Cyclic Plasticity Model Research Articles

Multiaxial fatigue of forged Inconel 718 at room and high temperature

This work investigates the effects of high temperature on the fatigue behavior of forged Inconel 718 under axial/torsional loading conditions. To this end, strain-controlled tension, torsion, and proportional fatigue tests were performed at 20 °C and 450 °C on thin-walled tubular specimens extracted from an as-forged turbine disk. All tests were conducted with axial and shear strain ratios equal to zero, and the applied equivalent von Mises strain amplitude was such to result in fatigue lives within the range of 104 to 106 cycles, which is the typical fatigue life of the component of interest in this study. It was observed that for a given loading condition and prescribed equivalent strain amplitude, the fatigue lives of tests at 450 °C were longer than the room temperature tests. Moreover, the longest lives were observed in the torsion tests, followed by the proportional and tension tests in all temperature and prescribed equivalent strain amplitude tested. The capability of the cyclic plasticity model proposed by Chaboche in describing the cyclic response of Inconel 718 was also addressed. This model successfully simulated the stress–strain behavior of this material under all loading conditions, and for both temperatures investigated. In addition, the cracking behavior of the material was examined. For both temperatures, the tension tests failed by Mode I tensile cracks, while Mode II shear cracks were observed in the torsion and proportional tests. After a scanning electron microscope analysis, it was concluded that the transgranular propagation mode was the predominant failure mechanism of all tested conditions. The fatigue life of Inconel 718 was predicted by the Fatemi–Socie (FS) and the multiaxial version of the Smith–Watson–Topper (SWT) fatigue models, resulting in estimations within a factor-of-two and a factor-of-four, respectively. Moreover, crack directions were also determined by the critical plane models and compared with the orientation of the observed cracks. The SWT model correctly predicted the crack direction of the tension tests, while the FS model was more accurate in determining the orientation of the cracks seen in the torsion tests. None of the two models was able to correctly predict the angles of the critical plane in all tested loading conditions.

Measurement and modeling of deformation-induced martensitic transformation in a metastable austenitic stainless steel under cyclic loadings

Deformation-induced martensitic transformation (DIMT) under cyclic loading in metastable austenitic steel AISI 348 was in-situ monitored through the magnetic permeability method with a Feritscope. Stepwise cyclic loading tests under room temperature revealed nonlinear and non-monotonic variations of the magnetic permeability within single loading cycles. The magnetic response was confirmed to be influenced by internal stress and plastic deformation. Villari effect under cyclic loadings was systematically investigated in the metastable austenitic steel and a model was introduced to correlate the Feritscope output with effective stress. A phenomenological model was proposed to describe the variation of Feritscope output of martensitic phases under zero internal stress within single loading cycles. The band-like structure of α′-martensite was observed along the principal stress axis and forming a material with composite nature. A stress partitioning model based on the dual-phase concept was established and the macroscopic stress is distributed in constituent phases. Mechanical behaviors of both phases were modeled by the cyclic plasticity model and the obtained stress-strain curves match well with the experimental results. On knowing the evolutions of internal stresses in the martensitic phase, the variations of magnetic properties under both loaded and unloaded states were well modeled.

Temperature-dependent cyclic plastic deformation of U75VG rail steel: Experiments and simulations

To reveal the temperature-dependent cyclic plastic deformation of U75VG steel, the monotonic tension, strain- and stress-controlled cyclic deformation experiments are carried out at different temperatures. The results show that the U75VG rail steel shows the cyclic softening, cyclic hardening and cyclic softening at 278 K, 573 K and 873 K. Moreover, the U75VG rail steel exhibits obvious ratcheting behavior at differ-ent temperatures, and the ratcheting strain depends on the applied mean stress and stress amplitude. The ratcheting strain is restrained at 573 K due to the influence of dynamic strain aging, while it rapidly increases at 873 K due to increasing the viscos-ity at high temperatures. A temperature-dependent cyclic plastic model is constructed to consider the influence of dynamic strain aging on the cyclic plastic deformation. By comparing the simulation and experimental results, the prediction ability of the proposed model for U75VG rail steel under different temperatures is verified.

Anisotropic cyclic plasticity modeling for additively manufactured nickel‐based superalloys

AbstractThe additively manufactured materials show anisotropic mechanical properties. In the present paper, a constitutive model for a nickel‐based superalloy made by selective laser melting was established to characterize cyclic mechanical behaviors under multiaxial loading conditions. Detailed material tests revealed that the effects from the building orientation decrease with multiaxial cyclic loads. A cyclic constitutive model based on the Hill criterion was introduced for the superalloy and considered the orthotropic mechanical properties depending on loading cycles. The computation confirms the model can reasonably simulate the cyclic elastic‐plastic behavior under non‐proportional complex loading conditions and provides an applicable method for engineering applications.

A constitutive model of cyclic plasticity with Lode dependence for structural steels

A finite strain constitutive model is proposed to represent the cyclic elastoplastic response of structural steels. The model simulates the Lode angle dependence of plastic response, which has been recently observed in experimental studies. The model combines Frederick-Armstrong kinematic hardening rules with an exponential isotropic hardening rule, and a non-associated plastic flow rule. A Lode angle-dependent coefficient is defined to modify the isotropic hardening response and determine the shape of yield surface, with respect to the conventional von Mises surface. Stabilization of hysteresis for cyclic plasticity is achieved through a memory surface, defined in the plastic strain space. Analytical formulas for an implicit Return-Mapping algorithm are derived to realize the numerical implementation of this model via a UMAT user subroutine. The effect of Lode dependence of the plasticity response of structural steel Q235 is investigated through monotonic and cyclic experiments on flat shear specimens. A process for parameter identification is outlined, and model predictions are validated through comparison with experimentally-measured force–displacement curves on uniaxial and shear specimens.

Finite-Element Analysis of High-Strength Steel Extended End-Plate Connections under Cyclic Loading.

In order to examine the seismic behavior of high-strength steel extended end-plate connections, a three-dimensional efficient finite-element model in Abaqus was established subjected to cyclic loading at the beam end. Geometrical dimensions, boundary conditions, element types, contact properties between the bolts, end-plate and column flange, and material cyclic constitutive models were described in detail. Geometry and material nonlinearity were adequately considered. In particular, a cyclic plasticity model for high-strength steels was employed that was easily calibrated based on the tension coupon test, so as to describe the complicated cyclic hardening and softening response. The simulated results of the finite-element model were compared to the test ones in terms of both deformation modes and hysteresis loops. The results showed that the bending deformation of the end-plate and column flange was accurately captured, and the gap phenomena among the bolt nuts, the end-plate, and column flange was described in a satisfactory manner as well. The hysteresis loops from the simulation agreed well with the test results, reproducing the pinched shape due to the end-plate gap evolution under cyclic loading as well as the quite plump shape with stable energy dissipation when the panel zone dominated the cyclic response. Therefore, the accuracy of the finite-element model was verified and it provided a strong benchmark tool for investigating the cyclic or seismic performance of this kind of connection. The connection failure including the bolt fracture and cracking in the end-plate needs further numerical study by calibrating accurate material failure models for high-strength steels and bolts.

Homogenization based macroscopic model of phase transformations and cyclic plasticity in pearlitic steel

In this contribution macroscopic modeling of phase transformations and mechanical behavior of low alloy steels are developed and investigated. Such modeling is of importance in simulations of transient thermo-mechanical processes which can cause phase transformations, examples from the railway industry include train braking induced frictional heating as well as rail grinding and welding operations. We adopt a modeling approach which includes phase transformation kinetics and individual constitutive models for the phases in combination with different homogenization methods. Algorithmic implementations of the isostrain, isostress and self-consistent homogenization methods are presented and demonstrated in finite element simulations of a laser heating experiment. Stress field results from the different homogenization methods are compared against each other and also against experimental data. The importance of including transformation induced plasticity in the modeling is highlighted, as well as the multi-phase stages of the heating and cooling.

Mechanistically informed data-driven modeling of cyclic plasticity via artificial neural networks

A mechanistically informed data-driven approach is proposed to simulate the complex plastic behavior of microstructured/homogenized solids subjected to cyclic loading, especially to simulate the Masing effect. Our proposed approach avoids the complicated mathematical construction of an appropriate yield surface, and does not require a large amount of data for training, by virtue of its mechanistic character, which couples the methods and tools of data science to the principles of mechanics. Specifically, a data-processing method is herein advanced to extract specific internal variables that characterize cyclic plastic behavior, which cannot be measured directly via physical experiments. A yield surface, represented by an artificial neural network (ANN), is then trained by stress–strain data and the extracted internal variables. Finally, the ANN is integrated into a finite element computational framework to solve different boundary value problems (BVPs). Results for demonstrative examples are presented, which illustrate the effectiveness and the reliability of the proposed approach for solids containing voids and particles in their microstructure. Compared with direct numerical simulation (DNS), our approach seems to predict the average levels of stress and plastic strain under cyclic loading more efficiently, as well as the regions of strain localization. In addition, results for a homogenized three-dimensional truss structure demonstrate that our approach can accurately describe the evolution of key internal variables. Our mechanistic approach requires much less data than the general pure data-driven methods, which shows a possible computational efficiency compared with the pure data-driven approach. Limitations of our proposed approach are also discussed.

A fast method to estimate the multiaxial non-proportional elastic–plastic stress–strain in rail rolling contact fatigue problems

This paper aims to propose a new and fast method to estimate the multiaxial non-proportional elastic–plastic stress and strain time histories developed in rails due to rolling contact and evaluate its accuracy for fatigue analysis. The method has the pseudo-elastic stress time history as input, which is obtained by a coupled analytical and numerical method. Therefore, a method originally proposed for notch-root elastic–plastic stress–strain analysis was extended to the Rolling Contact Problem (RCF). The problem is solved incrementally and is established considering a set of equations composed by constitutive and multiaxial notch correction equations. Additionally, a kinematic cyclic plasticity model was included. An equivalent model based on the Finite Element Method was used for comparison purposes. The comparison was made in terms of multiaxial fatigue damage parameters in critical planes, according to fatigue analysis models developed by Matake and Brown & Miller. The more relevant advantage of the method over the non-linear FEM analysis is the possibility to readily obtain long elastic–plastic stress and strain histories and to perform material parameter and load case studies. The method proposed agrees with the equivalent FEM and proved to be a powerful tool for fast wheel-rail failure analysis, especially in RCF problems.

An Approximate Method for Calculating Elastic-Plastic Stress and Strain on Notched Specimens.

The paper deals with an approximate method for calculating elastic–plastic stresses and strains on the surface of notched samples. The method is based on the Abdel–Karim–Ohno cyclic plasticity model. The plane stress condition is considered within the evaluation. The output of the approximation on several multiaxial axial–torsion load paths is compared to our own experimental results. Experiments were carried out on samples of two notch types manufactured from the 2124-T851 aluminum alloy. Strain distribution in the notch area was measured by digital image correlation. The comparison between computational solution and measured response shows that the new method allows for obtaining reasonably good approximation, even for relatively complicated multiaxial load cases.

Assessment of cyclic plasticity models

The mechanical features of the Chaboche model (Chaboche et al., 1979; Chaboche, 1989, 2008) are analyzed definitely. Then, it will be revealed that the Chaboche model is not a physical model but merely ad hoc primitive model to be the polynomial approximation of test data including a lot of material constants without clear physical meaning and thus possesses a lot of physical and mathematical defects. All these defects are solved out in the subloading-overstress model.

Cyclic plasticity models and fatigue criteria for exhaust manifold life assessment in the context of limited material data available

ABSTRACT The work focuses on predictive capabilities of fundamental cyclic plasticity and fatigue life models, which can be calibrated using limited amount of experiments as specific ones needed for more advanced models are often absent. The analyses are conducted for the synthetic case of exhaust manifold made from cast iron. The thermal boundary conditions from the forced convection were obtained from the computational fluid dynamics considered as a conjugate heat transfer problem. Two rate-independent and temperature-dependent material models were calibrated for structural analyses. Both were validated with experiments on isothermal and anisothermal levels. Sequential thermal–mechanical finite element simulations were performed. Two fatigue life models were employed. The first was a temperature-dependent strain-based fatigue life criterion calibrated from uniaxial data. The second was a temperature-independent energy-based fatigue life criterion resulting in twice lower life than the strain-based criterion, while none of the plasticity models made a significant difference in that prediction.

On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems

In this work the finite element (FE) implementation of the small strain cyclic plasticity is discussed. The family of elastoplastic constitutive models is considered which uses the mixed, kinematic-isotropic hardening rule. It is assumed that the kinematic hardening is governed by the Armstrong–Frederick law. The radial return mapping algorithm is utilized to discretize the general form of the constitutive equation. A relation for the consistent elastoplastic tangent operator is derived. To the best of the author’s knowledge, this formula has not been presented in the literature yet. The obtained set of equations can be used to implement the cyclic plasticity models into numerous commercial or non-commercial FE packages. A user subroutine UMAT (User’s MATerial) has been developed in order to implement the cyclic plasticity model by Yoshida into the open-source FE program CalculiX. The coding is included in the Appendix. It can be easily modified to implement any isotropic hardening rule for which the yield stress is a function of the effective plastic strain. The number of the utilized backstress variables can be easily increased as well. Several validation tests which have been performed in order to verify the code’s performance are discussed.

Neural network constitutive model for uniaxial cyclic plasticity based on return mapping algorithm

Structures are subjected to cyclic loading during earthquakes. Therefore, to develop accurate constitutive models for simulating structural response to earthquakes, the cyclic plasticity of structural steels should be considered. Neural network constitutive models reproduce the plastic behavior of materials by applying the learning capability of neural networks. Although numerous monotonic loading models have been developed, there have been relatively few applications of neural network constitutive models to cyclic plasticity. In this study, a neural network constitutive model with good generalization ability and high computation efficiency was developed to model the stress and strain history of materials under cyclic loading. The model employs a feed forward neural network as part of an implicit stress integration scheme implemented by the return mapping algorithm for the hardening model proposed by Chaboche. An appropriate network architecture was constructed using numerical results to set the number of neurons in the hidden layer and the batch size. The results obtained by the trained neural network under random loading agreed well with those obtained by a return mapping algorithm, along with a 70% reduction in calculation time.

A new thermodynamically based model for creep and cyclic plasticity

Creep and cyclic plasticity are two common mechanical behaviors in engineering, and their interaction significantly affects the performance and degradation of corresponding components and structures, especially at high temperatures. How to build a physically based model for describing materials’ mechanical response under complex loading is still a challenge. This study proposes a thermodynamically based model for describing complex creep plasticity behaviors, such as cyclic plasticity and creep. Unlike existing models, the proposed model can describe time-dependent cyclic plasticity and clarify the contribution of various creep mechanisms. Starting from the fundamental thermodynamic laws, Helmholtz free energy and dissipation analysis considering different creep mechanisms are introduced. Then, constitutive equations are derived according to the physical hypothesis of normality of dissipation space. In the proposed model, plastic deformation is thought to depend on static plasticity and creep, which is further decomposed into three parts based on diffusion and dislocation activities, and the contribution of each creep mechanism is explicitly described. Finally, a series experimental data of Ti-6-4 is used to verify the utility of the proposed model. Satisfactory modeling results are obtained, including primary creep, steady creep, power-law breakdown, and creep cyclic plasticity interactions, confirming the validity of the proposed model.

Implementation of Sobol’s sensitivity analysis to cyclic plasticity model with parameter uncertainty

Though modeling material cyclic plasticity in a probabilistic way can yield a more accurate result than deterministic modelling method, it is quite hard to perform uncertainty quantification for all the material parameters. In this paper, Sobol’s global sensitivity analysis is applied to cyclic plasticity model to investigate how the variation of these parameters affect fatigue reliability evaluation. A machine learning algorithm is proposed to improve the computational efficiency for failure probability assessment. The results of global sensitivity analysis show that fatigue damage parameters, elastic modulus and initial yield stress are very influential to fatigue reliability analysis while others are not.

Cyclic Metal Plasticity Model Parameters with Limited Information: Constrained Optimization Approach

AbstractTensile test data for structural steels are ubiquitous. However, the information monotonic loading provides with respect to the material’s characteristics is limited. Notably, features of i...

Modelling of cyclic plasticity and phase transformations during repeated local heating events in rail and wheel steels

Short term local friction heating events in railway operations might lead to phase transformations in pearlitic rail and wheel steels. A modelling framework for phase transformations combined with cyclic plasticity for the individual phases is presented. The phase transformation kinetics include e.g. austenitization due to heating, martensite formation due to rapid cooling and martensite tempering. The modelling framework has been calibrated against cyclic dilatometry test data and cyclic mechanical experiments. Simulations of a double heating event followed by rolling contact loadings show phase transformations and how cyclic residual stresses develop in the different phases.

Constitutive modeling of cyclic plasticity at elevated temperatures for a nickel-based superalloy

During the operation of turbines in jet engines or in power plants, high thermal and intermittent mechanical loads appear, which can lead to high-temperature fatigue failure if thermal and mechanical loads vary at the same time. Since fatigue testing is a time-consuming process, it is important to develop realistic material models with predictive capabilities that are able to extrapolate the limited experimental results for cyclic plasticity within a wide range of temperatures. To accomplish this, an approach based on a representative volume element (RVE), mimicking the typical γ/γ′ microstructure of a Ni-based single crystal superalloy, is adopted for cyclic loading conditions. With the help of this RVE, the temperature- and deformation-dependent internal stresses in the microstructure can be taken into account in a realistic manner, which proves to be essential in understanding the fatigue behavior of this material. The material behavior in the elastic regime is described by temperature-dependent anisotropic elastic constants. The flow rule for plastic deformation is governed by the thermal activation of various slip systems in the γ matrix, the γ′ precipitate and also by cube slip along the γ/γ′ microstructure. This phenomenological crystal plasticity/creep model takes different mechanisms into account, including thermally activated dislocation slip, the internal stresses due to inhomogeneous strains in different regions of γ matrix channels and in γ′ precipitates, the softening effect due to dislocation climb, the formation of 〈112〉 dislocation ribbons for precipitate shearing, and Kear-Wilsdorf locks.This constitutive law is parameterized based on experimental data for the CMSX-4 single-crystal superalloy by applying an inverse analysis to identify the material parameters based on many low cycle fatigue tests in the intermediate temperature and high stress regime. The identified material parameters could predict cyclic plasticity and low cycle fatigue behavior at different temperatures. The model does not only reliably reproduce the experimental results along different crystallographic loading directions, but it also reveals the relative importance of the different deformation mechanisms for the fatigue behavior under various conditions.

The tension-compression behavior of gradient structured materials: A deformation-mechanism-based strain gradient plasticity model

Gradient structured (GS) metals can simultaneously achieve high strength and high ductility, which is the pursuit of structural materials. Abundant studies have pointed out that significant kinematic hardening is key to their strength-ductility combination. Unfortunately, few constitutive models were established to simulate and analyze the characteristic kinematic hardening behavior of GS metals. Thus, a systematic and deep understanding of the relationship between graded microstructure and the resulting macroscopic response needs further effort. In this work, we develop a strain gradient plasticity model that considers plasticity heterogeneities from the grain to the sample scale. A back stress model, which accounts for the dependency of dislocation pileups on grain size, is established to describe the cyclic deformation properties of GS materials. The established model unifies the concepts of geometrically necessary dislocations accommodating plasticity heterogeneities, grain size-dependent back stress, and reversible dislocation motion during reverse loading into a strain gradient plasticity framework. A finite element implementation of the model quantitatively predicts the uniaxial tensile and tensile-compressive responses of a GS copper bar as well as of homogeneously grained reference samples. The simulation indicates that the enhanced kinematic hardening of GS copper results mainly from fine grains in the GS layer and contributes to the considerable ductility of the GS material. The strain gradient cyclic plasticity model enables future investigation of the cyclic/fatigue behavior of GS materials, which is vital for the engineering application.