Cyclic Hardening Model Research Articles

A Direct Method on the Evaluation of Cyclic Steady State of Structures With Creep Effect

This paper describes a new extension of the linear matching method (LMM) for the direct evaluation of cyclic behavior with creep effects of structures subjected to a general load condition in the steady cyclic state, with the new implementation of the cyclic hardening model and time hardening creep constitutive model. A benchmark example of a Bree cylinder and a more complicated three-dimensional (3D) plate with a center hole subjected to cyclic thermal load and constant mechanical load are analyzed to verify the applicability of the new LMM to deal with the creep fatigue damage. For both examples, the stabilized cyclic responses for different loading conditions and dwell time periods are obtained and validated. The effects of creep behavior on the cyclic responses are investigated. The new LMM procedure provides a general purpose technique, which is able to generate both the closed and nonclosed hysteresis loops depending upon the applied load condition, providing details of creep strain and plastic strain range for creep and fatigue damage assessments with creep fatigue interaction.

Constitutive modeling of dense gravelly soils subjected to cyclic loading

SUMMARYA constitutive model for dense gravelly soils was developed to reproduce their responses under cyclic loadings. Its application aims at nonlinear dynamic analyses of earth structures involving gravelly soils, such as rockfill dams and railroad ballasts. The framework of generalized plasticity was modified to incorporate the concept of stress distance for better simulation of unloading and reloading responses. It was then combined with the theory of critical state soil mechanics to develop the constitutive model. The model has the following important features: unified simulation of particle breakage through translating critical state line, smooth transition from unloading to reloading in the stress space, and proper modeling of cyclic hysteresis, cyclic densification, and cyclic hardening of dense gravelly soils. Most of the model parameters can be obtained through simple calculation using conventional triaxial test results, and their calibration process was discussed. The model was used to simulate the cyclic responses of three gravelly soils with satisfactory accuracy. Copyright © 2014 John Wiley & Sons, Ltd.

Evolution of the crystal stress distributions in face-centered cubic polycrystals subjected to cyclic loading

Due to the heterogeneous nature of polycrystalline metals, the stress distribution at the crystal level is influenced by the complex interplay of factors such as the orientations of the crystal lattices, the elastic and plastic mechanical properties, the interactions between neighboring crystals, and the type of loading conditions. In this paper, we investigate the evolution of the crystal scale stress and elastic strain distributions under cyclic loading. More specifically, we examine the orientation dependent lattice strains in face-centered cubic polycrystals under fully reversed, strain-controlled cyclic loading using a cyclic hardening model implemented within a crystal-based finite element formulation. The directional strength-to-stiffness ratio and the single crystal yield surface (SCYS) topology are used to provide a quantitative explanation of the observed hysteresis behavior when the lattice strains are plotted as a function of the macroscopic stress. The directional strength-to-stiffness ratio influences the progression of yielding in the elastic–plastic transition regime, leading to a nonlinear response in the elastic–plastic transition regime and causing hysteresis behavior in the macroscopic stress versus lattice strain curves. The lattice strains after the elastic–plastic transition regime are influenced by the single crystal elastic moduli and the facet/vertex attributes of the SCYS. We found that the same trends hold in the absence of slip system hardening and in the presence of a strong rolling texture.

The Bauschinger effect in the supercooled austenite of SAE 52100 steel

During the heat treatment and the welding of steel components, the interactions between the thermal and phase transformation strains result in cyclic loading of the component, which often results in plastic deformation. Although this has long been a well-known fact, the cyclic hardening behavior of supercooled austenite was not investigated up to now. In this study, tension–compression tests were performed on the supercooled austenite of SAE 52100 ball bearing steel at several temperatures using Gleeble3500® thermomechanical testing machine. The results were compared with conventional hardening models used in heat treatment and welding simulation. The results indicate that the metastable austenite exhibits a complicated cyclic hardening behavior that can only be partially reproduced by commercial simulation software. In the outlook, it is concluded that more complicated cyclic hardening models should be implemented for better prediction of distortion and residual stresses after heat treatment or welding.

A numerical simulation model of cyclic hardening behavior of AC4C-T6 for LNG cargo pump using finite element analysis

This paper is concerned with the evaluation of cyclic hardening models within the stress–strain behavior of aluminum alloy AC4C-T6 that can be used to LNG cargo pump operating in cryogenic temperature. To insure the strength assessment of LNG cargo pump, material model of cyclic hardening and plasticity for aluminum alloy AC4C-T6 is investigated through FEA (Finite Element Analysis) with various hardening options including linear and non-linear hardening, isotropic and kinematic hardening, and combined hardening model. Monotonic tensile and cyclic tensile experiments for AC4C-T6 alloy were performed at room temperature and temperature of −165 °C. Parameters of each hardening model are obtained from the experimental data; thus five hardening models are numerically simulated thereafter. Appropriate hardening models which describe the cyclic stress–strain relationship are investigated through the simulations of cyclic hardening behavior by FEA. In order to verify the predicted behavior of cyclic hardening obtained by FEA, the results of FEA and those measured by experiments are compared.

Extremely low cycle fatigue tests on structural carbon steel and stainless steel

Cyclic material tests in the low and extremely low cycle fatigue regime were carried out to study the properties of structural carbon steel and stainless steel. A total of 62 experiments were performed in cyclic axial and bending configurations, with strain amplitudes up to ±15%. Materials from hot-rolled carbon steel (S355J2H), cold-formed carbon steel (S235JRH) and cold-formed austenitic stainless steel (EN 1.4301 and EN 1.4307) structural sections were tested and the results were compared. The strain–life data from the axial tests were used to derive suitable Coffin–Manson parameters for the three materials; two further extremely low cycle fatigue life prediction models were also considered. The results revealed that the three materials exhibit similar strain–life relationships despite significantly different elongations at fracture measured in monotonic tensile tests. The hysteretic responses of the materials at different strain amplitudes were used to calibrate a combined isotropic/kinematic cyclic material hardening model which can be incorporated into numerical models of structural members. The stainless steel specimens displayed significantly greater levels of cyclic hardening than the corresponding carbon steel samples. A relationship between the results obtained from axial and bending test arrangements was established through consideration of energy dissipation, enabling strain–life models to be derived from either means of testing.

지진시 지반의 반복경화/연화 현상에 의한 부지응답 특성 영향 연구

본 논문에서는 반복하중에 의한 반복 경화 및 연화 현상을 나타낼 수 있는 수정 IWAN 모델을 이용하여, 1차원 비선형 부지응답 해석프로그램(이하 KODSAP; Kaist One Dimensional Site-response Analysis Program)을 개발하였다. 개발된 프로그램은 지진하중 재하에 따른 지반의 반복경화 및 연화현상에 의한 부지응답 특성 변화를 재현할 수 있다. KODSAP을 이용하여 기반암 상부 40m인 모형지반의 반복경화 및 연화 정도, 지진가속도의 크기에 따른 부지응답특성 변화를 살펴 보았으며, 현재 실무에서 널리 적용되고 있는 등가선형, 비선형해석과 KODSAP 해석결과(지반의 반복경화 및 연화현상을 고려한)과의 차이점을 살펴 보았다. A one-dimensional site response analysis program (KODSAP) was developed using cyclic soil behavior model by using the modified parallel IWAN model. The model is able to predict the cyclic hardening and degradation of soil through the adjustment of the internal slip stresses of its elements beyond the cyclic threshold, and satisfies Bauschinger's effect and the Masing rule in terms of its own behavior characteristics. The program (KODSAP) used the direct integration method in the time domain. The elasticity of the base rock was considered as a viscous damper boundary condition. The effects of cyclic hardening or degradation of soil on site response analysis were evaluated through parametric studies. Three types of analyses were performed to compare the effect of analysis and cyclic parameter on site response. The first type was equivalent linear analysis, the second was nonlinear analysis, and a third was nonlinear analysis using the cyclic hardening or degradation model.

Strain localization and damage prediction during sheet metal forming

This work aims to study the strain localization in different sheet metal forming processesby the finite element method using advanced behaviour models. In order to improve the prediction of the formability limit of sheets under forming it is important to consider constitutive models that take into account the degradation of material properties due to large strain localization. For this purpose, an elastic-plastic model has been coupled with the classical damage model of Lemaitre and Chaboche [2, 3]. Two hardening models are considered in an attempt to more accurately reproduce the work-hardening phenomenon at large strains. The first one represents the classical cyclic hardening model of Chaboche-Marquis [3, 4] while the second corresponds to the so-called dislocation-based microstructural model of Teodosiu and Hu [5, 6]. These two models are able to reproduce some transient hardening phenomena at strain path changes – with a better description obtained with the microstructural model. The coupling with damage is carried out within the framework of continuum damage mechanics thanks to the introduction of a scalar variable describing the degradation of the elastic proprieties and consequently softening behaviour when damage occurs. The coupled elastic-plastic damage model is implemented into the Abaqus software using an implicit integration scheme. The resulting code is used for the prediction of forming limit diagrams.

A Consistent Soil Fatigue Framework Based on the Number of Equivalent Cycles

Cyclic soil degradation and hardening affects soil stiffness and strength, and is linked to an increase or decrease in the mean effective confining stress due to void ratio or pore pressure changes. This change of state can be explicitly modeled by using effective stress methods, or implicitly modeled using total stress methods. In the latter, this is achieved by using empirical functions based on the number of loading cycles that are derived from constant-amplitude stress or strain laboratory tests. To suite generalized loading conditions, these functions must be extrapolated to variable-amplitude loading. This falls under the general class of a fatigue-based problem. The main focus of this paper is to present a generalized consistent soil fatigue formulation for soils under cyclic loading. The paper then goes on to discuss the implementation of various cyclic soil degradation and hardening models reported in the literature, and highlights their important underlying assumptions, capabilities and limitations.

Improvement on the Modeling of Rate-Dependent Plasticity and Cyclic Hardening by Bodner-Partom Model

An additional isotropic internal variable is utilized to extend the Bodner Partom unified viscoplastic constitutive model(original B-P) to improve the modeling of rate dependent plasticity and cyclic hardening behaviors of metals. The extended model (new B-P) contains two isotropic internal variables: one plays the role of representing the fast hardening in smaller inelastic strain range, while the other evolutes at slower speed accompanied by larger accumulated inelastic deformation, such as cyclic hardening. To examine the validity of the extended constitutive model, the rate dependent plasticity of a Ni-base superalloy Udimet 720Li at 650°C and 700°C are characterized using both models. Not only numerical simulations are conducted for various loading conditions by implementing both models into ABAQUS using a user material subroutine, also a systematic comparison between two models is completed. Numerical results show that the extended material constants in the new model provide more flexible capability in modeling the inelastic behavior of the material with sound accuracy.

Integrity assessment of a 3D tubeplate using the linear matching method. Part 2: Creep relaxation and reverse plasticity

In an accompanying paper [Int J Pres Ves Pip, 2004], a 3D tubeplate in a typical AGR superheater header was analysed for the shakedown limit, reverse plasticity and ratchet limit based on the application of the linear matching method (LMM). Both the perfectly plastic model and the cyclic hardening model were adopted for the evaluation of the plastic strain range. In the present paper, based on the creep-reverse plasticity model, the accumulated creep strain during a creep dwell at the steady cyclic state is assessed by the LMM. The accumulated creep strains, the creep flow stresses as well as the elastic follow-up factors with differing dwell times are evaluated in detail. The total inelastic strain over the cycle at the steady cyclic state is calculated. By comparing these results with ABAQUS step-by-step inelastic analyses, the applicability of the methods is demonstrated.

Integrity assessment of a 3D tubeplate using the linear matching method. Part 1. Shakedown, reverse plasticity and ratchetting

The Linear Matching Method (LMM) has been developed recently for the integrity assessment for the high temperature response of structures. In this article, a complex 3D tubeplate in a typical AGR superheater header is analysed for the shakedown limit, reverse plasticity and ratchet limit based upon the LMM. At this stage, both the perfectly plastic model and the cyclic hardening model are adopted for the evaluation of the plastic strain range. Comparisons of LMM results with other results by ABAQUS step-by-step inelastic analyses for several material models are given. Further cyclic creep-reverse plasticity analyses are presented in an accompanying paper [Int. J. Pressure Vessels Piping (2004)].

Constitutive modeling of strain range dependent cyclic hardening

In this paper, a new approach for constitutive modeling of strain range dependent cyclic hardening is proposed by extending the kinematic hardening model based on the critical state of dynamic recovery. It is assumed that isotropic, as well as kinematic, hardening consists of several parts, and that each part of isotropic hardening evolves when the corresponding part of kinematic hardening is in the critical state of dynamic recovery. The extended model is capable of simulating the cyclic hardening behavior in which different characteristics of cyclic hardening appear depending on strain range. The model is verified by simulating the relatively large cyclic straining tests of 304 stainless steel at ambient temperature, in which cyclic hardening does not stabilize before rupture if strain range exceeds a certain value. The model is further verified by predicting the history dependence of cyclic hardening under incremental cyclic loading and the maximum plastic strain dependence of strain hardening in cyclic tension.

Representation of cyclic hardening and softening properties using continuous variables

Abstract Our aim is the modeling of cyclic hardening, cyclic softening, cyclic mean stress relaxation, and additional nonproportional cyclic hardening. We do so by means of hardening functionals for back stress and yield stress without employing additional memory surfaces. Rather, we suppose all quantities to evolve simultaneously during elastic-plastic loading in a continuous manner. The basic idea is to formulate evolution equations for the hardening variables, which are of the “hardening/dynamic recovery” format with respect to a transformed arc length. The corresponding transformation is influenced by continuously evolving parameters, measuring strain amplitude and nonproportionality during the recent process history. Although the resulting, model has a very simple structure, it is capable of describing the basic phenomena under quite general loading conditions.

Viscoplasticity theory based on overstress: the modeling of ratchetting and cyclic hardening of AISI type 304 stainless steel

At room temperature, annealed AISI type 304 stainless steel exhibits rate dependence that manifests itself in rate sensitivity, creep and relaxation. It is also the driving force behind incremental elongation under zero-to-tension load-controlled loading, called ratchetting. It is shown to increase with decreasing stress rate and is independent of stress rate sequence. Accumulated ratchet strain has the same hardening effect as the strain in a monotonic test. For cyclic loading with load or strain reversal, significant cyclic hardening is observed. It is well known that this hardening depends on the path and seems to be most pronounced under 90° out-of-phase cycling. Other paths show various degrees of cyclic hardening. At the same effective strain range, the hardening under nonproportional loading is much more pronounced than under proportional loading. Experiments show that the rate sensitivity is, as a first approximation, unchanged by the significant hardening, which is therefore rate independent. The small-strain, isotropic viscoplasticity theory based on overstress (VBO) is used to model these phenomena. The theory is of the unified type and does not employ yield or loading/unloading criteria. The inelastic strain rate is a function of the overstress, the difference between the stress and the equilibrium stress, which is a state variable of the theory. Its growth law is the repository for modeling nearly elastic regions and hysteresis. Under constant strain rate loading, the theory admits asymptotic solutions, which show that the stress is composed of viscous, rate-independent (plastic) and kinematic contributions. For the modeling of cyclic hardening, a growth law for the rate-independent contribution to the stress is formulated. It models a different type of growth for proportional and nonproportional as well as cyclic and monotonic loadings. Numerical experiments for homogeneous states of stress are performed by integrating the stiff, nonlinear ordinary differential equations using the IMSL routine DGEAR. They demonstrate the modeling capabilities for step-down and step-up two-amplitude loadings, for proportional and nonproportional cyclic loadings including elliptical and square paths as well as for ratchetting.

Effect of Temperature Variation on Cyclic Elastic-Plastic Behavior of SUS 304 Stainless Steel

Abstract The cyclic elastic-plastic behavior of SUS 304 stainless steel was investigated experimentally under various temperatures and temperature-changing conditions. The specimens were cyclically loaded between fixed axial strain limits at constant temperatures in the range from room temperature to 600°C. The effects of the cyclic strain amplitude on the saturation property of cyclic hardening were obtained at various temperatures. The effects of temperature variations on the cyclic hardening were examined under the temperature conditions of changing between two different temperatures. From these experimental results, the effects of the temperature variation on the saturation properties were found under several temperature conditions. The three different hardening models accounting for these cyclic hardening properties were proposed. The experimental results were compared with the results calculated by those three cyclic hardening models.

The Bauschinger effect and cyclic hardening in copper

The Bauschinger Effect and cyclic hardening were studied during the first few cycles in copper single crystals of an “easy glide” orientation. Dislocation etch pitting was used to augment the mechanical measurements. It was found that significant rearrangements of the dislocation distribution occurred during stress reversal. Sharply defined kink bands which formed during forward straining broadened, and the overall dislocation distribution became more uniform during subsequent cyclic deformation. For cycling at constant strain amplitude, it was found that hardening above the prestress level occurred almost as rapidly as during unidirectional deformation. However, the absence of hardening during increments of Bauschinger strain yielded anomalously low hardening in terms of the cumulative strain. A cyclic hardening model is proposed in which the Bauschinger strains below the prestress level result from relaxation of internal stresses whereas “hardening strains” occur only above the prestress level. The non-symmetry, which causes higher Compressive stresses than tensile stresses during cycling at constant strain amplitude, is shown to result from larger Bauschinger strains below the prestress levelduring tensile half-cycles. Cell sizes and bundle spacings reported in the literature for cyclic tests have been correlated with the corresponding flow stresses and are consistent with predictions of the Long Range Stress Theory.