Deformation Theory Of Plasticity Research Articles

Quasi - static and impact performance study of a three-dimensional negative Poisson's ratio structure with adjustable mechanical properties

The mechanical properties of most materials with a negative Poisson's ratio (NPR) cannot be flexibly adjusted after being designed to meet complex engineering requirements. To ensure the changes of those materials’ relative density are minimal when overcoming these limitations, this study proposes a novel method that adjusts the mechanical performance by grooving the structure and adjusting the angle of the diagonal support rod. Unlike traditional methods that involve adding 'ribs' to the structure for adjustability, this approach focuses on the design of the structure itself. To analyze the large deformation behavior of unit-cell lattices, we established a theoretical model based on plastic deformation theory and derive the relationship between the number of unit-cell lattices and the relative density of multi-cell lattices. Experimental samples were fabricated by using selective laser melting (SLM). Meanwhile, the accuracy of the finite element results was verified by quasi-static compression experiments and impact experiments. Then the validated finite element model is then utilized to discuss the influence of structural parameters on mechanical properties. In addition, we also studied the influence of medium and low-speed impact loads on the deformation characteristics, mechanical properties, and energy absorption (EA) of the structures. The results demonstrate the reliability of the design method, showcasing its potential to achieve on-demand adjustability of stress, stiffness, and strength to meet complex engineering requirements. Notably, the adjustment range of peak load is from 24.55 MPa at the lower limit α = 60° to 48.29 MPa at the upper limit α = 90°, with an adjustment range of 23.74 MPa. The adjustment range of the average platform stress is from 10.8 MPa at the lower limit of α = 60° to 24.34 MPa at the upper limit of α = 80°, and the adjustment range reaches 13.54 MPa. This study provides new insights on intelligent protection engineering and the adjustable mechanical properties of metamaterials.

Understanding and exploring anisotropy mechanism of mechanical properties for ferrous alloy under different cooling paths

To understand and illuminate the anisotropy mechanism of mechanical properties with respect to typical ferrous alloy, two different kinds of microstructures were fabricated by adopting thermo-mechanical controlled processing (TMCP) with identical rolling schedule and different cooling paths, named high coiling temperature process (HC) and low coiling temperature process (LC). The influences of microstructure together with distribution of crystallographic orientation on the anisotropy discipline were investigated, and the anisotropy mechanism were further explored on the basis of plastic deformation theory. Results indicated that the microstructure processed by HC was primarily composed of quasi-polygonal ferrite (QPF) and small fraction of bainitic ferrite (BF). While the LC-processed microstructure predominantly consisted of acicular ferrite (AF), BF as well as martensite-austenite island (M/A). The LC-processed alloy exhibited more obvious anisotropy performance indicated by tensile properties along different tensile directions compared to the HC-processed alloy. There was a phenomenon of uniform distribution of macro-texture and uneven distribution of micro-texture with respect to the both achieved microstructures, and the uneven distribution of micro-texture together with high density of dislocation for BF were responsible for the obvious anisotropy performance of the studied ferrous alloy.

Development of the theory of joint plastic deformation of different metals during steel strip rolling

Development of the theory of joint plastic deformation of different metals during steel strip rolling

Elasto-plasticity theory for large plastic deformation and its use for the material stiffness determination

In this paper, we present a finite elasto-plasticity theory for large plastic deformations. For the elastic part of the model, we use the St. Venant–Kirchhoff elasticity. The plastic part is described by the isomorphy concept, the yield condition is covered by the isotropic J2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_2$$\\end{document} theory of (Huber in Czas Techn 22:34,1904; von Mises in Math Phys 4:582–592, 1913) and (Hencky in ZAMM 9:215–220, 1924), and the yield condition uses the principle of maximum plastic dissipation. The numeric of this theory is discussed and finally implemented in a Fortran code to use it as material law in the UMAT subroutine of the finite element program Abaqus. The material law is validated using different test calculations like tensile and shear tests as well as a large deformation simulation compared to the Abaqus internal material law. Further, we apply this material model to determine the effective material stiffness tetrad of large deformed inhomogeneous materials. For these purposes, we additionally present an automated method for determining material stiffnesses of an arbitrary material in Abaqus.

Investigation of Passive Pile Groups’ Responses Induced by Combined Surcharge-Induced and Excavation-Induced Horizontal Soil Loading

Excessive lateral forces and the deformation of pile groups caused by adjacent surcharge loading and excavation can potentially lead to the failure or collapse of nearby pile foundations. This paper presents a simplified analytical method to investigate the lateral displacement of passive pile groups caused by combined surcharge-induced and excavation-induced horizontal soil loading and validates it by utilizing two published centrifuge tests and numerical modeling. Firstly, the passive load resulting from surcharge-induced horizontal soil loading is determined using the improved formula of Boussinesq and the theory of local plastic deformation. The additional horizontal force exerted on the pile axis subjected to excavation-induced horizontal soil loading is also taken into account using the Mindlin solution. Furthermore, the shielding effect between pile groups is also proposed to analyze the response of a laterally loaded pile group due to excavation unloading. Secondly, according to the Pasternak foundation model of soil–pile interaction, the equilibrium differential equations are solved by the finite difference method. Finally, parametric analyses are undertaken to evaluate the behavior of different constraints on the pile head and surcharge procedure. The results demonstrate that the capped-head pile groups can provide greater restraint compared to the free-head groups for the lateral displacement of pile groups. The front pile experiences greater forces than the rear one in passive pile groups as a result of the smaller soil pressure on the rear pile. Additionally, increasing the horizontal stiffness of the capped head with fully fixed ends can significantly decrease the horizontal deformation of the pile groups.

Lateral Deformation Response of an Adjacent Passive Pile under the Combined Action of Surcharge Loading and Foundation Excavation

With the increasing development of civil engineering in large cities, more and more excavations and surcharge loadings are being constructed or planned adjacent to existing building piles in crowded urban areas. Previous study on pile deformation has primarily focused on surcharge loading or foundation excavation and given little concern to the combined action of surcharge loading and foundation excavation. The article develops a two-stage process to assess the lateral displacement of nearby pile foundations induced by the combined action of surcharge loading and excavation. Firstly, the local plastic deformation theory and Boussinesq solution are used to accurately predict the passive loading of adjacent pile foundations caused by surcharge loading; Mindlin formulas are adopted to predict the passive pile’s additional lateral stress applied by excavation. Secondly, Pasternak models are adopted and the finite difference method is used to establish the deflection differential formula of the single passive pile. Last but not least, a parametric study is conducted to investigate the influence of the loading dimensions, loading magnitudes, and three-dimensional excavation dimensions. The findings of the calculations reveal that the loading magnitudes have a more significant impact on the lateral displacement of the pile compared to the loading dimensions. Therefore, a concentrated surcharge loading should be avoided. Additionally, the excavation depth has a greater influence on the lateral displacement of the pile compared to the excavation area. In order to mitigate this situation, a step excavation should be implemented for each layer of soil, with the soil excavated away from the pile foundation first.

Improving shape formation under conditions of plane tensile stress

Thin-walled axisymmetric truncated parts made of sheet billets are actively used in rocket and aerospace engineering. Improvement to their shape formation, based on directed material thickness change will ensure the production of parts with minimum thickness variation. This will also enable aviation and space industry enterprises to attain leading positions, as well as reduce labor costs. This work studies the possibility of obtaining thin-walled axisymmetric parts of truncated tapered shape using one of the methods of sheet metal stamping under flat tensile stress conditions (flanging). The mechanism was identified and the analysis of the stress-strain state of the billet during deformation was carried out. This takes into account the minimizing of the difference between the specified and technologically possible thicknesses. A mathematical model was developed to consider the shaping method based on the process of flanging. Theoretical studies were based on the principles of the plastic deformation theory of sheet materials. This was achieved by the following factors: approximate differential equations of force equilibrium; equations of constraint; plasticity conditions; and fundamental constitutive relations under given initial and boundary conditions. The process of flanging was simulated using the LS-DYNA software package with the following initial data of a conical billet made of 12Kh18N10T steel: cone angle 16.4°, thickness Sbillet = 0.3 mm. The aim was to eliminate errors in designing a tool for future implementation of the method on a manufactured die tooling, as well as to confirm the theoretical conclusions on the selection of technological parameters and achieve minimal thickness variation. The steps of computer modeling are presented, indicating the main process parameters such as material model, mechanical characteristics of the workpiece material, type of elements, kinematic loads, conditions of contact interaction of elements with each other, etc.

Ensuring the Safety of Steel Moment Frames Subjected to Uncertain Impacts

The article addresses the problem of safety evaluation of steel moment frames of civil buildings, e.g., warehouses, shops, garages, and multistory industrial buildings on deformable soil in the relevant case of an emergency impact. The case of accidental emergency impacts is considered when such parameters as the point, direction, and intensity of an impact cannot be predetermined. Such impacts are not expected to trigger the progressive collapse of currently implemented design solutions and the whole structure must maintain the property of survivability. To evaluate this property, several calculations are to be made in the quasi-static statement to identify the stress–strain state under the most dangerous accidental impacts. Further, final calculations are to be made in the dynamic statement. In this case, the problem of search is solved using the criterion of minimizing the integral safety margin of structural elements in a steel moment frame design. Calculations prevent the frame stability loss. The calculation is performed in the quasi-static statement using models made in compliance with the deformation theory of plasticity, while the calculation in the dynamic statement takes into account the associated plastic flow rule. The proposed procedures allow for designing steel moment frames that are resistant to accidental emergency impacts. Impact loading is analysed as pulse loading, which is statically equivalent to the dynamic effect of an inelastic impact of a stiff body on a structural system. The design and the efficiency evaluation of a steel moment frame of a two-story building are considered.

Effect of neutral layer migration on bending force of AZ31B magnesium alloy sheet during bending

In this paper, they are based on the micro-element stress equilibrium condition in the plastic deformation theory and the Yoon-2014 yield criterion, which can reflect the tension and compression asymmetry of AZ31B magnesium alloy, a bending force model is established to predict the required bending force at different angles according to the neutral layer migration in the bending process of magnesium plate. The offset and bending force values of the neutral layer were verified by FEM and corresponding experiments. The results show that the bending force of a magnesium plate is related to the geometrical size of the scale, the yield limit of the material, and the height of the elastic zone of deformation. The model’s prediction accuracy is better than that of the conventional calculation formula, which can realize the reliable prediction of the required bending force of the magnesium plate. In the bending process, the magnesium plate is affected by the asymmetry of tension and pressure, and the neutral layer migrates to the tensile side. The deviation degree of the neutral layer is the most obvious when the magnesium plate is bent to 90°, and the required bending force is the largest.

Patterns of localized deformation at pre-fracture stage in carbon steel – stainless steel bimetal

The work is devoted to the study of strain localization at macroscale level during parabolic mechanical hardening and pre-fracture under quasi-static loading of a carbon steel – stainless steel bimetal. The problem of estimating the scale of the phenomena that determine plasticity is decisive in the development of any theories of plastic deformation, in particular, dislocation theories. The main difficulty in constructing such theories is the reconciling the dislocation scales, characteristic for most deformation and mechanical hardening mechanisms, with macroscopic parameters of deformation processes. In the framework of the autowave model of localized plastic deformation, this problem can be reduced to the possibility of obtaining parameters from the results of macroscale observations of localized plastic flow development. During the experiments, it was confirmed that in a bimetal at any forming stage, a specific pattern of localization centers distribution is spontaneously generated - a pattern of localized plastic flow. The shape of such patterns is determined by the law of mechanical hardening acting in the material. It is shown that the observed localization patterns can be used as an informative feature in predicting the plasticity margin. In the process of uniaxial tension at the stage of parabolic mechanical hardening of the bimetal, the deformation mode is realized with the formation of several potential fracture centers. It was established that at the pre-fracture stage, during the time evolution of the wave pattern of deformation localization, the zone of active plastic deformation narrows, but the number of centers in it either remains the same with a decrease in the distance between them, or even increases. The result of this process is the formation of a macroscopic neck, and then fracture. At the pre-fracture stage, the collapse point indicates the place of future fracture and signals the need to stop the deformation process in order to avoid the fracture of the bimetallic material. Thus, the well-known manifestation of deformation macroscopic localization – formation of a neck – is preceded by complex phenomena of mutually coordinated motion of localized plasticity centers at the pre-fracture stage.

Physical nonlinearity in porous functionally graded kirchhoff nano-plates: Modeling and numerical experiment

In this paper, mathematical models of porous functionally graded inhomogeneous plates were constructed. The following hypotheses were used as the foundation: the kinematic Kirchhoff model was used; nano effects were considered by the modified couple stress theory; material properties depend on coordinates (x,y,z), and for metals, they also hinge on the stress-strain state at a point in the plate volume, i.e. there is a dependence σi(ei). This dependence can be any analytical function derived from experimentation, which means that it is possible to take into account elastic-plastic deformations according to the deformation theory of plasticity. The ceramic material is resilient. The required variational and differential equations and the boundary conditions were derived from the Lagrange functional. The plate material's porosity was characterised by six types. For numerical solutions, the methods of reduction of the partial differential equation to the ordinary differential equation were applied, as well as iterative methods nested one into another, based on the following techniques: variational iterations method (VIM), Agranovskii-Baglai-Smirnov method (ABSM) and Birger's method of variable parameters of elasticity. For each of these methods, there are theorems proving their convergence. Each problem that describes the stress-strain state of Kirchhoff nano-plates was solved using the following analytical methods: Exact Navier's solution (ENS), Bubnov-Galerkin method (BGM), Levy solution (LS), numerically analytical Kantorovich-Vlasov (KVM) methods, variational iterations method (VIM), Vaindiner method (VaM) and numerical finite difference method (FDM). The convergence of these methods was investigated and the optimal method for calculating such structures, both in terms of accuracy and speed, was determined for the elliptic 2D PDEs of arbitrary area Ω. Numerical results for both elastic nano-plates and elastoplastic nano-plates have been presented.

Construction of Forming Limit Diagram for Sheet Blanks from Aviation Aluminum Alloys

Introduction. The modern development of stamping aircraft manufacturing is inextricably linked with the assessment of the limiting capabilities of sheet blanks. However, the issue of defect-free forming of blanks made of aviation aluminum alloys is understudied. The importance of this issue is due to the fact that aluminum alloys are often used in the manufacture of thin-walled products for aviation purposes. During the implementation of shaping processes, various defects may appear, specifically, corrugation or unacceptable thinning. In this regard, the objective of the work was to construct a diagram of the limit deformations of the base aviation alloys and to conduct a comparative analysis of the limit deformation curves for these materials.Materials and Methods. Logarithmic deformations with the property of additivity were used to account for large deformations. The construction of the diagram of the limit deformations was carried out in the formulation of the deformation theory of plasticity. The issue of constructing a diagram of limit deformations was considered on the basis of the positivity criterion of the loading force derivative. In the area of negative values of the smallest major deformations, the Hill criterion was used to construct the limit deformation curve, and in the area of positive values of the smallest major logarithmic deformations, the Swift criterion was used. When constructing the limit deformation diagram, a power approximation of the hardening rule was used.Results. The curves of limiting deformations for the following aviation alloys were obtained: AMg6, D16AT, AMg2M, 1201-T, AMcM. According to the comparative analysis of the areas of safe forming, the values of deformations of the beginning of necking and their influence on the change in the position of the curve of the limiting deformation of blanks were compared: the greater the deformation of the neck formation, the higher the position of the curve of the limiting deformations. The concept of the Keeler's limit deformation diagram was described. Approaches to the construction of the Hill-Swift criteria used on the basis of the results of tensile testing of sheet specimens were presented.Discussion and Conclusions. Based on the constructed curves of limiting deformations for aviation alloys, AMg-6, D16AT, AMg2M, 1201-T, AMcM, the following has been found. AMg2M alloy has the largest area of safe forming, 1201-T alloy has the smallest one. That is explained by the difference in relative deformations of the beginning of neck formation. The conducted research made it possible to evaluate the possibilities of defect-free forming of thin-walled blanks made of basic aviation aluminum alloys. The use of the constructed diagrams of limiting deformation will provide predicting the appearance of breaks in the process of forming sheet blanks.

Calculation of the formation of normal cracks in a reinforced concrete element based on the deformation theory of plasticity of concrete by G.A. Geniev

The authors present a refined method of determining the moment of cracking in reinforced concrete bar constructions using the diagram of deformation of concrete built on the basis of the deformation theory of plasticity by G.A. Geniev in which the stress and strain invariants of concrete are linked by nonlinear dependences. In the resulting defining equations, the hypothesis of flat sections, as well as the premise of reaching the limit values of concrete deformations on the stretched fibers of the cross-section are used. Stresses in concrete are determined through deformation values in accordance with the nonlinear deformation diagram of concrete. On the basis of the assumptions accepted, analytical dependences for determining the moment of cracking in the sections of bending elements with single and double reinforcement have been acquired. The formulas obtained were used in the analysis of various factors influence on crack resistance of bendable reinforced concrete elements. It was found out that the moment of crack formation practically does not change when percentage of reinforcement of longitudinal tensile or compressed reinforcement changes. The most effective method of crack resistance improvement is the increase of concrete strength. The proposed methodology is verified by comparison with experimental results on reinforced concrete prototypes. It is concluded that the use of the diagram of nonlinear deformation of concrete on the basis of the theory of plasticity by G.A. Geniev allows to estimate more strictly the crack resistance of reinforced concrete rod elements.

Моделирование напряженно-деформированного состояния кирпичной кладки одноэтажного нежилого здания

The application of the finite element method (FEM) for the calculation of brick structures of a single-storey building at the design stage is considered. The stress-strain state of the critical masonry of the building is restored. For this purpose, the deformation theory of plasticity of A.A. Ilyushin, the dependence of stresses on deformations according to existing norms for the calculation of brickwork of buildings is applied. The results of full-scale testing using the method of non-destructive testing are analyzed. As a result of monitoring the technical condition of non-existing structures of the building under study, defects that appeared at the stage of construction of the building and during its operation were revealed. The results obtained by the two methods were compared, the degree of wear of masonry building structures was determined, after which recommendations were developed to improve the current technical condition of the brick building under consideration. It is established that after the completion of repair work and during the further operation of the construction object, it is necessary to comply with the requirements for the current constructive prevention of the building on the basis of the requirements of the current normative acts. The possibility of the superstructure of the second floor superstructure on existing structures was also analyzed. It is revealed that at the moment it is impossible to perform the superstructure, since in order to make it possible to perform the superstructure of the second floor, the conditions must be met to strengthen the structures for the safety of the operation of the lower floor with an increase in the load on it due to the support of an additional floor on it.

Elastic–plastic bifurcation analysis of cylindrical shells with axisymmetric variable thickness

This study focuses on the elastic–plastic bifurcation analysis of axial compressed thin-walled cylindrical shells with variable thickness. The general asymptotic formula of the elastic–plastic critical buckling load, which is a function of the Coefficient of the Thickness Variation (CTV) and the buckling load of shells with constant thickness, is derived based on the hybrid perturbation-weighted residual method. The general formula can be reduced to the classical elastic buckling solution in Koiter (1994) when considering the elastic case with the first-order term. Furthermore, a finite element bifurcation analysis procedure is also presented by adopting the incremental J2 deformation theory of plasticity through a custom user-defined subroutine appended to the nonlinear finite element software ABAQUS. The robustness of this numerical scheme and the theoretical formula is confirmed by the decent agreement with the available experimental results in the literature. In the end, the influence of the thickness variation parameter and D/t on the elastic–plastic buckling load of shells with varying thickness is also discussed.

On a thermodynamic foundation of Eyring rate theory for plastic deformation of polymer solids

ABSTRACTThe plastic deformation of almost all solid polymers can be represented by a thermally activated rate process involving the motion of cooperative mobile elements over potential barriers, based on the Eyring activated rate theory. The present study shows that the governing equations for the Eyring rate theory can be completely derived based on the principle of microscopic reversibility in the framework of non-equilibrium dynamics.

Determination of the bearing capacity of encentrally compressed concrete filled steel tubular columns on the basis of the deformation theory of concrete plasticity

Objective. The article proposes a method for finite element analysis of pipe-concrete columns in a physically nonlinear setting by reducing a three-dimensional problem to a twodimensional one based on the hypothesis of plane sections.Method.The equations of the theory of plasticity of concrete by G.A. Geniev are used. The technique was tested by comparing the solution with a calculation in a three-dimensional setting in the LIRA-SAPR software package, as well as with the experimental data of A.I. Sagadatov and calculation according to the current Russian design codes for steel-pipe concrete structures.Result. It has been established that the effective area of operation of columns with a circular cross section is small eccentricities of the longitudinal force.Conclusion. The proposed approach can be applied to the analysis of the stress-strain state and the bearing capacity of pipe-concrete columns of arbitrary section. There are no restrictions on the composition of concrete, and the shell material can be not only steel, but also fiberglass.

Microstructure based numerical simulation of the micromechanics and fracture in hypereutectic Al–Mg2Si composites

In the present study, both experimental and numerical examinations were performed to understand the hypereutectic Al–Mg2Si composite's microstructural morphology, mechanical properties and fracture correlation. The innovation of this research includes the micromechanics studies and failure initiation in hypereutectic Al–Mg2Si composite through the compiled induce stress, deformation plasticity and energy dissipation theory subjected to tension. Ultimate tensile strength (UTS), toughness and elongation have decreased, but the yield strength has increased up to 25% Mg2Si addition and then decreased at the composites with 30 wt% Mg2Si because the brittle fracture increases due to the presence of comparatively coarser and dendritic primary Mg2Si particles. Additionally, an increase in the microporosity with the increase in Mg2Si concentration also affects the same. Finite element analysis (FEA) was performed using the Ramberg-Osgood constitutive model and actual microstructure 2D representative volume elements model. The FEA and experimental results have a satisfactory agreement. The fractography unveils the presence of a mix-mode of fracture, i.e. the ductile and the brittle fracture of the composites. Mises and Tresca failure criteria reveal that the distribution of stress is non-homogeneous and stress is localized in the narrow eutectic and irregular Mg2Si phase region, which acts as a crack initiation site. Analysis of the stress triaxiality and equivalent plastic strain distribution shows that void initiation and growth take place during the deformation of the Al–Mg2Si composites. The plastic dissipated energy distribution in deformed RVEs interestingly consents to the von mises stress, plastic strain and stress triaxiality analysis findings.

Еxperimental determination of ratio of transverse and longitudinal deformations (Poisson's ratio) during longitudinal rolling

In the analysis of experimental data obtained according to the scheme of the plane stressed-deformed condition (during longitudinal rolling) the dependence of the ratio of transverse to longitudinal deformations coefficient, or Poisson’s ratio for plane stressed-deformed condition are defined. Obtained values differ from the tabular data for the elastic deformed state and from the accepted value in the deformation theory of plasticity.

Experimental determination of ratio of transverse to longitudinal strains (Poisson’s ratio) in pure shear (upsetting of long strips in container)

Тhe values of the coefficient of the ratio of transverse and longitudinal strains, or Poisson's ratio, are determined depending on the type of stress-strain state when analyzing the experimental data obtained according to the pure shear scheme (during the upsetting of long narrow strips in a container). The data obtained differ from the tabular data for the elastic deformed state and from the value of 0.5 accepted in the deformation theory of plasticity.