Analytical formulation of an oscillatory system with hereditary-type dry friction and oscillation constraints

The dynamics of a shock-vibrating system is analyzed. The system consists of a pair of bodies of friction, one of which is under the effect of an external periodic force; the vibration of one of the bodies is limited by a rigid obstacle, and the hereditary-type dry friction forces during their interaction are taken into account. A numerical-analytical approach using the mathematical apparatus of the point mapping method is implemented to analyze the phase portrait structure of the mathematical model as a function of the characteristics of the sliding and state friction forces, as well as of the type and position of the vibration limiter. Based on the character of changes in the bifurcation diagrams, the authors have determined the main laws of changes in the motion regimes (occurrence of random complexity periodic motion regimes and possible transfer to chaos via the period doubling process) when changing the parameters. Analytical results with and without a vibration limiter are compared

A continual model of a damaged medium used for analyzing fatigue life of polycrystalline structural alloys under thermal-mechanical loading

International audienceThe main physical laws of thermal–plastic deformation and fatigue damage accumulation processes in polycrystalline structural alloys under various regimes of cyclic thermal–mechanical loading are considered. Within the framework of mechanics of damaged media, a mathematical model is developed that describes thermal–plastic deformation and fatigue damage accumulation processes under low-cycle loading. The model consists of three interrelated parts: relations defining plastic behavior of the material, accounting for its dependence on the failure process; evolutionary equations describing damage accumulation kinetics; a strength criterion of the damaged material. The plasticity model based on the notion of yield surface and the principle of orthogonality of the plastic strain vector to the yield surface is used as defining relations. This version of defining equations of plasticity describes the main effects of the deformation process under monotone cyclic, proportional and nonproportional loading regimes. The version of kinetic equations of damage accumulation is based on introducing a scalar parameter of damage degree and energy principles, and account for the main effects of nucleation, growth and merging of microdefects under arbitrary regimes of low-cycle loading. The strength criterion of the damaged material is based on reaching a critical value of the damage degree. The results of numerically modeling cyclic thermal–plastic deformation and fatigue damage accumulation in heat-resistant alloys (Nimonic 80A, Haynes 188) under combined thermal–mechanical loading are presented. Special attention is paid to the issues of modeling the processes of cyclic thermal–plastic deformation and fatigue damage accumulation for complex deformation processes accompanied by the rotation of the main stress and strain tensor areas. It is shown that the present damaged medium model accurately enough for engineering purposes describes the processes of cyclic isothermal and nonisothermal deformation and fatigue damage accumulation under combined thermal–mechanical loading and makes it possible to evaluate low-cycle fatigue life of heat-resistant alloys under arbitrary deformation trajectories

The dynamics of eccentric vibration mechanism (Part 1)

This paper presents a mathematical model of a new multi-striker eccentric shock-vibration mechanism (ESVM) with a crank-sliding bar vibration exciter (CSVE) and an arbitrary number of pistons. Analytical solutions for the parameters of the model are obtained to determine the regions of existence of stable periodic motions. Under the assumption of an absolutely inelastic collision of the piston, we derive equations that single out a bifurcational unattainable boundary in the parameter space, which has a countable number of arbitrarily complex stable periodic motions in its neighborhood. We present results of numerical simulations, which illustrate the existence of periodic and stochastic motions. The methods proposed in this paper for investigating the dynamical characteristics of the new crank-type conrod mechanisms allow practitioners to indicate regions in the parameter space, which allow tuning these mechanisms into the most efficient periodic mode of operation, and to effectively analyze the main changes in their operational regimes when the system parameters are changed

On the self-excitation of vibrations of a boring bar in the process of deep boring

The article presents equivalent mathematical models of a boring bar designed for deep boring, in a distributed and a discrete idealizations. A mathematical model describing coupled torsional and lateral vibrations of a boring bar is constructed in the form of a set of differential equations with lagging of the cutting process dynamics. A methodology for studying stability in small of the deep boring process using a characteristic quasi-polynomial is presented. The numerical-analytical results of the studies made it possible to discern stability regions in the parameter space of the model and to obtain relations for maximal cutting depth as a function of geometrical and technological parameters (stiffness, cutting velocity, feeding etc.) of the boring bar considered. It is noted that the obtained numerical-analytical results are in good agreement with experimental data

Strain-Rate Dependency of a Unidirectional Filament Wound Composite under Compression

This article presents the results of experimental studies concerning the dynamic deformation and failure of a unidirectional carbon fiber reinforced plastic (T700/LY113) under compression. The test samples were manufactured through the filament winding of flat plates. To establish the strain rate dependencies of the strength and elastic modulus of the material, dynamic tests were carried out using a drop tower, the Split Hopkinson Pressure Bar method, and standard static tests. The samples were loaded both along and perpendicular to the direction of the reinforcing fiber. The applicability of the obtained samples for static and dynamic tests was confirmed through finite element modeling and the high-speed imaging of the deformation and failure of samples during testing. As a result of the conducted experimental studies, static and dynamic stress-strain curves, time dependencies of deformation and the stress and strain rates of the samples during compression were obtained. Based on these results, the strain rate dependencies of the strength and elasticity modulus in the strain rate range of 0.001–600 1/s are constructed. It is shown that the strain rate significantly affects the strength and deformation characteristics of the unidirectional carbon fiber composites under compression. An increase in the strain rate by 5 orders of magnitude increased the strength and elastic modulus along the fiber direction by 42% and 50%, respectively. Perpendicular loading resulted in a strength and elastic modulus increase by 58% and 50%, respectively. The average strength along the fibers at the largest studied strain rate was about 1000 MPa. The obtained results can be used to design structural elements made of polymer composite materials operating under dynamic shock loads, as well as to build models of mechanical behavior and failure criteria of such materials, taking into account the strain rate effects

Mechanical Response Change in Fine Grain Concrete Under High Strain and Stress Rates

International audienceExperimental results on assessing the effects of strain and stress rates on the behavior of fine-grain concretes are presented. Specimens of fine-grain and fiberreinforced concretes were dynamically tested using the Kolsky method and its modification, the “Brazilian test”. As a result of the experiments, values of the Dynamic Increase Factor (DIF) were determined for both the materials studied. Their curves as a function of strain and stress rates were constructed. The experimental data is compared with the theoretically obtained values of DIF as a function of strain rate available in the literatur

Estimating Fatigue Related Damage in Alloys under Block-type Non-symmetrical Low-cycle Loading

International audienceProcesses of plastic deformation and damage accumulation in poly-crystalline structural alloys are investigated under block-type, nonstationary, non-symmetric cyclic loading. In the framework of damage mechanics, a mathematical model is proposed that effectively describes elastoplastic deformation and fatigue related damage accumulation processes under low-cycle loading. This model can be subsumed under three main parts: the relations defining elastoplastic behavior of the material; the equations describing damage accumulation kinetics; the strength criterion of the damaged material. For validating the model, we perform a numerical analysis and a comparison with the data from full-scale experiments. We demonstrate that the proposed model qualitatively and quantitatively describes the main effects of plastic deformation and damage accumulation processes in structural alloys under complex loading scenarios. Moreover, fatigue related lifetime of the structure is accurately captured by this model as well

Pantographic metamaterials: A view towards applications

The purpose of this article is to show the basic characteristics of the so-called pantographic metamaterial. Here we underline how the microstructure provides some exotic properties and, in principle, implies the second gradient nature of this type of metamaterial. Thanks to the development of additive manufacturing technology (especially in the field of metallurgy) we are now able to produce real samples and carry out experimental measurements to validate the proposed models. In this article we show some new experimental tests, obtained by considering pantographic structures printed in stainless steel. Numerical simulations are briefly shown to show the validity of the theoretical model developed to describe the pantographic metamaterial