Linear Strain Hardening Research Articles

Enhancing clay soil stability in seasonal freezing areas through waste cherry marble powder and geotextile reinforcement

In this study, the mechanical and durability performance of clay soils reinforced with different proportions of Cherry Marble Powder (CMP) and non-woven geotextile configurations, both independently and in combination, is investigated in detail at both the macro and micro levels. The effectiveness of reinforcement in the stabilization of clay soils in cold climates has been evaluated by means of Gray Correlation Analysis (GCA). The results show that as the CMP ratio and the number of geotextiles increase, the peak strength of the soil increases, with higher CMP levels showing perfect plastic behavior and more geotextiles showing linear strain hardening, particularly in combination. Substantial strength reductions post-7th cycle ranged between 91.09 % and 103.38 % for 12 % CMP and 219.83 % and 270.42 % for three-layered geotextile groups. Cohesion increased by 59.76 % and 179.41 %, while the internal friction angles remained stable and decreased after F-T cycles, except with additives. Failure modes shifted with CMP content, F-T cycles and confining pressure. The transition was from strain hardening to strain softening, with increased shear fracture planes and brittleness. The energy absorption capacity (EAC) increased with the CMP ratio, with the geosynthetic reinforcement increasing the EAC by a factor of 1.5 before and after the F-T cycles. The combined use of CMP and geotextiles in soil stabilization improved the engineering properties in areas of frost, with the optimum gradation being three layers of geotextile and a CMP ratio of 12 %, which effectively mitigated the effects of the maximum F-T cycle.

Ternary medium constitutive model of frozen rubber-reinforced expansive soil

The application of waste rubber for soil improvement is feasible, and the static and dynamic properties of rubber-reinforced soils have been extensively studied. However, the mechanical properties of frozen rubber-reinforced expansive soils have not been effectively studied due to the complexity of multiphase media under the action of multiple fields, and no applicable constitutive models describe them. In this paper, the stress-strain relationship model for frozen rubber-reinforced expansive soils is investigated over a range of strain rates from 0.18% to 0.3% and the following conclusions were obtained: (1) The structural model of the frozen rubber-reinforced expansive soil can be considered a ternary medium model that consists of elasto-brittle bonding elements, elasto-plastic friction elements and elastic friction elements. (2) The stress-strain relationship can be divided into three stages: linear elastic stage, elasto-plastic stage and strain softening (RC ≤ 15%) or hardening (RC = 20%) stage. (3) The rubber content has a greater influence on the stress-strain relationship. When the rubber content reaches 20%, the expression of the stress-strain curve changes from strain softening to strain hardening, at which time the rubber dominates. (4) The maximum shear strength of frozen rubber-reinforced expansive soil is obtained at 10% rubber content.

Structural behavior of stainless steel anchor channels embedded in concrete under perpendicular and longitudinal shear

Stainless steel anchor channels with channel bolts (SSAC-CBs) have been chosen as alternatives to conventional carbon steel anchor channels to enhance corrosion resistance, ductility, and load-bearing capacity. This study evaluated the shear performance of SSAC-CBs embedded in concrete members under perpendicular and longitudinal shear loads using static monotonic tests. The failure modes and shear capacities of the specimens were compared with those obtained by finite element analysis (FEA) models established using ABAQUS. Concrete edge breakout failure accompanying the channel flexural yielding and channel bolt fracture dominated in the SSAC-CBs under perpendicular shear. The load–displacement curves for perpendicular shear exhibited four salient stages: initial linear elasticity, slippage, strain hardening, and damage and failure. Under longitudinal shear, the SSAC-CB specimens exhibited a failure of the serrations in the contact area between the serrated channel bolt head and channel lips and slip failure between the hook-type channel bolt and channel lips. In addition, the numerical analysis results indicated that the load-bearing capacities, initial elastic stiffnesses, and failure modes obtained through the FEA models were consistent with the test results. Furthermore, theoretical formulas were proposed for the shear capacity for SSAC-CBs under perpendicular and longitudinal shear. The research outcomes provide valuable guidance for the design and application of SSAC-CBs in engineering.

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.

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.

Stress-strain state of coal wells Karaganda basin

The article considers the problem of determining the thermoelastic stresses that arise when drilling a coal seam with a depth of at least 800 m. The stress-strain state is a term that has penetrated from the mechanics of a deformable solid body into various areas, both natural and technological. Usually, three types of stress-strain state are distinguished: the first type of elastic work - up to 35% of the breaking load; the second type of elastic-plastic work - up to 75% of the breaking load, while cracks appear and their number increases with increasing load; the third type of destruction - cracks appear like an avalanche and every detail is destroyed. For the first time, we succeeded in solving analytically the Stefan problem for a cylinder of finite dimensions, with a moving interface, by selecting an integral transformation. A similar solution for a well in coal seams (as well as for other applications) gives an analytical solution to the deformation-wave process in a rock mass, discovered experimentally in the late 70s of the last century (scientific discovery of 1985, priority of 1978). Our experimental and theoretical results fit into the model of macroscopic localization of plastic flow. This model shows that the localization of plastic flow in solids (and in a coal seam) has a pronounced wave character. At the same time, at the stages of easy slip, linear and parabolic strain hardening, as well as at the stage of preliminary destruction, the observed patterns of localization are different types of wave processes.

Autowave description of the temperature effect during deformation of FCC metals

The data of comparative studies of the development of plastic flow in pure aluminum and iron-based austenitic alloy (Fe-Cr-Ni) are presented. Deformation patterns were studied during tests in the temperature range 143≤ T≤420 K. It was found that the effect of temperature is different for these two cases. When a stationary dissipative structure appears at the stage of parabolic strain hardening, the effect of temperature is determined by the change in the length of the localized plasticity autowave. At the stage of linear strain hardening, when a phase autowave of localized plasticity is formed, the effect is associated with an exponential increase in its rate with temperature. Keywords: plastic deformation, localization, metals, Debye temperature.

Автоволновое описание температурного эффекта при деформации ГЦК металлов

The data of comparative studies of the development of plastic flow in pure aluminum and iron-based austenitic alloy (Fe-Cr-Ni) are presented. Deformation patterns were studied during tests in the temperature range 143-420 K. It was found that the effect of temperature is different for these two cases. When a stationary dissipative structure appears at the stage of parabolic strain hardening, the effect of temperature is determined by the change in the length of the localized plasticity autowave. At the stage of linear strain hardening, when a phase autowave of localized plasticity is formed, the effect is associated with an exponential increase in its rate with temperature.

Nonlinear Finite Element Analysis of Fiber Reinforced Concrete Slabs

This paper presents a study on the behavior of fiber reinforced concrete slabs using finite element analysis. A previously published finite element program is used for the nonlinear analysis by including the steel fiber concrete properties. Concrete is represented by degenerated quadratic thick shell element, which is the general shear deformable eight node serendipity element, and the thickness is divided into layers. An elastic perfectly plastic and strain hardening plasticity approach are used to model the compression behavior of concrete. The reinforcing bars were smeared within the concrete layers and assumed as either an elastic perfectly plastic material or as an elastic-plastic material with linear strain hardening. Cracks initiation is predicted using a tensile strength criterion. The tension stiffening effect of the steel fibers is simulated using a descending parabolic stress degradation function, which is based on the fracture energy concept. The effect of cracking in reducing the shear modulus and the compressive strength of concrete parallel to the crack direction is considered. The numerical results showed good agreement with published experimental results for two fibrous reinforced concrete slabs.

Implementation and validation of true material constitutive model for accurate modeling of thick-walled cylinder swage autofrettage

The fatigue life prediction and associated fail-safe design of autofrettaged tubes require accurate stress modeling of each specific high-strength thick-walled cylinder during and after the autofrettage process, which depends largely on the elastoplastic behavior of the original steel tubes. However, the complex material behavior is dominated by the Bauschinger effect. Modeling swage autofrettage of such steel tubes remains problematic. This is a crucial issue that has not been resolved by any available modeling software. Therefore, the modeling and design of the autofrettage process for current and future materials depends upon extending the capability of current software.This research aims to develop a user-programmable function (UPF), USERMAT, to realize a user-defined material model that features true material constitutive behavior with the corresponding algorithms for accurate stress analysis of high strength thick-walled cylinders during the autofrettage process. The material constitutive model to be implemented can be formulated with high accuracy via an available material characterization, which can adapt to both nonlinear and linear strain hardening during the initial tensile loading, while the elastic modulus can be reduced during reversed-loading. It also incorporates the Bauschinger effect as a function of the prior tensile plastic strain during the nonlinear compressive reversed-loading phase and fits the experimental data of the true material model. Swage autofrettaged thick-walled cylinder case studies were reported. The results for residual radial and hoop stress and for elastic strain components were compared with independent, available neutron diffraction measurements, and they are in good agreement. Developing and integrating such a UPF into a standard finite element analysis software package is potentially the most significant unsolved fundamental modeling issue relating to re-yielding, fracture and fatigue of modern autofrettaged cylinders and pressure vessels. It can not only provide a fundamental understanding of the deformation mechanism and stress development within the high strength steel tubes during the autofrettage process, but also provide guidance for the design and optimization of the autofrettage manufacturing processes and of material selection for high intensity pressure vessels, a potential market of billions of dollars.

Effect of X46Cr13 Microstructure on the Ultrasound Rate Propagation under Plastic Deformation

The change in ultrasound rate in the plastic deformation of high-chromium X39Cr13 stainless steel with ferrite–carbide structure (initially), martensite structure (after quenching), and sorbite structure (after high tempering) is investigated. The loading curve is different for each state. In the initial state, the loading curve is practically parabolic. In the martensitic state, linear strain hardening is the only stage. In the sorbitic state, a three-stage curve is observed. The structure of the steel after different types of heat treatment is studied by optical and scanning probe microscopy. In parallel with the recording of the loading curve, the change in properties of the ultrasound surface waves (the Rayleigh waves) in the steel under tension is measured. The structure of the steel determines not only the type of deformation curve in uniaxial extension but also the dependence of the ultrasound rate on the strain.

Geometrical and Material Nonlinear Finite Analysis of Fiber Reinforced Concrete Slabs

Geometrical nonlinearity arises from the continuous change of shape under increasing loads on thin or long span members, and the materials nonlinearity due to the nonlinear behavior of the materials composing the structural element. In this study the finite element method is used to analyze fibrous reinforced concrete slabs, material and geometric nonlinearities were considered. Concrete is represented by degenerate quadratic thick shell element. Concrete behavior in compression is modeled by elastic perfectly plastic or strain hardening plasticity. A tensile strength criterion is used to follow crack initiation and propagation. A parabolic stress degradation function, which is based on the fracture energy concept, is used to model the tension stiffening effect of steel fibers. The reinforcement is considered as smeared within the concrete layers, and assumed as either an elastic perfectly plastic material or as an elastic-plastic material with linear strain hardening. Von Karman assumptions which is based on the total Lagrangian approach is used for the geometric nonlinearity. The numerical results using for both normal and lightweight fiber reinforced concrete slabs were predicted satisfactorily. The average predicted failure load of the investigated cases to the experimental failure load was 0.899 with a standard deviation of 0.092.

A Finite Similitude Approach to Scaled Impact Mechanics

The response characteristics of large-scale structures subjected to impact loading can in principle be determined by scaled experiments. Unfortunately, scaling suffers from scale effects and for impact mechanics, the non-scalability of strain rate and strain hardening can diminish the effectiveness of scaled trials. To resolve this difficulty, a new scaling method has recently appeared in the open literature called finite similitude. The theory is founded on the metaphysical concept of space scaling, where the idea is that by expanding or contracting space, changes in the governing mechanics can be assessed.In this paper the finite-similitude theory is further developed, where it is demonstrated how the constraints imposed by dimensional analysis can be broken. A new form of similarity is introduced but at the cost of requiring two scaled experiments at distinct scales. It is shown however, how the theory is able to combine the information from the two scaled trials to predict outcomes that can be markedly superior to what can be achieved with experiments at a single scale. All scale dependencies are accounted by the theory and consequently the new formulation attempts to capture scale effects, so provides a more realistic approach to scaled experimentation.Unlike dimensional analysis, the new first-order finite similitude theory can simultaneously target two independent physical properties of common dimension (e.g. initial-yield stress and linear strain hardening). The advantage offered by this feature is demonstrated analytically and numerically in the paper with a focus on axisymmetrical tube buckling and energy absorption. The analytical model serves to expound the theory and the numerical highlights its capabilities and the kinds of accuracy achievable with the new approach.

Deformation behavior of stainless steel under uniaxial tension

The present work is devoted to the study of the laws of macroscopic localization of plastic deformation of austenitic stainless steel AISI 321 at low and high temperatures. The studies of AISI 321 steel found that at the stages of linear strain hardening, the propagation velocity of the localized plastic deformation centers and the spatial period of local elongation change when test temperature increases by the exponential law. Patterns of plastic strain localization as single bands are due to the Portevin – Le Chatelier effect on jerky flow.

LOCALIZED PLASTIC DEFORMATION AND PERIODIC TABLE

: We consider the autowave mechanism of evolution of a localized plastic deformation of crystalline solids of different origins. It is found that localization of the plastic flow is determined by the relation between elastic and plastic phenomena in deforming materials. The origin of this relation is explained using general thermodynamic concepts. It is shown that parameters of plastic flow localization at the stage of linear strain hardening in the process of solid body deformation are closely related to characteristics of the electronic structure of metals. Inverse of the product of wavelength and velocity of the localized plasticity autowave grows linearly with the number of conduction electrons per unit cell of the metal. The obtained data directly indicate that the nature of the electron-gas contribution to hindering of dislocations is more complicated. Thus, the parameters of plastic flow localization are defined by the position of metal in the Mendeleev periodic table.

Influence of soil\u2013structure interaction on seismic pounding between steel frame buildings considering the effect of infill panels

The present research aims to study the influence of the soil–structure interaction (SSI) and existence or absence of masonry infill panels in steel frame structures on the earthquake-induced pounding-involved response of adjacent buildings. The study was further extended to compare the pounding-involved behavior versus the independent behavior of structures without collisions, focusing much on dynamic behavior of single frames. The effect of SSI was analyzed by assuming linear springs and dashpots at the foundation level. The infill panels were modeled using equivalent diagonal compression struts. The steel frames were assumed to have elastic–plastic behavior with 1% linear strain hardening. The dynamic contact approach was utilized to simulate pounding between the adjacent buildings. Nonlinear finite element analysis was performed for two adjacent multi-story structures with four different configurations representing cases that can exist in reality. The seismic response of the studied cases generally emphasized that ignoring the soil flexibility and/or the contribution of the infill panels may significantly alter the response of adjacent structures. This may result in a false expectation of the seismic behavior of buildings exposed to structural pounding under earthquake excitation.

On the role of anisotropic expansion and yield stress on crack tip precipitates

This pilot study uses a Landau-Lifshitz phase field model to study the growth of a precipitate originating from a crack tip. A boundary layer giving a remote square root singular elastic stress field is applied. The materials are assumed to be elastic-plastic with linear strain hardening. The precipitate is assumed to expand in a simplified anisotropic manner, meaning that the hydride is assumed to grow with an orientation giving maximum expansion perpendicular to the crack plane. The results show that the anisotropic expansion has a strong effect on the shape of the hydride. For anisotropic materials the hydride becomes wedge like. The resulting shapes for the anisotropic cases are in line with observations of internal crack tip hydrides in zirconium. The shapes resemble earlier results for Einstein-Smoluchowski stress driven diffusion using discrete models and simplified modelling of the growth process. The crack tip shielding caused by both precipitation and plastic yielding is examined using the J integral. It shows that the near tip value is a around a quarter of its remote value for elastic isotropic materials and around a half for anisotropic materials.

Strain gradient crystal plasticity with evolving length scale: Application to voided irradiated materials

A micromorphic crystal plasticity model is used to simulate slip band localization in single crystals under simple shear at finite deformations. Closed form analytical solutions are derived for single slip in the case of positive, zero and negative strain hardening. Linear negative strain hardening, i.e. linear softening, leads to a constant localization slip bandwidth, while non linear softening and saturating behaviour results in an increasing bandwidth. An enhanced model is therefore proposed in order to maintain a bounded localization slip bandwidth when considering an exponential softening behaviour. Analytical solutions are used to validate finite element computation of the same boundary value problems. The enhanced micromorphic crystal plasticity model is then applied to predict the interaction between localized slip bands and voids encountered in porous irradiated materials. For that purpose, periodic porous unit cells are loaded in simple shear with a strain gradient crystal plasticity matrix material. The finite element simulation results show that, for a given void volume fraction, the larger the voids, the wider the localization band. However, for a given void size, the larger the void volume fraction, the narrower the localization band. In addition a satisfactory qualitative agreement of the rotation and elongation of the voids with the experimental observations made in irradiated materials is observed, where small voids are shown to remain ellipsoidal for larger shear strains. Large voids deform into peanut-like shapes.

Understanding structure-mechanics relationship of high density polyethylene based on stress induced lattice distortion

The relationship between the macroscopic non-linear mechanics and the microscopic crystal structural evolution of pre-oriented high-density polyethylene (HDPE) is investigated by in situ synchrotron radiation wide-angle X-ray diffraction (WAXD) measurement over a wide temperature range from −10 to 130 °C. With the concept of stress-induced disordering of crystal, the ratio (φa/b) of lattice parameters a to b is defined as a new structural variable, which can reflect the lattice distortion and then the microscopic stress state of orthorhombic crystal (O-crystal). According to the temperature-dependent non-linear variation of φa/b with strain, the contributions of O-crystal and monoclinic crystal (M-crystal) to the macroscopic mechanics including linear elasticity, yielding, stress softening and strain hardening are clarified. It is found that M-crystal bears the main extensional stress once formed, although it survives within a limited strain window relying on temperature. By further combining the extensional phase diagram constructed in strain-temperature space, the HDPE deformation is recognized to undergo successively one-dimensional (1D) chain segments rotation of crystal, two-dimensional (2D) crystal plan shearing or slipping and three-dimensional (3D) recrystallization along with increasing strain or stress, demonstrating a multiscale structural transition and energy dissipation mechanism.

Entropy Interpretation of the Elastic–Plastic Strain Invariant

An interpretation of the nature of the relation between elastic and plastic strains, called the elastic–plastic strain invariant, is proposed which takes into account the change in the entropy of the system during autowave generation at the stage of linear strain hardening. It is shown that this approach consistently explains the nature of the invariant and its role in the description of plasticity.