Physical Mesomechanics

The problem of the strength of a plate made of a brittle material with through mode I cracks is discussed. In contrast to the approach based on the singular solution of the classical theory of elasticity for a plane with a crack and on linear fracture mechanics, we propose to use nonsingular solutions obtained within the generalized elasticity theory and, as a result, to implement a method, conventional for the strength estimation of solids with stress concentration, based on the maximum stress criterion. The maximum stress is determined from a nonsingular solution of the generalized elasticity equations for a plane with a crack. The reported experimental results for plates with cracks under tension and bending confirm the solution obtained by the proposed method and allow it to be compared with a solution based on linear fracture mechanics. In fact, a new concept of fracture mechanics is put forward, which is free of singular solutions and allows the problems of fracture mechanics to be treated as problems of stress concentration. Comparison of the obtained analytical solutions with the experimental data has shown that the scale factor of generalized elasticity determines the critical state in fracture mechanics with no less accuracy than the critical stress intensity factor and therefore can be used as a fracture criterion. The resulting explicit nonsingular solutions allow the prediction of the stress concentration caused by a crack.

Inclined multiple cracks may appear in composite laminates and sandwich structures. In this paper, we solve the fracture problem of a three-layer sandwich structure which contains multiple inclined cracks in the central layer under tension and antiplane shear. Three types of crack configurations are considered: an isolated crack, a periodic array of inclined cracks with the same length, and two parallel cracks with different lengths. In these cases, we examine the interaction among the cracks under mixed I–II mode and pure mode III based on the stress intensity factors. Then, we apply the solutions to fibre-reinforced composite laminates. The results show that the stress intensity factors of the multiple cracks are significantly affected by the constraining effect of the outer sublaminates and the shielding effect among cracks. For cracks with significantly different sizes, the long crack dominates the stress concentration. This work reveals the influences of the laminate configuration, crack distribution, crack orientation and crack size on the stress concentration at the tips of inclined cracks in the three-layer composite laminate, and the results may be used to analyze the crack propagation in the laminates.

The paper studies the effect of the annealing temperature on microstructural transformation and micro-hardness variation in an internally oxidized vanadium alloy V—Cr—ZrO₂ deformed by high-pressure torsion in Bridgman anvils. It is shown that the development of large plastic strains and subsequent annealing of the particle-reinforced V—Cr—ZrO₂ alloy lead to the formation of a fine-grained structure (with about 1 µm grain size) with a high density of high-angle boundaries pinned by ZrO₂-based nanoparticles. Such high-defect states are characterized by a more than twofold increase in microhardness with the major contribution of grain boundary hardening. The conducted research has revealed the main relaxation features of V—Cr—ZrO₂ alloy deformed by high-pressure torsion at room temperature. The heat treatment of the studied material at 800°C is shown to activate recovery and polygonization. Primary recrystallization is observed upon temperature increase to S00°C. A further increase in temperature in the interval 950–1050°C intensifies collective recrystallization, due to which the fraction of equi-axed grains increases significantly. Secondary recrystallization is activated at 1200°C and, as a result, individual grains grow in size. These processes are accompanied by a decrease in the V—Cr—ZrO₂ alloy microhardness from 3500 to 2000 MPa. Dispersion and substructural hardening are analyzed, and their contribution to the strength is studied. It is shown that the high thermal stability of the nanostructural and fine-grained states is ensured by the high density of uniformly distributed ZrO₂-based nanoparticles (of size 3–10 nm) that pin the high-angle grain boundaries.

In the work, we develop and implement force and deformation models of the strain and damage accumulation rates in creep with the use of the ANSYS finite-element analysis software. Numerical calculations are performed on a plane plate with a rectilinear through crack under biaxial loading and on a three-dimensional compact specimen under eccentric tension. The obtained stress-strain fields are used to calculate the contour I_n integral in the vicinity of the crack tip as well as the distribution of the stress intensity factor at the creep stages. It is found that these parameters behave differently depending on the damage function formulation. It is shown that the creep stress intensity factor can be used as a fracture resistance characteristic that is sensitive to the used model and accumulated damage level, the biaxial loading type and material properties.

A new concept in mechanics is proposed based on the notions of space, time, and energy. The energy is represented by the sum of thirteen terms expressed as products of invariants of the Lagrangian equations of motion and scalar factors corresponding to the physical properties of materials. Differential equations of motion and equilibrium are derived from the frame indifference condition for energy, in which the Eulerian variables are the sought functions and the Lagrangian variables are the arguments. Assumptions are made under which these equations can be transformed into the Poisson and Laplace equations. The law of conservation of energy is used to obtain dependences between the Lagrangian stresses and strains in the reversible deformation region; they are compared with the expressions used in the theory of elasticity. It is discussed whether the point of reference for the mean stresses may be chosen with regard to the volume energy density of particles in their initial state, as well as whether elastic deformation can be described using a single constant. As an example, the energy model and the equations of motion in the Lagrangian form are applied to describe the transition from reversible to irreversible deformation. The developed model differs from the classical one by using two independent infinitesimal operators for the time and space. It is shown that Newton’s law of inertia can be regarded as a variant for the determination of the generalized forces characterizing the kinetic energy change in a body with increments in the distance between the origin of the observer coordinate system and the center of mass of the body. The application of the Lagrangian variables and the superposition principle for describing any spatial motions (including for absolutely rigid bodies), which can be used in the dynamic analysis of linkages and other mechanisms, is validated. The multiple choice of generalized forces for absolutely rigid bodies, including when passive forces arise, is considered. The method of dynamic analysis of mechanisms developed on the basis of the energy model allows the law of conservation of energy to be satisfied for any part of the studied system in an arbitrary time interval.