Deformation Theory Of Plasticity Research Articles

Упругопластическая модель механического конусно-раструбного соединения труб

Background One of the problems of the industrial pipelines is the protection against internal corrosion. This article discusses the mechanical cone-spigot steel pipe joint with an internal protective coating and the conditions for achieving equal strength at different combinations of mechanical properties of metals and sizes of the pipe. There were investigated the basic laws of cone-spigot connections strength, the requirements of a maximum pressure rating at different combinations of input data; there was offered an algorithm for the calculation of process parameters. Aims and Objectives To investigate the strength of the cone-spigot connections under the different factors that determine the dissimilarity of the connected pipes on the mechanical properties and dimensions within standard tolerances. To improve the calculation method to ensure the uniform strength. To evaluate the effect of operating pressure on strength. Methods The Genki-Ilyushin provisions of deformation theory of plasticity were used in the mathematical apparatus. The calculations were carried out by the finite element method in conjunction with the methods and iterations of successive approximations. Results There were investigated the influence of the following properties of the pipe: the ratio of diameters and wall thicknesses, the mechanical properties of metals within the elastic and plastic deformations, as well as the operating pressure on the mechanical strength of the cone-spigot connections. There were made the recommendations, allowing to provide uniform strength of cone-spigot connection with various combinations of initial parameters.

Nonlinear elastic/plastic buckling analysis of thick/thin skew plates under uniaxial and biaxial loading

In this study, elastic/plastic buckling analysis of thick skew plates subjected to uniaxial compression or biaxial compression/tension loading using the generalized differential quadrature method is presented for the first time. The governing differential equations are derived based on the incremental and deformation theories of plasticity and first-order shear deformation theory. The elastic/plastic behavior of the plates is described by the Ramberg–Osgood model. Generalized differential quadrature discretization rules in association with an exact coordinate transformation are simultaneously used to transform and discretize the equilibrium equations and the related boundary conditions. The results are compared with the previously published data to verify the established methodology and procedures. The effect of skew angle and thickness ratio on the convergence and accuracy of the method are studied. Moreover, the effects of aspect, loading and thickness ratios, skew angle, incremental, and deformation theories and different types of boundary conditions on the buckling coefficients are presented in detail. The results show that the difference between the incremental and deformation theories becomes greater with increasing thickness ratio and constraints at boundary conditions. Furthermore, the skew angle also has an important effect on differences between those theories.

Calculation of the Pull-Out Force of Ni<sub>47</sub>Ti<sub>44</sub>Nb<sub>9</sub> Shape Memory Ally Pipe Coupling

Investigation of mechanical state of shape memory alloy pipe-coupling had an important significance in engineering field. Theory of plastic deformation was used to analyze the coupling force in the tube connecting process of NiTiNb shape memory alloy, in this paper. Based on the analyzed results a mechanical modeling and formula calculation were carried out, the radial pressure of the SMA tube was calculated, in this paper. The results show that, when the temperature doesn’t reach to contact temperature, the pipe coupling of TiNiNb shape memory alloy has no radial pressure; when the temperature reaches to inverse martensite phase transformation temperature, the radial pressure increases; with the decreasing of temperature, the radial pressure increases a little. The radial pressure and push-out force increase with the increasing of the wall thickness. Thus, to improve the strength of connection, the wall thickness of pipe coupling can be properly increased.

Investigation of localized necking in substrate-supported metal layers: Comparison of bifurcation and imperfection analyses

Localized necking is often considered as precursor to failure in metal components. In modern technologies, functional components (e.g., in flexible electronic devices) may be affected by this necking phenomenon, and to avoid the occurrence of strain localization, elastomer substrates are bonded to the metal layers. This paper proposes an investigation of the development of localized necking in both freestanding metal layers and elastomer/metal bilayers. Finite strain versions of both rigid–plastic flow theory and deformation theory of plasticity are employed to model the mechanical response of the metal layer. For the elastomer, a neo-Hookean constitutive law is considered. Localized necking is predicted using both bifurcation (whenever possible) and Marciniak–Kuczynski analyses. A variety of numerical results are presented, which pertain to the prediction of localized necking in freestanding metal layers and metal/substrate bilayers. The effects of the constitutive framework and the presence of an elastomer substrate on strain localization predictions have been specifically highlighted. It is demonstrated that the addition of an elastomer layer can retard significantly the occurrence of localized necking. It is also demonstrated that the results of the Marciniak–Kuczynski analysis tend towards the bifurcation predictions in the limit of a vanishing size for the geometric imperfection.

Elastoplastic buckling analysis of rectangular thick plates by incremental and deformation theories of plasticity

In this study, the elastoplastic buckling behavior of thick plates under uniaxial, biaxial compression/tension, pure shear and combined shear, and uniaxial compression loading are analyzed using a stability analysis based on generalized differential quadrature method. Based on first-order shear deformation plate theory and incremental and deformation theories of plasticity, the nonlinear equilibrium equations are developed. Various combinations of clamped, simply supported, and free boundary conditions are considered. The governing equations and solution domain are discretized by the generalized differential quadrature method. The results are compared with known solutions in literature to verify the established methodology and procedures. The effects of aspect, loading and thickness ratios, shear correction factor, different boundary conditions, and behavior of material on the buckling coefficient are discussed. Finally, some mode shapes of various loading and boundary conditions are illustrated.

A new basis for the application of the $$J$$ J -integral for cyclically loaded cracks in elastic–plastic materials

Fatigue crack propagation is by far the most important failure mechanism. Often cracks under low-cycle fatigue conditions and, especially, short fatigue cracks cannot be treated with the conventional stress intensity range \(\Delta K\)-concept, since linear elastic fracture mechanics is not valid. For such cases, Dowling and Begley (ASTM STP 590:82–103, 1976) proposed to use the experimental cyclic \(J\)-integral \(\Delta J^{\exp }\) for the assessment of the fatigue crack growth rate. However, severe doubts exist concerning the application of \(\Delta J^{\exp }\). The reason is that, like the conventional \(J\)-integral, \(\Delta J^{\exp }\) presumes deformation theory of plasticity and, therefore, problems appear due to the strongly non-proportional loading conditions during cyclic loading. The theory of configurational forces enables the derivation of the \(J\)-integral independent of the constitutive relations of the material. The \(J\)-integral for incremental theory of plasticity, \(J^{\mathrm{ep}}\), has the physical meaning of a true driving force term and is potentially applicable for the description of cyclically loaded cracks, however, it is path dependent. The current paper aims to investigate the application of \(J^{\mathrm{ep}}\) for the assessment of the crack driving force in cyclically loaded elastic–plastic materials. The properties of \(J^{\mathrm{ep}}\) are worked out for a stationary crack in a compact tension specimen under cyclic Mode I loading and large-scale yielding conditions. Different load ratios, between pure tension- and tension–compression loading, are considered. The results provide a new basis for the application of the \(J\)-integral concept for cyclic loading conditions in cases where linear elastic fracture mechanics is not applicable. It is shown that the application of the experimental cyclic \(J\)-integral \(\Delta J^{\exp }\) is physically appropriate, if certain conditions are observed.

Elastic/plastic Buckling Analysis of Skew Thin Plates based on Incremental and Deformation Theories of Plasticity using Generalized Differential Quadrature Method

Abstract In this study, generalized differential quadrature analysis of elastic/plastic buckling of skew thin plates is presented. The governing equations are derived for the first time based on the incremental and deformation theories of plasticity and classical plate theory (CPT). The elastic/plastic behavior of plates is described by the Ramberg-Osgood model. The ranges of plate geometries are 0.5 £ a/b £ 2.5 and 0.001 £ h/b £ 0.05 under uniaxial uniform compression or biaxial compression/tension. GDQ discretization rules in association with an exact coordinate transformation are simultaneously used to transform and discretize the equilibrium equations and the related boundary conditions. Based on comparison with previously published results, the accuracy of the results is shown. Finally, the effects of aspect, loading and thickness ratios, skew angle, incremental and deformation theories and different types of boundary conditions on the buckling coefficient are presented. Moreover, the effect of skew angle and thickness ratio on the convergence and accuracy of the method are studied. Due to the lack of published solutions for plastic buckling of skew thin plates and the high accuracy of the present approach, the solutions obtained may serve as benchmark values for further studies.

An elastic–plastic constitutive model for ceramic composite laminates

Existing phenomenological constitutive models are unable to capture the full range of behaviors of ceramic composite laminates. To ameliorate this deficiency, we propose a new model based on the deformation theory of plasticity. The predictive capabilities of the model are assessed through comparisons of computed and measured strain and displacement fields in open-hole tension tests. The agreements in the magnitude of strains and in the size and shape of shear bands that develop around a hole are very good over most of the loading history. Some discrepancies are obtained at high stresses. These are tentatively attributed to non-proportional stressing of some material elements: a feature not captured by the present model.

Elastic/plastic buckling analysis of skew plates under in-plane shear loading with incremental and deformation theories of plasticity by GDQ method

The present study is concerned with the elastic/plastic buckling analysis of a skew plate under in-plane shear loading. The governing equations for moderately thick skew plates are analytically derived based on first-order shear deformation theory, whereas the incremental and deformation theories of plasticity are employed. Two types of shear loads, i.e. rectangular shear (R-shear) and skew shear (S-shear) have been investigated. The buckling coefficient values are significantly affected by the direction of stresses. Since the problem is geometrically and physically nonlinear, the generalized differential quadrature method as an accurate, simple and computationally efficient numerical tool is adopted to discretize the governing equations and the related boundary conditions. Then, a direct iterative method is employed to obtain the buckling coefficients of skew plates. To demonstrate the accuracy of the present analytical solution, a comparison is made with the published experimental and numerical results in literature. The influences of the aspect and thickness ratios, skew angle, incremental and deformation theories and various boundary conditions are examined for R-shear and S-shear buckling coefficients. Finally, some mode shapes of the skew thick plates are illustrated. The present results may serve as benchmark solutions for such plates.

Fast Plastic Integration Algorithms for Forming Process Simulations

This paper presents a fast plastic integration algorithm and compares it with other algorithms for forming process simulations. The iterative Return Mapping Algorithm (RMA) is widely used owing to its accuracy and efficiency, but it is still time consuming and may cause divergence problems. Another algorithm based on the Incremental Deformation Theory (IDT) was proposed, using the deformation theory of plasticity by piecewise; it is very fast but could not well consider the loading history, leading to notable errors. The new Direct Scalar Algorithm (DSA) based on the flow theory of plasticity is proposed in this paper. The basic idea is to transform the constitutive equations in terms of the unknown stress vectors into a scalar equation in terms of the equivalent stresses which can be determined by using the experimental tensile curve; thus, the plastic multiplier λ can be directly calculated without iterative solution. The DSA is a fast and robust plastic integration algorithm. The comparison of the results obtained by using the three algorithms shows the accuracy and efficiency of the DSA.

Plastic bifurcation buckling of lined pipe under bending

Abstract Linepipe used in offshore and other operations is often protected from corrosive contents by lining internally a carbon steel carrier pipe with a thin layer of corrosion resistant material. In many applications the lined pipeline can experience bending or compression severe enough for the liner to buckle and collapse inside an intact carrier pipe. This paper presents a solution procedure for establishing the onset of the first bifurcation buckling of such a lined pipe under bending. Bending induced differential ovalization of the two shells causes partial separation of the liner from the carrier pipe. The compressed liner intrado at some stage buckles into periodic wrinkles. This bifurcation check is established numerically using the J 2 -deformation theory of plasticity. It is shown to occur at bending strain levels very similar to those of the liner shell bent alone but smaller than those of lined pipe under uniform compression. The post-buckling behavior of the lined pipe under bending was subsequently studied by introducing to the liner initial imperfections in the form of the wrinkling buckling mode. Under increasing bending the wrinkle amplitude grows eventually yielding to a second diamond-type buckling mode that results in local collapse. Collapse, while shown to be imperfection sensitive, occurs at a much higher bending strain than the critical wrinkling bifurcation values and it should thus be the failure mode governing design.

A different approach to estimate the process parameters in tube hydroforming

An enhanced unfolding inverse finite element method (IFEM) has been used together with an extended strain-based forming limit diagram (FLD) to develop a fast approach to predict the feasibility of tube hydroforming process of concept part and determine where the failure or defects can occur. In tube hydroforming, the inverse IFEM has been used for estimating the initial length of tube, axial feeding and fluid pressure. The already developed IFEM algorithm used in this study is based on the total deformation theory of plasticity. Although the nature of tube hydroforming is three-dimensional deformation, in this article a modeling technique has been used to perform the computations in two-dimensional space. Therefore, compared with conventional forward finite element methods, the present computations are quite fast with no trial and error process. In addition, the solution provides all the components of strain. Using the extended strain-based forming limit diagram, the components of strain can lead us to measure the potentials for failures during the deformation. The extended strain-based FLD based on the Marciniak and Kuczynski (M-K) model has been computed and used to predict the onset of necking during tube hydroforming. The extended strain-based FLD is built based on equivalent plastic strains and material flow direction at the end of forming. This new forming limit diagram is much less strain path dependent than the conventional forming limit diagram. Furthermore, the use and interpretation of this new diagram is easier than the stress-based forming limit diagram. The results of analysis for free bulging and square bulging have been compared with some published experimental data and the results obtained by conventional commercial software. The results indicate that the fluid pressure estimated by this method is 2.7 % greater than the results obtained by the experiment in the square bulging sample. In addition, the fluid pressure estimated in the free bulge sample is 5.6 % greater than the experimental results.

Theory for plasticity of face-centered cubic metals.

The activation of plastic deformation mechanisms determines the mechanical behavior of crystalline materials. However, the complexity of plastic deformation and the lack of a unified theory of plasticity have seriously limited the exploration of the full capacity of metals. Current efforts to design high-strength structural materials in terms of stacking fault energy have not significantly reduced the laborious trial and error works on basic deformation properties. To remedy this situation, here we put forward a comprehensive and transparent theory for plastic deformation of face-centered cubic metals. This is based on a microscopic analysis that, without ambiguity, reveals the various deformation phenomena and elucidates the physical fundaments of the currently used phenomenological correlations. We identify an easily accessible single parameter derived from the intrinsic energy barriers, which fully specifies the potential diversity of metals. Based entirely on this parameter, a simple deformation mode diagram is shown to delineate a series of convenient design criteria, which clarifies a wide area of material functionality by texture control.

On the Advantages of the Theories of Plasticity with Singular Loading Surface

This paper analyzes the peculiarities of plastic flow of metals for the case of non-proportional loading when the loading path consists of two portions—uniaxial tension and subsequent infinitesimal pure shear (torsion). The issue is discussed from the point of view of the hardening rules governing the kinetics of loading surface. Three cases are considered, flow plasticity theory with isotropic and kinematic hardening rule, as well as the synthetic theory of plastic deformation. As a result, the synthetic theory leads to the results that correlate with experiments, whereas the former two theories associated with smooth loading surfaces give a principal discrepancy with experimental data.

Springback of Extruded 2196-T8511 and 2099-T83 Al-Li Alloys in Stretch Bending

Al-Li alloys extrusions improve the performance of advanced aircraft due to their low density and high stiffness. In order to determine whether 2196-T8511 and 2099-T83 Al-Li alloys extrusions with high ultimate tensile strength/Young's modulus ratios, also exhibit significant elastic recovery, the springback behaviors of the two Al-Li alloys extrusions under displacement controlled cold stretch bending are addressed, using the simple plasticity deformation theory, the explicit/implicit FEM and the physical experiments. The results show that applied post-stretch strain affects springback of extrusions. The two Al-Li alloys extrusions show time-dependent springback at room temperature. The analytical solution and finite element simulation are effective means to assess the impact of material and process parameters on springback in stretch bending.

A thermostatistical theory for solid solution effects in the hot deformation of alloys: an application to low-alloy steels

The hot deformation of low-alloy steels is described by a thermostatistical theory of plastic deformation. This is based on defining a statistical entropy term that accounts for the energy dissipation due to possible dislocation displacements. In this case, dilute substitutional and interstitial atom effects alter such paths. The dislocation population is described by a single parameter equation, with the parameter being the average dislocation density. Solute effects incorporate additional dislocation generation sources. They alter the energy barriers corresponding to the activation energies for dislocation recovery, grain nucleation and growth. The model is employed to describe work hardening and dynamic recrystallization softening in fifteen steels for a wide range of compositions, temperatures and strain rates. Maps for dynamic recrystallization occurrence are defined in terms of processing conditions and composition.

Research on causes and mitigation measures of bright band on hot rolled strip

An experimental and theoretical approach for analysing the causes of bright band on the hot rolled strip combined with plant data is presented. Based on multiple tests in a hot rolling mill, the occurrence regularity and characteristics of bright band were summarised. Tests for recognising bright band’s microstructure and mechanical properties were performed to determine its origin. Comparison experiments were performed such as emergency stop of coiler, opening of pinch roll gap and influence detection of supporting roller to track the formation process of bright band. A theoretical explanation is given by combining plastic deformation theory with the characteristics of bright band. Mitigation measures were developed and carried out in the mill, and improvements were achieved.

Springback Analysis in Sheet Metal Forming Using Modified Ludwik Stress-Strain Relation

This paper deals with the springback analysis in sheet metal forming using modified Ludwik stress-strain relation. Using the deformation theory of plasticity, formulation of the problem and spring back ratio is derived using modified Ludwik stress strain relationship with Tresca and von Mises yielding criteraia. The results have been representing the effect of different value of or ratio, different values of Strain hardening index (), Poisson’s ratio (), and thickness on spring back ratio (). The main aim of this paper is to study the effects of the thickness, ratio, and Poisson’s ratio in spring back ratio.

Meshless methods for the inverse problem related to the determination of elastoplastic properties from the torsional experiment

The problem of determining the elastoplastic properties of a prismatic bar from the given experimental relation between the torsional moment M and the angle of twist per unit length of the rod’s length θ is investigated as an inverse problem. The proposed method to solve the inverse problem is based on the solution of some sequences of the direct problem by applying the Levenberg-Marquardt iteration method. In the direct problem, these properties are known, and the torsional moment is calculated as a function of the angle of twist from the solution of a non-linear boundary value problem. This non-linear problem results from the Saint-Venant displacement assumption, the Ramberg–Osgood constitutive equation, and the deformation theory of plasticity for the stress–strain relation. To solve the direct problem in each iteration step, the Kansa method is used for the circular cross section of the rod, or the method of fundamental solutions (MFS) and the method of particular solutions (MPS) are used for the prismatic cross section of the rod. The non-linear torsion problem in the plastic region is solved using the Picard iteration.

Springback Analysis of Rectangular Sectioned Bar of Non Linear Work-Hardening Materials under Torsional Loading

This paper deals with the springback problems of rectangular section bars of non-linear work-hardening materials under the torsional loading. Using the deformation theory of plasticity, a numerical scheme based on the finite difference approximation has been proposed. The growth of the elastic-plastic boundary and the resulting stresses while loading, and the springback and the residual stresses after unloading are calculated. The results are verified experimentally with mild steel bars having a rectangular cross-section and the experimental results have been found to agree well with the theoretical results obtained numerically.