Kinematic Hardening Parameters Research Articles

Cyclic behavior and constitutive relations of HRB400E steel under large strain range

To study the differences in material performance between HRB400E steel and conventional strength steel, this paper performed monotonic and cyclic loading tests on HRB400E and Q355B steels under a series of loading protocols. Additionally, the self-designed fixtures were used to achieve large strain rate loading. The ductility, monotonic behavior and hysteretic characteristics of HRB400E and Q355B steels were assessed, along with the energy dissipation capacity evaluated through the energy dissipation coefficients. The cyclic skeleton curves of both steels were fitted using the Ramberg-Osgood model, with further investigation into the influence of kinematic hardening parameters on hysteretic curves. The combined hardening parameters of the Voce-Chaboche model were calibrated based on the experimental results, and the hysteretic curves were simulated under different loading protocols via ANSYS. The analysis results reveal that the energy dissipation coefficients of HRB400E steel are larger than that of Q355B steel, yet smaller than those of Q460D, LYP100, LY100, LY160, and LY225 steels. Both HRB400E and Q355B steels demonstrate significantly improved material strength under cyclic loading. Excellent agreement between simulated and experimental curves is achieved when using four pairs of kinematic hardening parameters. Additionally, the hysteretic performance of HRB400E and Q355B steels under different cyclic loading protocols can be precisely simulated by employing calibrated combined hardening parameters. Through this paper, the cyclic behavior and constitutive relations of HRB400E steel are comprehensively understood, which provides a reliable theoretical basis for engineering design and structural analysis. Furthermore, this research provides a scientific basis for material applications of HRB400E steel.

Residual Stresses in Surgical Growing Rods.

The treatment of early-onset scoliosis using surgical growing rods suffers from high failure rate. Fatigue resistance can be improved by inducing compressive residual stresses within the near surface region. An in-depth investigation of the residual stresses profile evolution is performed through the sequence of material processing steps followed by surgeons handling operations, in connection to material properties. The final goal is to guide further improvements of growing rod lifetime. Residual stress evaluation was carried out on Ti6Al4V rods using digital image correlation applied to micro-beam ring-core milling by focused ion beam. This provided experimental stress profiles in shot-peened rods before and after bending and demonstrated that compressive residual stresses are maintained at both concave and convex rod sides. A finite element model using different core and skin conditions was validated by comparison to experiments. The combination of an initial shot peening profile associated to a significant level of backstress was found to primarily control the generation of compressive stresses at the rod surface after bending. Guidelines to promote larger compressive stresses at the surface were formulated based on a parametric analysis. The analysis revealed the first order impact of the initial yield strength, kinematic hardening parameters and intensity of the shot peening operation, while the bending angle and the depth of shot peening stresses were found to be of minor importance. Materials exhibiting large kinematic hardening and low yield strength should be selected in order to induce compressive residual stresses at key fatigue initiation location.

A method to calculate seismic behavior of a corroded beam-to-column joint considering distribution randomness of corrosion depth

When conventional uniform corrosion method and equivalent material property method are applied to predict the seismic performance of corroded steel beam-to-column joints, distribution randomness of corrosion depth can't be considered, once damage occurs at a position where there is a large corrosion pit, there will be a great error between the actual damage and the damage predicted by the two methods. The current work aims to overcome this problem. Firstly, accelerated corrosion test was conducted on mild steel coupons. Secondly, topography of the corrosion pits was scanned, and distribution characteristic of the corrosion depth was obtained. According to the distribution characteristic, a FE modeling method (namely, stochastic corrosion method) that considers distribution randomness of the corrosion depth was proposed. The proposed method, together with uniform corrosion method and equivalent material property method were then applied on the seismic performance prediction of a corroded steel beam-to-column joint. The results show that 1) The depth of the corrosion pits on the specimens subjected to accelerated corrosion approximately obeys lognormal distribution. 2) The corroded steel beam-to-column joints' hysteretic behavior predicted by stochastic corrosion method is more accurate than those predicted by the other two methods. Compared with uniform corrosion method, the maximum calculation accuracy improvement of stochastic corrosion method can reach 90%. 3) The reason which leads to prediction error of uniform corrosion method is that localized buckling of some positions on the structural member is overlooked, while the reason leads to prediction error of equivalent material property method is that the kinematic hardening parameter C is assumed to increase with the increase of corrosion time period. Both the prediction errors of the two methods increase with the increase of corrosion time.

Comparison of the continuum damage and fracture mechanics in fatigue assessment of components containing residual stresses

In the present study, the fatigue crack growth life of standard and smooth notched specimens containing residual stresses are evaluated based on the continuum damage and fracture mechanics approaches. It is indicated that fatigue crack growth lives assessed by the continuum damage model are closer to the experimental results, with a difference of <10% in the specimens containing residual stresses. The total stress intensity factor range is used to consider the effects of residual stresses in the estimation of fatigue crack growth life based on the fracture mechanics. It is found that in existing residual stresses, the stress intensity factor is not a proper parameter to evaluate crack tip zone. Fatigue crack initiation life is experimentally obtained based on assessing variations of the slope of unloading curve in the force-displacement diagram of fatigue experiments. The cycle including a change in the slope is considered as fatigue crack initiation event. Isotropic and kinematic hardening parameters of ASTM A516 pressure vessel steel are considered in finite element analyses. Tensile residual stresses are introduced into the notched specimens by employing four-point-bending with a magnitude of around 90% of the yield stress of the material. The results indicate that at least 65% of the fatigue life of the specimens is decreased due to the presence of tensile residual stresses. Tensile residual stresses are measured using the hole-drilling technique.

Application of continuum damage mechanics in fatigue assessment of A516 steel specimens considering residual stresses

The present study evaluates the effects of tensile residual stresses on fatigue behaviour of ASTM A516 pressure vessel steel specimens. In this regard, fatigue specimens containing a smooth notch region are studied. A damage coupled elastic-plastic constitutive material model is developed to investigate effects of residual stresses on fatigue life. Isotropic and kinematic hardening parameters of the material are experimentally determined. Additionally, the damage model parameters are specified from fatigue experiments conducted on standard specimens in different stress ratios. Tensile residual stresses are introduced into the smooth notched specimens through employing four-point-bending method. The hole drilling technique is utilized to measure the residual stress magnitudes. The results indicate that about two third of fatigue life of the specimens is decreased due to the existed tensile residual stresses. Furthermore, fatigue crack initiation and propagation behaviour in the specimens containing residual stress are studied based on the developed continuum damage model.

Parameter Identification of Chaboche Model for Aluminum Alloy Sheets Based on Differential Evolution Algorithm

Springback prediction is one of the most challenging in finite element analysis for sheet metal forming processes. The demand requests the development of a kinematic hardening model and parameter identification. This study presents a schematic strategy to identify parameters of Chaboche’s kinematic hardening model based on a differential evolution optimization method. To this goal, several tension-compression (TC) tests were conducted to observe the Bauchinger’s effects and kinematic hardening behaviors of two aluminum alloy sheets: AA6022-T6 and AA7075-T76. A Python code is developed to apply the proposed method in identifying parameters of the kinematic hardening model. The calibrated material models were implemented in Abaqus software to simulate V-bending and U-bending tests for the investigated materials. The predictions for springback amount match well with the experimental measurements, which verifies the effectiveness of the presented identificationstrategy.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

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.

Constants and parameters of the damage accumulation model with isotropic and kinematic hardening for 25Cr1Mo1V steel

This article describes the methodology for determining the parameters and constants of the Lemaitre-type damage model based on 25Cr1Mo1V steel. The model implements the Voce isotropic hardening and Armstrong-Frederick kinematic hardening laws. The algorithm for identifying constants and parameters is based on standard uniaxial tension tests to describe isotropic hardening, and low-cycle fatigue tests to determine damage model constants and kinematic hardening parameters. The method is valid for all alloys whose behavior patterns can be described by the presented model representations. On the basis of the found constants and parameters, cyclic loading of cylindrical specimens was simulated with the finite element method and a fatigue curve for 25Cr1Mo1V steel was obtained. A good agreement between the experimental and predicted fatigue life was achieved.

Seismic performance of welded flange plate (WFP) connections in composite steel structures

This paper studies the seismic behavior of welded flange plate (WFP) connections of steel beams to H-shaped columns with composite floors. Nonlinear finite element models of exterior beam-column connections under monotonic and quasi-static cyclic loadings are developed in ABAQUS commercial software. Geometric, material, and contact nonlinearities are considered in the models, and the specimens are loaded up to the final failure point. The von-Mises J2-plasticity model with bilinear kinematic hardening and ductile damage parameter is employed to simulate steel constitutive behavior, and reinforced concrete is modeled by the Concrete Damage Plasticity (CDP) model enhanced with embedded steel rebars. Load-carrying capacity, ductility, failure modes, strain distribution, and energy dissipation capacity of the specimens are compared, and various effects of composite action are studied. The research represents the importance of considering the composite action in the design process, which contrasts with the common practice. Based on these observations, a novel reduced beam section detailing is proposed, which circumvents the issues with current design configurations, and provides an optimal seismic behavior for WFP composite connections.

Laser Shock Peening Induced Back Stress Mitigation in Rolled Stainless Steel

Abstract Laser shock peening (LSP) is investigated as a potential tool for reducing tensile back stress, shown here applied to rolled and annealed 304L austenitic steel. The back stress of treated and untreated dog-bone samples is extracted from hysteresis tensile testing. Electron back-scatter diffraction (EBSD) and orientation imaging microscopy (OIM) analysis quantify the geometrically necessary dislocation (GND) density distribution of unstrained and strained as well as unpeened and peened conditions. Finite element analysis (FEA) simulation models back stress and residual stress development through tensile testing and LSP treatment using known LSP pressure models and Ziegler's nonlinear kinematic hardening law. Nonlinear regression fitting of tensile testing stress–strain in as-received specimens extracts the kinematic hardening parameters that are used in numerical study. This research shows LSP may be used to overcome manufacturing design challenges presented by yield asymmetry due to back stress in rolled steel.

Improvement of the Arcan Setup for the Investigation of Thin Sheet Behavior Under Shear Loading

Accurate predictions of thin sheet material springback during forming processes are of great interest in the forming industry. However, thin sheets are susceptible to buckling under shear loading. The present research aims at improving the so-called Arcan setup for testing thin (1-5 mm) sheet samples with large gauge areas (i.e., width about 21 mm) by introducing anti-buckling devices to mitigate sample buckling. Three monotonic and one cyclic shear tests were carried out on 1 mm thick C60 high carbon steel. The use of the proposed anti-buckling device resulted in the suppression of sample buckling. Numerical analyses of the experiment where buckling was eliminated revealed predominant shear stress states in the gauge area (i.e., stress triaxiality = 0), which highlights minor influences of the anti-buckling device on the sample stress state. To suppress buckling, the use of anti-buckling devices was essential. Moreover, the friction coefficient between the sample and the proposed devices was calibrated ( $$\mu = 0.33$$ ) in addition to kinematic hardening parameters.

Finite Element Simulation Technique for Evaluation of Opening Stresses Under High Plasticity

Abstract The crack closure phenomenon is important to study as it estimates the fatigue life of the components. It becomes even more complex under low-cycle fatigue (LCF) since under LCF high amount of plasticity is induced within the material near notches or defects. As a result, the assumptions used by the linear elastic fracture mechanics (LEFM) approach become invalid. However, several experimental techniques are reported on the topic, the utilization of numerical tools can provide substantial cost and time-saving. In this study, the authors present a finite element simulation technique to evaluate the opening stress levels for two structural steels (25CrMo4 and 30NiCrMoV12) under low-cycle fatigue conditions. The LCF experimental results were used to obtain kinematic hardening parameters through the Chaboche model. The finite element analysis (FEA) model was designed and validated, following the fatigue crack propagation simulation under high plasticity conditions using abaqus. Crack opening displacement versus stress data were exported from abaqus, and 1.5% offset method was employed to define opening stress levels. Numerical simulation results were compared with the experimental results obtained earlier through the digital image correlation (DIC) technique. To conclude, FEA could be a valuable tool to predict crack closure phenomena and, ultimately, the fatigue life of components. However, analysis of opening stresses using crystal plasticity models or extended finite element method (XFEM) tools should be explored for a better approximation in future studies.

Inelastic Material Models of Type 316H for Elevated Temperature Design of Advanced High Temperature Reactors

In this paper, the inelastic material models for Type 316H stainless steel, which is one of the principal candidate materials for elevated temperature design of the advanced high temperature reactors (HTRs) pressure retained components, are investigated and the required material parameters are identified to be used for both elasto-plastic models and unified viscoplastic models. In the constitutive equations of the inelastic material models, the kinematic hardening behavior is expressed with the Chaboche model with three backstresses, and the isotropic hardening behavior is expressed by the Voce model. The required number of material parameters is minimized to be ten in total. For the unified viscoplastic model, which can express both the time-independent plastic behavior and the time-dependent viscous behavior, the constitutive equations have the same kinematic and isotropic hardening parameters of the elasto-plastic material model with two additional viscous parameters. To identify the material parameters required for these constitutive equations, various uniaxial tests were carried out at isothermal conditions at room temperature and an elevated temperature range of 425–650 °C. The identified inelastic material parameters were validated through the comparison between tests and calculations.

A Novel Approach for Determination of Hardening Parameters of an Aluminum Alloy under Cyclic Loading with High Amplitudes

An optimization procedure for the determination of combined nonlinear isotropic/kinematic hardening parameters for strain rate-independent cyclic plasticity has been investigated. With this procedure, it is offered that only nine material parameters, including Young’s modulus, yield stress, Poisson’s ratio, two isotropic hardening parameters, and four kinematic hardening parameters, will be sufficient to perform cyclic plasticity analysis with high accuracy in well-known FE programs (e.g. ABAQUS) even for separate strain range amplitudes. The procedure has been performed to calculate such parameters for aluminum alloy EN AW-6082, which is frequently used in vehicle bodies and simulation results are compared with experiment results. The determined parameters lead highly accurate simulation results in FE routines.

Inverse Method to Determine Fatigue Properties of Materials by Combining Cyclic Indentation and Numerical Simulation

The application of instrumented indentation to assess material properties like Young’s modulus and microhardness has become a standard method. In recent developments, indentation experiments and simulations have been combined to inverse methods, from which further material parameters such as yield strength, work hardening rate, and tensile strength can be determined. In this work, an inverse method is introduced by which material parameters for cyclic plasticity, i.e., kinematic hardening parameters, can be determined. To accomplish this, cyclic Vickers indentation experiments are combined with finite element simulations of the indentation with unknown material properties, which are then determined by inverse analysis. To validate the proposed method, these parameters are subsequently applied to predict the uniaxial stress–strain response of a material with success. The method has been validated successfully for a quenched and tempered martensitic steel and for technically pure copper, where an excellent agreement between measured and predicted cyclic stress–strain curves has been achieved. Hence, the proposed inverse method based on cyclic nanoindentation, as a quasi-nondestructive method, could complement or even substitute the resource-intensive conventional fatigue testing in the future for some applications.

Micromechanics based modelling of fatigue crack initiation of high strength steel

The cyclic behaviour and fatigue crack initiation in low cycle regime of dual phase (DP) steel grade 590 were characterized. Experimental strain-controlled tension–compression tests and corresponding simulations using representative volume elements were carried out. The Chaboche kinematic hardening parameters were determined for each individual phases. The damage model based on accumulated inelastic hysteresis energy was incorporated for describing crack onset mechanism in the microstructure. Damage parameters were calibrated with experimental strain-life curves for crack initiation state. Effects of pre-strain on crack occurrence of steel were studied. Observed crack initiation and its life were well predicted by the proposed modelling scheme.

Numerical Study on the Variability of Plastic CTOD.

This paper presents a numerical study on the influence of material parameters and loading variability in the plastic crack tip opening displacement (CTOD) results. For this purpose, AA7050-T6 was selected as reference material and a middle-cracked tension specimen geometry was considered. The studied input parameters were the Young’s modulus, Poisson’s ratio, isotropic and kinematic hardening parameters and the maximum and minimum applied loads. The variability of the input parameters follows a Gaussian distribution. First, screening design-of-experiments were performed to identify the most influential parameters. Two types of screening designs were considered: one-factor-at-a-time and fractional factorial designs. Three analysis criteria were adopted, based on: main effect, index of influence and analysis of variance. Afterwards, metamodels were constructed to establish relationships between the most influential parameters and the plastic crack tip opening displacement (CTOD) range, based on two types of designs: Face-Centered Central Composite Design and Box-Behnken design. Finally, the metamodels were validated, enabling the expeditious evaluation of the variability in the plastic CTOD range; in addition, the variability in the fatigue crack growth rate was also evaluated.

Effect of kinematic hardening parameters on fatigue crack growth

The parametric study of the effect of material properties on fatigue crack growth (FCG) rarely has been addressed in literature. The consideration of plastic CTOD as crack driving force opened the opportunity to predict FCG rate numerically and therefore to develop parametric studies focused on the effect of loading, geometrical and material parameters. The objective here is to study the effect of kinematic saturation stress, XSat, and kinematic saturation rate, CX, on FCG using this numerical approach. The increase of the kinematic parameters reduced the plastic CTOD and therefore the FCG rate. The variation is non-linear and the rate of variation of δp decreases with the increase of XSat and CX. The effect of the kinematic saturation stress, XSat, is more relevant than the effect of kinematic saturation rate, CX. On the other hand, a small effect of kinematic hardening parameters on crack closure was found. Finally, the increase of the number of load cycles between crack increments produced a great reduction of crack closure but no effect of plastic CTOD on models without contact of crack flanks.

Fuzzy logic enhancement of material hardening parameters obtained from tension\u2013compression test

This paper presents the determination of material hardening parameters with the use of the fuzzy set theory. The hardening parameters were initially predicted from measurements taken in the cyclic tension–compression test. The experimental hysteresis loop was compared to numerical one obtained by the integration of the plastic flow rule. The nonlinear combined hardening model—Voce isotropic hardening and Frederick–Armstrong kinematic hardening—was considered here. After the initial selection, the hardening parameters were adjusted in the optimization problem using the least-squares method. An approximation error of the hysteresis loop was minimized. Finally, nonlinear isotropic and kinematic hardening parameters were assumed to be fuzzy variables. Hardening parameters obtained in the optimization problem were randomly scattered up to 20%, and the membership functions associated with them were computed. The approximation error of the hysteresis loop was found for each selection of the hardening parameters providing the output membership function associated with this error. The upalpha -level optimization method was used as the main numerical tool, while the extension principle was tested only as the reference solution. In the defuzzification process, the most reliable hardening parameters were found.

Basic Kinematic Hardening Rules Applied to 304 Stainless Steel and the Advantage of Parameters Evolution

Cyclic plasticity models for the description of the deformation characteristics of austenitic stainless steel 304 at a room temperature have been studied with the focus on its industrial use. The main objective of this work is to investigate the capabilities of the classical Chaboche model with four terms which is commonly used in practice, and to compare those capabilities with the same model enriched with the evolution of some kinematic hardening parameters. The incorporation of parameters evolution brings significant number of necessary parameters to be determined, compared to the classical Chaboche model with four terms. To overcome excessive number of necessary parameters, also two terms Chaboche model with parameters evolution is used. Presented paper evaluates the time and temperature independent modeling possibilities of Chaboche combined nonlinear kinematic hardening model and isotropic hardening model with von Mises yield criterion.