Strain-controlled Cyclic Loading Research Articles

Mechanistic model for hydrogen accelerated fatigue crack growth in a low carbon steel

Fracture by hydrogen accelerated fatigue crack growth is a severe type of environmental failure. Although fatigue crack growth has been the subject of intense investigation over several decades, a complete mechanistic and predictive model is still lacking. Such a crack growth model is even more rare in the case of hydrogen in view of the lack also of constitutive models for material deformation under cycling loading that account for the hydrogen effect. In this study, we present a model for fatigue crack propagation induced by alternating crack tip plastic blunting and re-sharpening, which in the presence of hydrogen can be accelerated by hydrogen enhanced dislocation motion and generation. The Chaboche constitutive model, which is a nonlinear kinematic hardening model capable of capturing many features of material behavior under cyclic loading, is used for the calculation of the stress and strain fields at the propagating crack tip. The Chaboche model is calibrated using a sequence of experimental data from uniaxial strain-controlled cyclic loading tests and uniaxial stress-controlled ratcheting tests with a low carbon steel, JIS SM490YB, in the absence and presence of hydrogen. The numerical simulation results indicate that the proposed crack propagation model can predict Paris law behavior and can successfully demonstrate acceleration of fatigue crack growth in the presence of hydrogen. Significantly, the profiles of the steady-state opening stress and strain ahead of the fatigue crack tip in a compact tension (C(T)) specimen were found to have sections over which they vary as ln(1/r) with distance r from the crack tip, consistent with the crack-tip strain field for a non-stationary crack.

A Constitutive Model for Asymmetric Cyclic Hysteresis of Wrought Magnesium Alloys under Variable Amplitude Loading

A cyclic plasticity constitutive model was developed for materials with asymmetric cyclic behavior to explain the stabilized stress–strain response under variable amplitude loading. The proposed constitutive model incorporated the von Mises yield function with an adjustment to accommodate asymmetric yielding under tension and compression. A combined isotropic–kinematic hardening model was proposed to describe the evolution of the yield surface in the reference uniaxial frame and the actual frame. The history of plastic deformation is memorized by introducing internal variables, accumulated slip, and residual twins, which govern the cyclic flow behavior in the subsequent reversal. The additional conditions required to predict the stabilized hysteresis response of a material under variable amplitude loading were set out and incorporated into the constitutive model. The model was numerically implemented and programmed into a user material (UMAT) subroutine to run with the commercial finite element program, Abaqus/Standard 2019. The model was calibrated using the stabilized hysteresis response of ZEK100 and AZ31B sheets under constant amplitude strain-controlled cyclic loading for different strain amplitudes. To verify the model, constant amplitude and four different variable amplitude load spectra tests were performed and the stabilized stress–strain hysteresis response predicted by the model was compared with test results. It was demonstrated that the results are in very good agreement.

Investigating the deformation and microstructural evolution of laser powder-bed fusion of Hastelloy X during high temperature fatigue loading

This study investigates the fatigue behaviour of samples made by laser powder-bed fusion of Hastelloy X (LPBF-HX) with as-built and machined surface conditions at 700 °C under fully reversed strain-controlled cyclic loading. Samples with both surface conditions exhibited initially cyclic hardening followed by cyclic softening under large strain amplitude testing, where a slight continuous hardening was observed for tests with smaller strain amplitudes. The samples with machined surfaces showed longer endurance and higher stress ranges than those with as-built surfaces. Post-fatigue-test EBSD analysis showed the formation of the Goss texture and extensive local strain accumulation in the samples tested under high strain amplitude at 700 °C. Fractography investigations revealed that early crack initiation in the samples with as-built surfaces was from stress concentrations induced by valleys on the rough surface. No evidence of crack initiation induced by pre-existing defects was observed in the machined samples, and the excessive slip activity at the surface was found to be responsible for the crack initiation.

Experimental study on pure-shear cyclic deformation of dielectric elastomer at different temperatures

A series of pure-shear cyclic tests were performed on VHB™4910 dielectric elastomer at various temperatures, and the investigations were focused on the influence of temperature variations on the cyclic deformation of the elastomer and the influences of loading level and loading rate on the temperature-dependent cyclic deformation. The results demonstrate that the temperature-dependent deformation of VHB™4910 dielectric elastomer primarily manifests its viscoelasticity, while the hyper-elastic part shows comparatively weaker temperature-dependence. At different temperatures, the elastomer exhibits a cyclic softening during the strain-controlled cyclic loading. Both the peak stress and residual strain reduce with increasing the temperature and reach a stable state more rapidly at higher temperatures. A more pronounced temperature-dependence is exhibited in the stress response of the elastomer at a high loading rate; while a lower rate-dependence is observed at a high temperature. The ratchetting of the elastomer presented in the stress-controlled tests becomes more prominent as the temperature increases, but the rate-dependence of ratchetting is weaker at higher temperatures. Moreover, the temperature-dependence of ratchetting is more significant at a high-stress level as compared to that at a low-stress level.

Research on multi-scale failure mechanism of gradient nanostructured 316L steel under strain-controlled fatigue at 650 °C

Gradient nanostructured materials have excellent fatigue resistance. At present, there are few research on the fatigue properties of gradient nanostructured (GNS) materials at high temperature. Herein, the multi-scale failure mechanism of GNS 316L steel at 650 °C is studied, and the high temperature fatigue tests under different strain amplitudes are conducted. Then, post-test microstructure observations were carried out to reveal the damage mechanisms, and the fatigue behavior was numerically simulated by crystal plasticity model. The experimental results show that the strength of the GNS 316L steel is still higher than that of the coarse-grained (CG) 316L steel at 650 °C, and the fatigue life of the GNS 316L steel is also higher than that of the CG one under strain fatigue loadings. The fatigue fracture results show that the fatigue crack presents a mixed propagation mode, and the crack source of GNS 316L transfers from surface to subsurface under low strain amplitude. The numerical results directly reflect the influence of the GNS surface layer on the plastic slip behavior. The fatigue failure mechanism of GNS 316L steel under strain-controlled cyclic loading at 650 °C was explained from a multi-scale perspective. This study provides data and method support for the application of GNS 316L steel at high temperature.

Suffusion in gap-graded granular soils subjected to strain-controlled cyclic loading with coupled CFD-DEM method

The suffusion mechanism of gap-graded soils subjected to cyclic loading, which is common in foundations of transportation engineering and marine structures, has not been fully understood. This paper employs the coupled computational fluid dynamics and discrete element method (CFD-DEM) to investigate the effect of cyclic loading on suffusion. The cyclic loading is simulated in a strain-controlled way, by which, samples with different frequencies (i.e., 0.5 Hz, 1 Hz, and 2 Hz) and strain amplitudes (i.e., 0.5 %, 1 %, 2 %) undergo erosion of 20 s duration with a constant hydraulic gradient and confining pressure. The influence of cyclic loading on suffusion is examined from both the macroscopic and microscopic perspective through the capture of erosion mass, void ratio variation, particle velocity field, fines trajectory, and force chain. Results indicate that the higher the cyclic frequency and strain magnitude, the more severe the loss of the fines. The vibratory compaction of dynamic loading could lead to the clogging of the sample, decreasing the hydraulic conductivity. In addition, the different micromechanisms of fines erosion during loading and unloading is presented.

A tunnelling crack density evolution model for FRP laminates subjected to cyclic multi-axial strain-controlled loading

A multi-scale stochastic crack density evolution model for tunnelling cracks under multi-directional cyclic loading is presented. The damage model proposed utilizes a multi-scale stress-based criterion for crack initiation and a triple unit cell approach with inputs from the GLOB-LOC model for crack-front growth rate. Biaxial cruciform specimens subjected to strain-controlled cyclic loading are used to calibrate the crack initiation SN curve and the Paris-Erdogan type of law required for crack growth. Additionally, uniaxial force-controlled cyclic tests are used to calibrate the stochastic parameters associated with crack initiation and crack growth. The performance of the damage model in predicting the crack-front growth compared well with experimental data and 3D finite element analyses. The damage model includes a crack element discretisation scheme which allows for multiple collinear cracks to initiate and coalesce. The model also accounts for the growth of damage outside the window of a primary representative volume element. The crack density predictions of the model are compared with measurements from cruciform specimens. It is shown that the damage model captures the trend of the crack density evolution well and provides a conservative prediction of the crack saturation level.

Loading history effect on ratcheting behavior: Modelling and simulation

In this paper, an elastoplastic constitutive model is developed to describe the effect of loading history on the ratcheting. The loading history variable is introduced to record stress history variation during cyclic loading, such as equivalent peak stress and equivalent stress amplitude. Based on Ohno-Wang model, an improved kinematic hardening rule is proposed to simulate the ratcheting effect by establishing the nonlinear evolution equation of ratcheting parameter. A new memory evanescence term is introduced to the plastic strain range memory surface. The evanescence term is activated to describe the difference of yield stress evolution during ratcheting and strain-controlled cyclic loading as the plastic strain range radius exceeds a certain threshold. Compared with the experiments and existing models, the results show that the proposed model can better capture the ratcheting effect with loading history.

Sensitivity of local cyclic deformation in lath martensite to flow rule and slip system in crystal plasticity

The prediction of the cyclic deformation behaviour in lath martensite-based high-strength steels requires constitutive models that reflect the local stress and strain fields as accurately as possible. At the same time, the constitutive models should act as efficiently as possible in order to achieve the required high number of cycles in a finite time. Only few research works have studied the sensitivity of the local cyclic deformation in lath martensite to the power law-based flow rule (Hutchinson or Chaboche–Cailletaud) and the active body-centred cubic (bcc) slip systems ({110}〈111〉 and {112}〈111〉) in the crystal plasticity finite element method (CPFEM). This paper, therefore, aims to provide some guidance in the selection of suitable flow rule and slip systems. Based on full-field micromechanical modelling of a medium-carbon steel under symmetric strain-controlled cyclic loading, it can be shown that the two most commonly used flow rules according to Hutchinson and Chaboche–Cailletaud are equally capable of predicting the local stress and strain distributions within the hierarchical martensitic microstructure. However, using the Hutchinson flow rule increases the computational performance for the quasi-rate-independent problem considered here. The local distributions found differ strongly from those in the parent austenitic microstructure. If plastic deformation is assumed not only on the slip systems {110}〈111〉, as often done, but also on the {112}〈111〉 type, a redistribution of the bimodal distributed local stresses occurs at a significantly lower stress level. The unimodal distributed local strains are less affected by this. In addition, it is found that slightly different critical resolved shear stress (CRSS) values for both slip system types influence the local stress and strain distributions less severely than the additional plastic slip activation in the material.

Hysteresis behavior of EQ56 high strength steel: Experimental tests and FE simulation

The probability of offshore platforms suffering to extreme cyclic loads, such as storm surges and typhoons, increases highly at deep sea. It is essential to achieve the hysteresis behavior of steel material for evaluating the dynamic response of offshore platform under cyclic load. A total of 18 coupons are fabricated from the EQ56 high strength steel (HSS) plate to investigate the monotonic and cyclic behaviors. Loading protocols include monotonic tension, constant amplitude and changing amplitude strain-controlled cyclic loadings. It is revealed that the visco-plastic behavior of EQ56 HSS is insignificant under the monotonic tension at room temperature. The EQ56 HSS presents obvious Bauschinger effect, non-masing rule, stress hardening/softening behavior and strain history memory effect under strain-controlled cyclic loading. The prior loading history at low strain-amplitude levels has little effect on the saturation stress of EQ56 HSS while stress hardening can be reactivated to a new saturation level when the applied strain-amplitude is increased. The monotonic and the cyclic hysteresis curves of EQ56 HSS were compared, and hysteretic skeleton curves are fitted using the Ramberg-Osgood model. The essential parameters of the Chaboche combined hardening model are calibrated to describe the cyclic behavior of EQ56 HSS. The comparison between FE simulation and test results demonstrates that this model cannot characterize effectively the hysteretic behavior of EQ56 HSS because the strain history memory effect and coupled behavior of cyclic stress softening and hardening are ignored in its constitutive equation.

Fatigue of hybrid fibre-reinforced plastics.

Understanding the fatigue behaviour of hybrid fibre-reinforced plastics is desirable for exploiting their features in safe, durable and reliable industrial components. The fatigue performance of hybrid composites has not been extensively investigated yet. The paper presents an overview of the available knowledge on the fatigue of hybrid fibre-reinforced plastics, and, more specifically, reports the fatigue behaviour of a quasi-isotropic pseudo-ductile all-carbon fibre interlayer hybrid composite by experimental measurements and observations, with emphasis on the damage development. The fatigue conditions are tension-tension stress- and strain-controlled cyclic loading. The results include fatigue life for different maximum stress and strain levels, stiffness evolution and damage observations by X-ray micro-computed tomography. The studied hybrid all-carbon fibre quasi-isotropic composite exhibits pseudo-ductility in quasi-static testing. For stress-controlled fatigue, the fatigue load over the limit of elastic response is not sustained. Contrary to that, the composite retains its load-carrying ability in the pseudo-ductile regime for a strain-controlled regime, albeit with lowered stiffness. This article is part of the theme issue 'Ageing and durability of composite materials'.

Experimental Analysis and Constitutive Modeling of Cyclic Behavior of 304 L Stainless Steel: Introduction of Isotropic Hardening Fading Effect

Abstract In this study, the mechanical behavior of austenitic stainless steel 304 L under low cycle fatigue was investigated under different uni-axial strain-controlled loadings of 0.5%, 0.8%, 1.0%, 1.2%, and 1.5%. The analysis of the experimentally determined strain versus stress hysteresis curves was carried out to achieve stress quantities such as amplitude stress, peak effective stress, and peak back stress. It was observed that in the early stage of cyclic loading, material underwent initial hardening, followed by softening phenomena which were more considerable in the lower strain range. Before the failure, the secondary hardening was observed at the final stage. In addition to accumulated plastic strain, it was shown that the peak back stress and peak effective stress which is associated with isotropic hardening and kinematic hardening behavior, respectively, are influenced by the strain range effect. Therefore, the coefficient of recall term that appeared in the Armstrong–Frederick nonlinear kinematic hardening model was considered to be dependent on the radius of the memory surface. Furthermore, to increase the ability of the plasticity constitutive model to show a smooth transition between various hardening stages, the radius of the yield surface which is associated with the isotropic hardening rule was equipped with the fading effect. Finally, by the comparison of numerical and experimental results, the capability of the rate-dependent constitutive model over classical rate-independent plasticity in the prediction of mechanical behavior of steel 304 L under strain-controlled cyclic loading was revealed.

Propagation of tunnelling cracks in composite materials under strain and force-controlled cyclic loading

In this paper, the propagation of tunnelling cracks in composite laminates subjected to uniaxial force-controlled and strain-controlled cyclic loading is analysed considering both interacting and non-interacting cracking scenarios. Glass fibre reinforced polymer laminates with [Formula: see text] layup are used in the analysis. For non-interacting cracks, a strain-controlled test under a single strain value is found to be sufficient to produce the slope of the Paris-Erdogan law type curve relating the crack front growth rate (CGR) with the energy release rate (ERR), but within a limited range of ERR. Whereas, a force-controlled test is found more suitable when characterising the variation of the CGR at a certain ERR value. For closely spaced cracks, commonly seen crack interaction scenarios are identified and the CGR of the crack front is investigated for both loading control modes. It is found that the CGR decreases when volume averaged stresses are reduced ahead of the crack front due to shielding effect at high crack densities. A relationship between these two parameters is presented. It is further found that the CGR of two collinear crack fronts growing towards each other for coalescence do not influence each other. But when the two crack fronts are not collinear the CGR of the crack fronts is significantly affected after they have grown past each other.

A universal constitutive model for hybrid stress-strain controlled creep-fatigue deformation

On account of stress relaxation, the conventional strain-controlled creep-fatigue interaction (CCFI) tests make it difficult to obtain the creep-dominated data. To make up for this deficiency, a novel hybrid stress-strain controlled creep-fatigue interaction (HCFI) loading which is capable of controlling the ratio between fatigue damage and creep damage is developed. Besides, extensive comparisons of two CFI responses give better understanding of the newly proposed HCFI loading. Experimental results show that the cyclic creep behaviors under the two CFI loading conditions are obviously different. The creep strain for HCFI tests accelerates with cycle number and increases with test parameters significantly, while the creep strain decelerates with cycle number during CCFI loadings and it is not sensitive to dwell conditions. Besides, HCFI tests show a pronounced difference in failure life as the test parameters vary. These different phenomena challenge the current constitutive models, and thus, towards developing a simulation-based design methodology for high temperature components, a universal viscoplastic constitutive model based on Walker model is proposed, in which the self-adaptive hardening parameters and dynamic recovery factors are incorporated to capture the distinct cyclic deformation behaviors during HCFI and CCFI loadings. Good agreements between the experimental and simulated results verify the robustness of the proposed model in capturing various cyclic loadings, including strain-controlled cyclic loading (low cycle fatigue and CCFI), stress-controlled ratcheting-creep loading and HCFI loading, of P92 steel and Inconel 718 at different temperatures. Accordingly, apart from a loading profile able to generate wide ranges of CFI damage, this work also gives a universal constitutive model, which may provide a new solution for existing CFI design from loading waveforms to modeling methods.

Dynamic Properties of Biopolymer-Treated Loose Silty Sand Evaluated by Cyclic Triaxial Test

Abstract Improvement in certain soil properties because of biopolymer treatment has been found to imply that it could help in liquefaction mitigation. In this study, the effect of confining pressure on cyclic strength properties of agar biopolymer treated and untreated silty sand has been explored so that their behavior at varying depths, subjected to varying overburden stress, could be known. The agar-treated and untreated soils subjected to effective confining stresses of 100, 150, and 200 kPa were tested under consolidated undrained, strain-controlled cyclic triaxial loading, keeping the other parameters constant. The pore water pressure response, stress-path behavior, and effect on dynamic soil parameters were studied. The excess pore pressure and secant shear modulus were found to increase with the increase in confining pressure, whereas there wasn’t much of an effect on damping characteristics. The confining pressure had a positive effect on treated soil subjected to cyclic loading in terms of strength and stiffness because of the densification caused from confinement. In addition, durability characteristics of the treated soil were evaluated by cyclic wetting and drying tests. The N2-Brunauer-Emmett-Teller surface area test revealed that the surface area and pore volume decreased upon treatment, the results of which were supported by scanning electron microscopy images also.

Studies on the experimental and simulated cyclic-plastic response of structural mild steels

Experimental investigations have been conducted on the cyclic-plastic response of a structural mild steel (Grade YST210) under varying strain amplitudes (εa) under symmetric strain-controlled cycling. The results on the investigated YST210 steel and the reported results on four similar grades of steels (E250A, Q235, SS400, and GR345 steel) under symmetric strain-controlled cyclic loading are analyzed using a suggested approach based on Chaboche isotopic-kinematic hardening (CIKH) model. The parameters of the CIKH model are estimated from the stabilized hysteresis loops, and the obtained parameters are subsequently optimized using genetic algorithm to obtain closer predictions for the experimental cyclic-plastic response. The experimental fatigue response of YST210 steel reveals cyclic softening, and the estimated softening factor (SF) varies from 10% to 22% when εa alters from 0.25% to 2%; the magnitude of SF at εa = 2% decreases from 22% to 17.5% as the strain rate increases from 5 × 10−4 s−1 to 5 × 10−2 s−1. The efficacy of the suggested approach was estimated using the maximum root mean square error (Ferror) between predictions and experimental results. For the YST210 steel at different εa, the magnitude of Ferror is <4.5%, while for the other steels it is <3%. The suggested approach inherits the merit that it considers only a single set of parameters for different test conditions unlike multiple set of parameters often being used in the reported simulations. But still the results of simulations for E250A and SS400 steels depict an improvement of more than 40% over the available reports of simulations for the same steels.

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.

Modeling the Hydrogen Effect on the Constitutive Response of a Low Carbon Steel in Cyclic Loading

Abstract Hydrogen-accelerated fatigue crack growth is a most severe manifestation of hydrogen embrittlement. A mechanistic and predictive model is still lacking partly due to the lack of a descriptive constitutive model of the hydrogen/material interaction at the macroscale under cyclic loading. Such a model could be used to assess the nature of the stress and strain fields in the neighborhood of a crack, a development that could potentially lead to the association of these fields with proper macroscopic parameters. Toward this goal, a constitutive model for cyclic response should be capable of capturing hardening or softening under cyclic straining or ratcheting under stress-controlled testing. In this work, we attempt a constitutive description by using data from uniaxial strain-controlled cyclic loading and stress-controlled ratcheting tests with a low carbon steel, Japanese Industrial Standard (JIS) SM490YB, conducted in air and 1 MPa H2 gas environment at room temperature. We explore the Chaboche constitutive model which is a nonlinear kinematic hardening model that was developed as an extension to the Frederick and Armstrong model, and propose an approach to calibrate the parameters involved. From the combined experimental data and the calibrated Chaboche model, we may conclude that hydrogen decreases the yield stress and the amount of cyclic hardening. On the other hand, hydrogen increases ratcheting, the rate of cyclic hardening, and promotes stronger recovery.

DEM study on the development of the earth pressure of granular materials subjected to lateral cyclic loading

The discrete element method (DEM) is adopted to study the development of the lateral earth pressure of granular materials subjected to lateral strain-controlled cyclic loading, which is imposed by integral abutments due to temperature variation. Clumped particles are used to simulate the nonspherical granular particles. The simulation results show that there is continuing buildup of lateral stresses with cycling for both loose and dense samples, while the loose sample experiences a substantial decrease in volume and the dense sample shows slight dilation. The simulated macro-response is qualitatively consistent with the laboratory observations. The micro-response is further investigated, and a unique relationship is revealed between the deviator stress ratio on the macro-scale and the deviator fabric of strong contacts on the micro-scale, which is not influenced by the initial porosity, vertical stress, or loading path. Although the cyclic lateral strain is small, a number of cycles can result in a certain micro-structure that can support large lateral stresses, which can also be achieved by lateral monotonic loading to large strains. The influence of the particle shape on the macro- and micro-responses of an assembly is highlighted by performing lateral cyclic loading test on a sample with spherical particles.

A crystal plasticity-based constitutive model for ratchetting of cyclic hardening polycrystalline metals

A crystal plasticity-based constitutive model is developed by modifying the second item of Armstrong–Frederick (A–F) nonlinear kinematic hardening rule and introducing self-hardening and latent hardening representing the dislocation interaction between slip systems. With the help of β scale-transition rule, the cyclic stress–strain responses of polycrystalline metals can be obtained from the single crystal constitutive model. Then the developed model is applied to describe the cyclic deformation behavior of a face-centered cubic polycrystalline metal, i.e., 316L stainless steel. The predicted results of the model compared with the experiments of 316L stainless steel show that the model can not only simulate the uniaxial and multiaxial ratchetting of the face-centered cubic crystal material during the asymmetrical stress-controlled cyclic loading, but also describe the cyclic hardening characteristics of materials under symmetrical strain-controlled cyclic loading. Meanwhile, the model is capable of predicting uniaxial ratchetting of different orientations at single crystal scale.