A rate-dependent constitutive model for saturated frozen soil considering local breakage mechanism

A rate-dependent constitutive model for saturated frozen soil is vital in frozen soil mechanics,especially when simultaneously describing the nonlinearity,dilatancy and strain-softening characteristics.The distribution of the non-uniform strain rate of saturated frozen soil at the meso-scale due to the local icecementation breakage is described by a newly binary-medium-based homogenization equation.Based on the field-equation-based approach of the meso-mechanics theory,the interaction expression of the strain rate at macro-and meso-scale is derived,which can give the strain rate concentration tensor at different crushed degrees.With the thermodynamics and empirical assumption,a breakage ratio in the rate-dependent form is determined.This overcomes the limitations of the existing binary-medium-based models that are difficult to simulate rate-dependent mechanical response.Based on these assumptions,a newly binary-medium-based rate-dependent model is proposed considering both the ice bond breakage and material composition characteristics of saturated frozen soil.The proposed constitutive model has been validated by the test results on frozen soils with different temperatures and strain rates.

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.

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.

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.

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.

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.

A Rate-Dependent Peridynamic Model for the Dynamic Behavior of Ceramic Materials

In this study,a new bond-based peridynamic model is proposed to describe the dynamic properties of ceramics under impact loading.Ceramic materials show pseudo-plastic behavior under certain compressive loadings with high strain-rate,while the characteristic brittleness of the material dominates when it is subjected to tensile loading.In this model,brittle response under tension,softening plasticity under compression and strain-rate effect of ceramics are considered,which makes it possible to accurately capture the overall dynamic process of ceramics.This enables the investigation of the fracture mechanism for ceramic materials,during ballistic impact,in more detail.Furthermore,a bond-force updating algorithm is introduced to perform the numerical simulation and solve the derived equations.The proposed model is then used to analyze the dynamic response of ceramics tiles under impact loading to assess its validity.The results of damage development in ceramic materials are calculated and compared with the experimental results.The simulation results are consistent with the experiments,which indicates that the proposed rate-dependent peridynamic model has the capability to describe damage propagation in ceramics with good accuracy.Finally,based on a comparison between simulation and experimental results,it can be concluded that the damage results are in better agreement with experimental results than non-ordinary state-based peridynamic method.

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.

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.

Experimental study on uniaxial ratchetting-fatigue interaction of extruded AZ31 magnesium alloy with different plastic deformation mechanisms

The uniaxial ratchetting-fatigue interaction of extruded AZ31 magnesium(Mg)alloy is investigated by uniaxial stress-controlled cyclic tests at room temperature and with addressing the roles of different plastic deformation mechanisms.Different stress levels are prescribed to reflect the cyclic plasticity of the alloy controlled by diverse deformation mechanisms(i.e.,dislocation slipping,deformation twinning and detwinning ones),and then the influences of stress level and stress rate on the ratchetting and fatigue life are discussed.The experimental results demonstrate that different evolution characteristics of whole-life ratchetting and fatigue life presented during cyclic tests with various mean stresses,stress amplitudes and stress rates are determined by the dominated plastic deformation mechanisms.It’s worth noting that the ratchetting can occur in the compressive direction even in the cyclic tests with a positive(tensile)mean stress,and the fatigue life increases first and then decreases with the increase of mean stress on account of the interaction between dislocation slipping and twinning/detwinning mechanisms.Comparing the fatigue lives obtained in the asymmetric stress-controlled and symmetrical strain-controlled cycle tests,it is seen that the ratchetting deformation causes an additional damage,and then leads to a shortening of fatigue life.

Implementation of OpenMP Parallelization of Rate-Dependent Ceramic Peridynamic Model

A rate-dependent peridynamic ceramic model,considering the brittle tensile response,compressive plastic softening and strain-rate dependence,can accurately represent the dynamic response and crack propagation of ceramic materials.However,it also considers the strain-rate dependence and damage accumulation caused by compressive plastic softening during the compression stage,requiring more computational resources for the bond force evaluation and damage evolution.Herein,the OpenMP parallel optimization of the rate-dependent peridynamic ceramicmodel is investigated.Also,themodules that compute the interactions betweenmaterial points and update damage index are vectorized and parallelized.Moreover,the numerical examples are carried out to simulate the dynamic response and fracture of the ceramic plate under normal impact.Furthermore,the speed-up ratio and computational efficiency by multi-threads are evaluated and discussed to demonstrate the reliability of parallelized programs.The results reveal that the totalwall clock time has been significantly reduced after optimization,showing the promise of parallelization process in terms of accuracy and stability.

CRITERION FOR JUDGING SATISFACTION OF CONSISTENCY CONDITIONS IN RATE-DEPENDENT CONSTITUTIVE RELATIONS

Based on irreversible thermodynamics, the criterion for judging the satisfaction of consistency conditions in rate-dependent constitutive relationship is deduced by introducing four basic hypotheses. Formulas for solving internal variables are given. It makes the rate-dependent model applicable no matter whether the consistency conditions can be satisfied or not.

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.

Modeling of ratcheting accumulation of secondary deformation due to stress-controlled high-cyclic loading in granular soils

An objective of this work is to develop a validated computational model that can be used to estimate ratcheting accumulation behavior of granular soils due to high-cyclic loading. An accumulation model was proposed to describe only the envelope of the maximum plastic deformations generated during the cyclic loading process, which can calculate the accumulated deformation by means of relatively large load cycle increments. The concept of volumetric hardening was incorporated into the model and a so-called overstress formulation was employed to describe the evolution of the accumulated volumetric deformation as a state parameter. The model accounted for ratcheting shakedown and accumulation such as a pseudo-yield surface(a shakedown surface) associated with loading inside the current virgin yield surface which was implemented into the well-known modified Cam-clay model. Finally, the model was calibrated using data from the stress-controlled drained cyclic triaxial tests on homogeneous fine grained sands. It is seen that the model can successfully represent important features of the ratcheting accumulation of both volumetric and deviatoric deformation caused by repeated drained loading over a large number of cycles.

Constitutive Model for Multiaxial Ratcheting Predictions of Cyclic Softening Weld Metal

A series of fully reversed axial, torsional strain-controlled cyclic tests and two multiaxial ratcheting tests were conducted on weld metal specimens using an Instron8521 tension-torsional servo-controlled testing machine. The weld metal showed clear cyclic softening under axial, torsional and multiaxial loading. A modified kinematic hardening rule was proposed in which a multiaxial-loading-dependent parameter incorporated the radial evanescence term of the Burlet-Cailletaud mode with the Ohno-Wang kinematic hardening rule to predict the multiaxial ratcheting effects. The introduction of yield stress evolved with accumulated plasticity strain enables the model to predict cyclic plasticity behavior of cyclic softening or cyclic hardening materials. Thus modified model considers the isotropic hardening as well as kinematic hardening of yield surface, and it can present description of plasticity behavior and ratcheting of cyclic softening and cyclic hardening materials well under multiaxial loading.

Selective liquid directional steering enabled by dual-scale reentrant ratchets

Achieving well-controlled directional steering of liquids is of great significance for both fundamental study and practical applications, such as microfluidics, biomedicine, and heat management. Recent advances allow liquids with different surface tensions to select their spreading directions on a same surface composed of macro ratchets with dual reentrant curvatures. Nevertheless, such intriguing directional steering function relies on 3D printed sophisticated structures and additional polishing process to eliminate the inevitable microgrooves-like surface deficiency generated from printing process, which increases the manufacturing complexity and severally hinders practical applications. Herein, we developed a simplified dual-scale structure that enables directional liquid steering via a straightforward 3D printing process without the need of any physical and chemical post-treatment. The dual-scale structure consists of macroscale tilt ratchet equipped with a reentrant tip and microscale grooves that decorated on the whole surface along a specific orientation. Distinct from conventional design requiring the elimination of microgrooves-like surface deficiency, we demonstrated that the microgrooves of dual-scale structure play a key role in delaying or promoting the local flow of liquids, tuning of which could even enable liquids select different spreading pathways. This study provides a new insight for developing surfaces with tunable multi-scale structures, and also advances our fundamental understanding of the interaction between liquid spreading dynamics and surface topography.