Advanced Cyclic Plasticity Model Research Articles

Numerical simulation of the mechanical behaviour of steel pipe bends under strong cyclic loading

The present study uses advanced numerical tools to examine the mechanical behavior of steel pipe bends (elbows), subjected to strong cyclic loading, associated with repeated plastic deformations of alternate sign. The elbows are modeled with finite elements, accounting for the measured elbow geometry and the actual properties of steel elbow material. The main feature of the present work is the simulation of material response using an advanced cyclic-plasticity model, based on the bounding-surface concept, implemented through an in-house material subroutine. Upon appropriate calibration with material tests in strip specimens, extracted from the bends under consideration, the constitutive model is employed for predicting the mechanical response of large-scale physical laboratory experiments. Very good predictions are obtained in terms of global load-displacement response, as well as in terms of local strains and their accumulation over the loading cycles (ratcheting) at specific elbow locations. This indicates that the bounding-surface model can be an efficient tool for predicting accurately the mechanical response of piping components under severe cyclic loading conditions. Finally, using the validated numerical models, extensive results are obtained, focusing on the effects of internal pressure on strain accumulation at specific locations of the elbow, for three values of pipe thickness.

Automated calibration of advanced cyclic plasticity model parameters with sensitivity analysis for aluminium alloy 2024-T351

The plasticity models in finite element codes are often not able to describe the cyclic plasticity phenomena satisfactorily. Developing a user-defined material model is a demanding process, challenging especially for industry. Open-source Code_Aster is a rapidly expanding and evolving software, capable of overcoming the above-mentioned problem with material model implementation. In this article, Chaboche-type material model with kinematic hardening evolution rules and non-proportional as well as strain memory effects was studied through the calibration of the aluminium alloy 2024-T351. The sensitivity analysis was performed prior to the model calibration to find out whether all the material model parameters were important. The utilization of built-in routines allows the calibration of material constants without the necessity to write the optimization scripts, which is time consuming. Obtaining the parameters using the built-in routines is therefore easier and allows using the advanced modelling for practical use. Three sets of material model parameters were obtained using the built-in routines and results were compared to experiments. Quality of the calibration was highlighted and drawbacks were described. Usage of material model implemented in Code_Aster provided good simulations in a relatively simple way through the use of an advanced cyclic plasticity model via built-in auxiliary functions.

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.

Implementation of MAKOC cyclic plasticity model with memory

This paper deals with the description of implementation of the advanced cyclic plasticity model called MAKOC, which is based on the AbdelKarim–Ohno kinematic hardening rule, the isotropic hardening rule of Calloch and a memory surface introduced in a stress space in accordance with the Jiang-Sehitoglu concept. The capabilities of the MAKOC model are compared with the Chaboche model included in some FE codes. Cyclic plasticity models commonly included in commercial FE software cannot accurately describe the behavior of the material, especially in the case of additional hardening caused by non-proportional loading of the material. This fact is presented on the experimental data set of aluminum alloy 2124T851. Steady state material behavior is studied with regard to the subsequent application in computational fatigue analysis. The cyclic plasticity model developed was implemented into the FE code ANSYS 15.0 using Fortran subroutines for 1D, 2D as well as 3D elements. The integration scheme is described in detail including the method of implementing the model and determining an error map for the proposed MAKOC and Chaboche models. The numerical tangent modulus is proposed to ensure parabolic convergence of the Newton-Raphson method for the MAKOC model. An axisymmetric analysis of 3D Hertz problem was performed to show convergence in the local as well as global iterations.

Evaluation of AF type cyclic plasticity models in ratcheting simulation of pressurized elbow pipes under reversed bending

The ratcheting behavior was studied experimentally for Z2CND18.12N elbow piping under cyclic bending and steady internal pressure. Dozens of cyclic plasticity models for structural ratcheting responses simulations were used in the paper. The four models, namely, Bilinear (BKH), Multilinear (MKIN/KINH), Chaboche (CH3), were already available in the ANSYS finite element package. Advanced cyclic plasticity models, such as, modified Chaboche (CH4), Ohno-Wang, modified Ohno-Wang, Abdel Karim-Ohno and modified Abdel Karim-Ohno, were implemented into ANSYS for simulating the experimental responses. Results from the experimental and simulation studies were presented in order to demonstrate the state of structural ratcheting response simulation by these models. None of the models evaluated perform satisfactorily in simulating circumferential strain ratcheting response. Further, improvement in cyclic plasticity modeling and incorporation of material and structural features, like time-dependent, temperature-dependent, non-proportional, dynamic strain aging, residual stresses and anisotropy of materials in the analysis would be essential for advancement of low-cycle fatigue simulations of structures.

A simplified cyclic plasticity model for calculating stress-strain response under multiaxial non-proportional loadings

Abstract Given the dependence of many fatigue damage parameters on both stress and strain values, being able to produce accurate stress-strain estimations is an essential first step when performing a fatigue life analysis. However, more advanced cyclic plasticity models, capable of capturing complex material behavior under multiaxial non-proportional loadings, often require the determination of a large number of material constants from experimental data that are not always available to the analyst. Therefore, in this study, a simplified Armstrong-Frederick-Chaboche style plasticity model, based on the assumption of Masing material behavior and a newly proposed transient hardening formulation, was evaluated in terms of its ability to predict stress-strain response under complex multiaxial loading conditions. To do this, experimental stress-strain data were generated for 2024-T3 aluminum alloy using both constant and variable amplitude multiaxial block loading histories designed to reflect a wide variety of stress states that might be encountered in any given service loading history. Stress-strain predictions were performed both with and without the consideration of non-proportional hardening effects in order to provide a baseline for evaluating the results. Although all stress-strain predictions were found to agree well with the experimental data, both quantitatively and qualitatively, it was shown that, in general, predictions for axial stress amplitudes and mean axial stresses were consistently better than those for shear stress.

Hertz Contact Problem between Wheel and Rail

Rail-wheel contact problems have been analyzed by the use of the three-dimensional finite element models. Based on these models, the paper presents a study regarding the applicability of the Hertz contact to rail-wheel contact problems. Beside a standard rail, the study also considers a crane rail and a switching component. The bodies of the contact problem are the standard rail UIC60 and the standard wheel UICORE. The maximum contact pressure which the material can support in the elastic range in steady state conditions is known as the shakedown limit. With an operating contact pressure below the shakedown limit the rail would be expected to remain elastic a long period of its lifecycle. However, examination of rail cross-sections shows severe plastic deformation in a sub-surface layer of a few tens of microns thickness; the contact patch size is in tens of millimeters. Three-dimensional elastic-plastic rolling contact stress analysis was conducted incorporating elastic and plastic shakedown concepts. The Hertzian distribution was assumed for the normal surface contact load over a circular contact area. The tangential forces in both the rolling and lateral directions were considered and were assumed to be proportional to the Hertzian pressure. The elastic and plastic shakedown limits obtained for the three-dimensional contact problem revealed the role of both longitudinal and lateral shear traction on the shakedown results. An advanced cyclic plasticity model was implemented into a finite element code via the material subroutine. Finite element simulations were conducted in order to study the influences of the tangential surface forces in the two shear directions on residual stresses and residual strains. The Hertz theory is restricted to frictionless surfaces and perfectly elastic solids, but it is the best method for determining deformations and stress from pitch of contact. Form change due to wear and plastic deformation of a rail can reduce the service life of a track. The purpose of this investigation was to study the development of these damage mechanisms on new and three years old rails in a commuter track over a period of two years.

Effect of Non-Steady State Loading on Rolling-Sliding Contact Stress

The stresses, strains, and deformations produced by repeated, two-dimensional non-steady state rolling-sliding contact were analyzed using an elastic-plastic finite element model. An advanced cyclic plasticity model was used. The non-steady state rolling contact was restricted to a harmonic variation of the normal Herztian contact pressure. Repeated rolling and sliding were simulated by multiple translations of a set of varying normal and tangential surface tractions across an elastic-plastic semi-infinite half space. The non-steady state loading considered results in a wavy contact surface profile. The surface displacements and wave depth of the wavy deformation increase with increasing rolling passes, but the increases in wave depth per rolling pass (ratchetting rate) decay. The residual stresses and strains near the wave trough of the residual wavy deformation are higher than those near the wave crest. The results are in agreement with the experimental observations. The tangential force has a greater influence on the residual strains than on the residual stresses.

Elastic-Plastic Finite-Element Analysis of Repeated, Two-Dimensional Wheel-Rail Rolling Contact under Time-Dependent Load

A study was performed using a finite-element model to obtain stresses, strains, and deformations for repeated, two-dimensional rolling contact of a locomotive driving wheel and a rail under time-dependent load. An advanced cyclic plasticity model was used with a commercial finite element code via a material subroutine. The time-dependent load was considered a harmonic variation of the wheel-rail normal contact force. The normal contact pressure was assumed to follow the Hertzian distribution and the tangential force followed the Carter distribution. A wavy profile is formed on the running surface of the rail subjected to the harmonic variation of the normal (vertical) contact force. The developed wavelength of the profile corresponds to the frequency of the normal contact force for the actual train speed. The creepage or rolling-sliding condition plays an important role in the residual strains and deformations, but its influence on the residual stresses is insignificant. The residual stresses at the surface decrease with increasing rolling passes and gradually tend to stabilize. The residual strains and surface displacements increase with increasing rolling cycle, but the increases in residual strain and surface displacement per rolling pass (ratchetting rate) decay. The residual stresses, strains, and deformations near the wave trough of the residual wavy deformation are larger than those near the wave crest. For any given creepage including zero value, when the number of rolling passes increases, the surface depth of the wavy-deformed surface increases but the ratchetting rate decays. The results are useful in investigating the influence of plastic deformation on rail corrugation.

A Study of Early Stage Self-Loosening of Bolted Joints

Both experimental investigation and finite element analysis were conducted to explore the mechanisms for the early stage self-loosening of bolted joints under transverse cyclic loading. The nuts were glued to the bolts using a strong thread locker in the self-loosening experiments to ensure that no backing-off of the nut occurred. Depending on the loading magnitude, the clamping force reduction ranged from 10% to more than 40% of the initial preload after 200 loading cycles. Three-dimensional elastic-plastic finite element analysis was conducted with the implementation of an advanced cyclic plasticity model. The finite element results revealed that the local cyclic plasticity occurring near the roots of the engaged threads resulted in cyclic strain ratcheting. The localized cyclic plastic deformation caused the stresses to redistribute in the bolt, and the result was the gradual loss of clamping force with loading cycles. The finite element results agreed with the experimental observations quantitatively. When the two clamped plates started to slip and the slip displacement was controlled, both experiments and finite element simulations suggested that the friction between the clamped plates has an insignificant influence on the early stage self-loosening.

Three-Dimensional Elastic-Plastic Stress Analysis of Rolling Contact

Three-dimensional elastic-plastic rolling contact stress analysis was conducted incorporating elastic and plastic shakedown concepts. The Hertzian distribution was assumed for the normal surface contact load over a circular contact area. The tangential forces in both the rolling and lateral directions were considered and were assumed to be proportional to the Hertzian pressure. The elastic and plastic shakedown limits obtained for the three-dimensional contact problem revealed the role of both longitudinal and lateral shear traction on the shakedown results. An advanced cyclic plasticity model was implemented into a finite element code via the material subroutine. Finite element simulations were conducted to study the influences of the tangential surface forces in the two shear directions on residual stresses and residual strains. For all the cases simulated, the p0/k ratio (p0 is the maximum Hertzian pressure and k is the yield stress in shear) was 6.0. The Qx/P ratio, where Qx is the total tangential force on the contact surface in the rolling direction and P is the total normal surface pressure, ranged from 0 to 0.6. The Qy/P ratio (Qy is the total tangential force in the lateral direction) was either zero or 0.25. Residual stresses increase with increasing rolling passes but tend to stabilize. Residual strains also increase but the increase in residual strain per rolling pass (ratchetting rate) decays with rolling cycles. Residual stress levels can be as high as 2k when the Qx/P ratio is 0.6. Local accumulated shear strains can exceed 20 times the yield strain in shear after six rolling passes under extreme conditions. Comparisons of the two-dimensional and three-dimensional rolling contact results were provided to elucidate the differences in residual stresses and ratchetting strain predictions.