Additional Cyclic Hardening Research Articles

Multiaxial fatigue life prediction method based on the back-propagation neural network

The study was devoted to developing a reliable multiaxial fatigue life prediction method with the effect of additional cyclic hardening considered. Based on the original assumptions of traditional critical plane methods, a new characteristic plane (subcritical plane) was defined to describe the particularity of additional cyclic hardening under non-proportional loading condition. On the new defined subcritical plane, a new multiaxial fatigue damage control parameter containing the effect of additional hardening was also built, by which the dynamic path of stress spindle, combining material property and loading environment, was fully analysed. In addition, a multiaxial fatigue life prediction back-propagation neural network (BPNN), as an alternative to the traditional physical model, was proposed to calculate the fatigue life under multiaxial loading. To calculate the multiaxial fatigue life of different materials, a more simplified combination parameter σb/E for different types of materials was chosen as input parameter in BPNN training. The availability of the proposed method was validated by reasonable correlations with experimental data of six alloy steel materials and two Non alloy steel materials under diverse loading paths.

A Novel Damage Parameter for Fatigue Life Assessment under Non-Proportional Loading

As is well-known, the loading non-proportionality has a significant influence on fatigue process, since the rotation of principal stress/strain axes can lead to additional cyclic hardening. In order to accurately reflect the effect of additional cyclic hardening on the predicted lifetime, Vantadori has recently formulated a strain-based fatigue criterion which implements a novel strain factor (function of material constants and degree of non-proportionality) in the damage parameter relationship. By considering some experimental data available in the literature, the goal of the present paper is to discuss the accuracy of the present criterion in estimating fatigue lifetime of metallic components, especially under non-proportional loading.

Three-level model based on physical theories of plasticity: Formulation, implementation algorithms, results of application to the study of cyclic loading

The physical and mechanical properties of metals and alloys, as well as, the operational characteristics of products made of them, are known to be significantly determined by the meso- and microstructure of materials. Therefore, physically oriented models that can be used to analyze the material structure evolution have been intensively developed and widely applied in recent decades for the study of thermomechanical processing of metals and alloys. These models are based on the introduction of internal variables, theories of crystal plasticity (elastoviscous plasticity), and a multilevel approach. In this paper, we consider the structure, mathematical formulation and algorithm for implementing a three-level (macro-, meso-1, and meso-2 levels) dislocation-oriented model designed to study the behavior of a representative macrovolume (macrosample) of mono- and polycrystalline alloys under cyclic deformation paths. The loading is given, and the Voigt (Taylor) hypothesis is used to connect the macro- and mesolevel-1. The mesolevel-2 submodel operates with the densities and velocities of full and split edge dislocations on slip systems. Interactions of dislocations of various systems, such as annihilation, hardening due to forest dislocations, formation of barriers of a dislocation nature (Lomer–Cottrell, Hirt) are taken into account. At mesolevel-1, the description is carried out in terms of shear stresses and shear rates along slip systems, determined by the Orowan equation using the mesolevel-2 data. A rigid moving coordinate system associated with a crystal lattice is introduced to evaluate the rotation of crystallites. The response of the material at the macro level is determined by averaging the stresses in crystallites. The results of applying the model to the study of deformation of alloy macrosamples with different values of stacking fault energy along simple and complex deformation trajectories are presented. It is shown that the materials with low stacking fault energy demonstrate the effect of additional cyclic hardening when loaded along complex deformation trajectories.

A Novel Multiaxial Strain-Based Criterion Considering Additional Cyclic Hardening.

The present paper is dedicated to the theoretical evaluation of a loading feature, that may have a significant influence on fatigue phenomenon: non-proportionality. As a matter of fact, considerable interactions between dislocations, leading to the formation of dislocation cells, cause additional cyclic hardening of material. Such a phenomenon is experimentally observed for materials sensitive to non-proportionality. In such a context, the present paper is aimed to propose a novel multiaxial strain-based criterion, the refined equivalent deformation (RED) criterion, which allows to take into account, in fatigue life estimation, both strain amplitude and additional cyclic hardening. The accuracy of the novel criterion is evaluated by considering experimental tests, performed on Ti-6Al-4V specimens, subjected to multiaxial LCF loading.

A new multiaxial fatigue life prediction model for aircraft aluminum alloy

Considering the frequent failure of aircraft caused by the multiaxial fatigue damage, it is very necessary to develop a reliable mathematical model to predict the multiaxial fatigue life for aircraft aluminum alloy. In our study, a new multiaxial fatigue life prediction model was proposed for both thin-walled tubular and notched specimens. In presented model, a new characteristic plane (subcritical plane) was defined to describe the particularity of additional cyclic hardening under non-proportional loading condition. On the new defined subcritical plane, a corresponding damage parameter containing the effect of additional hardening was also built, by which the dynamic path of stress spindle, combining material property and loading environment, was fully analysed. Finally, in order to verify the effectiveness of the new model for the multiaxial fatigue life prediction of aircraft aluminum alloy, multiaxial fatigue experiment for 2A12 aluminum alloy in four types of fatigue specimens was employed for the material fatigue failure simulation of the aircraft. Through the comparison result with three traditional models, it was evident the stability and accuracy of the new proposed model were much superior to those of the other three traditional models.

Prediction of multiaxial fatigue life for complex three‐dimensional stress state considering effect of additional hardening

AbstractIn engineering practice, it is generally accepted that most of components are subjected to multiaxial stress‐strain state. To analyse this complicated loading state, different types of specimens of 2A12 (2124 in the United States) aluminium alloy were tested under multiaxial loading conditions and a new multiaxial fatigue analysis method for the state of three‐dimensional stress and strain is proposed. Elastic‐plastic finite element method (FEM) and a proposed vector computing method are used to describe the loading state at the critical point of specimen, by which the parameter ΓT is calculated at the new defined subcritical plane to consider the effect of additional cyclic hardening. Meanwhile, the principal equivalent strain is still calculated at the traditional critical plane. The new damage parameter is composed of different process parameters, by which the dynamic path of strain state, including loading environments and material properties, are fully considered in one loading cycle. According to experimental verifications with 2A12 aluminium alloy, the results show that the proposed method shows satisfactory, accurate, and reliable results for multiaxial fatigue life prediction in the state of three‐dimensional stress and strain.

Low-cycle fatigue behaviour of an aero-engine disk alloy under non-proportional loading

The quest for higher efficiency and fuel economy has pushed aeroengines to challenging levels. In order to become more efficient, engines must run at higher bypass ratios and temperatures, resulting in extreme operating conditions for their hottest section. Nickel based superalloys have been used for this application for the past 50 years due to high fatigue strength at elevated temperatures. This paper investigates the deformation behaviour and fatigue lives of a powder metallurgy Nickel-based superalloy developed for discs of high-pressure turbines, i.e. the most demanding section of aeroengines. For that six different non-proportional load paths were carefully selected, where five of them present the same degree of load non-proportionality, to explore load path dependency and the effects of non-proportional multi-axial loading on fatigue lives. Results confirm an additional cyclic hardening caused by load non-proportionality and its detrimental effect on fatigue life. Lives for non-proportional tests were around three times shorter than fatigue lives for proportional tests at comparable stress levels.

A survey on multiaxial fatigue damage parameters under non‐proportional loadings

AbstractIn this paper, several multiaxial fatigue damage parameters taking into account nonproportional additional hardening are reviewed. According to the way nonproportional additional hardening is considered in the model, the damage parameters are classified into 2 categories: (1) equivalent damage parameters and (2) direct damage parameters. The equivalent damage parameters usually define a nonproportional coefficient to consider nonproportional additional cyclic hardening, and make a combination of this nonproportional coefficient with stress and/or strain quantities to calculate the equivalent damage parameters. In contrast, the direct damage parameters are directly estimated from the stress and strain quantities of interest. The accuracy of 4 multiaxial fatigue damage parameters in predicting fatigue lifetime is checked against about 150 groups of experimental data for 10 different metallic materials under multiaxial fatigue loading. The results revealed that both Itoh's model, one of equivalent damage parameters, and Susmel's model, which belong to direct damage parameters, could provide a better correlation with the experimental results than others assessed in this paper. So direct damage parameters are not better than the equivalent damage parameters in predicting fatigue lifetime.

Multiaxial Cycle Deformation and Low-Cycle Fatigue Behavior of Mild Carbon Steel and Related Welded-Metal Specimen

The low-cycle fatigue experiments of mild carbon Q235B steel and its related welded-metal specimens are performed under uniaxial, in-phase, and 90° out-of-phase loading conditions. Significant additional cyclic hardening for 90° out-of-phase loading conditions is observed for both base metal and its related weldment. Besides, welding process produces extra additional hardening under the same loading conditions compared with the base metal. Multiaxial low-cycle fatigue strength under 90° out-of-phase loading conditions is significantly reduced for both base-metal and welded-metal specimens. The weldment has lower fatigue life than the base metal under the given loading conditions, and the fatigue life reduction of weldment increases with the increasing strain amplitude. The KBM, FS, and MKBM critical plane parameters are evaluated for the fatigue data obtained. The FS and MKBM parameters are found to show better correlation with fatigue lives for both base-metal and welded-metal specimens.

Prediction of non-proportional cyclic hardening and multiaxial fatigue life for FCC and BCC metals under constant amplitude of strain cycling

The fatigue lives are reduced accompanying an additional cyclic hardening under strain controlled non-proportional cyclic loading in which principal directions of stress and strain are altered within a cycle. This study predicts non-proportional cyclic hardening and multiaxial fatigue life for several BCC and FCC metals under constant amplitude strain cycling. A novel procedure to determine non-proportional cyclic hardening form uniaxial tensile properties has discussed in this study. Standard plastic strain energy density based fatigue criteria with considering the non-proportional cyclic hardening effect successfully predicts multiaxial fatigue lives. The predictions of non-proportional cyclic hardening and multiaxial fatigue life through models are validated by experimental results of various BCC and FCC metals which are collected from literatures.

Multiaxial Fatigue Damage Prediction and Life Estimation of a Centrifugal Impeller for a Turboshaft Engine

The rotating gas turbine engine component such as centrifugal compressor is subjected to various static and dynamic loads during service. These service loads introduce multiaxial stress-strain states and inflict severe structural damage and hence reduce compressor efficiency and service life. In many cases, the service loads are non-proportional which introduces additional cyclic hardening depending on the loading path and the material used (Wu et al., Int J Fatigue 59:170–175, 2014). Studies have revealed that fatigue life is drastically reduced as a result of this additional cyclic hardening phenomenon. In recent decades, numerous multiaxial fatigue damage theories (which are strain based) have been developed taking into account the factors influencing fatigue like operating temperature, anisotropy, microstructure, nature of loading (proportional or non-proportional), and environmental effects. In general, these theories envisage crack nucleation and propagation to take place at a critical plane, but differ from one another the way critical planes are defined and damage parameters are proposed. To estimate the fatigue life under the multiaxial loading conditions, these theories relate multiaxial stress-strain components to uniaxial fatigue properties obtained from test data. But, it is observed that most of these theories are limited in application to a particular material or loading conditions. No general consensus is available on the best available fatigue damage theory for a particular application. Further, literature shows that most of these theories are applied and compared on tubular and notched test specimens under proportional and non-proportional loading conditions. Literatures are seldom available which compares these theories at the application level and validate through experiments. The objective of this paper is to estimate the low-cycle fatigue life of a centrifugal impeller used in a gas turbine application using different multiaxial fatigue damage models in the literature and propose a methodology which closely fits the experimental results. For applications such as gas turbine engines, the margin of safety (with respect to 0.2% PS) varies in the range of 1.05 to 1.15 (Stephens et al. in Metal fatigue in engineering. Wiley, New York, 2001). For this, it is extremely important to estimate the life and damage mechanism affecting the life of the components accurately to ensure the flight safety, reliability, and total service life of the gas turbine engine. The centrifugal impeller was designed for a pressure ratio of 3.2 and maximum rotational speed of 52,500 rpm. The titanium alloy Ti6Al4V was chosen as the possible material for the impeller as it has high strength and stiffness to weight ratio and is widely used in aerospace application (Wu et al., Int J Fatigue 44(12):14–20, 2012). The entire analysis can be divided into three main modules. Firstly, the stress and strain history on the centrifugal impeller was determined under actual operating condition. Finite element structural analysis packages were used for this purpose. Secondly, the stress-strain histories obtained from FE analysis were post-processed using several multiaxial fatigue damage models like Maximum von Mises strain model (Kalluri and Bonacuse in In-Phase and Out-of-Phase Axial-Torsional Fatigue Behavior of Haynes 188 at 760 °C. NASA Technical Report 1991, 91-C-046, 1991), which is based on the equivalent strain and the Smith-Watson-Topper (SWT) model (Shamsaei and McKelvey, Int J Fatigue 59:170–175, 2014), Kandil-Brown-Miller (KBM) model (Kandil et al., Met Struct 280:203–210, 1988), Fatemi and Socie (FS) model (Fatemi and Socie, Fatigue Fract Eng Mater 11(3):149–166, 1987), which are based on the critical plane approach to obtain the fatigue life. Finally, a prototype of the centrifugal impeller was made and tested at our sophisticated cyclic spin test facility to validate the Low-Cycle Fatigue life.

Multiaxial and Thermomechanical Fatigue of Materials: A Historical Perspective and Some Future Challenges

Abstract Many engineering components in aircraft gas turbine engines, reusable space propulsion systems, and automotive engines must endure cyclic mechanical forces and deformations in multiple directions and non-isothermal conditions. For the design and safety of such engineering components, durability needs to be estimated with robust multiaxial fatigue life prediction models that are validated under such non-isothermal conditions. In this paper, a historical review is presented on the evolution of uniaxial fatigue (thermal, isothermal, bithermal, and thermomechanical) and isothermal, multiaxial fatigue leading to multiaxial, thermomechanical fatigue with several examples on testing techniques and fatigue life prediction methodologies. The necessity for multiaxial, thermomechanical fatigue testing of structural and engine materials, additional cyclic hardening and reduction in fatigue life observed under such service conditions, and ramifications of estimating multiaxial, thermomechanical fatigue life with isothermal multiaxial fatigue data at the greatest temperature of the cycle are discussed. Finally, some of the potential future challenges associated with experimental characterization of materials and fatigue life estimation under these complex but realistic service conditions are highlighted.

Investigation of the features of polycrystals complex loading using a two-level crystal plasticity theory

The article considers a two-level mathematical model of inelastic deformation of metal polycrystals taking into account evolution of the structure. The structure of the model was considered, some special features of its application to describe the intensity of inelastic deformations were marked. The need for a careful physical analysis of the hardening laws construction was highlighted. To evaluate the applicability of multi-level models to describe the known experimental effects of cyclic deformation a number of results of field experiments on the complex proportional and disproportional cyclic deformation was considered, some specific effects that appear in these processes were identified: stresses amplitude output at the stationary value; additional cyclic hardening at a disproportionate loading, which magnitude depends on the so-called degree of disproportionality. Numerical experiments on the disproportionate cyclic loading were carried out, the possibility of modified hardening laws to describe access to the stationary values of the stress intensity was noted, and also the possibility of a qualitative description of the effect of additional cyclic hardening was demonstrated. The A.A. Ilyushin hypothesis by isotropy and the principle of vector properties delay at the turn of the deformation path were validated.

Multiaxial effects on LCF behaviour and fatigue failure of AZ31B magnesium extrusion

Multiaxial cyclic tests were performed on wrought AZ31B magnesium extrusion. Axial, torsional and multiaxial cyclic behaviours of the material are presented. Effects of phase angle on stress–strain response, cyclic hardening and fatigue life are discussed. It was found that the material exhibits additional cyclic hardening due to non-proportional loading. However, the phase angle has no pronounced effect on fatigue life. Fatigue cracking behaviour was examined and two characteristics of crack geometry, i.e., size and orientation, are presented. Multiaxial fatigue lives using the Fatemi–Socie and the Smith–Watson–Topper models were predicted. In addition, the Jahed–Varvani energy model was used for fatigue life prediction and was shown to have a potential to be evaluated at plane of maximum axial strain energy density. Reverse analysis for predicting fatigue life by pre-defined critical plane as the observed plane is discussed in details.

Multiaxial fatigue: An overview and some approximation models for life estimation

A brief overview of some important issues in multiaxial fatigue and life estimation is presented. These include damage mechanisms and damage quantification parameters, material constitutive response and non-proportional hardening, cycle counting and damage accumulation in variable amplitude loading, and mixed-mode crack growth. It is shown that capturing the correct damage mechanism is essential to develop a proper damage quantification parameter for robust multiaxial fatigue life estimation. Additional cyclic hardening of some materials under non-proportional multiaxial loading and its dependence on the load path as well as material microstructure is also discussed. It is argued that critical plane damage models with both stress and strain terms are most appropriate since they can reflect the material constitutive response under non-proportional loading. Importance of a proper cycle counting method to identify cycles in a variable amplitude load history, and capability of the linear cumulative damage rule to sum damage from the counted cycles are also discussed. As mixed-mode crack growth can constitute a significant portion of the total fatigue life, analysis of crack growth rates and correlations under combined stresses is presented. Several models as well as some simple approximations in capturing the aforementioned effects in multiaxial fatigue life estimations are also described. The approximation models include an estimation model for obtaining material non-proportional cyclic hardening coefficient, and a simple multiaxial fatigue life estimation model for steels based on hardness as the only required material property.

Material dependence of multiaxial low cycle fatigue lives under non-proportional loading

This study discusses evaluation of material dependence of multiaxial low cycle fatigue to develop a suitable strain parameter for life estimation under non-proportional loading. It has been reported that fatigue lives are reduced accompanying an additional hardening under strain controlled non-proportional loading in which principal directions of stress and strain are changed in a cycle. Strain controlled multiaxial low cycle fatigue tests under proportional and non-proportional strain paths were carried out using hollow cylinder specimens of several materials. The reduction in low cycle fatigue life due to non-proportional loading is discussed relating to the additional cyclic hardening behaviors and its material dependence. Material constant, α, used in strain parameter for life estimation under non-proportional multiaxial low cycle fatigue is also discussed.

Low-cycle fatigue life prediction of various metallic materials under multiaxial loading

This paper proposed a simple life prediction model for assessing fatigue lives of metallic materials subjected to multiaxial low-cycle fatigue (LCF) loading. This proposed model consists of the maximum shear strain range, the normal strain range and the maximum normal stress on the maximum shear strain range plane. Additional cyclic hardening developed during non-proportional loading is included in the normal stress and strain terms. A computer-based procedure for multiaxial fatigue life prediction incorporating critical plane damage parameters is presented as well. The accuracy and reliability of the proposed model are systematically checked by using about 300 test data through testing nine kinds of material under both zero and non-zero mean stress multiaxial loading paths.

A modification of Shang–Wang fatigue damage parameter to account for additional hardening

Based on the critical plane approach, the Shang–Wang fatigue damage parameter is analyzed. It is discovered that the effect of the additional cyclic hardening on fatigue life cannot be reflected by the normal strain excursion well. In order to solve this problem, this fatigue damage parameter is modified by using the Huber–Mises criterion. The modified damage parameter combined maximum shear strain range with normal strain range on the critical plane, and a new stress-correlated factor is introduced to account for the additional cyclic hardening. It is demonstrated that the modified criterion gives satisfactory results for all the six checked materials.

A New Multiaxial Fatigue Life Prediction Model Under Proportional and Nonproportional Loading

Based on the critical plane approach, the drawbacks of the Wang–Brown (WB) model are analyzed. It is discovered that the normal strain excursion in the WB model cannot account for the additional cyclic hardening well. In order to solve this problem, a new damage parameter for multiaxial fatigue is proposed. In the meantime, the procedure for multiaxial fatigue life assessment incorporating critical plane damage model is presented as well. In the new damage parameter, both strain and stress components are considered, and the effect of the additional cyclic hardening on the fatigue life during nonproportional loading is taken into account as well. In addition, the proposed model is modified when the mean stress is existence. It is convenient for engineering application because of no material constants in this parameter. The capability of fatigue life assessment for the proposed fatigue damage model is checked against the experimental data found in literature for tubular specimens of 1045HR steel, hot-rolled 45 steel, S460N steel, GH4169 alloy at elevated temperature, and the notched shaft of SAE 1045 steel, which is under cyclic bending and torsion loading. It is demonstrated that the proposed criterion gives satisfactory results for all the five checked materials.

Geometrically necessary dislocation structure organization in FCC bicrystal subjected to cyclic plasticity

Crystal plasticity finite element analysis of cyclic deformation of compatible type FCC bicrystals are performed. The model specimen used in the analysis is a virtual FCC bicrystal with an isotropic elastic property; therefore, the effect of constraint due to elastic incompatibility does not appear. The results of the analysis show the strain-amplitude-dependence of both the organization of the GND structure and the stress–strain behavior. The calculated stress–strain curve with the largest strain amplitude shows additional cyclic hardening. The microscopic mechanisms of the strain-amplitude-dependent organization of the GND structure and additional cyclic hardening behavior are discussed in terms of the activation of secondary slip system(s). Finally, the effects of the elastic anisotropy, the lattice friction stress and the interaction between dislocations are also argued.