Linear Hardening Research Articles

Fast Prediction for Dynamic Response of Cellular Material under Dynamic Crushing

In this study, a dynamic enhancement stress model for cellular materials was derived from kinematics perspective, which directly reflected the influence of inertia effect on dynamic stress. Based on the proposed dynamic enhancement stress model, a densification strain calibration (DSC) analytical model with wider applicability for cellular materials was established, in which stress-dependent densification strain was employed. FE simulations for linear hardening and power hardening material under dynamic impact were conducted to validate DSC model. Comparing with idealized model (rigid, perfectly-plastic, locking model), dynamic plateau stress obtained by using of DSC model matched better with numerical results. Moreover, experimental results in published literature were employed to further confirm the reliability of DSC model in predicting projectile deceleration and final crushing depth. Finally, DSC model was used to predict dynamic response of gradient PVC foam, and the relative errors of final crushing depth to numerical results was within 8%.

A data-driven physics-constrained deep learning computational framework for solving von Mises plasticity

Current work presents an efficient data-driven Physics Informed Neural Networks (PINNs) computational framework for the solution of elastoplastic solid mechanics. To incorporate physical information for the elastoplastic problem, a multi-objective loss function has been carefully designed consisting of the residual of governing partial differential equation (PDE), constitutive relations, flow rules, consistency conditions, and various boundary conditions. In addition, data-driven physical knowledge fitting terms from the high-fidelity Finite Element Method (FEM) solutions for various elastoplastic field variables have been included for the construction of the total loss function. Utilizing multiple densely connected independent ANNs, the model obtains the elastoplastic solution by minimizing the proposed loss function. To demonstrate the strength of the proposed model, two test cases including von Mises perfectly plastic and isotropic linear hardening models are solved under plane-strain condition. Performance in terms of accuracy and robustness illustrates the superiority of the current framework showing excellent agreement with numerical solutions. Furthermore, for better accuracy of field variables with a lesser degree of data-driven estimate and accelerated training, the applicability of transfer learning (TL)-based approach has been illustrated to extend the solution for different sets of boundary conditions and material parameters. The present work highlights an efficient application of the custom-design PINNs model that leverage features from the data-driven solutions to guide the construction of an accurate and robust neural network for the solution of elastoplastic problems.

In-plane dynamics of circular cell hexagonally packaged honeycombs in two principal axes

The in-plane deformation modes, stress–strain curves and energy absorption characteristics of circular cell hexagonally packaged honeycombs with the linear elastic and plastic base material with linear strain hardening are numerically investigated under crushing velocities in two principal axes. Three deformation modes are observed and the empirical formulas for critical velocities of deformation mode transition are derived. With increasing crushing velocities, the fluctuation of stress becomes more intense in the plateau stress phase of stress–strain curves, which appears from low-crushing velocities in x2 direction, while in x1 direction at high velocities. Densification strain is linear with t/R ratio for a given crushing velocity, and becomes larger with increasing velocities approximately in a linear relationship under a deformation mode for a given t/R ratio. The law of mean plateau stress is consistent with a one-dimensional shock wave model and static plateau stress is proportional to the square of relative density. Three types of empirical expressions of mean plateau stress are derived. Crushing force efficiency is approximately independent of t/R ratio and sensitive to crushing velocity. Crushing force efficiency becomes smaller and then reduces with increasing velocities, and fluctuates around a level under dynamic mode.

The Macroscopic Phenomena in Plasticity

In this paper, the fundamental principles of plastic flow localization are briefly outlined. During the development of plastic flow, there is a changeover in the localization patterns conforming to the corresponding stage of work hardening based on the autowave nature of plastic flow localization. In particular, the evolution of plastic flow from yield point to fracture involves the following four stages of autowave generation: switching autowave → phase autowave → stationary dissipative structure → collapse of autowave. The most intriguing localization pattern is attributed to a phase autowave, which forms at the stage of linear work hardening. The characteristics of the phase autowave (propagation velocity, dispersion, and grain size dependence of the wavelength) have been determined experimentally. Moreover, an elastic-plastic strain invariant is introduced to describe the elastic and plastic properties of the deforming medium, as well as to establish the above characteristics of autowaves. A hypothetic quasi-particle, corresponding to the autowave of localized plasticity, is considered and its potential properties are estimated to interpret the localization process characteristics.

Fretting wear behavior of Inconel 718 alloy manufactured by DED and treated by UNSM

Alloy 718 is commonly used in the maritime and aerospace industries due to its strength and durability, particularly in engine rotating components such as disks, fan blades, and high-pressure compressors. As a new type of 3D printing technology, directed energy deposition (DED) can employ lasers to melt metal powders or wires to fabricate arbitrary-shaped workpieces directly from customized data, thereby making machining more synergistic and intuitive. However, the surface properties of the DED-printed alloy 718 samples, such as surface roughness and wear resistance, are typically subpar. By introducing severe plastic deformation to the near-surface, ultrasonic nanocrystal surface modification (UNSM) can be used as a post-processing method and results in altered properties. The uniaxial tensile test reveals that the UNSM-treated alloy 718 exhibits a higher mechanical property. Moreover, using a fretting test rig in accordance with the cylinder-on-plane agreement, a higher wear resistance for UNSM-treated alloy 718 is observed. This study employs the finite element method to fully comprehend the effect of UNSM on wear performance. The fretting wear process of Inconel 718 alloy is established using an energy-based finite element model. Considering the severe practical scenarios, the Johnson–Cook constitutive model is implemented, with the linear isotropic hardening model capturing the plastic behavior. In comparison to experimental measurements, the finite element results demonstrate unprecedented wear loss consistency with an error of less than 2%. Therefore, we conclude that the finite element model built in this study exhibits a high accuracy and can be used to analyze the effect of UNSM on fretting wear behavior. According to finite element analysis, as the normal load increases, the improvement in wear resistance induced by UNSM decreases. Given that the finite element model is based on the energy method, the effects of coefficient of friction (COF) and wear coefficient modified by UNSM are investigated separately. According to the findings, the UNSM-modified COF and wear coefficient play a significant role in determining the wear characteristics. Due to the removal of a substantial amount of material from the central area of the alloy 718 surface by wear, it is also possible to observe that severe plastic strains are primarily concentrated at the edges of the wear scars.

Elastoplastic bifurcation analysis for the lateral–torsional buckling of straight beams

This paper deals with the lateral–torsional buckling of elastoplastic steel beams under pure bending considering various cross-section geometries. Critical buckling moment expressions for elastic beams are well documented. In contrast, less attention has been devoted to the lateral–torsional buckling phenomenon in elastoplastic regime. When considering short beams (with sufficiently low slenderness), plastic zones will develop before buckling occurs. The problem being faced here is however much more complex than the classical problem of an elastoplastic beam subjected to an axial compressive force. Under such loading, plasticity occurs instantaneously and evolves uniformly over the cross-section and along the beam length whereas, in the other case, plasticity will spread gradually and the plastic zones will change with the loading. The main objective of the present paper is to develop original analytical solutions for the elastoplastic lateral–torsional buckling of perfectly straight beams. A general formulation based on a previously developed 3D plastic bifurcation theory is first proposed and then applied to the cases of two specific cross-section geometries, namely rectangular and I profiles. For the sake of simplicity, transverse shear strains are neglected in the analysis. The von Mises yield criterion with a linear isotropic hardening is adopted. In the case of a rectangular cross-section, closed-form solutions are obtained for the elastoplastic critical buckling moment, which is shown to depend on the geometric and material parameters of the beam, including the yield stress. For validation purposes, all the analytical solutions are compared against the results of numerical computations performed with an in-house program based on a shell finite element formulation. Analytical and numerical results are in very good accordance, making the analytical method presented here an efficient and precise tool to analyze the elastoplastic lateral–torsional buckling phenomenon.

Пластическое течение в твердых растворах Cu-Ni как автоволновой процесс

The influence of Ni content in Cu-Ni alloys on the localization of plastic flow under uniaxial tension has been studied. The regularities of localization of plastic deformation during linear and parabolic deformation hardening, as well as at the yield point, depending on the Ni content in the solid solution, have been studied by the speckle photography method. The influence of the Ni content on the duration of the stages of parabolic deformation hardening in alloys of different composition was found. The dependence of the spatial period of localization of plastic deformation (the length of the localization autowave) on the Ni content in the studied alloys is established. Keywords: localization of plastic deformation, autowaves, copper-nickel alloys, structure, mechanical properties, deformation and impurity hardening.

A Unified Framework for Full-Duplex Massive MIMO Cellular Networks With Low Resolution Data Converters

In this work, we provide a unified framework for full-duplex (FD) massive multiple-input multiple-output (MIMO) cellular networks with low-resolution analog-to-digital and digital-to-analog converters (ADCs and DACs). An objective of this work is to derive an accurate model to account for a wide variety of network irregularities and imperfections, including loopback self-interference (SI) that arises in full-duplex systems and quantization error from low-resolution data converters. Our contributions for forward and reverse links include (1) deriving signal-to-quantization-plus-interference-plus-noise ratio (SQINR) under pilot contamination, linear minimum mean square error (LMMSE) channel estimation and channel hardening; (2) deriving closed-form and approximate analytical expressions of spectral efficiency; (3) deriving asymptotic results and power scaling laws with respect to the number of quantization bits, base station antennas, and users, as well as base station and user equipment power budgets; and (4) analyzing outage probability and spectral efficiency vs. cell shape, shadowing, noise, cellular interference, pilot contamination, pilot overhead, and frequency reuse. Cell shapes include hexagonal, square, and Poisson Point Process (PPP) tessellations. In simulation, we quantify spectral and energy efficiency as well as the impact of SI power, inter-user interference, and cell shape on outage probability. We carry out the analysis for sub-7 GHz long term evolution (LTE) bands and then extend the framework to support millimeter wave (mmWave) bands.

ИССЛЕДОВАНИЕ ТЕХНОЛОГИИ ПРОИЗВОДСТВА ТВЕРДОСПЛАВНЫХ МАТЕРИАЛОВ

X-ray phase analysis, scanning electron spectroscopy, scanning electron microscopy and chemical analysis have been used to study the production technologies of carbide materials with high performance properties. It is established that in the process of processing metal materials acquire the required properties. The addition of tungsten - cobalt increases the density of the workpiece depending on the temperature and duration of the processes. Reduction of linear dimensions and hardening of workpieces occurs adequately.

Plastic flow in Cu-Ni solid solutions as an autowave process

The influence of Ni content in Cu-Ni alloys on the localization of plastic flow under uniaxial tension has been studied. The regularities of localization of plastic deformation during linear and parabolic deformation hardening, as well as at the yield point, depending on the Ni content in the solid solution, have been studied by the speckle photography method. The influence of the Ni content on the duration of the stages of parabolic deformation hardening in alloys of different composition was found. The dependence of the spatial period of localization of plastic deformation (the length of the localization autowave) on the Ni content in the studied alloys is established. Keywords: localization of plastic deformation, autowaves, copper-nickel alloys, structure, mechanical properties, deformation and impurity hardening.

Constitutive modeling of high strength steels; application to the analytically strengthening of thick-walled tubes using the rotational autofrettage

This paper focuses on high-strength and hardness steels which are used as an upgraded material in the construction of high-pressure vessels. Their mechanical behavior shows that these steels have perfectly plastic or linear hardening behavior with slight slopes during their loading phase. In contrast, their reversed loading behavior is nonlinear and quite easily affected by the prior plastic strain, in a way that the Bauschinger effect factor, trend, and nonlinearity degree of the reversed loading plastic part are strongly dependent on the prior plastic strain level. At first, a constitutive model was proposed to capture the test data of the nonlinear part of the stress-strain curve and the Bauschinger effect factors, as a function of prior plastic strain. Furthermore, this model should be proposed so that its application in solving boundary value problems such as thick-walled tubes leads to a closed-form analytical solution. To this end, the proposed model was adjusted to find a closed-form analytical solution for the analysis of thick-walled tubes under rotational autofrettage. In the following, the optimum autofrettage level for strengthening a thick-walled tube made of high-strength steel is obtained for proposed and other simplified constitutive models. By comparing the results, it was concluded that consideration of the dependency of mechanical behavior of this material on the prior plastic strain makes significant changes on the equivalent stresses.

Peculiarities of deformation and destruction of porous titanium nickelide alloys at stretching, compression and bending

The analysis of experimental data obtained during quasi-static tension, compression and bending of anisotropic and structurally inhomogeneous porous titanium nickelide alloys obtained by the method of self-propagating high-temperature synthesis (SHS) is carried out. It is shown that the studied porous titanium nickelide alloy near room temperature is in a pre-martensitic state and experiences a reversible martensitic transformation (MT) under the action of an external load. The influence of geometric anisotropy on the deformation behavior under tension and bending is shown. By means of quasi-static tension and three-point bending to failure of lamellar samples of porous titanium nickelide with a porosity of 60–70%, it was shown for the first time that all obtained strain curves are qualitatively self-similar and contain a basic block of two linear hardening sections and a yield section between them. It is shown for the first time that a decrease in the effective cross section and a decrease in the degree of geometric anisotropy of the deformation zone lead to the appearance of an additional yield region on the deformation curves of quasi-static tension. This indicates a significant dependence of the contribution of reversible martensitic deformation to the total deformation on the geometric anisotropy of porous titanium nickelide. An analysis of fracture surfaces showed the effect of the type and rate of loading on the ratio of brittle martensitic and ductile austenite phases in a multiphase matrix of a porous titanium nickelide alloy. The research was carried out with financial support of the Russian Science Foundation under the Grant No. 22-72-10037, https://rscf.ru/project/22-72-10037/.

Axial-flexural behaviours of concrete-filled square GFRP tubular columns under low temperatures

This study reported experimental investigations on the axial-flexural behaviours of concrete-filled square glass fiber-reinforced polymer (GFRP) tubular (CFSFT) columns at low temperatures. Twenty CFSFT columns under eccentric loads and two-point loading were conducted to evaluate the influences of low temperatures (T = 20 and −60 °C) and eccentricity ratios (e/r = 0.00, 0.25, 0.50, and 0.75). Failure modes, load–displacement behaviours, and load–strain behaviours at low temperatures have been reported. Test results indicated the load-vertical displacement curves of CFSFT columns under eccentric loads exhibited three different stages, i.e., linear, transition, and strain hardening or softening stage. Meanwhile, the bilinear load–deflection curves were observed for CFSFT columns under four-point bending. Based on these test results, the experimental axial load-moment (NT-MT) curves of CFSFT columns were obtained. These curves indicated that decreasing the temperature from 20 to −60 °C observably increased both the ultimate axial load (NuT) and ultimate bending moment (MuT) of CFSFT columns. However, the increment of both ultimate axial load and ultimate bending moment gradually decreased with the increasing eccentricity ratios.

Thermotropic yield characteristic of the ceramic–alloy composite beam induced by a unilateral heat source

AbstractThermotropic yield characteristic of the ceramic–alloy composite beam induced by a unilateral heat source is investigated by using the Hamilton principle and the variation method based on the first‐order shear deformation theory. The mathematical essence of the yield problem of the composite beam is that the variation of the Lagrange function of the system to the space coordinates equals zero. The Tamura–Tomota–Ozawa model and the linear rule of mixtures are used to simulate the composite material properties of functionally graded material (FGM), and the constitutive equations are established with the linear hybrid hardening model. The von‐Mises yield condition is introduced to judge whether the beam enters the yield state. The governing equations are established by using the Hamilton principle and variation method. The thermotropic yield surfaces, the yield stresses, and the critical temperature rises of the yield functionally graded beam are obtained, and the deflections of the beam are calculated by analytical method. The results reveal that the yield interfaces, the yield stresses, the critical temperature rises, and the deflections of the beam vary with material parameters, geometric parameters, and so on.

Data-driven estimation of plastic properties in work-hardening model combining power-law and linear hardening using instrumented indentation test

Data-driven estimation of plastic properties in work-hardening model combining power-law and linear hardening using instrumented indentation test

Justification of fracture criteria for salt rocks

The study of salt rocks deformation and fracture processes is an essential part of mining parameters justification for mineral salt deposits. The results of uniaxial compression tests on large salt rock specimens are presented as a loading curve and diagrams of the transverse-longitudinal displacements at various distances from the side faces. Based on an isotropic elastoplastic model, a multivariant numerical simulation was performed. Its purpose was to select of fracture criteria that accurately describe the loading diagram of specimen and its transverse-longitudinal deformations. The following fracture criteria are considered: Tresca with the associated plastic flow rule, the associated and non-associated Mohr-Coulomb, the parabolic analogue of Mohr-Coulomb criterion and the volumetric fracture criterion. Numerical simulation was carried out by the displacement-based finite element method. Three-dimensional hexahedral eight-node isoparametric elements were used for discretization of the solution domain. It has been established that within the elastoplastic model of media the process of uniaxial compression of a large cubic salt rock specimen is adequately described by the linear Mohr-Coulomb fracture criterion with the non-associated plastic flow, as well as by the associated volumetric parabolic yield criterion with the linear isotropic hardening.

Numerical and analytical investigation of square timber columns confined with steel and carbon fiber reinforced polymer external jacket

This paper numerically investigated the timber confinement of columns with carbon fiber reinforced polymer (CFRP) and steel tubes under axial compression. An elastic-plastic model with linear hardening, a CFRP hashin damage, and a timber damaged anisotropic elastic-plastic model, respectively, are used to simulate the inelastic behavior of the steel tube, CFRP layers, and timber core. In addition, a comprehensive numerical study was conducted using a wide range of cross-sections, thicknesses, lengths, and the number of CFRP layers developed to varying degrees (0, 45, and 90). To confirm the accuracy of the current FEM model, numerical data is compared to the experimental model’s final strengths, behavior, and failure mechanisms. Additionally, the ultimate strengths of timber-steel and CFRP are compared to various standards and design formulas. The results reveal that columns with thicker steel tubes and more CFRP layers have an average of about 42% and 12% greater load-bearing capacity and ductility. The degree of CFRP affected the load-bearing capacity of timber columns, which increased by around 10% from 45 to 90. In comparison to specimens with equal cross-sections and thickness, shorter specimens with greater cross-sections typically have 40% higher stiffness. According to parameter studies, the AISC 360-16 American standard design approaches can be safely extended to anticipate the ultimate strength of timber-steel columns. Meanwhile, both the ACI-440 and Ilki et al. design formula predictions are the most precise, particularly at 45° with high ultimate strength.

Singularity analysis of linear hardening V-notch by asymptotic expansion coupled BEM

In this paper, a general numerical method by the asymptotic expansion coupled the boundary element method (CBEM), considering the singular term and the higher order terms, is developed to analyze the complete singular stress field of linear hardening elastic–plastic material with a V-notch. The method firstly transforms the singularity analysis for the governing equation of the V-notch tip into an ordinary differential eigenvalue equation, which is then solved by the interpolating matrix method. Then, the complete singular stress field and the notch stress intensity factors (SIFs) can be obtained by coupling the asymptotic expansion of the elastic–plastic singular stresses at the V-notch tip with the conventional boundary elements method for the remaining region of the structure. Two types of examples are analyzed for the V-notch problem of linear hardening material. It is shown that the elastic–plastic singular stress field can be evaluated by the equivalent Young’s modulus and Poisson’s ratio. The proposed new approach is found to be accurate and effective in evaluating singular stress fields in a V-notch structure with linear hardening material.

Plastic zones in the pin connection of the laminated lattice girder

The paper deals with a static reanalysis of the existing ice-rink bearing steel structure which proves all the bearing members of the object after additional loading by new roof coat. In addition to experimental measurements carried out to diagnose the bearing roof steel structure and its elements needed for static assess the structure’s current state, pressure coefficients in individual parts of the structure were defined by means of ANSYS software and consequently used in static analysis of wind effects. According to the static analysis results, the repair of initial state was designed and realized, with designing of details needed to be modified. By means of ANSYS software, the detail of pin joint support of laminated lattice-girders was 3D-modeled with volume elements. The deformation-stress analysis of the mentioned detail was also performed by considering of elastic-plastic material with linear hardening.

A state-of-the-art review on mechanical performance characterization and modelling of high-performance textile reinforced concretes

• A detailed discussion on the constituents and design parameters of TRC is presented. • The mechanical properties of TRC are critically reviewed under various loading conditions. • The fracture mechanisms and modes under different loadings are discussed. • The outcome of the review highlights the research gap and perspective of TRC. Textile reinforced concrete (TRC) is becoming an emerging high-performance construction material due to its outstanding load-bearing capacity, corrosion resistance, and durability. However, the influences of textile type and design parameters on the mechanical performance of TRC have not been fully understood. Therefore, this study aims to enhance the understanding of the mechanical performance of TRC and identify further research needs. The tensile, compressive, and flexural performances of TRC are first discussed based on the literature review. It is found that the mechanical properties of TRC are highly dependent on the shape, geometry, woven type, and yarn properties of the textile. The failure patterns of TRC under tensile and flexural loadings generally include three stages: linear elastic (before the first crack), strain hardening (with multiple cracking), and softening (with fracture failure). The bonding performance of the textile embedded in the cementitious matrix is also reviewed using the pullout test results. The geometric parameters and surface characteristics of the textile significantly affect the interfacial bonding strength. Currently, the analytical models for the mechanical analysis of TRC and the numerical analysis for the 2D and 3D textile-reinforced concrete are available to predict their mechanical behaviours. This study can provide a valuable reference for further investigations on TRC materials and promote their applications in civil engineering.