Cyclic Plasticity Model Research Articles

Cyclic plasticity model for fatigue with softening behaviour below macroscopic yielding

Experimental observations have evidenced the insufficiency of yield surface definition via monotonic loading to guarantee adequate description of material behaviour under fatigue tests. Therefore, mechanical property characterisation through simple experimental tests such as uniaxial monotonic extension/compression is favoured, considering different responses due to cyclic loading. Herein, a phenomenological cyclic plasticity model is formulated to capture the correct generation of plastic deformation under cyclic loading conditions, even for stress states lower than the yield stress. The unconventional extended subloading surface model is modified to include an additional internal variable describing the strain-softening phenomenon typical of low- to high-cycle fatigue problems. Implicit integration strategies, in the form of the cutting-plane and closest projection point return mapping algorithms, are implemented to reduce the computation time. The solution accuracies are compared to that of a forward Euler integration scheme, and exhibit fast and accurate performance.

Understanding strain controlled low cycle fatigue response of P91 steel through experiment and cyclic plasticity modeling

In this paper, constitutive models for cyclic plasticity, namely, Chaboche and the Ohno-Wang models, are used to simulate the low cycle fatigue response of tempered ferritic-martensitic P91steel. A series of uniaxial strain-controlled low cycle fatigue tests are conducted at room temperature to evaluate various fatigue parameters. P91 steel shows cyclic softening behavior at all strain amplitudes. The analysis of the shape of hysteresis loops reveals that P91 steel deviates from Masing behavior. Plastic strain energy is used as a parameter to characterize the fatigue damage. The Morrow energy model estimates experimental average plastic strain energy density accurately. Remnant tensile properties are evaluated to quantify the damage during low cycle fatigue loading. The evaluation of back stress components and material Jacobian are implemented through a user defined subroutine UMAT into the commercial finite element package ABAQUS. Ohno-Wang material model predicts the hysteresis loop shape, area, and cyclic softening nature better than the Chaboche model. The predicted fatigue lives by simulation correlates well with the experimental fatigue lives within ± 200 cycles. These results suggest that energy based parameters can provide a reliable alternative to strain based approach in evaluating the fatigue damage of P91 steel.

Finite Element Implementation of a Temperature-Dependent Cyclic Plastic Model for SA508-3 Steel

A new temperature-dependent cyclic plastic model, combining the nonlinear cyclic softening and kinematic hardening rules is established for a nuclear material of SA508-3 steel. A modified isotropic hardening rule is proposed to capture the temperature-dependent cyclic softening, and a modified kinematic hardening rule is established to improve the prediction of the ratcheting behavior by introducing an exponential function related to the accumulated plastic strain. The stress is updated by the radial return mapping algorithm based on the backward Euler integration. A new expression of consistent tangent modulus for the equilibrium iteration is derived, and then the proposed model is implemented into the finite element software ABAQUS by using the user material subroutine (UMAT) to simulate the temperature-dependent ratcheting behaviors of SA508-3 steel. Finally, the ratcheting evolutions of notched bars at elevated temperature are obtained by uniaxial stress-controlled cyclic tests, and the nonuniform strain fields on the surface of plates with a center hole is measured by using the digital image correlation (DIC) technology. Comparisons between experimental and simulated results of a material point and structural examples show that the implemented model can provide reasonable predictions for ratcheting behaviors and nonuniform strain fields of structures at different temperatures for SA508-3 steel.

Material Modelling in Multi-Physics FEM Simulation

Nowadays virtual prototyping has a great impact in the design process of an industrial component. Numerical techniques based on the Finite Element Method (FEM) are mature to provide computational tools that permit complex phenomena to be accurately simulated, even when dealing with multi-physical problems. This work puts in evidence that an inaccurate assessment of the material properties may compromise the benefit of such complex modelling techniques. For this purpose, firstly the case of thermo-mechanically loaded structures will be presented. Considering fire walls for naval applications, the influence of the rock wool elastic modulus in the safety behavior will be emphasized. In the case of steel making component, the paper proofs that only a correct cyclic plasticity model of the material (copper alloy) permits a durability analysis to be accurately performed. Finally, in the case of an energy-harvesting device, the importance of taking into account the orthotropic properties of the material will be highlighted.

Cyclic plasticity modeling of nickel-based superalloy Inconel 718 under multi-axial thermo-mechanical fatigue loading conditions

High temperature components work mainly under thermo-mechanical loading conditions. Recent investigations reveal significant effects of the thermo-mechanical coupling on material behavior. In the present work, extensive experiments are performed for nickel-based superalloy Inconel 718 under both isothermal and thermo-mechanical loading conditions. Within the framework of the Ohno-Wang cyclic plasticity, a modified constitutive model is suggested to describe cyclic hardening/softening, non-proportional hardening, non-masing effects observed in the experiments. The implicit integration algorithm is developed and implemented into a commercial finite element code. Comparison between experiments and computations confirms that the suggested model can predict the cyclic plastic behavior under most different varying temperatures and multi-axial loading paths reasonably.

A Simplified Transient Hardening Formulation for Modeling Stress–Strain Response Under Multiaxial Nonproportional Cyclic Loading

Accurate estimation of material stress–strain response is essential to many fatigue life analyses. In cases where variable amplitude loading conditions exist, the ability to account for transient material deformation behavior can be particularly important due to the potential for periodic overloads and/or changes in the degree of nonproportional stressing. However, cyclic plasticity models capable of accounting for these complex effects often require the determination of a large number of material constants. Therefore, an Armstrong–Frederick–Chaboche style plasticity model, which was simplified in a previous study, was extended in the current study to account for the effects of both general cyclic and nonproportional hardening using a minimal number of material constants. The model was then evaluated for its ability to predict stress–strain response under complex multiaxial loading conditions by using experimental data generated for 2024-T3 aluminum alloy, including a number of cyclic incremental step tests. The model was found to predict transient material response within a fairly high overall level of accuracy for each loading history investigated.

A cyclic small-strain plasticity model for wrought Mg alloys under multiaxial loading: Numerical implementation and validation

Basal-textured wrought magnesium alloys are inherently prone to mechanical twinning/de-twinning during cyclic deformation at room temperature. They, subsequently, exhibit distinctive flow curve attributes, which are impossible to describe using conventional plasticity models developed for symmetric/isotropic metals, deforming mainly by slip. A continuum plasticity model is herein proposed, in such way that accounts for various asymmetric/anisotropic aspects of cyclic flow response of wrought magnesium alloys. The proposed model entails an isotropic von Mises yield function which evolves in stress space according to a generalized anisotropic kinematic hardening rule, based on Ziegler's rule. The phenomenological concept of plastic moduli matrix introduced in the proposed kinematic rule is viewed as the key factor in representing material yield/hardening behaviour in different directions. The components of this matrix can independently be calibrated by conducting uniaxial cyclic experiments along each direction. An efficient and stable numerical algorithm is developed and then coded into UMAT to use within Abaqus®/Standard finite element software. Thereafter, model validation has been successfully done using proportional and non-proportional biaxial axial-torsional cyclic tests on AZ31B, AZ61A, and AM30 Mg alloy extrusions.

Low-Cycle Fatigue, Fractography and Life Assessment of EN AW 2024-T351 under Various Loadings

The paper provides extensive experiments on aluminium alloy 2024-T351. Those cover the uniaxial strain- and stress-controlled tests using cylindrical specimens. Then, multiaxial tests were conducted via strain- and stress-controlled tensile–torsional loading on tubular specimens, which also cover the following non-proportional test – the 3-step experiment carried out in order to document the additional hardening. The paper also provides a fractography using the scanning electron microscopy and the life assessment. A novel approach to fatigue life prediction is presented, based on replacing the plastic part of the strain-life curve by the non-linear term in order to provide more variability and approximation ability. The broad experimental base will serve as a basis for future calibration and simulation using advanced cyclic plasticity models within the finite elements.

Low cycle fatigue analysis of ferrite-martensite dual-phase steel using advanced cyclic plasticity models

A computational model has been developed to predict the low cycle fatigue (LCF) characteristics of ferrite-martensite dual phase (DP) steel. LCF results of DP steel performed at strain amplitudes varying from 0.3% to 1.5% show initial cyclic hardening followed by cyclic softening behavior. Finite element simulation employing Chaboche model fails to capture the initial cyclic hardening behavior specifically at lower strain amplitudes. To predict the observed cyclic hardening and softening characteristics of DP steel with a progressive number of cycles, Ohno-Wang cyclic plasticity model has been modified by altering the yield function, which is formulated by incorporating a memory stress function. All the material parameters have been calibrated considering hysteresis loop of the first cycle of LCF result of ±1.5% uniaxial strain. The developed material model has been integrated with ABAQUS 6.14 finite element package to perform the LCF simulation. A comparison between simulation and experimental results for all strain amplitudes reveals that the proposed model has the better capability to predict the overall LCF characteristics of DP steel.

A robust frame element with cyclic plasticity and local joint effects

A robust elasto-plastic element is developed for analysis of frame structures. The element consists of a beam member with end joints with properties permitting representation of the effect of section forces in adjoining members, like axial forces. By use of the equilibrium formulation the deformations of beam member, plastic hinges and joints become additive and can be expressed in explicit form. The plastic deformations of the beam and the joints are represented by separate plastic mechanisms, described by the same generic cyclic plasticity format. This format is defined by an energy function, a yield surface, and a plastic flow potential for each plastic mechanism. In the cyclic plasticity model each component is characterized by the elastic stiffness, the yield capacity, the additional flexibility at initial yield, the ultimate capacity and a shape parameter describing the curvature of the hysteresis curve. The yield surface is represented by a recently developed generic format, combining the section forces into a homogeneous function of degree one and permitting smooth transition between regions with large and more moderate curvature. A robust return algorithm of approximately second order is developed, using a mid-step state to obtain representative information about the return path. The element is implemented in a co-rotational large-deformation computer program for frame structures. The formulation is illustrated by application to a couple of typical offshore frame structures, and comparison of different representations of the plastic effects illustrates the importance of a robust element with realistic representation of the cyclic plastic mechanisms.

Experimental and numerical investigation of strain rate effect on low cycle fatigue behaviour of AA 5754 alloy

The present study deals with evaluation of low cycle fatigue (LCF) behavior of aluminum alloy 5754 (AA 5754) at different strain rates. This alloy has magnesium (Mg) as main alloying element (Al-Mg alloy) which makes this alloy suitable for Marines and Cryogenics applications. The testing procedure and specimen preparation are guided by ASTM E606 standard. The tests are performed at 0.5% strain amplitude with three different strain rates i.e. 0.5×10-3 sec-1, 1×10-3 sec-1 and 2×10-3 sec-1 thus the frequency of tests vary accordingly. The experimental results show that there is significant decrease in the fatigue life with the increase in strain rate. LCF behavior of AA 5754 is also simulated at different strain rates by finite element method. Chaboche kinematic hardening cyclic plasticity model is used for simulating the hardening behavior of the material. Axisymmetric finite element model is created to reduce the computational cost of the simulation. The material coefficients used for “Chaboche Model” are determined by experimentally obtained stabilized hysteresis loop. The results obtained from finite element simulation are compared with those obtained through LCF experiments.

Accelerated cyclic plasticity models for FEM analysis of steelmaking components under thermal loads

Steelmaking components are often subjected to thermo-mechanical loads applied cyclically. In this case the choice of a suitable cyclic plastic model to be used in the numerical simulation is a crucial aspect in design. Combined (kinematic and isotropic) model permits the cyclic material behavior to be captured accurately. On the other hand, such model often requires unfeasible computational time to arrive at complete material stabilization. Simplified or accelerated models have then been proposed to make simulation faster. In this work, the thermo-mechanical analysis of a round mold for continuous casting is addressed as a case study. Due to axi-symmetry, a plane model can be adopted. This permits a finite element (FE) analysis with a combined model to be performed until complete stabilization. A comparison with other models able to speed up the simulation (accelerated models with increased values of saturation speed, Prager and stabilized models) was performed. It was found that only accelerated models give equivalent strain range values that do not significantly differ from the (reference) combined model, independently from the speed of saturation adopted.

A new accelerated technique for validation of cyclic plasticity models

This contribution presents a new methodology of fatigue tests evaluation based on digital image correlation application. The full-field strain analysis brings the possibility of 3D strain measurement evaluation on a curved part of specimen standardly used under axial-torsional loading. Resulting strain response curves can subsequently serve for evaluation of cyclic plasticity model predictions. The crucial idea is the way of FE model creation to can evaluate simulation in the same points of the structure as in the DIC measurement. The new methodology saves amount of material and leads to a shorter experimental time.

Modelling of cyclic plasticity and martensitic transformation for type 304 austenitic stainless steel

Isothermal monotonic tension and cyclic tests are conducted on type 304 austenitic stainless steel at 20, 50 and 80 °C from which stress-strain curves and martensite volume fraction were evaluated. The obtained data showed that deformation induced martensitic transformation was highly temperature dependent in monotonic tensile and cyclic tests. In cyclic test, stagnation of martensitic transformation was observed during the Bauschinger region, which imply that the transformation was triggered by austenite stress rather than the plastic strain. Finally, constitutive model based on stress induced hypothesis was proposed and it was validated by comparing the experimental results and the calculation with the conventional Stringfellow model.

A Cyclic-Plasticity-Based Mechanistic Approach for Fatigue Evaluation of 316 Stainless Steel Under Arbitrary Loading

In this paper, a cyclic-plasticity-based fully mechanistic fatigue modeling approach is presented. This is based on time-dependent stress–strain evolution of the material over the entire fatigue life rather than just based on the end of live information typically used for empirical S∼N curve-based fatigue evaluation approaches. Previously, we presented constant amplitude fatigue test based related material models for 316 stainless steel (SS) base, 508 low alloy steel base, and 316 SS-316 SS weld which are used in nuclear reactor components such as pressure vessels, nozzles, and surge line pipes. However, we found that constant amplitude fatigue data-based models have limitation in capturing the stress–strain evolution under arbitrary fatigue loading. To address the aforementioned limitation, in this paper, we present a more advanced approach that can be used for modeling the cyclic stress–strain evolution and fatigue life not only under constant amplitude but also under any arbitrary (random/variable) fatigue loading. The related material model and analytical model results are presented for 316 SS base metal. Two methodologies (either based on time/cycle or based on accumulated plastic strain energy (APSE)) to track the material parameters at a given time/cycle are discussed and associated analytical model results are presented. From the material model and analytical cyclic plasticity model results, it is found that the proposed cyclic plasticity model can predict all the important stages of material behavior during the entire fatigue life of the specimens with more than 90% accuracy.

Resetting scheme for plastic strain surface in constitutive modeling of cyclic plasticity

AbstractA resetting scheme is proposed for correctly evaluating the plastic strain range to analyze structural components subjected to regular cyclic loading following pre‐loading. In this scheme, a plastic strain surface, referred to as the plastic‐strain‐range surface in the present paper, is reset to a point and re‐evolves every cycle, with its size at the end of the last cycle considered to be the plastic strain range of the current cycle. This resetting scheme provides a definite value for the evolution parameter of the plastic‐strain‐range surface irrespective of the amounts of cyclic hardening, pre‐straining, and ratcheting. The resetting scheme is implemented in a cyclic viscoplastic model in finite element methods, and is applied to analyze a notched bar subjected to cyclic loading at its ends. Furthermore, the validity of the resetting scheme for non‐proportional cyclic loading is examined by analyzing the cyclic behavior along elliptic and rhombic strain paths. It is shown that the resetting scheme allows the use of a definite value for the evolution parameter of the plastic‐strain‐range surface in the presence of any cyclic hardening and/or ratcheting. Moreover, it is shown that the resetting scheme can be valid for cyclic loading with a certain degree of non‐proportionality.

Cyclic plasticity using Prager’s translation rule and both nonlinear kinematic and isotropic hardening: Theory, validation and algorithmic implementation

Finite element analysis of structures under elasto-plastic nonproportional cyclic loadings is useful in seismic engineering, fatigue analysis and ductile fracture. Usual models with nonlinear stress–strain curves in cyclic behavior are based on Mróz multisurface plasticity, bounding surface models or models derived from the Armstrong–Frederick rule. These models depart from the associative Prager’s rule with the main purpose of modeling aspects of cyclic nonlinear hardening. In this paper we develop a model for cyclic plasticity within the framework of the associative classical plasticity theory using Prager’s rule accounting for anisotropic nonlinear kinematic hardening coupled with nonlinear isotropic hardening. We include the validation of the theory against several uniaxial and multiaxial cyclic experiments and an efficient fully implicit radial return algorithm. The parameters of the model are obtained directly by a discretization of the uniaxial stress–strain behavior. Remarkably, both the presented theory and the computational algorithm automatically recover classical bi-linear plasticity and the Krieg and Key algorithm if the user-prescribed stress–strain curve is bilinear.

The Yield-Point Phenomenon and Cyclic Plasticity of the Console Beam

In the paper, the influence of the yield-point phenomenon (YPP) on cyclic plasticity of the console beam is presented with the objective to demonstrate the impact of the YPP on the local cyclic plasticity. The influence of the YPP and its dependence on cyclic material hardening or softening was studied through experiments and numerical simulations. Console beams are made from the low-alloy EN 42 CrMo 4 steel in its normalized state (184 HV), which exhibits cyclic hardening, and in its tempered state (296 HV), which is subject to cyclic softening. Numerical simulations were performed on constitutive model of cyclic plasticity taking into account the kinematic hardening, isotropic hardening or softening and formulations of the YPP which are based on the change of the elastic region surface in the stress space at first transition into the stress plateau. Analysis of the results shows the importance of taking into account the YPP equations in constitutive models of cyclic plasticity as well as the influence of the YPP on cyclic plasticity of the console beam.

A compact cyclic plasticity model with parameter evolution

The paper presents a compact model for cyclic plasticity based on energy in terms of external and internal variables, and plastic yielding described by kinematic hardening and a flow potential with an additive term controlling the nonlinear cyclic hardening. The model is basically described by five parameters: external and internal stiffness, a yield stress and a limiting ultimate stress, and finally a parameter controlling the gradual development of plastic deformation. Calibration against numerous experimental results indicates that typically larger plastic strains develop than predicted by the Armstrong–Frederick model, contained as a special case of the present model for a particular choice of the shape parameter. In contrast to previous work, where shaping the stress-strain loops is derived from multiple internal stress states, this effect is here represented by a single parameter, and it is demonstrated that this simple formulation enables very accurate representation of experimental results. An extension of the theory to account for model parameter evolution effects, e.g. in the form of changing yield level, is included in the form of extended evolution equations for the model parameters. Finally, it is demonstrated that the model in combination with a simple parameter interpolation scheme enables representation of ratcheting effects.

A Novel Methodology to Estimate Life of Gas Turbine Components Under Multiaxial Variable Amplitude Loading

A novel and highly effective methodology is presented in this study to estimate the stresses and strains and also the life of gas turbine components operating in multiaxial variable amplitude loading conditions. The methodology uses a cyclic plasticity model based on multilinear kinematic hardening (MLKH) for estimation of stress-strain response and Wang and Brown algorithm for counting the reversals in the loading cycle. The stress and strain response extracted for each reversal using the MLKH model where then integrated with multiaxial fatigue damage model based on critical planes (Wang and Brown model) suitable for LCF applications, to predict the fatigue life. The proposed methodology was initially compared with experimental test results of 42CrMo4 low alloy steel specimen, under different loading conditions like proportional, non-proportional and sequential loadings available in the literature. To reinforce the life prediction capability of the methodology, an application level study was undertaken. An air-cooled high-pressure turbine disk of an aero gas turbine engine was used as the model for this study. The fatigue life obtained from the multiaxial fatigue damage model was then compared with the experimental LCF life of the disk obtained from the field data. In order to be conservative in approach, lower bound of the 95% confidence limit of the fatigue data fitted using Weibull probability distribution function was used to compare the numerical life. The study shows a good correlation between the fatigue life arrived experimentally and the predicted life using the proposed methodology.