Cyclic Plasticity Research Articles

Microstructural Evolution and Mechanical Properties of Reeled X65 Pipeline Steel during Cyclic Plastic Deformation and Natural Aging

The reel laying is recognized as a cost‐effective installation process for offshore pipelines. However, the mechanical properties are modified due to plastic deformation during the reel laying and lowering process of reeled pipelines and the subsequent natural aging in service. Cyclic plastic deformation (CPD) is conducted on X65 pipeline steel to simulate the strain experienced in the reel‐laying and lowering process, and then, the CPD specimen is aged at 250 °C to simulate natural aging in service. The dislocation configurations gradually evolve from dislocation lines and tangles into dislocation walls and cells due to the increase in strain level. After CPD and aging, the tensile strength increases by about 25 MPa, which is not significantly affected by the last introduced load direction and strain level. At the end of compressive loading, the yield strength and yield ratio decrease, but the uniform elongation increases significantly. In contrast, at the end of tensile loading, the yield strength and yield ratio increase, but the uniform elongation decreases slightly. The yield strength further increases as the strain level increases from 2 to 3%. Therefore, CPD and aging modify the mechanical properties of X65, considerably depending on the last introduced load direction and strain level.

Anisotropy cyclic plasticity constitutive modelling for Ni-based single-crystal superalloys based on Kelvin decomposition

Nickel-based single-crystal (SC) superalloys exhibited excellent exceptional mechanical properties at high temperatures due to the elimination of internal grain boundaries, contributed a strong orientation-dependent material response. The anisotropy of SC superalloys was modeled viscoplastically from a macroscopic viewpoint based on the Kelvin decomposition theory [1] which was a decomposition of the stress space according to the elastic matrix eigen-directions to control the viscoplastic flow by Kelvin stress decoupled from each other. Compared to the classical phenomenological macro model, the proposed model effectively captures the slip deformation mechanism of SC superalloys with the inherent ability to simulate anisotropic because of the two criterions framework controlled by Kelvin stress. Compared with others, the proposed model was able to simulate time-dependent inelastic deformation and cyclic deformation behavior under complex loading. The kinematic hardening and isotropic hardening models incorporated microscopic quantities, such as dislocation density and channel phase width, connecting the macroscopic mechanical response with the microscopic state to achieve multiscale constitutive modelling. The parameter identification and finite element implementation were conducted on a SC superalloy [2]. Simulation results demonstrated the accuracy of the proposed model in predicting deformation behavior under various orientations, rate-dependent effects, isothermal and non-isothermal cyclic deformation. Comparison with the classical anisotropic matrix macroscopic phenomenological approaches highlights the superior capability of the proposed model to simulate the orientation-dependent mechanical properties of single-crystal alloys.

Assessment of dwell-fatigue properties of nickel-based superalloy coated with a multi-layered thermal and environmental barrier coating

A three-layered experimental thermal and environmental barrier coating (TEBC) was deposited using air plasma spraying technology on cylindrical specimens of nickel-based superalloy MAR-M247. TEBC consists of mullite (Al6Si2O13) and hexacelsian (BaAl2Si2O8) upper layer, Y2O3 stabilised ZrO2 interlayer and CoNiCrAlY bond coat deposited on the grit-blasted surface of MAR-M247. The cyclic plastic response and damage mechanisms in uncoated and TEBC-coated MAR-M247 have been studied in isothermal dwell-fatigue tests conducted under strain control with constant strain amplitude at 900 °C. In each cycle, 5-minute dwells were introduced in both tensile and compression peaks of the hysteresis loop. Fatigue hardening/softening curves, stress relaxation curves, cyclic stress-strain curves and fatigue life curves are reported. Ceaseless mild softening has been found in both uncoated and TEBC-coated MAR-M247. TEBC-coated MAR-M247 showed an improved lifetime in the whole range of tested strain amplitudes. Data obtained from stress relaxation curves were used to assess the fraction of creep damage. The generalised damage accumulation rule was used to evaluate damage due to fatigue-creep-environment interaction. A study of the surface relief and internal microstructure using SEM and TEM helped to interpret the specifics of fatigue behaviour of uncoated and TEBC-coated material. The effectiveness of this newly developed TEBC, together with the dwell sensitivity of MAR-M247, were discussed from the perspective relevant to dwell-fatigue cyclic straining.

Fatigue Crack Growth Monitoring and Investigation on G20Mn5QT Cast Steel and Welds via Acoustic Emission

The fatigue crack growth properties of G20Mn5QT cast steel and corresponding butt welds, using compact tension specimens, were monitored and investigated via acoustic emission (AE) techniques. Fatigue crack growth is a combination of cyclic plastic deformations before the crack tip, tensile crack fractures, and shear crack fractures. The cyclic plastic deformations release the maximum amount of energy, which accounts for half of the total energy, and the second-largest number of AE signals, which are of the continuous-wave type. The tensile crack fractures release the second-largest amount of energy and the largest number of AE signals, which are of the burst-wave type. The shear crack fractures release the least amount of energy and the lowest number of AE signals, which are similar to the burst type, albeit with a relatively longer rise time and duration. Crack tip advancement can be regarded as a discontinuous process. The critical area before the crack tip brittlely ruptures when the fatigue damage caused by cyclic plastic deformations reaches critical status. The ruptures produce a large number of tensile crack fractures and rare shear crack fractures. Through fractography observation, the shear crack fractures occur probabilistically around defects caused by casting or welding, which lead to stress and strain in the local complex.

Bayesian protocols for high-throughput identification of kinematic hardening model forms

Constitutive models are essential for assessing the mechanical response of complex materials, yet uncertainties in model forms and parameters persist due to the influence of micromechanisms and microstructural features. We develop Bayesian protocols to iteratively refine both model forms and the associated material properties for complex constitutive models. Our aim is to provide rigorous, probabilistically informed evaluations of improvements achieved with increasing model complexity. Leveraging high-throughput experimental microindentation data, the protocols involve three steps: (i) emulating FE simulations using multi-output Gaussian process surrogate models, (ii) calibrating an initial simple constitutive model against experimental data, and (iii) progressively enhancing model complexity by iteratively improving agreement between simulations and experiments. The various model forms are compared using model form probabilities and aggregate discrepancies. Sobol indices are used to quantify the identifiability of material properties, aiming to prevent parameter proliferation. We apply this protocol to identify the optimal form of cyclic plasticity models for duplex Ti-6Al-4V. Although tailored for cyclic plasticity models, these protocols hold promise for calibrating and refining nonlinear constitutive models across diverse material classes.

Influence of Continuous Rotation and Optimal Torque Reverse Kinematics on the Cyclic Fatigue Strength of Endodontic NiTi Clockwise Cutting Rotary Instruments.

Objectives: The objective of the present study was to evaluate the cyclic fatigue strength of clockwise cutting rotary endodontic instruments when subjected to two different kinematics: continuous clockwise rotation and clockwise reciprocation movement under optimum torque reverse (OTR) motion. Methods: New ProTaper Next X1 (n = 20) and X2 (n = 20) instruments were randomly divided into two subgroups (n = 10) based on kinematics (continuous rotation or OTR). The specimens were tested using a custom-made device with a non-tapered stainless-steel artificial canal measuring 19 mm in length, featuring a 6 mm radius and an 86-degree curvature. All instruments were tested with a lubricant at room temperature until a fracture occurred. The time to fracture and the length of the separated fragment were recorded. Subsequently, the fractured instruments were inspected under a scanning electron microscope for signs of cyclic fatigue failure, plastic deformation, and/or crack propagation. The subgroup comparisons for time to fracture and instrument length were performed using the independent samples t-test, with the level of statistical significance set at 0.05. Results: When using OTR movement, the ProTaper Next X1 increased the time to fracture from 52.9 to 125.8 s (p < 0.001), while the ProTaper Next X2 increased from 45.4 to 66.0 s (p < 0.001). No subgroup exhibited plastic deformations, but both showed dimpling marks indicative of cyclic fatigue as the primary mode of failure. Additionally, OTR movement resulted in more metal alloy microcracks. Conclusions: The use of OTR motion extended the lifespan of the tested instruments and resulted in a higher number of metal microcracks. This suggests that OTR motion helped to distribute the mechanical stress more evenly across the instrument, thereby relieving localized tension. As a result, it delayed the formation of a single catastrophic crack, enhancing the overall performance of the instruments during the experimental procedures.

Enhanced Cyclically Stable Plasticity Model for Multiaxial Behaviour of Magnesium Alloy AZ31 under Low-Cycle Fatigue Conditions.

Magnesium alloys, particularly AZ31, are promising materials for the modern automotive industry, offering significant weight savings and environmental benefits. This research focuses on the challenges associated with accurate modelling of multiaxial cyclic plasticity at small strains of AZ31 under low-cycle fatigue conditions. Current modelling approaches, including crystal plasticity and phenomenological plasticity, have been extensively explored. However, the existing models reach their limits when it comes to capturing the complexity of cyclic plasticity in magnesium alloys, especially under multiaxial loading conditions. To address this gap, a cyclically stable elastoplastic model is proposed that integrates elements from existing models with an enhanced algorithm for updating stresses and hardening parameters, using the hyperbolic tangent function to describe hardening and ensure a stabilised response with closed hysteresis loops for both uniaxial and multiaxial loading. The model is based on a von Mises yield surface and includes a kinematic hardening rule that promises a stable simulation of the response of AZ31 sheets under cyclic loading. Using experimental data from previous studies on AZ31 sheets, the proposed model is optimised and validated. The model shows promising capabilities in simulating the response of AZ31 sheet metal under different loading conditions. It has significant potential to improve the accuracy of fatigue simulations, especially in the context of automotive applications.

Fatigue life predictions for welded boiler water walls

Boiler water walls experience in-phase thermo-mechanical loading during start-ups and shut-downs, leading to low cycle fatigue (LCF) failure. This study aims at establishing an FEA-based failure prediction method for estimating the fatigue performance and service life of the welded water walls. The developed model is validated for predicting failure in the defect-free uniaxial fatigue specimens. Stress-mechanical strain hysteresis loops and accumulated inelastic strain energy density per cycle parameters are extracted from fatigue tests at 0.4%, 0.6%, and 0.7% strains. A combination of cyclic plasticity and continuous damage mechanics (CDM) theory is utilized to predict fatigue crack initiation sites and estimate the specimen fatigue life. Accumulated damage has been calculated for the life cycle of each specimen. FEA model predicted failure and service life agrees well with the experimental results. The established failure analysis parameters are then transferred from the specimen level to the water wall component level, thereby estimating the service life of defect-free water walls at 750 cycles.

Analysis of high temperature and strain amplitude effects on low cycle fatigue behavior of pitting corroded killed E350 BR structural steel

High-tension structural steels are prone to accelerated fatigue damage from pitting corrosion and high-temperature. Despite adverse effects, research on their low cycle fatigue (LCF) behavior is limited. Specifically, studies analyzing temperature-dependent pit sensitivity effects, considering pit-related material’s susceptibility to surface topographic features variation and stress concentration are lacking. This study conducts LCF tests on pitting corroded killed E350 BR structural steel at multiple strain amplitudes and high temperatures. It develops temperature-dependent parameters, such as the cyclic softening pit sensitivity factor, suitable for integration into existing approaches like total cyclic plastic strain energy density (CPSED), power-law, average strain energy density (SED), Coffin-Manson, and pit stress intensity factor (pit-SIF). Further, it proposes multiple linear regression-based prediction models relating total CPSED and average SED with strain amplitude and temperature. Corroded specimens show higher plastic deformation and reduced peak stress, fatigue life, and total CPSED compared to uncorroded ones. The developed parameters, integrated with average SED approach, predicts LCF life within an error band of ±1.5, while power-law relationship reduces it to ±1.2. Moreover, pit-SIF approach estimates fatigue life within an error band of ±1.5. The findings provide critical knowledge for enhanced component design, leading to structural safety, performance, and fire resilience.

An adaptive fatigue crack growth model at the welded joints of steel bridge

Under the influence of random loads such as those from vehicles, the welded details in steel bridges tend to gradually develop into macrocracks, typically originating from manufacturing defects or stress concentration points. As the service life of the steel bridge increases, the continuous generation and propagation of fatigue cracks lead to a decline in the bridge's service performance, potentially resulting in catastrophic failures such as bridge collapse. Accurately analyzing the fatigue crack growth patterns at welded joints is a prerequisite for reliably assessing the structural service performance. The analysis of fatigue crack propagation depends on both the crack growth step size and the cyclic stress–strain response at the welded joint under loading. Considering the complexity of the material properties and stress concentration at the welded joint, which leads to a lack of analytical solutions for the cyclic stress–strain characteristics at the crack tip, numerical analysis was employed to obtain the cyclic stress–strain response at the crack tip of the welded joints. Using the size of the cyclic plastic zone at the crack tip as an adaptive crack growth step size, a model for fatigue crack growth was developed based on the plastic strain energy of the cyclic plastic zone. Fatigue test specimens extracted from the welded toe of cruciform welded joints were tested, providing cyclic stress–strain (Ramberg-Osgood material parameters) and fatigue damage characteristics (Manson-Coffin material parameters) of the material at the welded toe. High-cycle fatigue tests using cruciform welded joint specimens determined a good correlation between the crack propagation characteristic dimensions obtained from the adaptive numerical analysis model and the experimental results. The experimental findings confirmed the applicability of the established adaptive numerical analysis model for studying fatigue crack growth in cruciform welded joints. The parameters introduced in this model are physically meaningful, easy to obtain, and suitable for engineering applications.

Elucidating the effect of cyclic plasticity on strengthening mechanisms and fatigue property of 5xxx Al alloys

The strength of non-heat-treatable 5xxx Al alloys is derived from solid solution strengthening and strain hardening, the absence of a precipitation strengthening response results in their lower strength. In this study, significant improvements in strength can be achieved by subjecting three different Mg concentrations 5xxx Al alloys to cyclic plasticity. A quantitative analysis of the respective contributions to the yield strength has been conducted by combining transmission electron microscopy and atom probe tomography. Additionally, the fatigue performance and fatigue mechanism of the cyclic strengthened 5xxx Al alloys have been thoroughly studied due to its transformation from non-heat-treatable to precipitation strengthening. We demonstrate that the high-cycle fatigue (HCF) strength of the cyclically strengthened state only experiences a minor improvement compared to the as-received state, which is significantly disproportionate to the enhancement in tensile strength. This disparity is primarily attributed to the changes in microstructure and fatigue mechanisms, resulting in a reduction in fatigue ratio. This study provides important insights for expanding research on cyclic plasticity methods in fatigue performance, and can aid in the development of improved processes for optimal fatigue resistance.

Experimental investigation and computational modelling of 304LN stainless steel under constant and variable strain path multiaxial loading conditions

This study investigates the fatigue behavior of 304LN stainless steel under constant and variable strain path multiaxial loading conditions. Experimental methods and computational modelling were used to analyze the response of the material to different loading scenarios. Experimental investigations were conducted to gather empirical data, which were subsequently validated using a modified Ohno-Wang and Tanaka cyclic plasticity framework. Two models were used for the analysis: the MOT model and a modified model that incorporated a weighted function and fractional functions for hardening and softening. In contrast, the modified model offers significant improvements, accurately capturing primary hardening and secondary softening across all loading scenarios. Furthermore, the modified model effectively simulates transient behavior, including load alteration and recovery effects, due to the integration of load history memory regulating functions. Overall, this study emphasizes the importance of considering the complexities of cyclic loading and the sensitivity of the material behavior to the loading history.

Strengthening behavior and microstructure of 2195 Al-Cu-Li alloy under cycling loading

Cyclic strengthening process, as a newly developed aluminum alloy strengthening technique, has garnered significant attention due to its advantages of rapidity, efficiency, and superior mechanical properties. This study investigated the effects of strain amplitude and loading frequency on cyclic strengthening, including mechanical properties and microstructural evolution. At room temperature, the cyclic strengthening effect of the 2195 alloy increases with increasing strain amplitude, while the influence of loading frequency is pronounced within the elastic range but nearly negligible within the plastic range. Microstructural analysis reveals that cyclic strengthening behavior within the elastic range is attributed to the precipitation of clusters, whereas within the plastic range, it is attributed to the precipitation of clusters and dislocation multiplication. Unlike other plastic deformations, cyclic plastic loading generates dislocations primarily in the form of dislocation loops. The dynamic precipitation of clusters and the diffuse distribution of dislocation loops significantly enhance the alloy's strength with minimal sacrifice of elongation. Experimental investigations on the influence of loading frequency on these precipitation behaviors demonstrate a positive correlation with dislocation generation and a negative correlation with cluster precipitation. Comparison of specimens with different strain amplitudes reveals that larger strain amplitudes provide more energy for cluster precipitation, thereby promoting precipitation. However, excessively large strain amplitudes lead to the annihilation of vacancies due to the introduction of more dislocations, thus inhibiting cluster precipitation. This indicates that the precipitation of clusters during cyclic deformation is profoundly influenced by dislocation behavior. This study deepens the understanding of cyclic strengthening mechanisms and provides support for subsequent development of cyclic strengthening processes in other materials design.

A novel method simultaneously eliminating Portevin-Le Chatelier effect and enhancing strength in non-heat-treatable Al-Mg alloys

This study investigates the effects of cyclic plasticity on the tensile properties of AA5083 alloys. The low strength and Portevin-Le Chatelier (PLC) effect in Al-Mg alloys means they have found limited use in automotive outer panels. This work shows that by applying cyclic strengthening approach to AA5083, a high density of Mg-Al clusters can be formed in matrix resulting in increased yield and tensile strengths. Moreover, the introduction of cyclic plasticity also effectively suppresses the PLC effect, which is due to the formation of the clusters and the consequent reduction in the number of free Mg atoms in the solid solution. This method introduces the concept of particle strengthening in Al-Mg alloys without altering composition, while simultaneously eliminating the PLC effect. It suggests a potential path for using 5xxx series alloys in applications traditionally dominated by 6xxx series alloys, with added benefits for recycling and sustainability in the automotive industry.

Cyclic stress–strain behavior of additively manufactured gamma prime strengthened superalloy at elevated temperatures

The γ́-precipitation hardened nickel-based superalloy IN939 manufactured by laser powder bed fusion (L-PBF) was subjected to cyclic loading to determine the cyclic stress–strain curve by short-cut procedure. The effect of building on loading direction/orientation was investigated. 〈001〉 crystallographic texture along the building direction was observed. The cyclic stress–strain curves were measured at 800 °C and 900 °C and the differences in cyclic plasticity were revealed. The specimens prepared by L-PBF with a building direction parallel to the loading axis exhibited the highest cumulative plastic deformation at both temperatures, while L-PBF with a building direction perpendicular to the loading axis was the lowest. Elastic moduli were determined and the differences were attributed to the crystallographic texture. In addition, conventionally cast IN939 was investigated as the reference material. Minor microstructural changes due to cyclic straining were inspected by transmission electron microscopy.

Inverse Method to Determine Parameters for Time-Dependent and Cyclic Plastic Material Behavior from Instrumented Indentation Tests.

Indentation is a versatile method to assess the hardness of different materials along with their elastic properties. Recently, powerful approaches have been developed to determine further material properties, like yield strength, ultimate tensile strength, work-hardening rate, and even cyclic plastic properties, by a combination of indentation testing and computer simulations. The basic idea of these approaches is to simulate the indentation with known process parameters and to iteratively optimize the initially unknown material properties until just a minimum error between numerical and experimental results is achieved. In this work, we have developed a protocol for instrumented indentation tests and a procedure for the inverse analysis of the experimental data to obtain material parameters for time-dependent viscoplastic material behavior and kinematic and isotropic work-hardening. We assume the elastic material properties and the initial yield strength to be known because these values can be determined independently from indentation tests. Two optimization strategies were performed and compared for identification of the material parameters. The new inverse method for spherical indentation has been successfully applied to martensitic steel.

Multiaxial ratcheting-fatigue evaluation of pressurized elbow pipe under strong cyclic loading using damage-coupled cyclic plasticity model

Continuous damage mechanics (CDM) is based on the theories of continuous medium mechanics and continuous medium thermodynamics, which considers damage is an irreversible dissipative process within the materials, and employs the field-theoretic approach of image-only science to study the internal macroscopic damage evolution law of the materials and its influence on the deterioration of the macroscopic mechanical properties of the materials. Hence, within the framework of CDM, a damage-coupled cyclic plasticity constitutive model is proposed based on combined isotropic and Chen-Jiao-Kim (CJK) kinematic hardening rule for evaluating the ratcheting-fatigue behavior of 90° elbow pipes under strong cyclic loading in this paper. Stress return mapping and numerical solution procedures of the proposed model are formulated based on the backward finite difference method. Formulation of the consistent tangent operator is presented for the Finite Element implementation of the plasticity model in ABAQUS UMAT. The FE analysis of non-pressurized and pressurized elbow pipes under cyclic displacement-controlled loading is respectively performed using the implemented constitutive model. The results reveal that the predicted results of the damage-coupled cyclic plasticity constitutive model are better than combined isotropic-kinematic hardening model, and well consistent with the experimental data.

Failure analysis of fatigue crack propagation in specimens of AlSi10Mg aluminum alloy produced by L-PBF: Effect of different heat treatments

Fatigue crack growth behavior of AlSi10Mg aluminum alloy processed by laser powder bed fusion (L-PBF) was studied for three material conditions: as-built, stress relieved and hot isostatic pressed. An improvement in the fatigue crack growth resistance was found for the heat-treated conditions which was attributed to the residual stress relief induced by the heat treatments. The stress ratio did not affect the fatigue crack growth in regime II which was explained by the absence of crack closure. Fatigue crack growth rates were predicted using a model based on the cyclic plasticity of the tested aluminum alloy. The proposed model agreed well with the experimental results.

Modeling of crack tip fields and fatigue crack growth in fcc crystals

Predicting the mechanical behavior of polycrystalline materials containing a crack under both monotonic and cyclic loading conditions is crucial for accurately assessing the integrity of engineering materials. This study focuses on the deformation characteristics of face-centered cubic (fcc) grains within the crack tip field and their significant role in governing the driving force for fatigue crack growth during cyclic loading. We employ a cyclic crystal plasticity finite element (CPFE) model to analyze the mechanical response of austenitic 316L stainless steel polycrystals by accounting for nonlinear kinematic hardening effects. Through CPFE simulations, we investigate the deformation fields in 316L grains at the crack tip, considering two different grain orientations under plane strain conditions. Our CPFE results under monotonic loading align consistently with previous theoretical and experimental findings, particularly in comparing CPFE-simulated and experimentally observed plastic sectors consisting of different slip traces on the specimen surface near the crack tip. Based on a critical plastic work criterion for crack advancement, cyclic CPFE simulations are used to determine the fatigue crack growth rate as a function of stress intensity factor range for the two crack tip grain orientations in stainless steel. The simulated Paris law exponent matches experimental values. Furthermore, we compare cyclic CPFE results with those from cyclic J2 plasticity finite element simulations. This study demonstrates a cyclic CPFE approach for determining crack tip fields, accounting for crystallographic effects on plastic deformation of crack tip grains. Our approach can be applied to effectively evaluate fatigue crack growth rates in fcc polycrystalline metals.

Plastic behavior and shakedown limit of defected pressurized pipe under cyclic bending moment

Pipelines subjected to thermal or mechanical loads may fail due to plastic strain accumulation which leads to ratcheting. In this research, cyclic plastic behavior and shakedown limit are investigated experimentally and numerically for a defected pressurized pipe under cyclic bending moment. In the numerical model, the combined isotropic/kinematic hardening model based on the Chaboche model is adopted to represent the cyclic plastic flow of the material. The hardening parameters are determined experimentally and used in the finite element (FE) model. A four-point bending test rig is manufactured to test a pressurized API 5L steel pipe under cyclic bending. An elliptical defect is created by machining to depict corrosion pits in pipes. The plastic strains are measured experimentally and the results are used to tune the parameters of the FE model. The shakedown limit of the defected pipe is determined numerically by tracking the critical points behavior and the results are verified experimentally. Furthermore, the plastic work dissipated energy (PWD) is estimated within the defective structure to study the behavior of the pipe. By running this compatible model, it is found that the yield and the shakedown limits are lowered by mean values of 55% and 25% respectively due to the presence of metal loss defect occupying almost half of the pipe thickness.