Cyclic Hardening Model Research Articles

Cyclic deformation response of annealed low-carbon steel: Insights from ratcheting and LCF experiments

Low cycle fatigue (LCF) and ratcheting experiments were carried out on annealed low-carbon steel at room temperature within a laboratory environment, utilising stress and strain control modes. The annealed low-carbon steel consistently demonstrates a cyclic softening response over its LCF lifespan, across all tested strain amplitudes. Notably, it was observed that ratcheting strain rises while ratcheting life declines with both rising mean stress and stress amplitude. Annealed low-carbon steel, being entirely ferritic and lacking precipitation or substitutional solid solution strengthening or hard phase strengthening, exhibits a restricted ability to withstand or alleviate the accumulation of ratcheting strain, particularly under very low mean stress conditions. In both LCF and ratcheting, significant substructure formation was detected. Nevertheless, there was no discernible difference in substructure formation between LCF and ratcheting when employing electron channelling contrast imaging techniques. The existing mean stress-based fatigue life prediction model has successfully forecasted ratcheting and LCF life within the 102–105 cycles range. A novel approach utilising modulus is introduced to characterise the cyclic hardening/softening behaviour of alloys in stress and strain-controlled experiments. The cyclic hardening model based on modulus effectively captures the responses observed in cyclic hardening/softening during LCF and ratcheting experiments.

Using XFEM technique to predict the crack growth in the notched plate under high loading cyclic conditions

Our study delves into analyzing fatigue damage in notched structures, an essential field in structural mechanics. We aim to understand how geometric and dimensional variations in the notches affect fatigue damage under different modes and amplitudes of cyclic loading, focussing on the behavior of steel. Our research methodology integrates experimental and numerical approaches. Experimental validation encompasses material properties, mesh selection, and boundary conditions. The finite element method is tailored to address steel’s elastoplastic behavior, employing calibrated parameters for kinematic and isotropic cyclic hardening models within the numerical realm. Specific findings elucidate the cyclic response of notched structures, tracking damage progression to critical thresholds, including the number of cycles to failure (Nf) and the critical crack length ( Lc ). Hysteresis curves vividly depict stress–strain relationships, offering insight into material behavior under cyclic loading. Implications span engineering domains, focussing on reliability and durability in the aerospace, automotive, and civil engineering sectors. Future directions include real-world applications and advanced techniques such as the Extended Finite Element Method (XFEM). In conclusion, this research enriches our understanding of fatigue damage analysis in notched structures, poised to impact safety and robust engineering design.

Size effect on the cyclic deformation behavior of superalloy ultrathin sheet: Characterization and multiscale modelling

Superalloy ultrathin sheets have high strength, outstanding oxidation resistance, corrosion resistance and fatigue performance, and its thin-walled components occupy a considerable proportion in aeroengines. In the microforming process of aeroengine thin-walled components, the superalloy ultrathin sheet is often deformed under complex loading states and shows obvious springback. However, the forming and springback laws of superalloy ultrathin sheet in the microforming process are not clear and often affected by size effect. In addition, the existing nonlinear kinematic hardening models cannot accurately forecast the deformation and springback of superalloy ultrathin sheets. To address this issue, the cyclic shearing tests were performed to systemically explore the size effect on Bauschinger effect, permanent softening, transient hardening and work hardening stagnation of superalloy ultrathin sheets under cyclic loading states. The mechanism of size effect on cyclic mechanical response was systematically revealed through microstructure evolution combined with surface layer effect. In addition, a new multiscale cyclic hardening model was proposed based on the Y-U model and size effect on cyclic deformation behavior of superalloy ultrathin sheets. The new multiscale cyclic hardening model coupling surface layer effect and grain boundary strengthening effect was constructed by modeling the relationship between the cyclic mechanical response and size effect. Comparisons between the original Y-U model and the new proposed model on the characterization effect of shear stress-strain curves demonstrated that the proposed cyclic hardening model can accurately present the cyclic deformation behavior. To further verify the prediction capability of the proposed cyclic hardening model, the springback behavior of superalloy ultrathin sheet in U-bending test and hydroforming of seal ring was predicted via the proposed model combined with the decrease of elastic modulus and Yld2000–2d yield criterion, and the predicted results were compared with experimental ones. Comparative research revealed that the proposed cyclic hardening model can accurately describe the cyclic deformation behavior and springback of superalloy ultrathin sheets affected by size effect.

Cyclic deformation and dynamically induced short-range ordering in small particles reinforced Al composite

Cyclic deformation of an Al-Cu-Mg composite strengthened by small non-shareable particles was firstly investigated through strain controlled low-cycle fatigue (LCF) tests. In comparison with the reported Al-Cu-Mg composites, the in-situ TiB2/Al-Cu-Mg composite presented higher fatigue life at all the tested strain amplitudes. The composite exhibited cyclic hardening response, which was contributed by non-shareable particles, dislocations and dynamically deformation-induced short-range orderings in the Al matrix. Considering plastic strain evolution, the cyclic hardening model was established and well fitted with experimental results. When cyclic loading was controlled at higher strain amplitudes, the serrated flow occurred on stress-strain hysteresis loops and then it disappeared after the first few cycles related to the occurrence of dynamic strain aging. Onset of the stress serration on stress-strain hysteresis loop was greatly dependent on the strain amplitude rather than cumulative plastic strain. Finally, the correlative cyclic hardening model of small particles reinforced Al composite was analytically discussed based on microstructure evolution and cyclic stress-strain responses.

Verification of the Tanaka non-proportional isotropic cyclic hardening model under asynchronous loading

Non-proportional cyclic loading path induces intrinsic strain hardening to the low stacking fault energy materials. The hardening is manifested in increased stress response which underestimation leads to non-conservative life prediction. This study aims to verify the Tanaka non-proportional isotropic cyclic hardening model under a wide spectrum of multiaxial asynchronous loadings. The Tanaka model is coupled with the Chaboche kinematic hardening model for stress path estimation. Modeling results are compared with fatigue experiments for two non-alloyed steel grades, E235 and E355. The Tanaka model improves the performance of the Chaboche model and exhibits its applicability to asynchronous loading.

Numerical and Experimental Assessment of the Effect of Residual Stresses on the Fatigue Strength of an Aircraft Blade.

The work presents the results of numerical fatigue analysis of a turbine engine compressor blade, taking into account the values of initial stresses resulting from surface treatment-shot-peening. The values of the residual stresses were estimated experimentally using X-ray diffraction. The paper specifies the values of the residual stresses on both sides of the blade and their reduction due to cutting through the blade-relaxation. The obtained values of the residual stresses were used as initial stresses in the numerical fatigue analysis of the damaged compressor blade, which was subjected to resonant vibrations of known amplitude. Numerical fatigue ε-N life analysis was based on several fatigue material models: Manson’s, Mitchell’s, Baumel-Seeger’s, Muralidharan-Manson’s, Ong’s, Roessle-Fatemi’s, and Median’s, and also on the three models of cyclic hardening: Manson’s, Xianxin’s, and Fatemi’s. Because of this approach, it was possible to determine the relationship between the selection of the fatigue material ε-N model and the cyclic hardening model on the results of the numerical fatigue analysis. Additionally, the calculated results were compared with the results of experimental research, which allowed for a substantive evaluation of the obtained results. These results are of great scientific and practical importance. The problem of determining the fatigue life of blades with defects operating under resonance vibrations is one of the original tasks in the field of fracture mechanics and experimental mechanics. The results obtained are of great importance in the aviation industry and can be used during engine maintenance and inspections to assess the suitability of blades with defects in terms of the needs of further work. This aspect of engineering maintenance is of great importance from the aircraft safety point of view.

Cyclic plastic deformation mechanism and cyclic hardening model of Sanicro 25 steel welded joint

The low cycle fatigue (LCF) behaviors of Sanicro 25 steel welded joint were investigated under different total strain amplitudes (Δεt/2) at 700 °C. The results revealed that the stress amplitude increased with an increase in Δεt/2, while the fatigue life decreased. In addition, the cyclic hardening ratio first increased and then decreased with increasing Δεt/2. This abnormal trend was attributed to the variation in the cyclic yielding stress, indicating the evolution of the dislocation morphology. The microstructure analysis revealed a significant change in the cyclic plastic deformation mechanism from the dislocation tangle (0.2%–0.4%) to the entanglement of dislocations on the precipitate (0.5%) with an increase in Δεt/2. Furthermore, the cyclic hardening models considering the entanglement of dislocations on the precipitate and the dislocation tangle were unified according to the modified Taylor stress. The validated results indicated that the unified cyclic hardening model accurately calculated the maximum cyclic stress during LCF for a 316H welded joint.

Initial cyclic hardening behavior of cracked structures under large-amplitude cyclic loading

A new cyclic hardening model is proposed based on combined experimental and numerical analyses to simulate the deformation of a cracked structure under large amplitude cyclic loading. In the experiment conducted herein, compact tension specimen tests made of TP304 stainless steel were subjected to large-amplitude cyclic loading. Then, finite element (FE) analysis was performed using the ABAQUS debond option to develop a cyclic hardening model. In the proposed cyclic hardening law, isotropic hardening was calculated in the first loading cycle. To assess the unloading of the first cycle, a Chaboche combined hardening model was used. The model results agreed well with the experimental displacement data. The effects of hardening in the first loading cycle on the yield surface and equivalent plastic strains in the subsequent cycles are presented as well.

Modeling of cyclic hardening and evaluation of plastic strain range in the presence of pre-loading and ratcheting

An extended evolution equation of cyclic hardening is proposed to include the effect of maximum plastic strain due to pre-loading and ratcheting. A set of extended evolution equations is also proposed for a plastic strain surface to properly evaluate the cyclic plastic strain range in the presence of pre-loading and ratcheting. These extensions are verified by performing uniaxial cyclic experiments of 316 stainless steel at 600°C. The experiments are accurately simulated using a constitutive model with the extensions in addition to the resetting scheme of the plastic strain surface recently proposed by the authors. The extension for the plastic strain surface allows fairly good simulation of the experiments without recourse to the resetting scheme if the strain range does not markedly decrease with the number of cycles. The extended equations are further used to discuss the effect of maximum plastic strain considering previous experiments.

Viscoplastic Parametric Analysis of Cylindrical Specimen Under Cyclic Behaviour

The present study tries to present a cyclic hardening model with the aim to simulate quantitatively the material response under strain controlled cyclic loading in tension-compression, of specified axial deformation. A numerical study was carried out to investigate the cyclic constitutive behaviour of alloy Indium under viscoplastic deformation. The analysis was performed under prescribed symmetric strain-controlled cyclic loading. The model contains both isotropic and kinematic hardening components, while the analysis were performed using Comsol Multiphysics for only 60 seconds duration. The kinematic hardening was described by using multiple back stresses. Multiple back stresses can provide a smoother transition between the elastic and plastic deformation, and it improves the general shape of the hysteresis loop. Two cases (geometries) have been examined in this study. From the material model and finite element cyclic plasticity model results, it is found that for the same parameters, but different dimensions there is difference on the stress-strain curves as well as on the von Mises stresses.

Effect of damage evaluation method and cyclic hardening models on strain-based fatigue assessment to a piping system under seismic loads

In this paper, strain-based damage assessment based on elastic-plastic FE analysis was carried out for the piping system test under seismic loads conducted at Bhabha Atomic Research Center (BARC, India) to suggest relevant damage evlaution method and cyclic hardening model. For the damage evaluation method, the cumulative plastic damage and cumulative fatigue damage assessment methods, suggested in ASME BP53 % of the test result, and the use of the cumulative plastic damage method is found to be more conservative than the cumulative fatigue damage method. The effect of the hardening model on evaluation results is found to be not so significant.

Fracture Modeling Of Cracked Pipe Under Monotonic And Cyclic Loading

ABSTRACT The present work presents experiment and numerical modelling to quantify the effect of the loading type on ductile crack growth in circumferential through-wall cracked SA508 Gr.1a pipes. In tests, three types of loading conditions are considered; monotonic, displacement-controlled and load-controlled large-amplitude cyclic loading. Experimental data are compared with numerical crack growth simulation results based on the multiaxial fracture strain energy model. Simulated results show overall good agreements with experimental data for all loading types. Based on FE results, the effects of the loading type and cyclic hardening model on ductile crack growth are discussed.

Ductile tearing simulation of STS410 pipe fracture test under load-controlled large-amplitude cyclic loading: Part I—Effect of load ratio

Ductile fracture of circumferential through-wall cracked pipe under large-amplitude load-controlled cyclic loading with three different load ratios was simulated using a fracture strain energy damage model. Damage model parameters were determined from a tensile test and a pipe test under monotonic loading. Comparison of simulated and experimental data reveals that the simulation results depend on the cyclic hardening model. Further investigation confirmed that selection of an appropriate cyclic hardening model is more important under load-controlled cyclic loading then under displacement-controlled one.

Effect of strain rate induced M23C6 distribution on cyclic deformation behavior: Cyclic hardening model

Cyclic deformation mechanism of Sanicro 25 alloy was investigated under different strain rates (ε˙) at 700 °C. When ε˙ increased, the maximum stress amplitude σa decreased and the fatigue life Nf increased. The saturated hysteresis energy ΔWp first decreased and then increased with increasing ε˙. It is attributed to the variation of stress amplitude, which is related to the interaction of precipitates and dislocations. HAADF STEM analysis shows that the Cr23C6 precipitates were distributed around the NbCrN precipitate when ε˙ was less than 2 × 10−3 s−1. The local deformation mainly concentrated in the grain interior owing to the formation of the bowed dislocations. This structure can lead to an increase in the number of creep cavities owing to the increasing stress concentration around the Cr23C6 precipitates, which indicates that creep damage Dc increases. The Cr23C6 precipitates nucleated and grew at the interface between NbCrN precipitate and matrix at ε˙=4×10−3 s−1, which can lead to a small stress concentration. Therefore, it implies that the Dc decreases at the relatively high ε˙. Considering the interaction between dislocations, the interaction of precipitates and dislocations, and the interaction of dislocations and grain boundaries, a unified cyclic hardening model was established. In addition, for the interaction of precipitates and dislocations at ε˙=2×10−3 s−1, the effect of the precipitates with various sizes on the bowed dislocations was considered. The predicted maximum cyclic stresses are in good agreement with the experimental values.

Modeling the Strain-Range Dependent Cyclic Hardening of SS304 and 08Ch18N10T Stainless Steel with a Memory Surface

This paper deals with the development of a cyclic plasticity model suitable for predicting the strain range-dependent behavior of austenitic steels. The proposed cyclic plasticity model uses the virtual back-stress variable corresponding to a cyclically-stable material under strain control. This new internal variable is defined by means of a memory surface introduced in the stress space. The linear isotropic hardening rule is also superposed. First, the proposed model was validated on experimental data published for the SS304 material (Kang et al., Constitutive modeling of strain range dependent cyclic hardening. Int J Plast 19 (2003) 1801–1819). Subsequently, the proposed cyclic plasticity model was applied to our own experimental data from uniaxial tests realized on 08Ch18N10T at room temperature. The new cyclic plasticity model can be calibrated by the relatively simple fitting procedure that is described in the paper. A comparison between the results of a numerical simulation and the results of real experiments demonstrates the robustness of the proposed approach.

Influence of the Cyclic Hardening Model on the Results of the Numerical Analysis of Fatigue Life on Example of the Compressor Blade

Abstract The main goal of the presented work is to determine the impact of the cyclic hardening model on the numerical results of the ε-N fatigue test. As an object of study, compressor blade (from PZL-10W helicopter engine) was used. The examined blade was made of EI-961 alloy. In numerical analysis, a geometrical model of the blade with a preliminary defect was created. Geometrical defect – V-notch was created on the leading edge. This defect was introduced in order to weaken the structure of the element and the possibility of observing the crack initiation process (in experimental tests). Material data to ε-N analysis, based on Manson-Coffin-Basquin equation, were estimated for Mitchell’s model. This model was built based on strength data provided by the steel producer. Based on three different models of cyclic hardening (Manson, Fatemi, and Xianxin), a number of load cycles were calculated. Load cycle during numerical analysis was represented as resonance bending with an amplitude of displacement equal to A = 1.8 mm. Obtained results were compared with experimental data. Additionally, the analytical model of ε-N fatigue (depending on the cyclic hardening) was prepared. All the work carried out has been summarized by a comprehensive comparative analysis of the results. Obtained results and dependencies can be used in the selection of an appropriate model of cyclic hardening in further fatigue tests of many aerospace elements.

Fatigue crack initiation prediction using phantom nodes-based extended finite element method for S355 and S690 steel grades

The assessment of fatigue crack initiation behavior of steel structures is essential and important especially to improve the application of high strength steel in construction. For a complete understanding of fatigue endurance, it is necessary to combine the phenomenological damage model with finite element numerical approach. In this paper, phantom nodes-based extended finite element method is used to predict the fatigue crack initiation of steel material, considering a prediction by XFEM of coupon tests made of steel grades S355 and S690. A user-defined fatigue damage initiation subroutine based on Smith, Watson, and Topper (SWT) damage model combined with non-linear isotropic/kinematic cyclic hardening model is implemented to predict fatigue crack initiation. The proposed method is successfully validated based on fatigue coupon test results of both steel grades, S355 and S690.

Cyclic deformation behavior of an Fe-Ni-Cr alloy at 700 °C: microstructural evolution and cyclic hardening model

The cyclic deformation behavior of an Fe-Ni-Cr alloy was studied based on low-cycle fatigue (LCF) experiments at 700 °C with various total strain amplitudes Δεt/2 A cyclic hardening behavior was found for Sanicro 25 alloy. The increasing rate of stress amplitude increased first, and subsequently decreased with prolonged cycles. The cyclic hardening ratio increased when Δεt/2 increased. Microstructure observations revealed that the Cr23C6 in the grain interiors were mainly distributed around the NbCrN precipitate. Additionally, the Cr23C6 precipitate aggregated and coarsened with an increasing Δεt/2 The shape of Cr23C6 precipitate also changed from rectangular to circular. The fracture surface observation showed the precipitates can be observed at the crack initiation site and in the microcavities and dimples. It indicates that the precipitates affect the fatigue fracture. In addition, the fraction of deformed grains increases as Δεt/2 increases. Furthermore, based on the modified Fisher-Hart-Pry (FHP) back-stress influenced by precipitates with different radii, the influences of the glide strain, half spacing of precipitates, and radius of precipitates on FHP back-stress were investigated. The applied stress increases with increasing glide strain and radius of precipitates. When the half spacing of precipitates increases, the applied stress decreases.

Chaboche-based cyclic material hardening models for 316 SS–316 SS weld under in-air and pressurized water reactor water conditions

This paper discusses a material hardening models for welds made from 316 stainless steel (SS) to 316 SS. The model parameters were estimated from the strain-versus-stress curves obtained from tensile and fatigue tests conducted under different conditions (air at room temperature, air at 300°C, and primary loop water conditions for a pressurized water reactor). These data were used to check the fatigue cycle dependency of the material hardening parameters (yield stress, parameters related to Chaboche-based linear and nonlinear kinematic hardening models, etc.). The details of the experimental results, material hardening models, and associated calculated results are published in an Argonne report (ANL/LWRS-15/2). This paper summarizes the reported material parameters for 316 SS–316 SS welds and their dependency on fatigue cycles and other test conditions.

Application of steel equivalent constitutive model for predicting seismic behavior of steel frame

In order to investigate the accuracy and applicability of steel equivalent constitutive model, the calculated results were compared with typical tests of steel frames under static and dynamic loading patterns firstly. Secondly, four widely used models for time history analysis of steel frames were compared to discuss the applicability and efficiency of different methods, including shell element model, multi-scale model, equivalent constitutive model (ECM) and traditional beam element model (especially bilinear model). Four-story steel frame models of above-mentioned finite element methods were established. The structural deformation, failure modes and the computational efficiency of different models were compared. Finally, the equivalent constitutive model was applied in seismic incremental dynamic analysis of a ten-floor steel frame and compared with the cyclic hardening model without considering damage and degradation. Meanwhile, the effects of damage and degradation on the seismic performance of steel frame were discussed in depth. The analysis results showed that: damages would lead to larger deformations. Therefore, when the calculated results of steel structures subjected to rare earthquake without considering damage were close to the collapse limit, the actual story drift of structure might already exceed the limit, leading to a certain security risk. ECM could simulate the damage and degradation behaviors of steel structures more accurately, and improve the calculation accuracy of traditional beam element model with acceptable computational efficiency.