Account Plastic Deformations Research Articles

Elastic-plastic buckling of gold thin films into straight-sided blisters

We report on straight-sided buckles experimentally observed by optical and atomic force microscopies on gold ductile thin films deposited by physical vapor deposition on silicon wafers. It is shown that, whatever the buckle dimensions, their maximum deflections are higher than those expected by the elastic theory. Finite elements simulations taking into account plastic deformations in the film have been carried out. The numerical results are presented, discussed and compared to the experimental observations.

НЕЛИНЕЙНЫЙ АНАЛИЗ МАССИВНЫХ ЖЕЛЕЗОБЕТОННЫХ КОНСТРУКЦИЙ С УЧЕТОМ ТРЕЩИНООБРАЗОВАНИЯ

A finite element method, as well as the algorithm and the program for solid reinforced concrete structures analysis have been developed, taking into account plastic deformations of concrete. A modified Willam & Warnke failure criterion was used, supplemented by a flow criterion. Two models of volumetric deformation of concrete have been developed: an elastic model under brittle fracture and an ideal elastic-plastic model. An eight-node solid finite element with linear approximation of displacement functions, which implements the deformation models above mentioned, is constructed. This finite element is adapted to the PRINS computational software, and as part of this program it can be used for physically nonlinear analysis of building structures containing three-dimensional reinforced concrete elements. Modern building codes prescribe to carry out calculations of concrete and reinforced concrete structures in a nonlinear formulation, taking into account the real properties of concrete and reinforcement. To verify the developed finite element, a series of test calculations of a beam in the condition of pure bending was carried out. Comparison of the calculation results with experimental data confirmed the high accuracy and reliability of the results obtained.

PROBLEMS OF COMPUTER STRUCTURAL ANALYSIS AND REINFORCEMENT CALCULATION TECHNIQUES OF REINFORCED CONCRETE RIBBED SLABS

This paper proposes an overview of computer structural analysis and reinforcement calculation techniques of reinforced concrete ribbed slabs that are used in Ukraine. It considers the fundamental hypotheses and assumptions of these techniques and analyzes the possibility of implementation of the building codes’ requirements into automated calculations. Numerical experiments confirm the existence of a relationship between the normal stress distribution pattern in the rib’s cross section and the width of the slab zone, which participates in the rib’s bending. We conclude the need to develop a generalizing methodology of FEM structural analysis for such structures, which could be implemented in modern FEM-analysis packages implementing building information modelling technology (BIM).Design forces in the elements of monolithic ribbed floors are determined taking into account plastic deformations. This approach is based on the assumption of the formation with increasing load in statically indeterminate systems of plastic hinges, each of which leads to a decrease in the static indeterminacy of the system by one degree. The appearance of plastic hinges leads to a redistribution of bending moments, which is calculated using a static or kinematic method. In the general case, the sum of the span moment and half of the support moments for the span of a single-span beam is always equal to the span moment in a similar single-span beam. That is, the ratio of support and span moments does not affect the bearing capacity of the statically indeterminate system as a whole, but only determines the order of formation of plastic hinges.

Finite-element analysis of residual stresses in the TС4 titanium alloy treated by laser shock peening

Laser shock peening is an effective tool for generating deep compressive residual stresses (more than 1 mm) near the surface of metallic structures. This can improve their mechanical properties and fatigue performance. For this purpose, it is necessary to find optimal laser shock parameters. In this paper, the effect of laser intensity and peening pattern on the residual stress field in a Ti-6Al-4V titanium alloy is investigated through numerical simulations. The applied approach includes two steps. In the first stage, the modeling of elasto-plastic stress waves is performed. The second stage involves a solution of static equilibrium problem for residual stress distribution taking into account plastic deformation fields. The analysis was carried out for a square plate with a thickness of 3 mm, the central part of which is subjected to a series of square laser pulses. The pulse length was the same for all considered cases, and it was equal to 3 mm. The results of the analysis demonstrate that, when the laser pulse power density increases, the maximum value of compressive stress increases as well, and tensile stresses occur on the opposite side of the sample. The application of the two-sided laser peening (no overlap) or one-sided peening (50% overlap) can eliminate this effect. An increase in the maximum compressive stress is observed on both sides of the specimen in these cases. Due to an increase in the number of layers in the case of the one-sided peening (no overlap), the maximum compressive stress and penetration depth become greater. However, tensile stresses in the volume of the sample also increase.

NUMERICAL AND ANALYTICAL MODELING OF STRESS-DEFORMED STATE OF THE METAL RING SEAL OF THE TUBING HAGER

The article presents a numerical and analytical modeling of the stress-strain state of a metal ring seal of a tubing hanger under installation loads, as well as under the influence of well pressure. An analytical method for calculating strength and tightness within the elastic formulation is proposed. The calculation by the finite element method was carried out in order to take into account plastic deformations, which make it possible to study the influence of the geometry of the contact zone of the sealing ring on the width of the contact pad and the magnitude of the contact pressure. Comparison of the calculation results by the analytical method and the finite element method is carried out. It is shown that the analytical method, as less labor-intensive, can be used at the initial stages of designing this type of equipment.

КОМПЬЮТЕРНЫЙ АНАЛИЗ РЕСУРСА ТОНКОСТЕННЫХ КОНСТРУКЦИЙ, РАБОТАЮЩИХ В АГРЕССИВНЫХ СРЕДАХ

The problem of brittle fracture of thin-walled shell structures operating under conditions of combined thermomechanical and corrosive effects is considered. The task solution is based on linear fracture mechanics taking into account plastic deformations in the vicinity of the tip of a developing crack and the impact of an aggressive environment. A mathematical model of the corrosion process was built, an integral part of which is a mathematical model of the corrosion rate of structural material, based on experimental data using Lagrange interpolation polynomials. A numerical method for solving the problem is proposed. To determine the available resource and the parameters of the state of the structures under consideration, a step-by-step method is used, followed by refinement using the dichotomy method. At each step of the computational process, the Cauchy problem is solved for the main system of differential equations. The proposed method for solving the problem is implemented in the form of software. The results of a computer study of the bearing capacity and resource of a typical design of a chemical apparatus body are presented.

Properties of a multi-layer multi-span corrugated package

In this article we deal with the problem of cyclic compression of a multilayer multi-span corrugated package by using the finite element method (FEM) and a three-dimensional model (3-D model) of deformation in Ansys. We take into account plastic deformation of the package, as well as the complex law of its propagation and mutual elastic slippage with dry friction over tops of corrugation and in local regions at the tops of corrugation along the package tapes, valid for any geometrical shape of corrugation. This solution can be considered as the second part of the general complex nonlinear problem of cyclic compression of a multilayer multi-span corrugated package with dry friction on contact surfaces. The solution obtained makes it possible to construct any loading processes in the field of elastic-hysteresis package loops. The comparison of elastic-frictional characteristics of the package (EFCs) obtained by calculation and the experimental ones showed their good agreement. The influence of the corrugated package parameters on its EFCs was studied. A number of properties of the package were determined allowing us to draw conclusions and formulate recommendations that make it possible to define the number of package tapes, the required accuracy in the manufacture of corrugations of its tapes, and the choice of the geometric shape of corrugations in almost all cases of practical use of corrugated packages. The solution obtained can be used to determine the effectiveness of a bumper and other protective devices during crash tests of a car for frontal and side impacts and to determine the optimal parameters of these devices by calculating. Certain results and recommendations of this paper can be useful for the calculation of parameters of damping elements of a blisk, hollow wide-chord blades of aircraft GTE fans, ring dampers of rocket engine rotors, as their damping elements are made in the form of multilayer, multi-span corrugated packages.

PARC_CL 2.0 crack model for NLFEA of reinforced concrete structures under cyclic loadings

This paper presents the development of an updated version of PARC_CL 2.0 crack model implemented in Abaqus Code using subroutine UMAT.for. The PARC_CL 2.0 model is a fixed cracked model for the response prediction of reinforced concrete members. More refined material constitutive relationships were incorporated in the formulation of the model to take into account plastic deformations. Finally, to validate the model, reinforced concrete (RC) panels subjected to cyclic loads, available in literature, are modeled and compared with experimental observations. The PARC_CL 2.0 model was able to capture, with reasonable accuracy, the overall behaviour including cyclic shear stress vs. shear strain behaviour, shear stiffness, cyclic stiffness degradation, energy dissipation during the cycles and pinching effect.

Mathematical Model and Program Development for the Efficient Process Conditions Determination during FeC0.15Cr12Ni2 Steel Diamond Smoothing

In this paper the mathematical model and the program based on this model for efficient process conditions during a diamond smoothing is introduced. The mathematical model has been tested with heatproof martensite category steel FeC0.15Cr12Ni2 by the synthetic diamond DSB-1 using as a smoothing tool. The mathematical model takes into account plastic deformation degree which could have both smoothing and reinforcing nature. Through the smoothing conditions the surface has a microroughnesses crumpling but reinforcing conditions involve also surface layer microhardness increasing.

Method of Calculation of Strengthening of the Loaded Rod Structures Taking into Account Plastic Deformations

Article presents the variation method of calculation of rod systems, strengthened by the increase of the size of the cross-sections of elements, change of the structural scheme and the stress state of the constructions. The methods of accounting the influence on the stress-strain state of repair stresses, the introduction of the new pre-stressed structural elements, changing the calculation scheme of strengthened structures are described. Relations used to calculate the strengthened rod systems with elastic and elastic-plastic deformations are shared.

The Fatigue Surface Cracks Growth Model Taking into Account Plastic Deformations for a Cylinder of a Low-speed Long-stroke Compressor

The article dwells on a model of a surface crack growth for a cylinder of a long-stroke compressor taking into account plastic deformations in a crack tip and a type of loading. We have obtained experimental data for cross-shaped samples made of engineering material; the samples have been used to study the effect of biaxial loading on a crack growth rate. The crack growth has been examined comparing the results obtained under monoaxial tension and under biaxial compression-tension. The fracture in a fatigue crack tip is presented as a combination of brittle fracture on a crack tip and as a ductile fracture in a propagation zone of plastic deformations. The finite element method with linear hardening in a zone of plastic deformations have been used to explore a stress state in a crack zone. The formula is proposed to determine the growth rate of fatigue cracks taking into account brittle and ductile stress parameters in the crack tip.

Optimal shakedown design of steel framed structures according to standards

The paper considers the relationships between the optimization of perfectly elastic–plastic structures under repeated variable load and the valid structural design standards. The physical and geometrical properties of a structure are known in advance. The quasi-static cyclic loading is characterized by time-independent upper and lower bounds. The mathematical model for determining the optimal internal limiting force distribution of a structure at shakedown with strength, stiffness and stability constraints according to EC3 standard is presented. The model takes into account the ultimate and serviceability limit states of EC3 with corresponding reliability levels. The evaluation of the stability of the elements under compression takes into account plastic deformations in the shakedown process. The proposed methodology allows a more precise interpretation of the stability constraints in continuous optimization problems of mathematical programming. The results are valid for the assumption of small displacements. Numerical examples of the optimization of a portal and three storey steel frames are presented.

The Effect of Stress State Characteristics on the Surface Fatigue Cracks Growth Rate Taking into Account Plastic Deformations

The technique of fatigue tests of steel cross-shaped samples with a surface crack under biaxial loading is described. The sample and equipment for the implementation a biaxial tension and compression-tension in a working part of the sample are proposed. The sample and equipment for the implementation a biaxial tension and compression-tension in a working part of the sample are offered. Test results of structural steel 20 samples are presented. A stress effect parallel to a crack plane on its growth rate is determined. Crack tip plastic zone shape and sizes under various loading conditions are studied. The relationship of a fatigue crack growth rate and a plastic deformation area size is established. The formula to determine the growth rate of a surface crack under biaxial loading taking into account a plastic deformation is proposed.

10.5937/jaes12-5818 = Bearing capacity of steel I-sections under combined bending and torsion actions taking into account plastic deformations

In steel structures, the I-beams are in many cases exposed to combination of bending moment and bimoment actions. In the elastic stage of work, material strength check is based on maximum normal stresses, which for symmetric I-beams are the sum of moment and bimoment stresses. The maximum stresses are compared with calculated resistance. In both European codes and Russian standards for design of steel structures, calculation of members is performed considering the conditions in which the plastic deformations over the section are allowed. With the development of plastic strains, bearing capacity of section is higher than in the elastic stage. The existing normative documents for the design of steel structures in Russia do not include design coefficient taking into account development of plastic deformations in warping torsion. The article examines combined action of bending moment and bimoment on I-beam profiles throughout the theoretical and numerical solutions. Recommendations for checking their bearing capacity in accordance to Russian standards are given, taking into account development plastic deformations.

An Analytical Model for Evaluation of Bending Angle in Laser Forming of Metal Sheets

In this study, an analytical model is developed to evaluate the bending angle in laser forming of metal sheets. The model is based on the assumption of elastic-bending theory without taking into account plastic deformation during heating and cooling phases. A thermal field is first established, then the thermal component of deformation is calculated and it is used in the strain balance to evaluate the bending angle. The basic idea is that it is possible to use a two-layer model whereas the heated layer thickness depends on the effective temperature distribution along the sheet thickness. A comprehensive experimental study is carried out and the main process parameters, i.e., laser power, scanning speed, sheet thickness, were varied among several levels to evaluate the accuracy of the developed model. Model predictions were confirmed by experimental measurements especially on materials with low conductivity. The established analytical model has demonstrated to provide a great insight into the process parameters effects onto the deformation mechanism within pure temperature gradient mechanism and bucking to temperature gradient transition conditions.

Analytical model of the critical current of a bentNb3Sn strand

The critical current performance of a largeNb3Sn cable-in-conduit conductor (CICC) was degraded by periodic bending of strands due to alarge transverse electromagnetic force. The degradation of each strand due to this bendingshould be evaluated in calculations of the critical current of a CICC, but a suitable modelhas not been developed yet. Therefore, the authors have developed a new analytical modelwhich takes into account plastic deformation of copper and bronze and filamentbreakage. The calculated results were compared with test results for uniformly bentNb3Sn bronze-route strands. The calculated results assuming a high transverse resistance model(HTRM) show good agreement with the test results, a finding which confirms the validity of themodel. Because of a much shorter calculation time than for numerical simulation, the developedmodel seems much more practical for use in calculating the critical current performance of aNb3Sn CICC. In addition, simulation results show that since the neutral axis of a bent strandshifts to the compressive side due to plastic deformation of the copper and bronze, and/orfilament breakage, the strand is elongated by bending. This elongation may enhance thestrand’s critical current performance. Moreover, the calculated results indicate thatthe dependence of the critical current on the bending strain is affected by thebending history if the strand is excessively bent, especially when filaments arebroken. In a real magnet, since a strand in a CICC is normally subject to themaximum electromagnetic force prior to an evaluation of its performance at a lowerelectromagnetic force, the effect of over-bending should be taken into account incalculations of its critical current performance, especially when filament breakage occurs.

Validação de um modelo de dano para a análise não-linear de estruturas em concreto armado

This work presents a discussion on the employment of a damage model recently proposed for concrete and other damage models in the non-linear analysis of reinforced concrete structures. The validation of the model is obtained by the comparison between numerical responses and experimental ones. The model proposed by Pituba regards concrete as an initially isotropic medium that starts to present plastic deformations, bimodularity and anisotropy induced by the damage. The model proposed by Mazars considers concrete to be an elastic and isotropic medium. Next, the model proposed by La Borderie is presented. This isotropic damage model takes into account plastic deformations induced by the damage. In the second part of the work, the models are used in the analysis of reinforced concrete structures, where the numerical responses are compared with experimental ones. The results evidence the good performance of the damage models on the simulation of the behavior of reinforced concrete structures. In particular, the employment of the damage model proposed by Pituba is valid. It is noted that the simple formulations of damage models can present results with good accuracy leading to possible practical applications in Structural Engineering.

Plasto-Elastohydrodynamic Lubrication (PEHL) in Point Contacts

Elastohydrodynamic lubrication (EHL) is an important branch of the lubrication theory, describing lubrication mechanisms in nonconformal contacts widely found in many mechanical components such as various gears, rolling bearings, cams and followers, metal-rolling tools, traction drives, and continuous variable transmissions. These components often transmit substantial power under heavy loading conditions. Also, the roughness of machined surfaces is usually of the same order of magnitude as, or greater than, the estimated average EHL film thickness. Consequently, most components operate in mixed lubrication regime with significant asperity contacts. Due to very high pressure concentrated in small areas, resulted from either heavy external loading or severe asperity contacts, or often a combination of both, subsurface stresses may exceed the material yield limit, causing considerable plastic deformation, which may not only permanently change the surface profiles and contact geometry but also alter material properties through work hardening as well. In the present study, a three-dimensional plasto-elastohydrodynamic lubrication (PEHL) model has been developed by taking into account plastic deformation and material work-hardening. The effects of surface/subsurface plastic deformation on lubricant film thickness, surface pressure distribution, and subsurface stress field have been investigated. This paper briefly describes the newly developed PEHL model and presents preliminary results and observed basic behavior of the PEHL in smooth-surface point contacts, in comparison with those from corresponding EHL solutions under the same conditions. The results indicate that plastic deformation may greatly affect contact and lubrication characteristics, resulting in significant reductions in lubricant film thickness, peak surface pressure and maximum subsurface stresses.

Practical fatigue analysis of hydraulic cylinders – Part II, damage mechanics approach

The paper is continuation and extension of the previous article (Marczewska et al., 2006) [1] published in Journal of Fatigue in 2006. Our previous model of analysis (Marczewska et al., 2006) [1] was based on classical S–N curves and equivalent amplitude stress concept. Now more physically justified damage mechanics approach to fatigue analysis is applied. The analysis used in both our papers is based on particular application of the constitutive model described in Oller et al. [2]. Hydraulic cylinders investigated under E.C. project “PROHIPP” are analyzed. Modeling of fatigue crack propagation is performed. The new elements, in comparison with previous paper (Marczewska et al., 2006) [1] are: application of the thermodynamic basics of damage mechanics approach to fatigue analysis with taking into account plastic deformations, introduction of damage evolution surface in fatigue analysis, modification of analytical form of S–N curve proposed in Oller et al. [2] and fatigue crack propagation modeling using damage mechanics approach. As it was mentioned in Marczewska et al. [1] the “marriage” of stress analysis and fatigue data is still one of deficiencies in the current European Norm EN 13445, chapter 18: detailed assessment of fatigue life [3]. Our paper is an attempt to further reduce this deficiency.

Micro-Macro Description for Elastoplasticity of Materials with Lamellar Microstructure Using Anisotropic Eshelby Tensor

The elastoplastic behavior of dual-phase materials with lamellar microstructure is analyzed using a micro-macro approach. It involves the Hill's self-consistent scheme incorporating general anisotropic Eshelby tensor, and it can take into account both inherent and plastic deformation induced anisotropies. A high-precision numerical algorithm related to rotational ellipsoidal inclusion and anisotropic Eshelby tensors is developed. The elastoplastic behavior of both macroscopically anisotropic and isotropic materials is analyzed and compared with the result using isotropic Eshelby tensor. It shows that the difference between the result with an isotropic Eshelby tensor and that with an anisotropic Eshelby tensor is negligible if plastic deformation is not severe. The effect of the shape of the ellipsoidal lamellar inclusion on the material responses, the computation time and the convergence of numerical processes are also investigated. It shows that the convergence of the numerical process with a general anisotropic Eshelby tensor is as good as that with an isotropic Eshelby tensor, but for the former the computation time is much more. The shape of the ellipsoidal inclusion also strongly affects the computation time.