Showing papers in "Mechanics of Solids in 2012"
TL;DR: In this paper, a model of fracture evolution near a main longitudinal shear in the presence of normal stresses is studied, where an echelon structure of cracks feathering the main rupture is formed under the shear domination conditions.
Abstract: Fracture evolution the near a main longitudinal shear in the presence of normal stresses is studied. Experiments with model materials (gypsum, cheese) showed that a multiscale echelon structure of cracks feathering the main rupture is formed under the shear domination conditions. A system of small cracks in the initial echelon is replaced by an echelon of larger and sparser cracks. Intensive transverse compression along the normal to the shear plane, which imitates the initial stress concentrator, takes the fracture region away from the shear plane. A model of evolution development of the observed echelon structure along the main rupture front under the shear domination conditions is proposed.
21 citations
TL;DR: In this article, the symmetric transverse vibrations of a circular metal-polymer sandwich plate under a thermal impact are studied and the facesheets are assumed to satisfy the Kirchhoff hypothesis and the deformed normal in the low-density core is rectilinear and incompressible across thickness.
Abstract: Symmetric transverse vibrations of a circular metal-polymer sandwich plate under a thermal impact are studied. The plate is connected with an inertialess Winkler foundation. The facesheets are assumed to satisfy the Kirchhoff hypothesis and the deformed normal in the low-density core is rectilinear and incompressible across thickness. Analytical solutions are obtained and their numerical analysis is given.
20 citations
TL;DR: In this paper, a simplified model of an orbital cable system equipped with an elevator is considered, and the conditions for the existence of families of system periodic motions analytically depending on the arising small parameter and passing into some stable radial steady state motion of the unperturbed problem as the small parameter tends to zero.
Abstract: The motion of a dumbbell-shaped body (a pair of massive points connected with each other by a weightless rod along which the elevator, i.e., a third point, is moving according to a given law) in an attractive Newtonian central field is considered. In particular, such a mechanical system can be considered as a simplified model of an orbital cable system equipped with an elevator. The practically most interesting case where the cabin performs periodic “shuttle”motions is studied. Under the assumption that the elevator mass is small compared with the dumbbell mass, the Poincare theory is used to determine the conditions for the existence of families of system periodic motions analytically depending on the arising small parameter and passing into some stable radial steady-state motion of the unperturbed problem as the small parameter tends to zero. It is also proved that, for sufficiently small parameter values, each of the radial relative equilibria generates exactly one family of such periodic motions. The stability of the obtained periodic solutions is studied in the linear approximation, and these solutions themselves are calculated up to terms of the firstorder in the small parameter.
20 citations
TL;DR: In this article, an asymptotic solution of the problem is obtained at distances large compared with the plate width and some promising methods for its use, in particular, for calculating the coefficients in the boundary conditions of the plate elastic fixation which models a coating partially delaminated from the substrate, are outlined.
Abstract: An asymptotic solution of the problemindicated in the title is obtained at distances large compared with the plate width and some promising methods for its use, in particular, for calculating the coefficients in the boundary conditions of the plate elastic fixation which models a coating partially delaminated from the substrate, are outlined. The possibility of considering the delamination in the approximation of the plate weak bending (the plate approximation) and the possibility of neglecting the tangential stress action along the contact boundary are implemented. The substrate is considered as a half-infinite elastic solid. This solution was obtained by using the Fourier transform and the solution of the resulting equation by the Wiener-Hopf method. The obtained asymptotic solution can be used to study problems related to coating delamination, especially on soft thick substrata.
18 citations
TL;DR: In this paper, the authors consider a linear reduced Cosserat medium, whose point bodies possess kinematically independent translational and rotational degrees of freedom, but the strain energy does not depend on the gradient of rotation of particles.
Abstract: We consider a linear reduced Cosserat medium: a linear elastic continuum, whose point bodies possess kinematically independent translational and rotational degrees of freedom, but the strain energy does not depend on the gradient of rotation of particles In such a medium the force stress tensor is asymmetric, but the couple stress tensor is zero This model can be applied for description of soils and granular media Since for the time being the experimental technique for measurement of rotational deformations is not well developed, we investigate how the presence of rotational degrees of freedom affects the dynamics of translational displacements We consider the case of the spherical tensor of inertia and isotropy with respect to the rotational degrees of freedom Integration of the equation of balance of torques lets us in several cases to put in correspondence a linear reduced Cosserat continuum with the spherical tensor of inertia with a classical (non-polar elastic linear) medium with memory with the same equation for the balance of forces, written in terms of translational displacements This is possible for the isotropic case and also if the anisotropy is present only in the tensor of elastic constants corresponding to the classical strain tensor If the material is isotropic with respect to rotational deformations but the (anisotropic) coupling between rotational and classical translational strains is present, then the corresponding classical medium does not exist If we ignore the rotational degrees of freedom when this coupling is present, this will lead us to the conclusion that the principle of material objectivity is violated
18 citations
TL;DR: In this paper, the molecular mechanics (MM) method is used to determine the frequencies and natural vibration shapes of single-walled carbon nanotubes with twisted ends and the buckling critical parameters and the postcritical deformation shapes.
Abstract: The molecular mechanics (MM) method is used to determine the frequencies and natural vibration shapes and to determine the buckling critical parameters and the postcritical deformation shapes of single-walled carbon nanotubes with twisted ends. The following two variants of the MM method are used: the standard MM method and the mixed method of molecular mechanics/molecular structure mechanics method (MM/MSM). Computer simulation shows that the MM/MSM method allows one to obtain acceptable values of frequencies and natural vibration shapes as well as of critical angles of twist, appropriate buckling modes, and postcritical deformation configurations of nanotubes compared with the same characteristics of nanotube free vibrations and buckling obtained by the standard MM method.
15 citations
TL;DR: In this article, a model of thermal fluctuation crack formation in aweakened bond region on amaterial interface is proposed, where the weakened bond region is modeled by a bridged crack whose properties vary in time according to the thermal fluctuations mechanism.
Abstract: A model of thermal fluctuation crack formation in aweakened bond region on amaterial interface is proposed. The weakened bond region is modeled by a bridged crack whose properties vary in time according to the thermal fluctuation mechanism. It is assumed that at least one of the materials is a polymer and the crack part occupied by bridges (the end region) is not small compared with the crack length. The stresses in the bridges and the kinetic dependence of the bond density in the crack end region are determined by solving a system of singular integrodifferential equations. The condition for the crack-defect nucleation is the decrease to the critical value of the average bond density on the corresponding part of the weakened bond region. Numerical results permitting one to estimate the crack nucleation time and the typical levels of external loads for the chosen material parameters are presented.
14 citations
TL;DR: In this paper, the motion of a dynamically symmetric rigid body in a homogeneous field of gravity is studied and necessary and sufficient conditions for the stability of the body rotation about the vertical symmetry axis are given.
Abstract: The motion of a dynamically symmetric rigid body in a homogeneous field of gravity is studied. One point lying on the symmetry axis of the body (the suspension point) performs high-frequency periodic or conditionally periodic vibrations of small amplitude. In the framework of approximate equations of motion obtained earlier, we find necessary and sufficient conditions for the stability of the body rotation about the vertical symmetry axis and study the existence and stability of regular precessions of the body in the coordinate system translationally moving together with the suspension point.
14 citations
TL;DR: In this paper, the authors present experimental data showing that fatigue loading is accompanied by redistribution of the dissolved hydrogen concentration in the region of fatigue damage accumulation in a two-continuum medium.
Abstract: The paper presents experimental data showing that fatigue loading is accompanied by redistribution of the dissolved hydrogen concentration in the region of fatigue damage accumulation. Amodel description of this process as the manifestation of parametric instability of a two-continuum medium is given.
14 citations
TL;DR: In this paper, the authors considered the problem of parametric control of plane motions of a two-mass pendulum (swing) and proposed a control law of swing excitation and damping, which consists in continuously varying the pendulumsuspension length depending on the phase state.
Abstract: The problem of parametric control of plane motions of a two-mass pendulum (swing) is considered. The swing model is a weightless rod with two lumped masses one of which is fixed on the rod and the other slides along it within bounded limits. The control is the distance from the suspension point to the moving point. The proposed control law of swing excitation and damping consists in continuously varying the pendulumsuspension length depending on the phase state. The stability of various controlled motions, including the motions near the upper and lower equilibria, is studied. The Lyapunov functions that prove the asymptotic stability and instability of the pendulum lower position in the respective cases of the pendulum damping and excitation are constructed for the proposed control law. The influence of the viscous friction forces on the pendulum stable motions and the onset of stagnation regions in the case of its excitation is analyzed. The theoretical results are confirmed by graphical representation of the numerical results.
12 citations
TL;DR: In this article, the authors used the celestial-mechanics approach (the spatial version of the problem for the Earth-Moon system in the field of gravity of the Sun) to construct a mathematical model of the Earth's rotational-oscillatory motions.
Abstract: The celestial-mechanics approach (the spatial version of the problem for the Earth-Moon system in the field of gravity of the Sun) is used to construct a mathematical model of the Earth’s rotational-oscillatory motions. The fundamental aspects of the processes of tidal inhomogeneity in the Earth rotation and the Earth’s pole oscillations are studied. It is shown that the presence of the perturbing component of gravitational-tidal forces, which is orthogonal to the Moon’s orbit plane, also allows one to distinguish short-period perturbations in the Moon’s motion. The obtained model of rotational-oscillatory motions of the nonrigid Earth takes into account both the basic perturbations of large amplitudes and the more complicated small-scale properties of the motion due to the Moon short-period perturbations with combination frequencies.
TL;DR: In this article, the free vibrations of a heavy homogeneous cylinder rolling in a cylindrical cavity whose directing curve is a brachistochrone are considered, and the equation of motion of the cylinder is derived and the circular frequency of free vibrations at the cylinder center of mass is determined.
Abstract: Free vibrations of a heavy homogeneous cylinder rolling in a cylindrical cavity whose directing curve is a brachistochrone are considered. The equation of motion of the cylinder is derived and the circular frequency of free vibrations of the cylinder center of mass is determined. An analogy between the cycloidal pendulum with a rolling cylinder and the classical cycloidal pendulum in the form of a material point is obtained.
TL;DR: In this paper, a generalized model of reversible dynamic thermoelasticity is constructed as a theory of elasticity of an ideal (defect-free) nonsymmetric 4D-medium that is transversally-isotropic with respect to the time coordinate.
Abstract: The space-time continuum (4D-medium) is considered, and a generalized model of reversible dynamic thermoelasticity is constructed as a theory of elasticity of an ideal (defect-free) nonsymmetric 4D-medium that is transversally-isotropic with respect to the time coordinate. The definitions of stresses and strains for the space-time continuum are introduced. The constitutive equations of the medium model relating the components of nonsymmetric stress and distortion 4D-tensors are stated. Physical interpretations of all tensor components of the thermomechanical properties are given. The Lagrangian of the generalized model of coupled dynamic thermoelasticity is presented, and the Euler equations are analyzed. It is shown that the three Euler equations are generalized equations of motion of the dynamic classical thermoelasticity, and the last, fourth, equation is a generalized heat equation which allows one to predict the wave properties of heat. An energy-consistent version of thermoelasticity is constructed where the Duhamel-Neumann and Maxwell-Cattaneo laws (a nonclassical generalization of the Fourier law for the heat flow) are direct consequences of the constitutive equations.
TL;DR: In this paper, the structural-temporal approach and the incubation time criterion are used to study the threshold energy necessary to initiate erosion fracture of a material surface, and the behavior of the energy threshold values depending on the indentor geometry (ball, cylinder, and body of revolution) is analyzed.
Abstract: The structural-temporal approach and the incubation time criterion are used to study the threshold energy necessary to initiate erosion fracture of a material surface. The behavior of the energy threshold values depending on the indentor geometry (ball, cylinder, and body of revolution) is analyzed. The graphs of threshold energy versus impact pulse duration and radius are drawn. The difference in the behavior of energy for small particles in these cases is established.
TL;DR: In this paper, a closed-form solution is constructed for a growing parallelepiped under smoothly rigid heat-insulated fixation conditions for the stationary faces and the growing load-free face.
Abstract: A procedure for determining nonstationary vibrations of a discretely accreted thermoelastic body in the approximation of small deformations and thermal flows is developed. A closed-form solution is constructed for a growing parallelepiped under “smoothly rigid” heat-insulated fixation conditions for the stationary faces and the growing load-free face. The temperature field on the growing face is analyzed numerically for various accretion scenarios.
TL;DR: In this paper, a model that describes the spatial motion of a body of revolution in an elastoplastic medium (without flow separation and with nonsymmetric separation of the medium flow taken into account) is used to study the Lyapunov stability of rectilinear motion in the case of frozen axial velocity on a half-infinite time interval.
Abstract: A previously constructed model that describes the spatial motion of a body of revolution in an elastoplastic medium (without flow separation and with nonsymmetric separation of the medium flow taken into account) is used to study the Lyapunov stability of rectilinear motion of a body in the case of frozen axial velocity on a half-infinite time interval. Some stability criteria are obtained and the influence of tangential stresses is analyzed.
TL;DR: In this paper, a comparison of two models of interatomic interaction is carried out, one based on pairwise moment interaction, and the other based on the Brennermodel where the variation in the angles between the segments connecting the atom under study with three nearest neighbors is additionally taken into account.
Abstract: Plane problems of statics and dynamics of graphite lattice are considered in the linear approximation. Comparative analysis of two models of interatomic interaction is carried out. One of these models is based on pairwise moment interaction, and the other is the Brennermodel where the variation in the angles between the segments connecting the atom under study with three nearest neighbors is additionally taken into account. The lattice tensile and shear rigidity in two directions is studied by straightforward calculations. The propagation of harmonic tensile and shear waves it two directions is considered. In problems of both statics and wave propagation, the results are compared with similar results for the equivalent continuum. It turned out that in the problems of statics, the Brenner model (after averaging) leads to an isotropic momentless continuum, while the model with pair interaction lead to the moment Cosserat continuum. In problems of wave propagation, both of these models give the same qualitative results. The velocities of acoustic parallel extension-compression wave propagation in a lattice are close to the wave velocity in the continuum but do not coincide with it. The difference increases with decreasing wave length and depends on the wave propagation direction. In the case of shear wave propagation in a lattice, the velocity of acoustic shear wave propagation in the pair moment potential model significantly (in the leading terms) depends on the direction of its propagation. The optical short waves are discovered and some of their properties are described.
TL;DR: In this paper, a Gauss type quadrature formula for a Cauchy type integral whose density is the product of a Holder function by the weight function (1 − x) α (1 + x) β (Re α, Reβ > −1) of orthogonal Jacobi polynomials was presented.
Abstract: The present paper presents a Gauss type quadrature formula for a Cauchy type integral whose density is the product of a Holder function by the weight function (1 − x) α (1 + x) β (Re α, Reβ > −1) of orthogonal Jacobi polynomials. It is shown that at the roots of the function of the second kind corresponding to the Jacobi polynomial P n (α,β) (x), the quadrature formula with n nodes gives the exact value of a Cauchy type integral for an arbitrary polynomial of order k ≤ 2n. This formula was tested when solving several contact and mixed problems of the theory of elasticity.
TL;DR: In this paper, a dynamical experiment and theoretical modeling are used to illustrate the important role played by the sharp decrease in the resistance of a filled polymer material in unloading (in the millisecond time range).
Abstract: Determination of mechanical characteristics of filled polymer materials in shock wave processes is of interest in calculations of the strength of these materials. The standard computation methods are based on the use of the linear theory of viscoelasticity, where there is no distinction between the active and passive deformation processes. In the present paper, dynamical experiment and theoretical modeling are used to illustrate the important role played by the sharp decrease in the resistance of a filled polymer material in unloading (in the millisecond time range). The higher the degree of filling of this material, the more significant this effect is.
TL;DR: An analytic survey of experimental data and theoretical approaches characterizing the long-term strength of metals in complex stress state is given in this paper, where an equivalent stress σe is introduced as a characteristic of the stress state.
Abstract: An analytic survey of experimental data and theoretical approaches characterizing the long-term strength of metals in complex stress state is given. In Sections 2 and 3, the results of plane stress tests (with opposite and equal signs of the nonzero principal stresses, respectively) are analyzed. In Section 4, the results of inhomogeneous stress tests (thick-walled tubes under the action of internal pressures and tensile forces) are considered. All known experimental data (35 test series) are analyzed by a criterion approach. An equivalent stress σe is introduced as a characteristic of the stress state. Attention is mainly paid to the dependence of σe on the principal stresses. Statistical methods are used to obtain an expression for σe, which can be used to study various types of the complex stress state. It is shown that for the long-term strength criterion one can use the power or power-fractional dependence of the time to rupture on the equivalent stress. The methods proposed to describe the test results give a good correspondence between the experimental and theoretical values of the time to rupture. In Section 5, the possibilities of complicating the expressions for σe by using additional material constants are considered.
TL;DR: In this paper, the optimal turn problem for a rigid body with a spherical distribution of mass is considered in the quaternion setting and a functional combining the time and the integral magnitude of the control vector modulus used to turn the rigid body is used as the optimality criterion.
Abstract: The optimal turn problem for a rigid body with a spherical distribution of mass is considered in the quaternion setting. A functional combining the time and the integral magnitude of the control vector modulus used to turn the rigid body is used as the optimality criterion. This problem is solved analytically in the class of conical motions. An example of computations is given.
TL;DR: In this paper, the propagation of harmonic plane waves in a homogeneous anisotropic thermo-elastic diffusive medium in the context of different theories of thermoelastic diffusion was studied.
Abstract: This paper concentrates on the study of the propagation of harmonic plane waves in a homogeneous anisotropic thermoelastic diffusive medium in the context of different theories of thermoelastic diffusion. It is found that five types of waves propagate in an anisotropic thermoelastic diffusive medium, namely a quasi-elastodiffusive (QED-mode), two quasi-transverse (QSH-mode and QSV-mode), a quasi-mass diffusive (QMD-mode) and a quasi-thermo diffusive (QTD-mode) wave. The governing equations for homogeneous transversely isotropic diffusive medium in different theories of thermoelastic diffusion are taken as a special case. It is noticed that when plane waves propagate in one of the planes of transversely isotropic thermoelastic diffusive solid, purely quasitransverse wave mode(QSH) decouples from rest of the motion and is not affected by the thermal and diffusion vibrations. On the other hand, when plane waves propagate along the axis of solid, two quasi-transverse wave modes (QSH and QSV) decouple from the rest of the motion and are not affected by the thermal and diffusion vibrations. From the obtained results, the different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically for a single crystal of magnesium. The effects of diffusion and relaxation times on phase velocity, attenuation coefficient, specific loss and penetration depth has been studied. Some particular cases are also discussed.
TL;DR: In this article, it was shown that self-excited vibrations are also possible if, conversely, rolling friction prevails over sliding friction, but these vibrations then occur in the rolling plane.
Abstract: Torsional vibrations of a wheel about its leg axis arising in the carriage rectilinear motion were dubbed the shimmy phenomenon. Because of insufficient understanding of dry friction laws in the case of point contact, the causes of the shimmy phenomenon were explained by specific features of tyre deformation [1–3]. But this phenomenon is also observed in the case of rigid (for example, metallic) wheels. The recently developed theory of polycomponent dry friction [5–11] was used to explain the shimmy phenomenon in [4]. It was discovered there that the shimmy phenomenon arises if sliding friction prevails over rolling friction. In the present paper, it is shown that self-excited vibrations are also possible if, conversely, rolling friction prevails over sliding friction, but these vibrations then occur in the rolling plane. Such self-excited vibrations are close in their physical meaning to the vibrations studied in textbooks on the theory of oscillations in the problem called an oscillator with dry friction on an infinite belt [12]. In contrast to this problem, the order of the system considered below is greater, and, in addition to sliding friction, rolling friction is present as well.
TL;DR: In this article, the authors considered the problem of friction force measurement under conditions of cosmic experiment on the orbit of a moving element and the indenter, and the existence and stability conditions were obtained in terms of the mass-elastic parameters of the contact pair.
Abstract: Problems of friction force measurement under conditions of cosmic experiment on the orbit are considered. To increase the measurement accuracy, some arrangements should be made for preventing the onset of a self-vibration mode in mechanical systems with movable contact. Two self-vibration modes are studied. One of them occurs in the case of moderate relative slip velocities of the moving element and the indenter, and the other, in the case of small velocities. The existence and stability conditions are obtained in terms of the mass-elastic parameters of the contact pair.
TL;DR: In this article, it is shown that this transformation is not universal and its mathematical and physical justification depends on the conditions of the plate fixation and loading, and that this justification is absent for the most widely used problems of bending of a rectangular plate freely supported and fixed on the contour.
Abstract: The transformation of the torque into the transverse force is considered; this transformation is traditional in the educational literature [1] and was proposed by Kirchhoff [2] and Thomson and Tait [3] to match the order of the differential equation of the classical theory of plates with the number of boundary conditions. It is shown that this transformation is not universal and its mathematical and physical justification depends on the conditions of the plate fixation and loading. It is shown that this justification is absent for the most widely used problems of bending of a rectangular plate freely supported and fixed on the contour.
TL;DR: The results of studies concerned with new trabds in the development of intensive plastic deformation methods for manufacturing nanostructure metals and alloys are presented in this article, where much attention is paid to the mechanical properties of bulk nanomaterials.
Abstract: The results of studies concerned with new trabds in the development of intensive plastic deformation methods for manufacturing nanostructure metals and alloys are presented. Much attention is paid to the mechanical properties of bulk nanomaterials. Keywords: intensive plastic deformation, nanostructure material, gain boundary, mechanical property, microstructure, segregation.
TL;DR: In this paper, the problem of free and constrained torsion of a rod of solid circular cross-section is solved numerically using a tensor linear constitutive relation written in terms of the energy compatible Cauchy stress and Hencky logarithmic strain tensors.
Abstract: The problems of free and constrained torsion of a rod of solid circular cross-section are solved numerically using a tensor linear constitutive relation written in terms of the energy compatible Cauchy stress and Hencky logarithmic strain tensors. The only function used to determine the properties of the isotropic incompressible material of the rod is a power-law function that approximates the shear diagram and corresponds to an elastoplastic material with power-law hardening. The solution obtained shows that, despite the tensorial linearity of the state law, the use of the logarithmic strain measure allows one to describe qualitatively the effect of significant elongation of the rod in free torsion (the Poynting effect) as well as the arising normal longitudinal, radial, and circumferential stresses, whose values are commensurable, at large deformations, with the maximum tangential stresses in the cross-section. Computational dependences of the torsional moment on the angle of twist in free and constrained torsion are obtained. These dependences are found to be significantly different from each other; the limitmoment and the correspondingmaximum angle of twist for free torsion are found to be considerably lower than those for constrained torsion. It follows that the shear strength, which is traditionally calculated from the maximum torsional moment, becomes indeterminate. For constrained torsion, the dependence of the longitudinal compressive force on the angle of twist is obtained.
TL;DR: In this paper, the possibility of vibration localization in damaged regions and the influence of the localization on the damage development till the film separation are studied. And the conditions under which damage behavior is determined by the localized oscillating part of the solution are derived.
Abstract: In the process of deformation of such multilayer structures, significant stresses can arise on the foundation-coating interface because of the difference in their physical and mechanical properties, which can result in fracture or coating separation. The action of static or impact loads on damage onset and development in the adhesive layer in such multilayer structures has been investigated almost completely, but similar processes in the case of suddenly applied vibration loads have not been studied to a large extent. The latter draw attention because of the fact that even small variable actions can localize vibrations near the imperfections (inclusions, defects, etc.) and can be accompanied with an increase in the damage of the adhesion layer, which results in partial separation of the film. In the present paper, the possibility of vibration localization in damaged regions and the influence of the localization on the damage development till the film separation are studied. The first of the possible scenarios of the damage region behavior is its monotone increase. The second scenario of damage behavior is its constant stepwise growth. In this case, damage increases on some time intervals and is constant between the intervals. Under the conditions obtained in the paper, this second scenario can be transformed into the first one. The third scenario is that damage does not increase. This scenario can be realized under sufficiently large vibration load frequencies. Some conditions under which damage behavior is determined by the localized oscillating part of the solution are derived.
TL;DR: In this article, the classical mechanical problem on the motion on a system of two or several bodies is stated in terms of parameters of the 13-parameter extended Galilean group without using such traditional notions as “point” and “force.
Abstract: The classical mechanical problem on the motion on a system of two or several bodies is stated in terms of parameters of the 13-parameter extended Galilean group (translations, rotations, boosts, and gravitational transformations) without using such traditional notions as “point” and “force.”
TL;DR: In this article, a mathematical model for the description of bulk microfracture processes in metals, which are understood as nucleation and coalescence of submicrocracks, micro-cracks and short non-propagating microcracks is presented.
Abstract: A mathematical model for the description of bulk microfracture processes in metals, which are understood as nucleation and coalescence of submicrocracks, microcracks, and short nonpropagating microcracks, and of brittle macrofracture processes in metals is presented. This model takes into account the laws of formation and propagation of short propagating, medium, and significant microcracks. The basic notions of this model are the reduced length of cracks and the probability of micro- and macrofracture. The model is based on the mechanical parameters of metal strength and fracture, which are studied experimentally. The expressions for determining the probability in the case of one-dimensional symmetric loading are given. The formulas for determining the threshold number of cycles at the beginning of crack formation are obtained for cracks of each type. For the first time, the data on standard parameters of fatigue strength were used to construct the fatigue curve of metals and alloys for macrocracks.