Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

Experimental Study on Non-proportional Multiaxial Strain Cyclic Characteristics and Ratcheting of U71Mn Rail Steel

An experimental study was carried out on the strain cyclic characteristics and ratcheting of U71Mn rail steel subjected to non-proportional multiaxial cyclic loading. The strain cyclic characteristics were researched under the strain-controlled circular load path. The ratcheting was investigated for the stress-controlled multiaxial circular, elliptical and rhombic load paths with different mean stresses, stress amplitudes and their histories. The experiment shows that U71Mn rail steel features the cyclic non-hardening/softening, and its strain cyclic characteristics depend greatly on the strain amplitude but slightly on its history. However, the ratcheting of U71Mn rail steel depends greatly not only on the values of mean stress and stress amplitude, but also on their histories. In the meantime, the shape of load path and its history also apparently influence the ratcheting. The ratcheting changes with the different loading paths.

VISCO-PLASTIC CONSTITUTIVE MODEL FOR UNIAXIAL AND MULTIAXIAL RATCHETING AT ELEVATED TEMPERATURES

Based on the experimental results of the ratcheting for SS304 stainless steel, a new visco-plastic cyclic constitutive model was established to describe the uniaxial and multiaxial ratcheting of the material at room and elevated temperatures within the framework of unified visco-plasticity. In the model, the temperature dependence of the ratcheting was emphasized, and the dynamic strain aging occurred in the temperature range of 4 00-600℃ for the material was taken into account particularly. Finally, the prediction capability of the developed model was checked by comparing to the corresponding experimental results.

Uniaxial Time-Dependent Ratcheting of SS304 Stainless Steel at High Temperatures

The uniaxial time-dependent strain cyclic behaviors and ratcheting of SS304 stainless steel were studied at high temperatures （350 ℃ and 700 ℃）. The effects of straining and stressing rates, holding time at the peak and/or valley of each cycle in addition to ambient temperature on the cyclic softening/hardening behavior and ratcheting of the material were discussed. It can be seen from experimental results that the material presents remarkable time dependence at 700 ℃, and the ratcheting strain depends greatly on the stressing rate, holding time and ambient temperature. Some significant conclusions are obtained, which are useful to build a constitutive model describiog the time-dependent cyclic deformation of the material.

THE STRAIN CYCLIC CHARACTERISTICS AND RATCHETING OF U71Mn RAIL STEEL UNDER UNIAXIAL LOADING

An experimental study was carried out of the cyclic behavior of U71Mn rail steel subjected to uniaxial strain and stress. The effects of cyclic struin amplitude, mean struin,strain loading rate and their histories on the strain cyclic characteristics were studied.Under the asymmetrical stress cycling, the effects of stress amplitude, mean stress,stress loading rate and their histories on the ratcheting were analyzed. The interaction between strain cycling and stress cycling was also discussed. It is shown that either the cyclic characteristics under strain cycling or the ratcheting under asymmetrical stress cycling depends not only on the cumnt loading state, but also on the previous loading history. Some significant results are obtained.

Experimental Study on Uniaxial and Multiaxial Strain CyclicCharacteristics and Ratcheting of 316L Stainless Steel

An experimental study was carried out on the strain cyclic characteristics and ratcheting of 316L stainless steel subjected to uniaxial and multiaxial cyclic loading. The strain cyclic characteristics were researched under the strain-controlled uniaxial tension-compression and multiaxial circular paths of loading. The ratcheting tests were conducted for the stress-controlled uniaxial tensioncompression and multiaxial circular, rhombic and linear paths of loading with different mean stresses, stress amplitudes and histories. The experiment results show that 316L stainless steel features the cyclic hardening, and its strain cyclic characteristics depend on the strain amplitude and its history apparently. The ratcheting of 316L stainless steel depends greatly on the values of mean stress, stress amplitude and their histories. In the meantime, the shape of load path and its history also apparently influence the ratcheting.

Ratcheting Behavior of Weld Joints Under Uniaxial Cyclic Loading Using Miniature Specimen

Because of the size limitation of weld joints in different regions, the traditional standard bar specimen is not suitable to investigate the mechanical properties of weld joints. In this study, miniature specimens were extracted from specific regions(base metal, weld metal, and three heat-affected zones) of API X80 and X70 weld joints. Uniaxial tensile tests were conducted to obtain the mechanical properties of different regions, and then uniaxial ratcheting tests were conducted to investigate the ratcheting behaviors of the different regions under the same peak and nominal stresses. Under both the tensile tests and ratcheting tests, the weld joints exhibit heterogeneous results, such as different mechanical properties and ratcheting behaviors, which were region dependent. Furthermore, the yield strength and yield-to-tensile strength ratio contribute differently to the ratcheting response.

Fatigue limit assessment of a 6061 aluminum alloy based on infrared thermography and steady ratcheting effect

To quickly predict the fatigue limit of 6061 aluminum alloy,two assessment methods based on the temperature evolution and the steady ratcheting strain difference under cyclic loading,respectively,were proposed.The temperature evolutions during static and cyclic loadings were both measured by infrared thermography.Fatigue tests show that the temperature evolution was closely related to the cyclic loading,and the cyclic loading range can be divided into three sections according to the regular of temperature evolution in different section.The mechanism of temperature evolution under different cyclic loadings was also analyzed due to the thermoelastic,viscous,and thermoplastic effects.Additionally,ratcheting strain under cyclic loading was also measured,and the results show that the evolution of the ratcheting strain under cyclic loading above the fatigue limit undergone three stages:the first increasing stage,the second steady state,and the final abrupt increase stage.The fatigue limit of the 6061 aluminum alloy was quickly estimated based on transition point of linear fitting of temperature increase and the steady value of ratcheting strain difference.Besides,it is feasible and quick of the two methods by the proof of the traditional S-N curve.

The Ratcheting Behaviour of Plain Carbon Steel Pressurized Piping Elbows Subjected to Simulated Seismic In-Plane Bending

In this paper, cyclic loading behavior of carbon steel pressurized piping elbows are described. Effects of internal pressure and bending moment amplitude on the ratcheting rate are investigated. The AF kinematic hardening model is used to predict the plastic behavior of the elbows. Material parameters and stress-strain data have been obtained from several stabilized cycles of specimens that are subjected to symmetric strain cycles. The results show that the maximum ratcheting strain occurred mainly in the hoop direction at flanks. Hoop strain ratcheting was found at intrados for individual specimen. Ratcheting strain rate increases with increase of the bending loading level at the constant internal pressure. The results show that the initial rate of ratcheting is large and then it decreases with the increasing cycles. The FE model predicts the hoop strain ratcheting rate to be near that found experimentally in all cases that M/Ml≤1..

The Ratcheting Behaviour of Stainless Steel Pressurized Piping Elbows Subjected to Dynamic Out-of-Plane Moments

In this paper the ratcheting behavior of four pairs of stainless steel elbows is studied under conditions of steady internal pressure and dynamic conditions that induced out-of-plane external moments at frequencies typical of seismic excitations. The finite element analysis with the nonlinear kinematic hardening model has been used to evaluate ratcheting behavior of the piping elbows under mentioned loading condition. Material parameters have been obtained from several stabilized cycles of specimens that are subjected to symmetric strain cycles. The direction of maximum strain is at about 45° between the hoop and axial directions. The results show that the direction of highest ratcheting is along the hoop direction rather than the direction of maximum principal strain. Also, the initial rate of ratcheting is large and then it decreases with the increasing cycles. Also, the FE method gives over estimated values compared with the experimental data.

ADVANCES IN TRANSFORMATION RATCHETING AND RATCHETING-FATIGUE INTERACTION OF NITI SHAPE MEMORY ALLOY

The accumulation of inelastic deformation occurring in NiTi shape memory alloy under the stress-controlled cyclic loading condition is named transformation ratcheting, since it is mainly caused by the solid-solid transformation from austenite to martensite phase and vice versa. The transformation ratcheting and its effect on the fatigue life （i.e., transformation-fatigue interaction） are key issues that should be addressed in order to assess the fatigue of NiTi shape memory alloy more accurately. In this paper, the advances in the studies on the transformation ratcheting and rateheting-fatigue interaction of super-elastic NiTi shape memory alloy in recent years are reviewed： First, experimental observation of the uniaxial transformation ratcheting and ratcheting-fatigue interaction of super-elastic NiTi alloy under the stress-controlled cyclic loading conditions is treated, and the detrimental effect of transformation ratcheting on the fatigue life is addressed; Secondly, two types of cyclic constitutive models （i.e., a macroscopic phenomeno- logical model and a micromechanical one based on crystal plasticity） constructed to describe the transformation ratcheting of super-elastic NiTi alloy are discussed; Furthermore, an energy-based failure model is provided and dealt with by comparing its predicted fatigue lives with experimental ones; Finally, some suggestions about future work are made.

Stress-controlled LCF experiments and ratcheting behaviour simulation of a nickel-based single crystal superalloy with [001] orientation

Uniaxial ratcheting behaviour and low cycle fatigue(LCF)failure mechanism of nickel-based single crystal superalloy DD6 with[001]orientation are investigated through the stresscontrolled LCF tests with stress ratio of-1.Then the deformation behaviour during the wholelifetime from the beginning of the experiment to the fracture of the specimen,as well as the fractographic/metallographic morphology,are compared with the strain-controlled LCF experimental results.Through the scanning electron microscope(SEM)observations,it is shown that the failure characteristics under stress-controlled LCF loading are similar with those under strain-controlled loading.Nevertheless,unlike strain-controlled LCF loading,even under fully reversed cycle loading for stress-controlled LCF,DD6 shows significant ratcheting behaviour due to the tensioncompression asymmetry.In addition,the LCF lifetimes under stress control are significantly shorter than the LCF lifetimes under strain control,and the culprit might be the detrimental effect of ratcheting strain on LCF lifetime.Based on these phenomena,an improved crystal plasticity constitutive model on the basis of slip-based Walker constitutive model is developed through modifying the kinematic hardening rule in order to overcome the inaccurate prediction of decelerating stageand stable stage of ratcheting behaviour.Furthermore,combining the continuum damage mechanics,a damage-coupled crystal plasticity constitutive model is proposed to reflect the damage behaviour of DD6 and the accelerating stage of ratcheting behaviour.The simulation results for the stress-controlled LCF deformation behaviour including the whole-lifetime ratcheting behaviour show good agreement with the experimental data.

Ratcheting Behavior of SA508-3 Steel at Elevated Temperature:Experimental Observation and Simulation

A series of monotonic uniaxial tensile tests, strain-controlled and stress-controlled cyclic tests of SA508-3 steel were conducted from 25 to 350℃. Results showed that the steel exhibited temperature-dependent cyclic softening characteristic and obvious ratcheting behavior, and dynamic strain aging was observed in the range of 250-350℃. Based on experimental observations, a temperature-dependent cyclic plastic constitutive model was proposed by introducing the nonlinear cyclic softening and kinematic hardening rules, and the dynamic strain aging was also considered into the constitutive model. Comparisons between experiments and simulations were carded out to validate the proposed model at elevated temperature.

Tensile ratcheting behaviors of bronze powder filled polytetrafluoroethylene

A series of tensile and ratcheting experiments for compacted polytetrafluoroethylene （PTFE） and bronze filled PTFE （PTFE/bronze） were conducted on dynamic mechanical analyzer （DMA-Q800）. The effects of mean stress, stress amplitude and temperature on the ratcheting behaviors of PTFE and PTFE/bronze were investigated. It is found that the stress-strain response of PTFE/bronze is nonlinear and its elastic modulus is higher than that of pure PTFE. For uniaxial ratcheting test, the dissipation strain energy density （DSED） decreases rapidly in the first l0 cycles and approaches a constant after 20 cycles. The ratcheting strain and the DSED corresponding to 100 cycles increase with increasing mean stress, stress amplitude and temperature. Additionally, the DSED and ratcheting strain of PTFE/bronze are much lower than those of pure PTFE under the same experimental conditions. It is also found that both pure PTFE and PTFE/bronze present cyclic hardening characteristics. Above all, the addition of bronze can improve both the uniaxial tensile property and the cyclic property of PTFE.

Experimental observations on the nonproportional multiaxial ratchetting of cast AZ91 magnesium alloy at room temperature

The nonproportional multiaxial ratchetting of cast AZ91 magnesium (Mg) alloy was examined by performing a sequence of axial-torsional cyclic tests controlled by stress with various loading paths at room temperature (RT).The evolutionary characteristics and path dependence of multiaxial ratchetting were discussed.Results illustrate that the cast AZ91 Mg alloy exhibits considerable nonproportional additional softening during cyclic loading with multiple nonproportional multiaxial loading paths;multiaxial ratchetting presents strong path dependence,and axial ratchetting strains are larger under nonproportional loading paths than under uniaxial and proportional45°linear loading paths;multiaxial ratchetting becomes increasingly pronounced as the applied stress amplitude and axial mean stress increase.Moreover,stress-strain curves show a convex and symmetrical shape in axial/torsional directions.Multiaxial ratchetting exhibits quasi-shakedown after certain loading cycles.The abundant experimental data obtained in this work can be used to develop a cyclic plasticity model of cast Mg alloys.

Uniaxial Ratcheting Behaviors of Metals with Different Crystal Structures or Values of Fault Energy: Macroscopic Experiments

The uniaxial ratcheting behaviors of several metals with different crystal structures or values of fault energy were observed by the stress-controlled cyclic tests at room temperature. The prescribed metals included 316L stainless steel, pure copper, pure aluminum, and ordinary 20# carbon steel. The effects of applied mean stress, stress amplitude and stress ratio on the uniaxial ratcheting were also investigated. The observations show that different crystal structures or values of fault energy result in more or less different ratcheting behaviors for the prescribed metals. The different ratcheting behaviors are partially caused by the variation of dislocation mobility.

Ratcheting behavior of notched stainless steel samples subjected to asymmetric loading cycles

The ratcheting response of 316 stainless steel samples at the vicinity of notch roots under single-and multi-step loading conditions is evaluated.Multi-step tests were conducted to examine local ratcheting at different low–high–high and high–low–low loading sequences.The stress levels over loading steps and their sequences highly influenced ratcheting magnitude and rate.The change of stress level from low to high promoted ratcheting over proceeding cycles while ratcheting strains dropped in magnitude for opposing sequence where stress level dropped from high to low.Local ratcheting strain values at the vicinity of notch root were found noticeably larger than nominal ratcheting values measured at farer distances from notch edge through use of strain gauges.Ratcheting values in both mediums of local and nominal were promoted as notch diameter increased.To assess progressive ratcheting response and stress relaxation concurrently,the Ahmadzadeh-Varvani(A-V)kinematic hardening rule was coupled with Neuber’s rule enabling to calculate local stress at notch root of steel samples.Local stress/strain values were progressed at notch root over applied asymmetric stress cycles resulting in ratcheting buildup through A-V model.The relaxation of stress values at a given peak-valley strain event was governed through the Neuber’s rule.Experimental ratcheting data were found agreeable with those predicted through the coupled framework.

Ratcheting boundary of 316LN austenitic stainless steel under thermal aging

Previous studies,including ASME and RCC-MR standards,did not consider the influence of environmental factors on the ratcheting boundary of the material,and only a unified ratcheting boundary was proposed.In this paper,thermal aging was taken into consideration,and the effect of thermal aging time on the ratcheting boundary of 316 LN austenitic stainless steel was characterized by the efficiency diagram rule.The results show that,when the secondary ratio U is small,there is no significant difference in ratcheting boundary between the original material and the thermal aged material.When the secondary ratio U is large,the ratcheting boundary of the material presents a slight upward trend with the increase of thermal aging time.Compared with ASME and RCC-MR standards,it is found that RCC-MR is conservative.Based on the evolution of the efficiency index V with the number of cycles,it is more conservative and reasonable to choose the stage when the efficiency index V develops into a constant.

Application of engineered compressible inclusions to mitigating soilstructure interaction issues in integral bridge abutments

The thermally induced cyclic loading on integral bridge abutments causes soil deformation and lateral stress ratcheting behind the abutment wall due to the expansion and contraction of the bridge deck.The forward and backward movements of the abutment in response to the expansion/contraction of the bridge deck lead to the formation of settlement trough and surface heaving,frequently creating a bump at the bridge approach and increasing the lateral earth pressure behind the abutment.Measures to reduce the bump at the bridge approach,including several treatment methods,such as compaction of selected backfill materials,grout injection,installation of approach slab,and using a layer of compressible inclusion material behind the abutment were proposed.However,these guidelines still lack sufficient design details and there are limited experimental findings to validate design assumptions.In this paper,the use of engineered compressible materials to alleviate the lateral earth pressure ratcheting and settlement at the bridge approach is investigated.The comparative study is presented for the soil-inclusion,material-structure and soil-structure interactions for an integral bridge under three different backfill conditions,i.e.(a)sand,(b)sand and EPS geofoam,and(c)sand and Infinergy®.The study was conducted in a special large-scale test chamber with a semi-scale abutment to gain better insights into the soil-structure interaction(SSI).The kinematics and rearrangement of the soil during the cyclic loading have been investigated to identify the mitigating effects of compressible inclusions.The comparative study indicates that both compressible inclusions perform comparatively well,however,Infinergy®is a better alternative than the medium-density EPS geofoam,as it works more effectively to reduce the backfill settlement and heaving as well as soil ratcheting effects under cyclic translational movement.