Strain-hardening Model Research Articles

An Anisotropic Model for Granular Material Based on Experiments

Soil is a heterogeneous material and most natural soil deposits show a definite stratification. The mechanical behaviour of such material is generally different in different directions, especially in the direction parallel and perpendicular to the stratification. A series of isotropic compression tests were carried out to study the behavior of granular material produced under controlled stratification in the laboratory. These tests were conducted both on cylindrical and square prismatic tri-axial specimens. It was observed that for hydrostatic loading, the strain response was different in different directions, especially in directions parallel and perpendicular to the direction of soil deposition. A definite trend of anisotropy was observed in the deformation pattern. The observed anisotropy is modeled in this paper by treating soil-dilatancy as a variable quantity. The equation of the plastic potential surface of the model which obeys a non-associated flow rule, is assumed to be dependent on three main variables confining pressure ( $$\sigma_{3}$$ ), void ratio (e) and the angle of bedding plane orientation (δ) during deposition. The angle of bedding plane orientation (δ) was measured with respect to the direction of the major principal stress. The model has a cap yield surface in the isotropic stress direction, which is supplemented by a shear hardening Mohr–Coulomb surface in the deviator direction. This paper focuses on predicting the anisotropic strain response of stratified soil deposits subjected to isotropic compression. The proposed anisotropic model incorporates within an existing strain-hardening sand model, a modified cap yield surface and a modified plastic potential function related to the cap surface, to account for the anistropic response observed in isotropic compression tests. The two dimensional stress–strain model was extended to three dimensional Cartesian space. The strain anisotropy observed in the isotropic compression tests was predicted by the three dimensional anisotropic model proposed for granular materials.

Development of a Model for Dynamic Recrystallization Consistent with the Second Derivative Criterion.

Dynamic recrystallization (DRX) processes are widely used in industrial hot working operations, not only to keep the forming forces low but also to control the microstructure and final properties of the workpiece. According to the second derivative criterion (SDC) by Poliak and Jonas, the onset of DRX can be detected from an inflection point in the strain-hardening rate as a function of flow stress. Various models are available that can predict the evolution of flow stress from incipient plastic flow up to steady-state deformation in the presence of DRX. Some of these models have been implemented into finite element codes and are widely used for the design of metal forming processes, but their consistency with the SDC has not been investigated. This work identifies three sources of inconsistencies that models for DRX may exhibit. For a consistent modeling of the DRX kinetics, a new strain-hardening model for the hardening stages III to IV is proposed and combined with consistent recrystallization kinetics. The model is devised in the Kocks-Mecking space based on characteristic transition in the strain-hardening rate. A linear variation of the transition and inflection points is observed for alloy 800H at all tested temperatures and strain rates. The comparison of experimental and model results shows that the model is able to follow the course of the strain-hardening rate very precisely, such that highly accurate flow stress predictions are obtained.

Deformation-Induced Atomic Disordering and Reordering in Alloys with L12 Structure

The paper presents a mathematical model of thermal and strain hardening of alloys having L12 superstructure which allows calculating the atomic long-range order (LRO) parameter depending on the deformation degree under various temperature and loading conditions. The observed non-monotonic change in the atomic LRO parameter during plastic deformation occurs due to the two types of competitive processes. These processes are caused by the motion and accumulation of the deformation defects and their healing due to the migration of point defects of different nature. The competitiveness between these two types of processes leads to the periodical destruction and reconstruction of the atomic LRO parameter, while the equilibrium between them can stabilize it after which it continues to be stable despite the deformation.

Influence of material modeling on simulation accuracy of aluminum stampings

The best practice in modeling material yield, strain hardening and anisotropic behavior in plastic deformation has been analyzed for an AA 6016 aluminum alloy. The investigation was based on the extensive material property testing, stamping benchmarking and AutoForm simulations. For the material property testing, both the uniaxial tensile test and the hydraulic bulge test were conducted. The elliptic punch test and the cross die test served as the benchmarks to validate the simulation results. In the simulations, the material characteristics was modeled with the combinations of four strain-hardening models and three yield criteria. By comparing the simulation results with the experimental measurements, the influence of material modeling on aluminum stamping simulation accuracy was evaluated. It was concluded from this study that the yield criterion is the key factor in controlling the simulation accuracy. The simulation with the BBC2005 yield model predicts the most accurate results. It was also shown that the combined Swift/Hockett-Sherby strain-hardening model is most suitable to describe aluminum strain hardening behavior.

An analytical model for predicting permanent plastic deflection and strain distributions in aluminium-alloy plates under low velocity impact loading

This paper proposes a new analytical model to predict plastic deformation and strain distributions in aluminium-alloy plates under low velocity impact loading. The low velocity impact load on the fully clamped circular plate was idealized as a quasi-static normal point force acting at the centre of plate. Based on apt geometrical approximation and assumptions, governing equations were established to predict the out-of-plane deflection and the radial tensile, radial and circumferential flexure strains in fully clamped conditions. From the deformation theory of plasticity, a new formula was derived to estimate the impact load by incorporating strain-energy approach, bilinear strain-hardening constitutive model and the one-dimensional Tresca yield criterion. Low velocity impact tests were performed to confirm the proposed model and good correlation was achieved between the predictions and actual experiments, demonstrating the practical and effective use of the proposed model.

Structural behavior of a lightweight, textile-reinforced concrete barrel vault shell

Textile-reinforced concrete (TRC) as a novel composite material offers a wide range of capabilities and flexibility in the manufacturing of thin-walled, lightweight structures. The application of textile reinforcement in fine aggregate high-performance concrete has enabled the dimensioning of structural concrete in very small thicknesses. This possibility allows for the fabrication of thin-walled TRC shell structures with complex geometries. On the other hand, structural planning and construction require new modeling approaches to comprehend the structural behavior of such forms. In this paper, we present the fabrication procedure of a large-scale TRC vault shell, together with the performed experimental study. The shell structure was tested under a two-step loading scenario to study the load-bearing behavior. The particular focus of the paper is on the analysis of the structural behavior by means of an anisotropic strain-hardening material model specifically developed for the simulation of TRC shells. The prediction obtained using the nonlinear finite element simulation has been compared with the test results to validate the modeling approach. The performed studies are used to evaluate and discuss the structural redundancy included in the applied linear ultimate limit state assessment procedure.

Work Hardening Behavior of 1020 Steel During Cold-Beating Simulation

The present research of cold-beating formation mainly focused on roller design and manufacture, kinematics, constitutive relation, metal flow law, thermo-mechanical coupling, surface micro-topography and microstructure evolution. However, the research on surface quality and performance of workpieces in the process of cold-beating is rare. Cold-beating simulation experiment of 1020 steel is conducted at room temperature and strain rates ranging from 2000 to 4000 s−1 base on the law of plastic forming. According to the experimental data, the model of strain hardening of 1020 steel is established, Scanning Electron Microscopy(SEM) is conducted, the mechanism of the work hardening of 1020 steel is clarified by analyzing microstructure variation of 1020 steel. It is found that the strain rate hardening effect of 1020 steel is stronger than the softening effect induced by increasing temperatures, the process of simulation cold-beating cause the grain shape of 1020 steel significant change and microstructure elongate significantly to form a fibrous tissue parallel to the direction of deformation, the higher strain rate, the more obvious grain refinement and the more hardening effect. Additionally, the change law of the work hardening rate is investigated, the relationship between dislocation density and strain, the relationship between work hardening rate and dislocation density is obtained. Results show that the change trend of the work hardening rate of 1020 steel is divided into two stages, the work hardening rate decreases dramatically in the first stage and slowly decreases in the second stage, finally tending toward zero. Dislocation density increases with increasing strain and strain rate, work hardening rate decreases with increasing dislocation density. The research results provide the basis for solving the problem of improving the surface quality and performance of workpieces under cold-beating formation of 1020 steel.

Dislocation strengthening in FCC metals and in BCC metals at high temperatures

Till now, it was widely believed that the dislocation strengthening coefficients used in the Taylor-like relation were universal for a given crystallographic class of materials. In the present study, it is shown that this is actually untrue because of two effects that influence the strength of interactions between slip systems, namely the value of the Poisson ratio and the occurrence of doubly degenerated, asymmetric, junction configurations. New strengthening coefficient values for reactions between slip systems were determined using dislocation dynamics simulations on five representative FCC metals, plus germanium, and on five BCC transition metals for {110} and {112} slip systems at high homologous temperatures. The value of the Poisson ratio affects all the strengthening coefficients to various extents ranging from small to substantial. The effects of configuration asymmetry and Poisson's ratio are more marked in BCC metals than in FCC metals. These two major effects arise from a number of concurring dislocation mechanisms, which are discussed in some detail. It is expected that the use of accurate material-dependent coefficients will notably improve the predictive ability of current models for strain hardening.

A study on the liquefaction risk in seismic design of foundations

A fully coupled non-linear effective stress response finite difference (FD) model is built to survey the counter-intuitive recent findings on the reliance of pore water pressure ratio on foundation contact pressure. Two alternative design scenarios for a benchmark problem are explored and contrasted in the light of construction emission rates using the EFFC-DFI methodology. A strain-hardening effective stress plasticity model is adopted to simulate the dynamic loading. A combination of input motions, contact pressure, initial vertical total pressure and distance to foundation centreline are employed, as model variables, to further investigate the control of permanent and variable actions on the residual pore pressure ratio. The model is verified against the Ghosh and Madabhushi high acceleration field test database. The outputs of this work is aimed to improve the current computer-aided seismic foundation design that relies on ground’s packing state and consistency. The results confirm that on seismic excitation of shallow foundations, the likelihood of effective stress loss is greater in deeper depths and across free field. For the benchmark problem, adopting a shallow foundation system instead of piled foundation benefitted in a 75% less emission rate, a marked proportion of which is owed to reduced materials and haulage carbon cost.

Development of a force–resultant model for spudcan footings on loose sand under combined loads

Spudcans are typical foundations used in shallow to moderate-depth water oil and gas fields to support jack-up drilling units. Understanding the behaviour of spudcans under combined loadings is crucial to the overall response of the jack-up structure. This paper presents the development of a strain-hardening plasticity model for a spudcan footing on loose sand. Most of the model components are developed from direct centrifuge observations. The centrifuge tests were performed at an acceleration of 100 times that of the Earth’s gravity on a model spudcan footing subjected to combined vertical, horizontal, and moment loads. All the experiments have been designed and conducted to allow the results to be interpreted with a strain-hardening plasticity framework. Combined loads were applied by using a novel apparatus, which enables independent vertical, horizontal, and rotational movements of the footing. Test results also revealed the existence of a three dimensional sliding surface that intersects with the conventional yield surface. This additional surface has been defined analytically. Retrospective simulation of the experimental data using the plasticity model confirms the model’s capability for use in predicting the behaviour of larger spudcan applications offshore.

Modeling of Grain-Boundary Mobility and Nucleation Rate during Discontinuous Dynamic Recrystallization in Ni-Nb Alloys and a High-Purity Alloy Derived from SAE 304L

A simple mesoscale model has been developed for discontinuous dynamic recrystallization. Each grain is considered in turn as an inclusion, embedded in a homogeneous equivalent matrix, the properties of which are obtained by averaging over all the grains. The model includes: (i) a grain-boundary migration-equation driving the evolution of grain size via the mobility of grain boundaries, which is coupled with (ii) a single-internal-variable (dislocation density) constitutive model for strain hardening and dynamic recovery, and (iii) a nucleation equation governing the total number of grains by the nucleation of new grains. All the system variables tend to asymptotic values at large strains, in agreement with the experimentally observed steady-state regime.With some assumptions, both steady-state stress and grain-size are derived in closed forms, allowing immediate identification of the mobility of grain boundaries and the rate of nucleation. An application to Ni–Nb-pure-binary model alloys and high-purity 304L stainless steel with Nb addition is presented. More specifically on one hand, from experimental steady-state stresses and grain sizes, variations of the grain boundary mobility and the nucleation rate with niobium content are addressed in order to quantify the solute-drag effect of niobium in nickel. And on the other hand, the Derby exponents were investigated varying separately the strain rate or the temperature.

Impact erosion prediction using the finite volume particle method with improved constitutive models

Erosion damage in hydraulic turbines is a common problem caused by the high- velocity impact of small particles entrained in the fluid. In this investigation, the Finite Volume Particle Method is used to simulate the three-dimensional impact of rigid spherical particles on a metallic surface. Three different constitutive models are compared: the linear strainhardening (L-H), Cowper-Symonds (C-S) and Johnson-Cook (J-C) models. They are assessed in terms of the predicted erosion rate and its dependence on impact angle and velocity, as compared to experimental data. It has been shown that a model accounting for strain rate is necessary, since the response of the material is significantly tougher at the very high strain rate regime caused by impacts. High sensitivity to the friction coefficient, which models the cutting wear mechanism, has been noticed. The J-C damage model also shows a high sensitivity to the parameter related to triaxiality, whose calibration appears to be scale-dependent, not exclusively material-determined. After calibration, the J-C model is capable of capturing the material's erosion response to both impact velocity and angle, whereas both C-S and L-H fail.

Devising Strain Hardening Models Using Kocks–Mecking Plots—A Comparison of Model Development for Titanium Aluminides and Case Hardening Steel

The present study focuses on the development of strain hardening models taking into account the peculiarities of titanium aluminides. In comparison to steels, whose behavior has been studied extensively in the past, titanium aluminides possess a much larger initial work hardening rate, a sharp peak stress and pronounced softening. The work hardening behavior of a TNB-V4 (Ti–44.5Al–6.25Nb–0.8Mo–0.1B) alloy is studied using isothermal hot compression tests conducted on a Gleeble 3500 simulator, and compared to the typical case hardening steel 25MoCrS4. The behavior is analyzed with the help of the Kocks-Mecking plots. In contrast to steel the TNB-V4 alloy shows a non-linear course of θ (i.e., no stage-III hardening) initially and exhibits neither a plateau (stage IV hardening) nor an inflection point at all deformation conditions. The present paper describes the development and application of a methodology for the design of strain hardening models for the TNB-V4 alloy and the 25CrMoS4 steel by taking the course of the Kocks-Mecking plots into account. Both models use different approaches for the hardening and softening mechanisms and accurately predict the flow stress over a wide range of deformation conditions. The methodology may hence assist in further developments of more sophisticated physically-based strain hardening models for TiAl-alloys.

Cavitation-induced damage of soft materials by focused ultrasound bursts: A fracture-based bubble dynamics model.

A generalized Rayleigh-Plesset-type bubble dynamics model with a damage mechanism is developed for cavitation and damage of soft materials by focused ultrasound bursts. This study is linked to recent experimental observations in tissue-mimicking polyacrylamide and agar gel phantoms subjected to bursts of a kind being considered specifically for lithotripsy. These show bubble activation at multiple sites during the initial pulses. More cavities appear continuously through the course of the observations, similar to what is deduced in pig kidney tissues in shock-wave lithotripsy. Two different material models are used to represent the distinct properties of the two gel materials. The polyacrylamide gel is represented with a neo-Hookean elastic model and damaged based upon a maximum-strain criterion; the agar gel is represented with a strain-hardening Fung model and damaged according to the strain-energy-based Griffith's fracture criterion. Estimates based upon independently determined elasticity and viscosity of the two gel materials suggest that bubble confinement should be sufficient to prevent damage in the gels, and presumably injury in some tissues. Damage accumulation is therefore proposed to occur via a material fatigue, which is shown to be consistent with observed delays in widespread cavitation activity.

Strain hardening model of TWIP steels with manganese content

High Mn austenitic Fe–Mn–C steel is a superior material which exhibits excellent strain hardening behavior, with high strength and good ductility as a result of deformation-induced twinning. In this paper, a dislocation-based strain hardening model is developed by considering the effect of the Mn content on the mechanical behavior of TWIP steel. The Mn content varies in the range of 22–26wt%. In the model, the stacking fault energy (SFE) is considered to be dependent on the composition of the TWIP steel and the plastic strain. The driving force for twinning, which is controlled by the SFE, dominates the mechanical twin nucleation probability. The dislocation density evolution, which controls the strain hardening behavior, is influenced by the twinning volume fraction. The mechanical behaviors of TWIP steels with different Mn contents are tested in axisymmetric tension, and the microstructure evolution is observed in-situ by means of light-optical microscopy. The twinning volume fraction is determined on the basis of the observed twin area fraction. The predictions of the proposed model are verified by comparison with experimental data and the influence of the Mn content of the TWIP steel on the mechanical behavior is also analyzed.

Finite element simulation of the effect of loading rate on the stress-strain behaviour of Albany sand

In this research, the effect of strain rate on Albany sand has been studied by elastic visco-plastic constitutive model within the framework of three component model. Strain rate effect can be modelled by using any one of the (i) Isotach, (ii) TESRA (temporary effects of strain rate and acceleration) or Viscous Evanescent and (iii) P&N (positive and negative viscosity) models of the three component framework. Usually ‘Isotach’ is appropriate for clay and soft rock, ‘TESRA’ for sand and ‘P&N’ is appropriate for sand with less angularity like Albany sand. In this research triaxial compression (TC) test results of Albany sand at different strain rates have been modelled successfully into a commercially available package called ‘ABAQUS’. The P&N model was implemented into a generalised elasto-plastic isotropic strain-hardening non-linear model in C++. The model was then embedded in the finite element computer programme ABAQUS, which was used for the actual analysis. In order to define the P&N model user subroutine of ABAQUS ‘UMAT’ was written in C++ and used hereafter. ABAQUS is a robust FEM software that allows writing subroutines for describing different material behaviour. Generally UMAT is written in FORTRAN but in this study the main model is written in C++ and then it is called by FORTRAN with appropriate change in ABAQUS environment file. The effect of strain rate on the stress-strain behaviour of Albany sand has been modelled by using the TESRA model with the help of user subroutine UMAT of commercially available FEM software ABAQUS.

Strain-hardening behaviors of dual phase steels with microstructure features

Due to the inhomogeneous deformation of the microstructure, it becomes difficult as well as necessary to determine the mechanical behavior of multi-phase high strength steels precisely. In this study, the strain distribution of microstructure is obtained utilizing Point Interpolation Method (PIM). The strain of microstructure with an exponential function of overall strain presents greater deformation in Ferrite than Martensite. Considering the characteristic deformation of individual phases, a dislocation based combined strain-hardening model is proposed to describe the overall stress-strain relationship of the material. The agreement between theoretical model and experiment results is verified by DP800. Based on the model, the stress-strain response of DP steels to different grain sizes and volume fractions of individual phases is studied. The strength and strain hardening behavior of DP steels with finer Ferrite, coarser Martensite and higher content of Martensite are significantly improved. In addition, dislocation mean free path, dislocation density, strain-hardening rate and hardening exponent of individual phases are calculated to describe the strain-hardening mechanism of individual phases and DP steels.

A strain-hardening microplane damage model for thin-walled textile-reinforced concrete shells, calibration procedure, and experimental validation

Thin-walled shell structures made of textile-reinforced concrete (TRC) exhibit a high load-bearing capacity and considerable ductility. However, the material behavior exhibits several interacting mechanisms of material disintegration that result in a complex, highly nonlinear structural response. In this paper, an anisotropic material model for TRC will be discussed that is able to capture those effects. The calibration of the material model is performed based on an inverse analysis using the strain-hardening response measured in a uniaxial tensile test. Finally, we validate the material model through a finite-element simulation of three-point bending tests as well as the complex biaxial load-bearing behavior as observed in slab tests with central loading. In this context, further issues such as the influence of large deflections and geometrical nonlinearity will be investigated. The calibrated model provides a valuable tool for an in-depth analysis of the structural behavior of thin-walled TRC shell structures. This is especially important for a realistic prediction of the deflections in the cracked state as well as load-bearing reserves resulting from stress redistributions.

Incorporation of Dynamic Strain Aging Into a Viscoplastic Self-Consistent Model for Predicting the Negative Strain Rate Sensitivity of Hadfield Steel

A new multiscale modeling approach is proposed to predict the contributions of dynamic strain aging (DSA) and the resulting negative strain rate sensitivity (NSRS) on the unusual strain-hardening response of Hadfield steel (HS). Mechanical response of HS was obtained from monotonic and strain rate jump experiments under uniaxial tensile loading within the 10−4 to 10−1 s−1 strain rate range. Specifically, a unique strain-hardening model was proposed that incorporates the atomic-level local instabilities imposed upon by the pinning of dislocations by diffusing carbon atoms to the classical Voce hardening. The novelty of the current approach is the computation of the shear stress contribution imposed on arrested dislocations leading to DSA at the atomic level, which is then implemented to the overall strain-hardening rule at the microscopic level. The new model not only successfully predicts the role of DSA and the resulting NSRS on the macroscopic deformation response of HS but also opens the venue for accurately predicting the deformation response of rate-sensitive metallic materials under any given loading condition.

Role of oxide seed layer in plastic response of epitaxially grown textured metal films

The elastic/plastic mechanical behavior of freestanding polycrystalline {111}-textured Pt films with thicknesses 50–1000 nm and different combinations of grain size and film thickness, grown epitaxially on a 35–50 nm thick polycrystalline (100)-TiO2 (rutile) seed layer, was studied at uniaxial tension strain rates 10−6 - 10 s−1. The mismatch strain between the {111}-Pt films and the underlying (100)-TiO2 seed layer gives rise to an interfacial dislocation network, which, in turn, determines the initiation of plastic deformation in Pt. Experiments showed that the flow stress increases, while the plastic strain accumulation at failure decreases with decreasing Pt film thickness. A modified Thompson model that accounted for the combined effect of film thickness and grain size provided good predictions for the elastic limit of Pt films. However, the yield stress was underestimated by the same model; a Taylor strain hardening model was superimposed to the modified Thompson model to account for additional hardening as a result of dislocation interactions during plastic deformation, which provided good predictions for the evolution of flow stress with plastic strain.