relative modules, which characterizes the anisotropy of such structures.

In this paper, a model that takes into account the dependence of strength properties on the damage rate is considered for modelling of the impact failure of composite materials. The constants of the material model are determined on the basis of experimental diagrams to compression and shear impact loading of unidirectional composite, which exhibit a nonlinear dependence on the strain rate. The proposed model is implemented to the Abaqus finite element modeling software for the case of a three-dimensional stress state. As an example of numerical modeling, we consider tubular composite specimens made of carbon fiber with an epoxy matrix and layers of different orientations, which are commonly used for determining of characteristics of impact energy absorption. Diagrams of impact loading of the considered tubular specimens are obtained. The influence of the chamfer (taper of the cross-section) on the edge of a tubular specimen on the impact loading diagram at the initial stage of the process, which serves as the initiator of crushing, is studied. The proposed approach allows us to estimate the magnitude of the peak of the amplitude associated with the crushing of the chamfer. In addition, at the initial stage of loading, maximum strain rates occur, which entails the hardening of the material, also expressed in the loading diagram as an increase in the amplitude. If the analysis neglects the effects associated with the strain hardening of the material and the geometry of the chamfer, the result may be expressed in an underestimation of the reaction, especially at the initial stage of the process. The absence of the described effects in the model of composite structures may lead to significantly incorrect results with complete failure with zero reaction. The developed approach is effective in the design and testing of damping elements made of composite material with properties that are sensitive to the loading rate.

A mathematical model of reconstruction of the fields of residual stresses and plastic deformations in thin-walled cylindrical tubes in the delivery state and after bilateral surface plastic hardening was developed. It included a method for identification of the model parameters using the example of thin-walled mm tubes made of X18N10T steel based on experimental data for the axial and circumferential components of the residual stress tensor for samples in the delivery state and after bilateral mechanical ultrasonic hardening. The adequacy of the mathematical model for the reconstruction of residual stresses in the thin-walled tubes made of X18N10T steel was verified by the experimental data in the state of delivery and after bilateral surface plastic hardening, taking into account the anisotropy of the distribution of plastic deformation after hardening in the axial and circumferential directions. A method for calculating the two-way relaxation of residual stresses on the outer and inner surfaces of thin-walled tubes under creep conditions was developed based on the generalization of the corresponding method for unilateral hardening. The relaxation process in the thin-walled tubes made of 08X18N9 steel (an early analogue of X18N10T steel) under conditions of thermal exposure, axial tension, internal pressure and the combined action of axial tension and internal pressure was investigated on the basis of the constructed phenomenological creep theory for this steel. A detailed analysis of the kinetics of the fields of residual stresses during creep in the thin-walled samples in the delivery state and after bilateral hardening at different times was performed. It is shown that under these conditions, almost a complete relaxation of residual technological stresses occurs both in the samples in the delivery state and after bilateral surface plastic deformation within 50 hours.

During tension of samples of low-carbon steels and some other plastic materials, the sharp yield point and the yield plateau are fixed on the deformation diagram. In this case, Chernov-Luders bands appear on the surface of the sample in the local section, which then propagate along the tension axis. The physical nature of the sharp yield point is established: the drop in the load after reaching the (upper) yield limit occurs as a result of dislocations being an extraction out of the cloud of the embedded atoms and vacancies (Cottrell's cloud). At the occurrence of the sharp yield point , the plastic strain is limited to a small area. When the sample deformation increases, the plasticity zone (the yield plateau is marked on the diagram at this time) expands, and the stress-strain state in this zone becomes almost homogeneous, if we do not consider its boundary with the elastic region. At the end of the yield plateau, the entire sample experiences a uniform plastic deformation, excluding its ends (galtels). From this point on, the strain diagram shows the of material hardening; presumably, this hardening occurred from the very beginning, but was hidden under the yield plateau. This is evidenced by the resulting strain-induced anisotropy. After unloading the sample, when the plastic strain front (in the form of Chernov-Luders bands) has not yet passed through the entire sample, and the Bauschinger's effect is observed with the subsequent change in the stress sign. The fact that after the occurrence of the sharp yield point , the plastic strain is not localized in a certain volume, similar to what occurs during the neck formation, but spreads along the sample, serves as proof of the material hardening due to plastic deformation immediately after the load falls. Therefore, if the plastically deformable part of the sample did not have a hardening of the material due to the plastic strain growth, it would not be able to spread to the elastic part of the sample. This paper presents the experimental data of the sign-variable torsion of the thin-walled tubular samples of steel 45 in the annealed state. The deformation atdiagram of the occurrence and development of the yield plateau in distinct sections along the length of the test sample is obtained. The material hardening diagram hidden under the yield plateau is reconstructed using the well-known Masing's principle.

The paper considers a woven fabric (based on fiberglass) composite structure in the form of a foam core sandwich cylindrical shell reinforced with circular frames, under the action of local loads applied to the frames. A technique is described for obtaining a numerical solution (with the confirmed reliability) to the problem of the stress-strain state of this type of structure using two alternative computational models, one of which is based on the numerical integration method, and the other one is based on the finite element method. The first model is developed by adopting a scheme, in which the frames are considered as short cylindrical shells obeying the single normal hypothesis. The foam core sandwich sections connected to them are considered within the framework of the zig-zag theory of soft core sandwich shells based on the assumption of incompressibility of the core along thickness. In this case, the corresponding calculation problem is formulated in the form of systems of algebraic and differential (in partial derivatives) equations for each of the shell sections being considered, which are supplemented by kinematic and force conditions at their joints, as well as boundary conditions at the left and right ends of the structure. The problem solving for each harmonic number is reduced to solving a set of boundary value problems for systems of 8 and 12 linear ordinary differential equations of the first order, related by conditions at the specified joints and using the procedure for expanding the parameters of the stress-strain state and applied loads into Fourier series in the circumferential direction. The solution algorithm is constructed using the numerical integration procedure in the orthogonal sweep version combined with the displacement method procedure (to satisfy the conditions at the joints). The declared finite element model is built within the ABAQUS software package using S4 shell elements (for composite layers) and C3D20 volume elements (for frames and core). The formed model, when setting deliberately overestimated values of the corresponding elastic modules, can implement a situation close to fulfilling the set of hypotheses adopted when constructing the first model. Having fixed in such a situation the consistency of the calculation results on the basis of the alternative computational models constructed in this way and thereby confirming the reliability of the obtained numerical solution, we carry out the transition to the calculation using the real values of the mentioned modules and the analysis of their influence on the stress-strain state of the investigated sandwich shell. The presented example of the calculation of a composite sandwich cylindrical structure, one of the frames of which is under the action of two local axial loads, demonstrates the possibilities of the adopted modeling method.

Advanced design methods offer not only a number of methods of modeling structures but also quite profound optimization approaches. The topology optimization is one of such advantageous methods. There are several implementations of this type of structural analysis, but the most common option is to deal with the material density as a generalized parameter. The development of 3D printing technologies increases the interest in algorithms of this type. However, it mostly refers to printing with metal or plastic, which implies the material isotropy. Advances in continuous fiber printing systems and automatic placement machines using composite tapes make it possible for engineers to control not only a material’s position, but also to choose the local orientation of reinforcing elements. Such systems require optimization algorithms taking into account additional parameters characterizing the material anisotropy. In this case the traditional problem of the topology optimization should first be modified for the model of an orthotropic material with restrictions on the value of the angle of rotation of the reinforcement lines along the print path. In this paper, an idea of such a topology optimization algorithm is proposed, which is implemented using the Abaqus finite element modeling facilities, and examples of solving typical problems are considered.

The paper presents a comprehensive computational and experimental study of the crack growth rate during the creep-fatigue interaction in compact specimens of P2M steel at a temperature of 550 °C. The theoretical part of the study consisted in the formulation of the fracture resistance parameters through the classical and new constitutive equations of the cracked body state taking into account the accumulation of damage. Numerical calculations included the determination of the stress-strain state fields for the conditions of elasticity, plasticity, and creep, as well as the distributions of nonlinear stress intensity factors and the C*-integral along the crack length and along the crack front for each tested compact specimen. The interpretation of the experimental results for specimens of the same shape in plan but different thicknesses is given in terms of elastic and nonlinear stress intensity factors, taking into account the accumulation of creep damage. It was found that the crack growth rate under the fatigue and creep interaction increases monotonically as the crack size increases in comparison with harmonic fatigue by an order of magnitude or more on specimens of the same geometry. Taking into account the damage through the creep stress intensity factors causes differences in the cyclic fracture diagrams. The superposition of fatigue and creep contributions in terms of load holding time shows an order of magnitude increase in the total crack growth rate compared to the interpretation of the experimental data in terms of pure creep.