Cyclic Elastoplastic Behavior Research Articles

A modified cyclic elastoplastic constitutive model considering the variational dynamic recovery term of back stress for FGH95 under asymmetrical cyclic loading

The asymmetric cyclic loading process occurs in aero-engine turbine discs. A constitutive model that accurately describes the cyclic elastoplastic behaviour of the material is important for structural design and low cycle fatigue life prediction of turbine discs. In this paper, the low cycle fatigue test of FGH95 was carried out at 620℃ under 0.5%, 0.6%, 0.7%, 0.8%, 0.9%, 1.0% and 1.1% strain amplitude with strain ratio equal to 0. The material exhibited cyclic hardening followed by cyclic softening at high strain amplitudes and cyclic softening at low strain amplitudes. The mean stress relaxation rate was similar for each strain amplitude. In addition, the evolution of effective stress and back stress was obtained through the method of internal stress division. Then, the relationship between the change in stress amplitude and the change in internal stress was discussed. The results showed that with cyclic loading, cyclic hardening/softening of FGH95 was affected by the competition mechanism of back and effective stresses. Considering that slip deformation and crystal lattice rotation coexist in plastic deformation, the dynamic recovery term of the Abdel-Karim and Ohno model was used. In order to characterize the different magnitudes of back stress change in materials at different plastic strain intervals, a dynamic recovery term coefficient was introduced to the dynamic recovery term and the critical surface of the back stress. The modified model was used to compare with experimental results. Then, it gives a good description of the material’s mean stress relaxation and strain amplitude variation and gives good agreement on the hysteresis loop.

On the cyclic elastoplastic shakedown behavior of an auxetic metamaterial: An experimental, numerical, and analytical study

This article presents the first experimental, numerical, and analytical study of the elastoplastic shakedown response of an auxetic metamaterial structure that elucidates interactions between auxeticity and maximum shakedown loading capacity. The study aims to determine the safe elastoplastic shakedown limit of perforated auxetic aluminum sheet structures (AA5083-TO) with fixed void fraction (16.4%) under ambient cyclic asymmetric uniaxial loading conditions. The motivation is that shakedown-based designs can be used to expand the feasible design space under cyclic loading conditions compared to conventional yield-limited designs. Finite element analyses with calibrated hardening models are used to develop Bree load-interaction diagrams that are experimentally validated. It is found that shakedown occurs at stress levels up to almost four times the elastic limit of the structure for a fixed allowable equivalent strain level near three percent. This shakedown multiplier is also sensitive to the extent of auxeticity in the structure and a parametric study and analytical model are used to identify underlying mechanisms and a potential maximum condition.

Bayesian optimization-assisted approximate Bayesian computation and its application to identifying cyclic constitutive law of structural steels

A costly finite element model discourages Bayesian inference of the underlying parameters from noise-corrupted experimental datasets. This arises because the likelihood of such a model is often computationally intractable, leading to the impossibility of performing a large number of costly simulations. This study presents Bayesian optimization-assisted approximate Bayesian computation (BO-assisted ABC) and showcases its application to identifying the approximate posteriors of parameters for known statistical models and of cyclic elastoplastic parameters for structural steels. ABC bypasses likelihood evaluations by generating prior samples that are assigned as samples constituting the posterior if discrepancies between the experimental dataset and the corresponding simulated datasets do not exceed a small, positive threshold. With a modest number of costly simulations, BO facilitates ABC by intelligently constructing a Gaussian process model that approximates the discrepancy mean function. Identification results from illustrative examples show that the approximate posteriors by the proposed approach not only reproduce a given posterior with acceptable accuracy but also capture the true nominal parameters of a statistical model. Moreover, the approximate posteriors of material parameters can simulate the cyclic elastoplastic behavior of a steel specimen under different loading conditions. The dependence of identification results on definitions of BO acquisition function is also investigated.

Strain‐controlled fatigue loading of an additively manufactured AISI 316L steel: Cyclic plasticity model and strain–life curve with a comparison to the wrought material

AbstractLow cycle fatigue (LCF) regime was experimentally studied for a 316L steel additively manufactured by laser‐powder bed fusion (L‐PBF), a material widely used in sectors that require a reliable durability analysis. Material cyclic elastoplastic behavior is described by the Chaboche–Voce combined plasticity model, which displayed a great degree of accuracy. The fatigue life was modeled by both invoking the Manson–Coffin curve and other simplified models derived from static properties of the material; some of which showed remarkably good accuracy. A quantitative comparison with a wrought‐processed 316L steel displayed a markedly different cyclic elastoplastic response but comparable fatigue strengths.

Cyclic elastoplastic constitutive model for stainless steels compatible with multiple strengths

The application of stainless steel materials in civil engineering has begun to attract attention over the last decade. Nevertheless, most studies of stainless steel structures still use the oversimplified Chaboche model. Therefore a more accurate constitutive model is needed to describe the cyclic elastoplastic behavior of stainless steel. The model should be able to simulate stainless steel of varying strengths and should be easily calibrated for practical engineering purposes. This paper proposes a compatible constitutive model that meets these objectives. The constitutive model combines two forms of hardening, is dominated by isotropic and kinematic hardening, and accounts for the strain memory effect and the average stress relaxation effect. A complete numerical implementation scheme for the constitutive model is proposed and coded in the user material subroutine (UMAT) based on the implicit return mapping algorithm. Furthermore, simplified methods and recommendations for the calibration of material parameters are given. The simulation results of a detailed finite element model are compared with the results of the cyclic loading tests, and good agreements are obtained. The proposed constitutive model can be further used in seismic or other dynamic nonlinear analyses of stainless steel structures to correctly predict their strength, deformation, and energy dissipation capacity.

Bayesian optimization for inverse identification of cyclic constitutive law of structural steels from cyclic structural tests

Properly modeling the cyclic elastoplastic behavior of structural steels is essential for establishing accurate analyses of structures subjected to earthquake excitation. However, identifying the underlying parameters to simulate such behavior is commonly hindered by the computational burden of carrying out many nonlinear analyses. This work proposes using Bayesian optimization (BO) for solving an inverse problem by which certain parameters for the nonlinear combined isotropic/kinematic hardening model are inferred from cyclic responses of a specimen or a structural component. BO minimizes an error function that represents the difference between the simulated responses and those measured experimentally while providing a global optimization framework for parameter identification, reducing the number of simulations, and addressing observational noise. It is found that BO has higher robustness as compared with some population-based optimization algorithms when expending the same number of simulations. Identification results for a specimen and a cantilever show a good ability of identified parameters to capture the behavior of structural steels under different cyclic loadings. They also suggest a possibility of identifying the parameters for multiple materials from cyclic tests of a structural component that is remarkable because cyclic material tests are difficult and usually not carried out before structural tests. Experimental measures from various loading histories should be simultaneously used for identification as they can mitigate the bias toward a specific loading history, which may lead the parameters to inaccurate prediction of material behavior under other loading histories.

Elastoplastic response of a pipe bend using Prandtl operator approach in a finite element analysis

Structural components are subjected to variable thermomechanical loads during use. These loads can lead to fatigue failure therefore it is important to detect potential weak points in the structure already during early stages of the R&D process. Reliable results of the stress-strain response are of crucial importance during the structural analyses. In this paper, a metallic pipe bend is subjected to a variable thermomechanical load and its structural response is investigated. The loads reach beyond the yield stress of the material, therefore an elastoplastic stress-strain response is observed. Prandtl operator approach, implemented into the finite element analysis, is used to simulate the response of the pipe bend. The approach enables fast and accurate structural simulations using the material parameters gained from uniaxial low-cycle fatigue testing at few test temperatures. The approach considers a cyclic elastoplastic material behaviour with multilinear kinematic hardening at variable temperatures. Comparison with the commonly used Besseling model shows a comparable stress-strain path simulation, but ensures a 30 % shorter computational time. Fatigue lifetime estimation differs for 4 % at the critical control point for the analysed thermomechanical load history.

Cyclic elastoplastic behaviour of 2198-T8 aluminium alloy welded panels

The friction stir welding (FSW) process generally induces a gradient of properties and a softer behaviour along the welded joint. To design aeronautical structures welded by FSW in fatigue, it is necessary to study the impact of this localized soft behaviour on the overall structure. In this study, the 2198-T8 hardening structural aluminium alloy is considered. Monotonic and cyclic mechanical tests are performed by combining conventional extensometric measurements with digital image correlation (DIC) to measure the local displacement fields around the welded zone. Based on these experimental data, constitutive equations are proposed and identified, zone by zone, across the welded joint. In parallel, a quantification of T1 (\(\hbox {Al}_{\mathrm {2}}\)CuLi) strengthening precipitates is performed in different regions of the joint with a transmission electron microscope in order to identify a relationship between the microstructure and the mechanical parameters. Finally, once all the material parameters are identified, the model is validated by a 3D finite element analysis representative of FSW samples.

Elastoplastic topology optimization of cyclically loaded structures via direct methods for shakedown

For the first time, the lower bound shakedown theorem is integrated into a level set–based topology optimization framework to identify lightweight elastoplastic designs. Shakedown is a cyclic elastoplastic behavior in which, upon cycling beyond the elastic limit, the accumulation of plastic strain arrests and purely elastic behavior is recovered. In contrast to most elastoplastic topology optimization, the use of a lower bound shakedown limit allows elastoplastic shakedown limits to be rigorously estimated using only the elastic solution. Under small deformation assumptions, this amounts to solving one simple partial differential equation, avoiding the non-linearity associated with plasticity, and thus simplifying the resolution process. Numerical results are provided for several benchmark examples. The results highlight the design performance enhancements attributed to allowing elastoplastic shakedown to occur instead of designing to first yield. In particular, up to 10% reduction in weight is found for the simple structures considered.

Material models and mechanical properties of titanium alloys produced by selective laser melting

Modeling of additively manufactured titanium alloys behavior in loading conditions represents a step forward to understand its advantageous and favorable properties in various applications, such as medical implants, components for aerospace, automotive and process industry. The knowledge on their behavior is still very limited, especially if the focus is directed to modeling of the behavior of titanium alloys produced by selective laser melting (SLM), which opens many possibilities in achieving optimal design of titanium alloy components. Therefore, an overview of the selected properties of these materials has been detailed, in order to choose or develop appropriate material models suitable for their behavior modeling. By adapting existing or developing new constitutive material models, in further work the behavior of SLM antibacterial Ti-xCu titanium alloys will be modeled considering their microstructure and defects. In this study, state-of-the-art on mechanical properties of AM Ti6Al4V alloy is given, as well as Ramberg – Osgood (R – O) parameters for modeling of monotonic and cyclic elastoplastic behavior.

МОДЕЛИРОВАНИЕ УСТАЛОСТНОЙ ДОЛГОВЕЧНОСТИ КОНСТРУКЦИОННЫХ СПЛАВОВ ПРИ ДВУХЧАСТОТНОМ НАГРУЖЕНИИ

The processes of fatigue life of polycrystalline structural alloys under the combined action of low- and high-cycle fatigue mechanisms are considered. From the standpoint of damaged medium mechanics (DMM), a mathematical model has been developed that describes the processes of plastic deformation and the accumulation of fatigue damage. The DMM model consists of three interrelated parts: relations that determine the cyclic elastoplastic behavior of the material, taking into account the dependence on the fracture process; equations describing the kinetics of fatigue damage accumulation; criterion for the strength of the damaged material. Variant of the constitutive relations for elastoplasticity is based on the concept of a microplastic loading surface in the von Mises form and the principle of the gradient of the plastic strain rate vector to the surface at the loading point. This version of the equations of state reflects the main effects of the process of cyclic plastic deformation of the material for arbitrary complex loading trajectories. A variant of the kinetic equations for the accumulation of fatigue damage is based on the introduction of a scalar damage parameter, is based on energy principles and takes into account the main effects of the formation, growth and fusion of microdefects under arbitrary complex loading conditions. A unified form of the evolutionary equation for the accumulation of fatigue damages for low-cycle and high-cycle fatigue is proposed. As a criterion for the strength of the damaged material, the condition for reaching the critical value of the damage is used. To assess the reliability and determine the limits of applicability of the constitutive relations of the DMM, numerical studies of the processes of accumulation of fatigue damage by cyclic inelastic deformation and fatigue failure of steel 20 and 08Х18Н12Т were carried out under single-frequency loading of the upper frequency and two-frequency loading with different amplitude ratios. And the comparison of the obtained numerical results with the data of field experiments is carried out. The results of comparing the calculated and experimental data showed that the developed model of the damaged environment reliably describes the durability of structures under the action of low- and high-cycle fatigue mechanisms.

Towards exploiting inelastic design for Inconel 625 under short-term cyclic loading at 600∘C

Many industries rely on the Inconel 625 alloy to serve under thermomechanical operating conditions. Understanding the macroscopic cyclic inelastic behavior of this material is vital for accurate assessment of its load-carrying capacity at elevated temperatures. In this work, a uniaxial experimental program at 600∘C is conducted to demonstrate designing for cyclic elastoplastic behavior (shakedown) as opposed to more restrictive first-yield, while still avoiding ratchetting or alternating plasticity. In particular, a range of cyclic stress amplitudes are imposed at non-zero mean stresses while maintaining a constant maximum stress. In addition, the effect of dynamic strain aging (DSA) on the macroscopic shakedown behavior is established under load control. The inelastic work done per cycle is used as a measure of severity of the cyclic inelastic behavior, and is evaluated by monitoring the evolution of the hysteresis loop width. It is found that when the maximum stress is constant, larger mean stress tests approach shakedown behavior. Furthermore, for the range of stress amplitudes and mean stresses considered, the cyclic elastoplastic shakedown behavior is not affected by the DSA, and only depends on the mean stress and stress amplitude.

МОДЕЛИРОВАНИЕ УСТАЛОСТНОЙ ДОЛГОВЕЧНОСТИ ПОЛИКРИСТАЛЛИЧЕСКИХ КОНСТРУКЦИОННЫХ СПЛАВОВ ПРИ СОВМЕСТНОМ ДЕЙСТВИИ МЕХАНИЗМОВ МАЛО- И МНОГОЦИКЛОВОЙ УСТАЛОСТИ

Processes of fatigue life of polycrystalline structural alloys under a combined effect of low- and high-cycle fatigue are considered. In the framework of mechanics of damaged media (MDM), a mathematical model is developed, which describes processes of plastic deformation and fatigue damage accumulation. The MDM model consists of three interrelated parts: relations defining cyclic elastoplastic behavior of the material, accounting for its dependence on the failure process; equations describing fatigue damage accumulation kinetics; a strength criterion of the damaged material. The version of defining relations of elastoplasticity is based on the notion of yield surface and the principle of orthogonality of the plastic strain rate vector to the yield surface at the loading point. This version of equations of state reflects the main effects of the cyclic plastic deformation process of the material for arbitrarily complex loading trajectories. The version of kinetic equations of damage accumulation is based on introducing a scalar parameter of damage degree. The construction uses energy-based principles and accounts for the main effects of the process of nucleation, growth and merging of microdefects under arbitrarily complex multiaxial loading regimes. A combined form of the evolutionary equation of fatigue damage accumulation in the regions of low-cycle (LCF) and high-cycle (HCF) fatigue is proposed. It is shown that, under regular cyclic loading of the material, the stress amplitude of the cycle decreases by degrees during the transition from LCF to HCF and depends on the physical interaction of these mechanisms in the transition zone. The condition when the damage degree attains its critical value is taken as the strength criterion of the damaged material. A methodology of numerically determining parameters of the evolutionary equation of fatigue damage accumulation in the conditions of HCF is presented. To assess the reliability and the limits of applicability of the defining relations of MDM, processes of plastic deformation and fatigue damage accumulation in a number of structural alloys in cyclic tests have been numerically studied, and the obtained numerical results have been compared with the data of full-scale experiments. The results of comparison of the numerical and experimental data reveal that the developed model of mechanics of damaged media adequately describes durability of structures subjected to a combined effect of low- and high-cycle fatigue mechanisms. It is shown that the introduced MDM model qualitatively and, accurately enough for practical engineering purposes, quantitatively describes the main effects of the processes of plastic deformation and fatigue damage accumulation in structural alloys under cyclic loading.

Elastoplastic response of as-built SLM and wrought Ti-6Al-4V under symmetric and asymmetric strain-controlled cyclic loading

PurposeThe purpose of this paper is to examine the mechanical behaviour of additively manufactured Ti-6Al-4V under cyclic loading. Using as-built selective laser melting (SLM) Ti-6Al-4V in engineering applications requires a detailed understanding of its elastoplastic behaviour. This preliminary study intends to create a better understanding on the cyclic plasticity phenomena exhibited by this material under symmetric and asymmetric strain-controlled cyclic loading.Design/methodology/approachThis paper investigates experimentally the cyclic elastoplastic behaviour of as-built SLM Ti-6Al-4V under symmetric and asymmetric strain-controlled loading histories and compares it to that of wrought Ti-6Al-4V. Moreover, a plasticity model has been customised to simulate effectively the mechanical behaviour of the as-built SLM Ti-6Al-4V. This model is formulated to account for the SLM Ti-6Al-4V-specific characteristics, under the strain-controlled experiments.FindingsThe elastoplastic behaviour of the as-built SLM Ti-6Al-4V has been compared to that of the wrought material, enabling characterisation of the cyclic transient phenomena under symmetric and asymmetric strain-controlled loadings. The test results have identified a difference in the strain-controlled cyclic phenomena in the as-build SLM Ti-6Al-4V when compared to its wrought counterpart, because of a difference in their microstructure. The plasticity model offers accurate simulation of the observed experimental behaviour in the SLM material.Research limitations/implicationsFurther investigation through a more extensive test campaign involving a wider set of strain-controlled loading cases, including multiaxial (biaxial) histories, is required for a more complete characterisation of the material performance.Originality/valueThe present investigation offers an advancement in the knowledge of cyclic transient effects exhibited by a typical α’ martensite SLM Ti-6Al-4V under symmetric and asymmetric strain-controlled tests. The research data and findings reported are among the very few reported so far in the literature.

Determination of the RVE size for polycrystal metals to predict monotonic and cyclic elastoplastic behavior: Statistical and numerical approach with new criteria

Abstract The determination of the size of the Representative Volume Element “RVE” is extremely important to predict mechanical and physical effective properties of heterogeneous materials. In the present work, the optimal size of RVE for polycrystal materials, which is made–up of grains having a polyhedron Voronoi shape, is investigated for the prediction of an elastoplastic behavior using the crystal plasticity model. Ten realizations with a different number of grains ranging from 10 to 250 have been used in the numerical simulation. The homogenization technique combined with the Finite Element Method (FEM) is used to obtain the macroscopic strain and stress. Several new criteria are introduced as indicators for estimating the optimal RVE's size. Their formulation is based on the standard deviation with respect to the average value of different mechanical quantities. These criteria ensure that, for an optimal RVE size, the response of the crystalline aggregate is not sensitive to the orientations evolution and grains' dimensions. It turns out that, for the cyclic behavior, the influence of the loading mode is very important, in particular the asymmetrical stress mode. The influence of the value of strain or stress used to perform different simulation tests on the RVE size has been analyzed. The simulation results are in good agreement with the experimental results from the literature.

STABILITY EVALUATION OF STEEL BRACED FRAMES UNDER INELASTIC CYCLIC LOADING

This paper deals with the inelastic cyclic analysis and stability (strength and ductility) evaluation of steel braced frames. The inelastic cyclic performance of steel braced frames is examined through finite element analysis using the commercial computer program ANSYS. First some of the most important parameters considered in the practical design and ductility evaluation of steel braces are presented. Then the details of finite element modeling and numerical analysis are described. Later the accuracy of the analytical model employed in the analysis is substantiated by comparing the analytical results with the available test data in the literature. Finally, the effects of some important structural and material parameters on cyclic elastoplastic behavior of steel braced frames are discussed and evaluated. It is concluded that the numerical method and finite-element modeling employed in the numerical analysis can predict with a reasonable degree of accuracy the experimentally observed cyclic behavior of steel-braced frames.

Aluminum Alloy 7075 Ratcheting and Plastic Shakedown Evaluation with the Multiplicative Armstrong–Frederick Model

This work investigates experimentally and computationally the uniaxial ratcheting strain and plastic shakedown of aluminum alloy 7075-T6. The experimental results illustrate the existence of both plastic shakedown and cyclic hardening, proving that both kinematic and isotropic hardening should be included in modeling. Although the multicomponent Armstrong–Frederick model with multiplier has demonstrated high accuracy in aluminum ratcheting simulation, as well implementation ease, the present results demonstrate poor performance when plastic shakedown is considered. This is attributed to the limited flexibility in varying the model parameters to balance the loading/unloading branches in the hysteresis loops and decelerate ratcheting pace. To improve the ability of the multicomponent Armstrong–Frederick model with multiplier in simulating plastic shakedown, a modification was made within the framework of the model that includes multiple backstress components, with each obeying its own kinematic hardening. A linear kinematic hardening backstress was added in the formulation, enabling the control of ratcheting pace and the occurrence of plastic shakedown. Simulations with the modified multicomponent Armstrong–Frederick model with multiplier demonstrate a significantly improved capability for ratcheting and plastic shakedown. Moreover, the modified multicomponent Armstrong–Frederick model with multiplier improved the life prediction for an actual aerospace structure. This provides a strong indication of the importance of achieving plastic shakedown accuracy when simulating cyclic elastoplastic behavior.

Cyclic elastoplastic behaviour, hardness and microstructural properties of Ti-6Al-4V manufactured through selective laser melting

Additive manufacturing methods have been increasingly attracting the attention of researchers and engineers due to offered advantages in this regard. Selective laser melting (SLM) is an additive manufacturing process which is used to produce complex shaped parts. Limited research has been reported so far on the cyclic elastoplastic response of SLM Ti-6Al-4V, a technologically significant phenomenon affecting the low and high cycle fatigue performance of the fabricated parts. This research presents preliminary results obtained from an in-progress mechanical characterisation campaign conducted on SLM Ti-6Al-4V specimens. Experimental data from uniaxial strain controlled tests are presented in conjunction with surface hardness measurements and an examination of the microstructural characteristics of the materials. Wrought material data, obtained from testing and the literature are utilised for comparison. Preliminary findings of ongoing research provide an insight in the elastoplastic behaviour anticipated for this class of metals.

Numerical implementation of a multiaxial cyclic plasticity model for the Local Strain method in low cycle fatigue

Very often computations on structural elements or machine components subjected to variable loading require the use of an advanced finite element model. This paper reports the numerical implementation of a model for multiaxial cyclic elasto-plastic behaviour, developed to extend the tools of the Local Strain method to fatigue under multiaxial conditions. A basic computer code for axial–torsional loads was developed with the commercial software MATLAB and a more sophisticated one, for general multiaxial loads, was developed as a UMAT subroutine in ABAQUS. Stress integration was introduced in the two usual forms: implicitly and explicitly. A comparison of the results obtained with the implicit and explicit formulations revealed that, under certain loading conditions, the outcome of the process depends very much on the particular integration scheme used.

Modeling of fatigue life of materials and structures under low-cycle loading

A damaged medium model (DMM) consisting of three interconnected components (relations determining the cyclic elastoplastic behavior of the material, kinetic damage accumulation equations, and the strength criterion for the damaged material) was developed to estimate the stress strain state and the fatigue life of important engineering objects. The fatigue life of a strip with a cut under cyclic loading was estimated to obtain qualitative and quantitative estimates of the DMM constitutive relations under low-cycle loading. It was shown that the considered version of the constitutive relations reliably describes the main effects of elastoplastic deformation and the fatigue life processes of materials and structures.