Nonlinear Kinematic Hardening Models Research Articles

Mixed-mode crack growth analysis using a cyclic plasticity model

The effects of two singularity fields, namely, the HRR solution and modified form of the nonlinear kinematic hardening (NKH) solution, on the pure mode I and mixed mode I/II fatigue crack propagation were investigated. Experiments and computations were performed on compact tension shear (CTS) specimens of P2M steel, aluminium 7050, and Ti-6Al-4V with different monotonic and cyclic elastic–plastic properties. The analysis of the experimental data on the crack growth rate for all tested materials is given in terms of plastic stress intensity factors (SIFs) according to the HRR and NKH models. The elastic–plastic crack tip fields were obtained by FE computation as a function of the position along the curvilinear crack path for the monotonic condition and the first several cycles of fatigue deformation considering the Bauschinger effect. As a complement to the FE modelling, digital image correlation (DIC) measurements of the displacement and strain fields around the crack tip in the CTS specimens were performed. This study aimed to obtain more detailed information on the local cyclic strain ahead of the mixed mode crack tip by using DIC. From the sensitivity analysis, it was established that the DIC value depended significantly on the location along the crack direction of the pair of points selected before and behind the crack tip. In this study, acceleration or retardation of the crack growth rate in terms of the NKH plastic SIF with respect to the HRR model was observed because of the coupling effect of the mode mixity and cyclic plastic properties of the tested P2M steel, aluminium 7050, and Ti-6Al-4V.

Cyclic behavior of a slit damper proposed for precast concrete beam-column connections

Since the 2017 Puebla-Morelos Earthquake, interest in limiting damage to structural components has exponentially increased in Mexico. Consequently, the use of energy dissipation devices has received renewed attention. Following that line, this paper studies an attractive solution, which is a slit damper proposed as a passive energy dissipation device for, but not limited to, precast beam-column connections. Slit dampers have been studied for their cost-effectiveness and ease of application. They present stable hysteretic behavior and dissipate substantial amounts of energy under cyclic loading while maintaining less ductile elements essentially elastic. The structural behavior of the proposed device was evaluated theoretically, followed by experimental verification. Quasi-static incremental and constant-amplitude cyclic tests were conducted on eight specimens, with two of them having non-uniform struts. Test results are presented and discussed, emphasizing ductility and energy dissipation capacity. The proposed damper showed stable hysteretic behavior and adequate seismic performance. Using non-uniform struts significantly increased the damper's deformation capacity and fatigue performance, which is desirable for seismic zones where long-duration earthquakes are expected, such as in Mexico City. Numerical modeling techniques were also validated with finite element analyses. It was shown that the proposed damper's hysteretic response could be accurately predicted using the combined non-linear isotropic and kinematic hardening model.

Size effect on the cyclic deformation behavior of superalloy ultrathin sheet: Characterization and multiscale modelling

Superalloy ultrathin sheets have high strength, outstanding oxidation resistance, corrosion resistance and fatigue performance, and its thin-walled components occupy a considerable proportion in aeroengines. In the microforming process of aeroengine thin-walled components, the superalloy ultrathin sheet is often deformed under complex loading states and shows obvious springback. However, the forming and springback laws of superalloy ultrathin sheet in the microforming process are not clear and often affected by size effect. In addition, the existing nonlinear kinematic hardening models cannot accurately forecast the deformation and springback of superalloy ultrathin sheets. To address this issue, the cyclic shearing tests were performed to systemically explore the size effect on Bauschinger effect, permanent softening, transient hardening and work hardening stagnation of superalloy ultrathin sheets under cyclic loading states. The mechanism of size effect on cyclic mechanical response was systematically revealed through microstructure evolution combined with surface layer effect. In addition, a new multiscale cyclic hardening model was proposed based on the Y-U model and size effect on cyclic deformation behavior of superalloy ultrathin sheets. The new multiscale cyclic hardening model coupling surface layer effect and grain boundary strengthening effect was constructed by modeling the relationship between the cyclic mechanical response and size effect. Comparisons between the original Y-U model and the new proposed model on the characterization effect of shear stress-strain curves demonstrated that the proposed cyclic hardening model can accurately present the cyclic deformation behavior. To further verify the prediction capability of the proposed cyclic hardening model, the springback behavior of superalloy ultrathin sheet in U-bending test and hydroforming of seal ring was predicted via the proposed model combined with the decrease of elastic modulus and Yld2000–2d yield criterion, and the predicted results were compared with experimental ones. Comparative research revealed that the proposed cyclic hardening model can accurately describe the cyclic deformation behavior and springback of superalloy ultrathin sheets affected by size effect.

Application of a semianalytical strain assessment and multiaxial fatigue analysis to compare rolling contact fatigue in twin‐disk and full‐scale wheel/rail contact conditions

AbstractA semianalytical model is introduced to assess rolling contact fatigue problems in railway applications. The constitutive law is based on the nonlinear kinematic and isotropic hardening model of Chaboche–Lemaitre, which allows the cyclic elastoplastic strain under the contact surface to be evaluated. The much higher computational effectiveness in comparison with finite element (FE) analyses is quantified. The Dang Van multiaxial fatigue criterion is implemented to evaluate the rolling contact fatigue in the subsurface elastic region where cracking is relatively rare but more dangerous than surface cracks. The influence of the presence of sulfides in the wheel matrix in decreasing fatigue strength is also assessed by means of Murakami's approach. The model is used to compare conditions under small‐scale twin‐disk experiments to full‐scale wheel/rail contact conditions. It is found that, for the same Hertzian pressure, the small‐scale contact is more conservative in that it causes a deeper plasticized layer as compared with the elliptical full‐scale contact. In the investigated cases, crack initiation is also not expected according to Dang Van criterion in neither of the studied contact conditions.

Semi-Automated Procedure to Estimate Nonlinear Kinematic Hardening Model to Simulate the Nonlinear Dynamic Properties of Soil and Rock

The strain-dependent nonlinear properties of ground materials, such as shear modulus degradation (G/Gmax) and damping, are of significant importance in seismic-related analyses. However, the ABAQUS program lacks a comprehensive procedure to estimate parameters for a built-in model. In this study, a nonlinear kinematic hardening (NKH) model with three back-stress values was used, which allows better fitting to the backbone curves compared to the simplified nonlinear kinematic hardening (SNKH) model previously proposed. Instead of modeling in ABAQUS, a semi-automated procedure was implemented in MATLAB, which can predict shear stress–shear strain hysteretic loops, to find the fitting parameters to the target G/Gmax and/or damping curves. The procedure was applied for three soil and two rock samples, and the results indicate a good match between model and target backbone curves, which proves the application of the procedure and the NKH model in simulating the nonlinear properties of ground materials.

A method for the simultaneous identification of anisotropic yield and hardening constitutive parameters for sheet metal forming

Sheet metal forming processes and their simulations often require knowledge of both anisotropic yield and hardening constitutive parameters. The identification of these properties, however, involves a large number of homogeneous tests as well as various expensive testing machines. In this paper, a novel method is proposed to enable a simultaneous identification of the multiple anisotropic yield and hardening constitutive parameters from a single test and using the simplest uniaxial testing machine, which significantly simplifies the conventional complex constitutive identification procedures. In particular, the test configuration is elaborately designed to exhibit both heterogeneous stress states and insignificant buckling under compressive loadings based on the plate buckling theory. The virtual fields method is adopted as the inverse problem solution for the selected anisotropic yield and hardening laws, namely, Hill1948 and the nonlinear kinematic hardening models. The proposed identification scheme is first validated through the simulated full-field strain and load data of the designed bridge-like test configuration. Its identification sensitivity is analyzed with respect to the influences of measurement noise, type and combination of virtual fields. The results show that using the designed test configuration it is possible to identify all the target anisotropic parameters from a single test despite a noticeable level of error. This however can be markedly improved by combining the two tests performed in the rolling and transverse directions, and with the multiple virtual fields constraints, from which accurate and robust identification results are obtained for the selected models. The validity of this method is then illustrated experimentally with the application on the wrought magnesium alloy AZ31B sheet specimens. Finally, potential improvements and applications of this method are suggested.

Analysis of Undrained Seismic Behavior of Shallow Tunnels in Soft Clay Using Nonlinear Kinematic Hardening Model

In this study, a soil–tunnel model for clay under earthquake loading is analyzed, using finite element methods and a kinematic hardening model with the Von Mises failure criterion. The results are compared with those from the linear elastic–perfectly plastic Mohr–Coulomb model. The latter model does not consider the stiffness degradation caused by imposing cyclic loading and unloading to the soil, whereas the kinematic hardening model can simulate this stiffness degradation. The parameters of the kinematic hardening model are calibrated based on the results of experimental cyclic tests and finite element simulation. Here, two methods—one using data from cyclic shear tests, and the other a new method using undrained cyclic triaxial tests—are used to calibrate the parameters. The parameters investigated are the peak ground acceleration (PGA), tunnel lining thickness, tunnel shape, and tunnel embedment depth, all of which have an effect on the resistance of the shallow tunnel to the stresses and deformations caused by the surrounding clay soils. The results show that unlike traditional models, the nonlinear kinematic hardening model can predict the response reasonably well, and it is able to create the hysteresis loops and consider the soil stiffness degradation under the seismic loads.

Investigation of Seismic Behavior of Clay‐Pile Using Nonlinear Kinematic Hardening Model

In geotechnical mediums where the bearing capacity of upper layers of soil is not suitable for use of the shallow foundations, piles are usually used as deep foundations to transfer loads to the stronger lower layers. Here, the seismic behavior of single pile and pile group constructed in saturated soft kaolin clay under three different earthquakes using Abacus 3D software is investigated. The aluminum material considering the linear elastic model has been used for the piles, and the nonlinear kinematic hardening model with Von Mises failure criterion has been considered for clay. This model can consider the soil stiffness degradation by increasing the number of cyclic loading. Three different methods have been used to calibrate the model parameters, two of them are new methods. In all calibration methods, the cyclic shear and undrained cyclic triaxial tests are used. The results obtained from the numerical analysis of the soil‐pile model are in relatively good agreement with the centrifuge model results. According to the results, the variation of earthquake frequency and intensity affects the bending moment created along the pile and also the distance between piles in a pile group affects the amount of the interaction between them.

An Identification Method for Anisotropic Plastic Constitutive Parameters of Sheet Metals

In this work, the virtual fields method (VFM) was extended to simultaneously identify the constitutive parameters of Hill 1948 anisotropic yield criterion and nonlinear kinematic hardening models for rolled sheet metals from a low cycle tension-compression test. First, simulations of different specimens under loading were conducted to determine a specific configuration which exhibits both insignificant buckling effect and heterogeneous stress state. Then, the simulated data were utilized to retrieve the target anisotropic constitutive parameters in order to validate the proposed VFM identification scheme. The results show that the input parameters can be satisfactorily regained from the designed tension-compression configuration and the VFM algorithm, verifying the feasibility of using this method to real experiments.

Back-Stress Effect on the Mechanical Strength of TWIP-IF Steels Layered Sheet

Although back-stress contributes to the mechanical properties of materials, the degree of strength enhancement from back-stress is not easy to estimate. In this research, back-stress hardening of twinning-induced plasticity (TWIP) + interstitial free (IF)-layered steel sheets were estimated by implementing a non-linear combined isotropic and kinematic hardening model. High back-stress evolution occurs due to plastic strain incompatibility between a TWIP-steel core and IF-steel sheath, and the strength of TWIP + IF layered steel sheath is greater than the strength estimated by the rule-of-mixtures. A non-linear combined isotropic and kinematic hardening model was used to estimate the strength enhancement from back-stress hardening, and the simulation results were correlated with the experimental results. This result shows that the back-stress evolution in heterogeneous materials contributes to their strength, and that the non-linear combined isotropic and kinematic hardening should be included to estimate the degree of back-stress hardening.

Application of Noninteraction Constitutive Models for Deformation of IN617 Under Combined Extreme Environments

Next-generation, reusable hypersonic aircraft will be subjected to extreme environments that produce complex fatigue loads at high temperatures, reminiscent of the life-limiting thermal and mechanical loads present in large gas-powered land-based turbines. In both of these applications, there is a need for greater fidelity in the constitutive material models employed in finite element simulations, resulting in the transition to nonlinear formulations. One such formulation is the nonlinear kinematic hardening (NLKH) model, which is a plasticity model quickly gaining popularity in the industrial sector, and can be found in commercial finite element software. The drawback to using models like the NLKH model is that the parameterization can be difficult, and the numerical fitting techniques commonly used for such tasks may result in constants devoid of physical meaning. This study presents a simple method to derive these constants by extrapolation of a reduced-order model, where the cyclic Ramberg–Osgood (CRO) formulation is used to obtain the parameters of a three-part NLKH model. This fitting scheme is used with basic literature-based data to fully characterize a constitutive model for Inconel 617 at temperatures between 20 °C and 1000 °C. This model is validated for low-cycle fatigue (LCF), creep-fatigue (CF), thermomechanical fatigue (TMF), and combined thermomechanical-high-cycle fatigue (HCF) using a mix of literature data and original data produced at the Air Force Research Laboratory (AFRL).

Modeling the Cycle-Dependent Material Hardening Behavior of 508 low Alloy Steel

Chaboche-based material hardening models were used to investigate the cycle/time dependency of the elastic-plastic behavior of 508 low alloy steel (LAS), a commonly used material for light water reactor components. Strain-versus-stress curves were derived from uniaxial tensile and fatigue experiments conducted under various conditions, such as in-air at room temperature, in-air at 300 °C, and primary loop water conditions for a pressurized water reactor (PWR). These data were then used to estimate material parameters such as the elastic modulus, yield stress, and variables related to Chaboche-based linear and nonlinear kinematic hardening models. The results estimated from the fatigue test data suggest that the material behavior is highly sensitive to fatigue cycles, in addition to temperature. The authors anticipate that the findings of this research will help develop computer-based advanced modeling tools to extrapolate stress-strain evolution of reactor components under multi-axial stress states and, hence, will help predict their fatigue life more accurately.

Enhanced non-linear material modelling for analysis and qualification of rollover protective structures

Finite element simulations of a rollover protective structure are an important aspect in its design, as it provides a means of structural integrity qualification prior to the required destructive testing. A good understanding of the rollover protective structure behaviour under simulated loading offers engineering practitioners the opportunity to optimize the design. The testing conditions, which are outlined in the applicable standards, result in plastic deformation of the rollover protective structure, associated with material hardening of various areas of the structure. An accurate description of the material behaviour is important for finite element simulations of the structural response. This research examines some of the hardening models commonly used in simulations of rollover protective structures, which are available in most finite element commercial software, including linear and multi-linear isotropic and kinematic hardening models and non-linear kinematic hardening models. The numerical performance of the plasticity models in representing the material behaviour was compared with the experimental data for commonly used rollover protective structure material. Analysis revealed the potential benefits and drawbacks of the various models. Moreover, a damage-induced softening model was implemented at the structure joints in conjunction with the non-linear hardening models. Enhanced computational results were obtained through this modelling variation, highlighting the importance of material modelling at the primary structure and the joints of a rollover protective structure.

Chaboche-based cyclic material hardening models for 316 SS–316 SS weld under in-air and pressurized water reactor water conditions

This paper discusses a material hardening models for welds made from 316 stainless steel (SS) to 316 SS. The model parameters were estimated from the strain-versus-stress curves obtained from tensile and fatigue tests conducted under different conditions (air at room temperature, air at 300°C, and primary loop water conditions for a pressurized water reactor). These data were used to check the fatigue cycle dependency of the material hardening parameters (yield stress, parameters related to Chaboche-based linear and nonlinear kinematic hardening models, etc.). The details of the experimental results, material hardening models, and associated calculated results are published in an Argonne report (ANL/LWRS-15/2). This paper summarizes the reported material parameters for 316 SS–316 SS welds and their dependency on fatigue cycles and other test conditions.

FEA to assess plastic deformation of railhead material damage of insulated rail joints with fibreglass and nylon endposts

Railhead material becomes severely stressed due to localised cyclical wheel/rail contact loadings. The stress situation is more critical in the vicinity of the endpost of an insulated rail joint (IRJ). As the contact point moves towards the endpost, the wheel loading peak pressure increases sharply, not following the well-known Hertzian Contact Theory (HCT). With a view to finding a more suitable design of IRJs to bear the pressure singularity and reduce impact force and damage of railhead material, nylon 66 (ny) along with fibre-glass (fg) endposts in IRJs have been considered.This paper presents a 3D finite element analysis targeting damage and stress distributions in the railhead material near the endposts. The following design parameters are considered: 5mm endpost thickness in a 6-bolt IRJ centrally suspended between two sleepers. A non-linear isotropic and kinematic material hardening model is used to represent elastic-plastic behaviour. 2000 loading cycles in the form of wheel pressure using the amplitude function in ABAQUS are applied for this analysis. Critical strain and stress components are determined to quantify railhead damage. The effects of both fg and ny endpost material on the mechanical behaviour of IRJs are analysed to find the best design. In this regard, progressive damage parameter and von-Mises stresses are considered to determine plastic deformation and material degradation of the railhead material.

Effect of micro-cavities on different plastic zones at the fatigue crack tip of a compact tension specimen

Knowledge of cyclic plastic deformation response at the fatigue crack tip is crucial to understand the nature of cyclic damage acting on the crack tip. Interaction between crack and defect is equally important to understand the cyclic damage progression at crack tip; however isotropic hardening model was adopted in all existing literatures. Isotropic hardening model is suitable to model only the monotonic plastic zone and unable to model the cyclic/reverse plastic zone. Kinematic hardening model is suitable to model the key cyclic plastic deformation responses like Bauschinger effect, ratcheting, and mean stress relaxation. A non-linear kinematic hardening (Chaboche) model is used in this present investigation to represent the material’s cyclic stress–strain response accurately.Effect of micro-cavity positions (angle and distance from crack tip) and sizes on plastic zones near a crack tip is investigated in this study by two dimensional plane strain finite element model of a compact tension specimen. It is observed that the size and shape of the monotonic and cyclic plastic zones are affected by position and size of the micro-cavity. During asymmetric loading condition, the ratcheting strain accumulation direction is also affected by the position of micro-cavity.

Experimental measurement and analytical determination of shot peening residual stresses considering friction and real unloading behavior

This paper presents an analytical model to predict the residual stress distribution induced by Shot peening. The analytical approach is based on the work of Shen and Atluri (2006) [18] with some modifications. The modifications are related to the elasto-plastic unloading of shot impingements, friction coefficient effect and the fraction of kinetic energy transmitted to the treated material. In order to predict more realistic residual stresses, the elasto-plastic unloading phase of shot impacts is modeled using two nonlinear kinematic hardening models considering the Bauschinger effect. Moreover, the effect of the Coulomb friction between target surface and shots is evaluated. For this purpose, the interior stresses caused by tangential tractions of friction force are determined analytically. In this work, the effects of friction coefficient, hardening model in loading and unloading phases, the offset of determination of the yield points and the Bauschinger effect on the residual stress distribution are taken into account. Experiments are carried out on DIN 1.6582 medium carbon steel to validate the results obtained from the analytical model. The results of the comparison indicate that the analytical relations agree well with the experimental data.

On the applicability of multi-surface, two-surface and non-linear kinematic hardening models in multiaxial fatigue

On the applicability of multi-surface, two-surface and non-linear kinematic hardening models in multiaxial fatigue

On the applicability of multi-surface, two-surface and non-linear kinematic hardening models in multiaxial fatigue

In this work, a comparison between NLK and Mróz-Garud’s multi-surface formulations is presented. A unified common notation is introduced to describe the involved equations, showing that the Mróz-Garud model can be regarded as a particular case of the NLK formulation. It is also shown that the classic two-surface model, which is an unconventional simplified plasticity model based on the translation of only two surfaces, can also be represented using this formulation. Such common notation allows a direct quantitative comparison among multi-surface, two-surface, and NLK hardening models.

Residual Stresses in Cylindrical Roller Bearings – A Three-Dimensional Analysis Model

The author presents an accurate method to calculate the residual fields in case of non-hertzian elastic-plastic contact problems in roller bearings. This kind of analysis requires a complete three-dimensional investigation due to the finite length of the contacting bodies. Previous analyses carried out in two-dimensional case are not able to take into account the complexity of the problem and the so-called edge-effect that is known to reduce the bearing fatigue life. A semi-analytical code previously developed was adapted to account for three-dimensional line contact analysis. A non-linear rate independent isotropic and kinematic hardening model is implemented for the bearing steel plastic behavior. Closed form solutions for residual stresses during cyclic non-proportional loading are obtained from the plastic strains and they are considered as initial stresses at every loading cycle.