Том 19, № 1 (2016)

In his main book “Discorsie Dimostrazioni Matematiche, Intorno a Due Nuove Scienze” published in 1638 by Elsevier in Leiden, Galileo Galilei, “the Father” of modern science, put the material science and strength of materials on the first place. He introduced the notions of stress and strength that have been fundamental since then. Moreover, in unison with Plato’s theory of forms he found out the perfect shape of a force-bent beam we call today equistrong. This discovery laid the foundation for search of other perfect elastic bodies as a continuation of Galilei’s work. There are no theorems of existence for equistrong bodies so that the quest for them is like a gold-digging. In what follows, the shapes of the following heavy, equistrong beams were found out: a) beam of constant thickness and of variable width, simply supported at both ends, b) beam clamped at one end and loaded at the other end while having either constant thickness and variable width, or constant width and variable thickness, and c) equistrong shape of the profile of aircraft wings accounting for gravity and lift loads. The shape of equistrong rod at buckling under a compressive force is found in the Euler’s problem. Equistrong structures possess minimum weight for given safety factor or maximum safety factor for given weight.

This paper discusses multiscale models of inelastic deformation of single- and polycrystals, which are based on crystal plasticity theories, as applied to the verification and justification of Ilyushin’s isotropy postulate (in a special form) at large displacement gradients. Different approaches to motion decomposition on the macroscale into quasi-rigid (described by the motion of a corotational coordinate system) and strain-induced motion (a relatively moving coordinate system) are considered. The strain path is defined in terms of a moving coordinate system. Corresponding kinematic effects are defined in terms of a laboratory coordinate system. In this case, the loading process image is constructed and loading conditions are specified in terms of the moving coordinate system. Calculations are performed for two types of strain paths with different curvature by assuming two different hypotheses about quasi-rigid motion on the macroscale: (i) the spin of the moving coordinate system is equal to an averaged mesoscale spin, and (ii) the spin is equal to the macroscale vortex. It is shown that the isotropy postulate is more valid in the case of assuming the first hypothesis.

The mechanisms of propagation of oblique plane harmonic waves through the interface of Voigt and Maxwell viscoelastic media were studied in the context of field theory of defects which describes dislocation continuum dynamics. The defect field waves structure for different displacement wave polarizations was determined. Analytical expressions were derived for the reflection and refraction coefficients of displacement waves and defect field waves propagating in the media. The dependences of Fresnel coefficients on the incidence angle of a primary wave and parameters of the contacting media were analyzed.

The paper presents a molecular dynamics study to investigate the behavior of materials under loading by friction stir welding (FPW). The loading is simulated by assigning constant angular and forward velocities to a certain group of atoms, being a FPW tool. The joined materials are two defect-free Cu crystallites, Cu and Fe crystallites, and two crystallites of the same solid solution structured as D16 (2024) alloy. It is found that as the tool passes along the weld line, the crystal structure of the materials is rearranged with subsequent mixing of their surface atoms. Under certain loading conditions, the crystal lattice after passage of the tool recovers its regular order. Also analyzed is the influence of vibrations additionally applied to the FPW tool. The simulation results provide a better understanding of the processes involved in mechanically activated diffusion.

In the paper, elastic moduli of finite-sized graphene monolayers are computed in a nonsymmetric formulation using the lattice statics approach. The motion of atoms due to their interaction is not considered, lattice stability is not studied. The presence of covalent binding is assumed to preserve material structure and all atoms are assigned displacements that correspond to a homogeneous deformation gradient tensor. As a result, the deformation kinematics of graphene is strictly controlled and the material response is defined using a variant of the interatomic interaction potential of the Mie family. The dimensionless parameters of the potential are identified using the coincidence criterion of the experimentally determined Poisson ratio of graphene with an estimated value. The obtained potential parameters are used to determine the elastic properties of a graphene monolayer in a nonsymmetric formulation for low strains and low temperatures. It is shown that the graphene monolayer under homogeneous deformation goes to a nonequilibrium state. In order to provide the potential energy minimum of the specimen in the deformed state, it is necessary to assign displacements to a part of graphene atoms that form one of its “triangular” sublattices relative to atoms of another sublattice, with each sublattice being deformed homogeneously.

Stresses induced by welding are analyzed from the viewpoint of material deformation behavior. Strain gages are used to measure the residual stresses, and electronic speckle-pattern interferometry is used to analyze the response of the welded work to external force. A tensile load is applied to a butt-welded, thin-plate steel specimen, and the resultant strain field is analyzed with the electronic speckle-pattern interferometry. Comparison is made with the case of a nonwelded specimen of the same material and dimension. The analysis indicates that the residual stress due to welding makes the normal strain due to the external tensile load asymmetric. The asymmetry enhances shear and rotational modes of deformation, generating stress concentration at a point away from the weld where the residual stress is substantially negligible. The observed features are discussed based on physical mesomechanics. Analysis reveals plastic deformation like behavior in the response of the welded specimen to the external force.