Nonlinear Kinematic Hardening Research Articles

Application of efficient algorithm based on block Newton method to elastoplastic problems with nonlinear kinematic hardening

PurposeThe purpose of this study is to present the effectiveness and robustness of a numerical algorithm based on the block Newton method for the nonlinear kinematic hardening rules adopted in modeling ductile materials.Design/methodology/approachElastoplastic problems can be defined as a coupled problem of the equilibrium equation for the overall structure and the yield equations for the stress state at every material point. When applying the Newton method to the coupled residual equations, the displacement field and the internal variables, which represent the plastic deformation, are updated simultaneously.FindingsThe presented numerical scheme leads to an explicit form of the hardening behavior, which includes the evolution of the equivalent plastic strain and the back stress, with the internal variables. The features of the present approach allow the displacement field and the hardening behavior to be updated straightforwardly. Thus, the scheme does not have any local iterative calculations and enables us to simultaneously decrease the residuals in the coupled boundary value problems.Originality/valueA pseudo-stress for the local residual and an algebraically derived consistent tangent are applied to elastic-plastic boundary value problems with nonlinear kinematic hardening. The numerical procedure incorporating the block Newton method ensures a quadratic rate of asymptotic convergence of a computationally efficient solution scheme. The proposed algorithm provides an efficient and robust computation in the elastoplastic analysis of ductile materials. Numerical examples under elaborate loading conditions demonstrate the effectiveness and robustness of the numerical scheme implemented in the finite element analysis.

Application of efficient algorithm based on block Newton method to elastoplastic problems with nonlinear kinematic hardening

PurposeThe purpose of this study is to present the effectiveness and robustness of a numerical algorithm based on the block Newton method for the nonlinear kinematic hardening rules adopted in modeling ductile materials.Design/methodology/approachElastoplastic problems can be defined as a coupled problem of the equilibrium equation for the overall structure and the yield equations for the stress state at every material point. When applying the Newton method to the coupled residual equations, the displacement field and the internal variables, which represent the plastic deformation, are updated simultaneously.FindingsThe presented numerical scheme leads to an explicit form of the hardening behavior, which includes the evolution of the equivalent plastic strain and the back stress, with the internal variables. The features of the present approach allow the displacement field and the hardening behavior to be updated straightforwardly. Thus, the scheme does not have any local iterative calculations and enables us to simultaneously decrease the residuals in the coupled boundary value problems.Originality/valueA pseudo-stress for the local residual and an algebraically derived consistent tangent are applied to elastic-plastic boundary value problems with nonlinear kinematic hardening. The numerical procedure incorporating the block Newton method ensures a quadratic rate of asymptotic convergence of a computationally efficient solution scheme. The proposed algorithm provides an efficient and robust computation in the elastoplastic analysis of ductile materials. Numerical examples under elaborate loading conditions demonstrate the effectiveness and robustness of the numerical scheme implemented in the finite element analysis.

Modeling of LCF Behaviour on AISI316L Steel Applying the Armstrong–Frederick Kinematic Hardening Model

The combination of kinematic and isotropic hardening models makes it possible to model the behaviour of cyclic elastic-plastic steel material, though the estimation of the hardening parameters and catching the influence of those parameters on the material response is a challenging task. In the current work, an approach for the numerical simulation of the low-cycle fatigue of AISI316L steel is presented using a finite element method to study the fatigue behaviour of the steel at different strain amplitudes and operating temperatures. Fully reversed uniaxial LCF tests are performed at different strain amplitudes and operating temperatures. Based on the LCF test experimental results, the non-linear isotropic and kinematic hardening parameters are estimated for numerical simulation. On comparing, the numerical simulation results were in very good agreement with those of the experimental ones. This presented method for the numerical simulation of the low-cycle fatigue on AISI316 stainless steel can be used for the approximate prediction of the fatigue life of the components under different cyclic loading amplitudes.

An efficient 3D finite element procedure for simulating wheel–rail cyclic contact and ratcheting

Various models for simulating rail ratcheting behaviour were developed to study rolling contact fatigue (RCF) damage in rails. However, limitations remain in terms of the accuracy of wheel–rail contact modelling and computational efficiency of the cyclic loading simulation. This study developed an efficient 3D finite element (FE) procedure to simulate ratcheting in rails subjected to numerous load cycles. The procedure simulates a wheel rolling repeatedly over a rail section with updated stress–strain states, enabling automatically executed cyclic loading simulation given a predefined number of cycles. To ensure the accuracy of the contact modelling, the effect of meshing schemes on subsurface stress distribution was examined. In addition, the FE contact model with the selected meshing scheme, which balances accuracy and computational efficiency, was verified against the widely accepted CONTACT program. Subsequently, a non-linear kinematic hardening (NLKH) steel material was used in the FE model for ratcheting simulations with up to 100 wheel-loading cycles. The rail surface and subsurface stress states were replicated under partial-slip wheel–rail rolling contact conditions with traction coefficients of 0.10, 0.20 and 0.35, respectively. The ratcheting behaviour was extensively analysed in terms of plastic deformation, contact patch evolution, and ratcheting rates. The simulated plastic deformation was found to alter the contact geometry and thus contact stresses, which in turn affect further accumulation of plastic deformation and subsequent ratcheting strains. These findings highlighted the importance of considering the interplay between the rail ratcheting behaviour of the rail and evolving contact conditions for predicting ratcheting and RCF damage in rails.

Experimental investigation and numerical modelling of the cyclic plasticity and fatigue behavior of additively manufactured 316 L stainless steel

This study addresses the critical need for a constitutive model to analyze the cyclic plasticity of additively manufactured 316L stainless steel. The anisotropic behavior at both room temperature and 300 °C is investigated experimentally based on cyclic hysteresis loops performed in different orientations with respect to the build direction. A comprehensive constitutive model is proposed, that integrates the Armstrong-Frederick nonlinear kinematic hardening, Voce nonlinear isotropic hardening and Hill's anisotropic yield criterion within a 3D return mapping algorithm. The model was calibrated to specimens in the 0° and 90° orientations and validated with specimens in the 45° orientation. A single set of hardening parameters successfully represented the elastoplastic response for all orientations at room temperature. The algorithm effectively captured the full cyclic hysteresis loops, including historical effects observed in experimental tests. A consistent trend of reduced hardening was observed at elevated temperature, while the 45° specimen orientation consistently exhibited the highest degree of strain hardening. The applicability of the model was demonstrated by computing energy dissipation for stabilized hysteresis loops, which was combined with fatigue tests to propose an energy-based fatigue life prediction model.

The role of hydrogen in promoting differences in fatigue crack growth rates observed in Type 304/304L stainless steel at elevated temperature

Hydrogen has been postulated to affect fatigue crack growth rates (FCGRs) in Type 304/304L stainless steel during exposure to high purity water (HPW) environments at elevated temperature. To assess this mechanism, FCGR testing was performed at elevated temperature (260°C) in air and pressurized hydrogen gas. Initial results indicate the measured FCGRs in hydrogen are up to 8x lower than those measured in air under comparable fatigue loading conditions. Post-test evaluation of compact tension specimens indicates crack mouth opening displacements and fracture surface morphologies generated in hydrogen that are consistent with those generated in HPW environments. Observations of crack tip blunting suggest the reduced FCGRs in elevated temperature hydrogen occur due to a decrease in the effective ΔK. Finite element plasticity modeling, using a hydrogen-dependent nonlinear kinematic hardening approach, supports the hypothesis that crack tip blunting and retarded FCGRs are due to a hydrogen-based change in cyclic behavior (e.g. cyclic creep) occurring ahead of the fatigue crack tip.

Virtual laboratory enabled constitutive modelling of dual phase steels

Accurate and efficient characterization and modelling of deformation responses are critically essential in the development of advanced metal forming processes. This work presents a virtual laboratory enabled constitutive framework for modelling complex deformation responses of dual phase (DP) steels under complex stress states, based on multi-phase full-field crystal plasticity (CP) and advanced phenomenological modelling. In the CP based virtual testing method, kinematic hardening and degradation of elastic modulus are modelled in particular to improve the capability for describing evolving microstructure induced mechanical responses of DP steels. The workflow of this framework is completely built and numerically implemented, including (i) representative volume element (RVE) generation based on microstructure characterization, (ii) identification of multiphase CP model parameters, (iii) prediction of elastic modulus degradation, (iv) prediction of yield stresses and plastic potentials in uniaxial tension and biaxial tension with various stress ratios, and (v) prediction of stress–strain curves in reverse tension compression. Using DP780 and DP980 as case materials, the corresponding physical experiments are conducted to verify the accuracy of the virtual tests, showing a good agreement between the virtual and experimental approaches. Both experimental and virtual tests are used to calibrate advanced phenomenological constitutive models that include non-linear elasticity, anisotropic yielding, and kinematic hardening. The calibrated models are implemented into the finite element (FE) codes to predict complex deformation and springback behaviours of DP780 and DP980 sheets in U-bending processes. In comparison with forming experiments of U-channel parts, the virtually calibrated models are validated and show good performance in predicting deformation and springback behaviours, providing a high capability for process analysis. The findings support that the virtual laboratory enabled modelling approach could be a substitute for extensive, expensive, and hard-to-access physically mechanical experiments required in the model calibration for a more effective and efficient analysis of metal forming processes.

Uniaxial ratcheting and ductile damage in structural steel with a stochastic spreading of experimental data

AbstractThis paper provides new experimental data regarding inelastic strain accumulation in structural steel samples. The samples are subjected to stress‐controlled cyclic loading with positive mean stress within each cycle; the loading blocks are combined in a complex pattern to study the effect of load history. A large‐strain ratcheting model is constructed based on a material law with a nonlinear kinematic and isotropic hardening. A new rule of ductile damage accumulation is suggested and a class of models with hardening stagnation is introduced. We show that models which include the hardening stagnation describe the experimental data more accurately. Unfortunately, due to a large spread of mechanical properties from sample to sample, it is impossible to describe the entire set of experiments using a single set of parameters. To address this challenge, we have developed novel mathematical tools for parameter identification in the context of stochastic variations in mechanical properties. These tools include the concept of a collar of model responses and the notion of protrusion. We propose an extended parameter identification problem that rethinks the standard error functional. We demonstrate that the extended identification problem effectively accounts for the large spread observed in experimental data when applied to the developed ratcheting model.

On the simulation of the small punch creep test—applied to 316L(N) austentic steels

ABSTRACT This paper describes a numerical analysis to predict the deformation and time to rupture of the small punch creep test for 316 L(N) austenitic steel. The constitutive model incorporates elasto-plastic nonlinear kinematic hardening and creep with primary, secondary and tertiary creep calibrated to the RCC-MRx code data. The computations are assessed by comparing with experimental data for a 500 µm thick sample clamped with a diameter of 5 mm loaded with a force 300,400 and 500N at 700°C. The model predicts the experimental observations quite well with respect to minimum deflection rate and time to rupture and its location using a local critical strain criterion. A very important feature is that the deformation and total effective strain distribution at rupture are almost identical for all loads as function of the time divided by the time to rupture.

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.

A dual-scale elasto-viscoplastic self-consistent model for the cyclic behavior of polycrystalline materials considering combined nonlinear kinematic hardening

A dual-scale elasto-viscoplastic self-consistent model for the cyclic behavior of polycrystalline materials considering combined nonlinear kinematic hardening

A Back-stress deconvolution method towards modelling of low cycle fatigue behavior of type 316L(N) stainless steel at room temperature

A novel back-stress deconvolution method based on nonlinear-kinematic hardening plasticity theory is proposed to determine the minimum number of back-stresses required to model the low cycle fatigue (LCF) hysteresis loops of 316L(N) stainless steel at room temperature. The deconvoluted back-stresses at different threshold plastic strains corroborate that, three back-stresses can simulate the back-stress vs plastic strain response for all cycles at ± 0.6 % strain amplitude. The variation of kinematic hardening parameters with cycles indicates dynamic evolution of material microstructure and gross microstructural heterogeneity during LCF. The simulated stress–strain hysteresis loops show excellent match with the experiments.

Quasistatic anisotropic induced behaviour of a tatb-based plastic-bonded explosive

The constitutive law of a plastic-bonded explosive (PBX) based on TATB crystals is studied in the quasistatic loading range. The experimental data highlight a viscoelastic behaviour with damage, and an anisotropy induced by plastic flow. The existing models for PBXs being not appropriate, a constitutive law accounting for the observed mechanisms is proposed. The linear viscoelasticity is integrated in a microplane model describing an effective anisotropic damage. A multilayer viscoplasticity is used to yield a non-linear kinematic hardening. A von Mises yield criterion is defined on each surface and a dilatancy function describes the volumetric plastic yield. This law is implemented in the Abaqus/Standard finite element code in the form of a UMAT subroutine. The model is calibrated on ten tests. The simulations performed to compare the model to each experimental test correctly reproduce the behaviour of the studied explosive composition.

On the effect of microplasticity on crack initiation from subsurface defects in rolling contact fatigue

This work demonstrates numerically how microplasticity, i.e. the yielding behavior below the conventional 0.2% plastic strain threshold, can lead to initiation of cracks at subsurface defects, in rolling contact applications operating under realistic loads. A 3D elasto-plastic finite element model is employed to perform shakedown analysis of the bearing steel around a small spherical void with two different approximations of the steel constitutive behavior at the plastic micro-strain regime. When non-linear kinematic hardening is used to model a fast but smooth onset of plasticity, the fields of plastic strains and micro-residual stresses around the void evolve very distinctly to the case where a sharp transition is assumed. To further investigate the role of the tensile micro-residual stresses occurring in the former case on crack initiation, a planar circular crack is inserted at the equator of the void and an entire overrolling cycle is investigated by means of linear elastic fracture mechanics (LEFM). This analysis is repeated for different crack sizes and the respective stress intensity factors and their amplitudes, relevant for crack growth, are reported. The work also reports implementation details for the coupling of a 3D elasto-plastic model for shakedown analysis to a subsequent LEFM analysis model.

Constitutive modelling of plastically deformable self-healing materials

A novel elasto-plastic constitutive model of self-healing materials is proposed coupling continuum damage–healing mechanics (CDHM) framework with kinematic and isotropic hardening cases. A novel secondary damage internal variable is presented, eliminating an assumption in the existing literature that the healed area does not undergo damage again, thus improving the existing CDHM framework. The necessity of the proposed secondary damage variable is successfully demonstrated by a four spring material model. The improved CDHM framework is coupled with the three-dimensional elasto-plastic formulation containing nonlinear kinematic hardening and isotropic strain hardening effects. The proposed formulation is finally numerically implemented by return mapping approach employing the strain energy equivalence hypothesis from CDHM, and the macro-scale stress update is performed applying several different strain histories. A continuum tangent modulus expression is also derived, and a boundary value problem is successfully solved employing an in-house developed plane strain nonlinear finite element code. It is finally demonstrated, by the numerical results, that the secondary damage variable is crucial while obtaining the physically realistic stress–strain response of self-healing materials leading to the complete failure upon exhaustion of the healing capabilities.

Solid solution induced back-stress in multi-principal element alloys: Experiment and modeling

The kinematic and isotropic hardening behavior was investigated for high and medium entropy alloys with a single-phase face-centered cubic (FCC) structure. The cross-slip associated with screw dislocations in FCC structures is strongly influenced by local fluctuations in the spatial distribution of different atom species. The local atomic arrangements inhibit the movement of Shockley partial dislocations during plastic deformation, thereby lowering the probability of cross-slip and generating a higher back-stress. This study used a solid-solution induced back-stress model, which combines nonlinear kinematic and isotropic hardening, to investigate the effects of dislocation forest stress and back-stress in a non-equiatomic Cr12Fe42Mn24Ni22 medium entropy alloy. Based on the experimental results, numerical simulations by the finite element method were performed to validate this modeling approach.

Cyclic Behavior of Material after Single Loading of Cavitation Peening

Cavitation peening has great potential to gain popularity over shot peening in industrial applications for improving the fatigue performance of materials. Improvement in fatigue performance occurs due to the introduction of compressive residual stress. However, the roughening of the surface caused by cavitation peening remains a matter of concern. It has not been investigated adequately in the literature. The cyclic behavior of a material is well known to be adversely affected by surface roughness. An experimental investigation is quite tricky for exploring the underlying role played by the surface roughness and the residual stress. Thus, the current study aims at the numerical investigation of the cyclic behavior of material after cavitation peening load. The 304L austenitic stainless steel has been considered for the present investigation. Finite element simulations (3D) were performed in ABAQUS considering combined non-linear isotropic and kinematic hardening behavior along with ductile damage model. The cavitation peening load is represented by a Gaussian profile defined by peak pressure and radial extent. The effect of cavitation peening (single load) on the material’s elasto-plastic response and subsequent fatigue behavior is studied. The increment in the peak pressure (or the decrement in the radial size) of the peening load is found to shift the maximum stress/strain and damage initiation site from the sub-surface to the surface region. Moreover, the cyclic loading is found to unify the stress distribution along the depth near the surface.

Cyclic Behavior of Simple Models in Hypoplasticity and Plasticity with Nonlinear Kinematic Hardening

The paper gives insights into modeling and well-posedness analysis driven by cyclic behavior of particular rate-independent constitutive equations based on the framework of hypoplasticity and on the elastoplastic concept with nonlinear kinematic hardening. Compared to the classical concept of elastoplasticity, in hypoplasticity there is no need to decompose the deformation into elastic and plastic parts. The two different types of nonlinear approaches show some similarities in the structure of the constitutive relations, which are relevant for describing irreversible material properties. These models exhibit unlimited ratchetting under cyclic loading. In numerical simulation it will be demonstrated, how a shakedown behavior under cyclic loading can be achieved with a slightly enhanced simple hypoplastic equations proposed by Bauer