Material Ratcheting Research Articles

Ratcheting Simulation of Additively Manufactured Aluminum 4043 Samples through Finite Element Analysis

This study presents a finite element-based ratcheting assessment of additively manufactured aluminum 4043 samples undergoing asymmetric loading cycles. The Chaboche material model in ANSYS was utilized and the effects of mesh and element type were examined. Different element numbers were used in a thorough convergence study to obtain independent meshing structures. The coefficients of this model were defined through stress–strain hysteresis loops determined from the strain-controlled tests. The backstress evolution and the corresponding yield surface translation in the deviatoric stress space were discussed as three different mesh elements of linear brick, quadratic tetrahedron, and quadratic brick were adopted. The magnitude of backstress was affected as different element types were employed. The first-order brick elements resulted in the highest backstress increments, while the lowest backstresses were determined when quadratic brick elements were taken. Backstress increments are positioned in an intermediate level with the use of quadratic tetrahedron elements. The choice of the element type, shape, and number influenced material ratcheting response over the loading process. The use of quadratic brick elements elevated the simulated ratcheting curves. The quadratic tetrahedron and linear brick elements, however, suppressed ratcheting level as compared with those of experimental data. The closeness of the simulated ratcheting results to those of the measured values was found to be highly dependent on these finite element variables.

Effect of hydrogen on low-cycle fatigue behavior of HRB400 steel under asymmetric cyclic loading

This paper focuses on the study of ductility changes, ratcheting, and low-cycle fatigue behavior of materials after hydrogen charging. Hot-rolled ribbed bar 400 (HRB400) steel was electrochemically charged with H2SO4 solution, and the samples subjected to different hydrogen charging times were subjected to quasi-static tensile and low-cycle fatigue tests under asymmetric cyclic loading. The tests indicated that hydrogen charging changed the initial yield stress of the material, but the ultimate strength remained almost unchanged; hydrogen charging significantly changed the cyclic hysteresis behavior of the material, which increased the elastic range of the stable hysteresis curve; hydrogen charging changed the pattern of ratcheting deformation. The pattern of ratcheting deformation in the later stage was very different from that of the sample without hydrogen charging; hydrogen charging reduced the ductility of the material and resulted in a significant decrease in fatigue life. The fracturing of the hydrogen-charged samples exhibited apparent quasi-cleavage and intergranular fracture characteristics. The non-hydrogen-charged samples had two failure modes (fatigue failure and increased ratcheting deformation resulting in necking instability), whereas the hydrogen-charged samples had only one failure mode of fatigue failure. Based on the experimental analysis, a fatigue life equation that simultaneously considers the effect of hydrogen embrittlement index, mean stress, and stress amplitude is proposed. The equation was used to predict the low-cycle fatigue life of hydrogen-charged specimens under asymmetric cyclic loading, and the error between the results and the measured values was in the two-factor band.

Damage mechanism of a long-wavelength corrugated rail associated with rolling contact fatigue

Corrugation is a common rail damage, which seriously affects the safety and reliability of wheel-rail operation. In this study, the rolling contact fatigue (RCF) damage mechanism of an ex-service small radius rail with long-wavelength corrugation was explored. The results showed that the cracks in the side abrasion area propagated parallel to the rail surface with a very small depth due to the severe wear. While the formation mechanism of cracks in the gauge corner area was the ratcheting of material. The cracks propagated to large length along the plastic deformation flow of microstructure and stopped inside the plastic deformation layer. The cracks in the rail top area propagated first along the plastic deformation flow and then turned at the bottom of the plastic deformation layer into the bulk with the direction which was almost perpendicular to the rail surface. The deflection of cracks was due to the presence of the oxides. The presence of residual austenite in the white etching layer (WEL) and slight plastic deformation area beneath the WEL indicated that the main reason for the formation of WEL was the combination of temperature rise and sustained plastic deformation. It is worth noting that a large number of cracks produced by work hardening made the spalling in the trough severer, leading to the aggravation of rail corrugation.

An implicit numerical scheme for cyclic elastoplasticity and ratcheting under plane stress conditions

The paper reports the development of an implicit numerical scheme for plane stress cyclic elasto-plasticity, capable of integrating a wide range of hardening rules, and simulating multi-axial ratcheting in metal structural components. Constitutive relations account for von Mises yielding in combination with mixed hardening. Emphasis is given to the kinematic hardening part, which is described with an advanced multiple back-stress model suitable for multi-axial material ratcheting simulation. The constitutive equations are integrated implicitly, and the accuracy of the algorithm is assessed via iso-error maps. Two main novelties of the algorithm refer to the incremental update of the internal variables through the solution of a single scalar equation, and the explicit formulation of the consistent tangent moduli. The numerical scheme is implemented within the finite element environment as an external material subroutine, and its computational efficiency is demonstrated through the simulation of large-scale experiments on pipe elbows. Using the proposed computational framework, two kinematic hardening rules are employed to simulate the elbow response with emphasis on local strain amplitude and accumulation (“ratcheting”). The good comparison between numerical and experimental results demonstrates the computational efficiency of the numerical scheme and highlights some key issues concerning multi-axial ratcheting simulation.

A unified direct method for ratchet and fatigue analysis of structures subjected to arbitrary cyclic thermal-mechanical load histories

In this paper, the distinction between material ratchetting and structural ratchetting is clarified, and the concept of constant life diagram is extended to depict low cycle fatigue life boundary in structural design. To provide a novel one-stop solution for structural fatigue and ratchetting problems, a Unified Procedure for Fatigue and Ratchet Analysis (UPFRA) has been proposed. The UPFRA has been successfully applied to two different engineering structures considering complex geometry and temperature-dependent material properties. By comparing the results with ABAQUS step-by-step inelastic analysis, the UPFRA has been verified to be a robust engineering tool with great accuracy, usability, and efficiency.

Simulation of Cyclic Loading on Pipe Elbows Using Advanced Plane-Stress Elastoplasticity Models1

Abstract This work investigates the response of industrial steel pipe elbows subjected to severe cyclic loading (e.g., seismic or shutdown/startup conditions), associated with the development of significant inelastic strain amplitudes of alternate sign, which may lead to low-cycle fatigue. To model this response, three cyclic-plasticity hardening models are employed for the numerical analysis of large-scale experiments on elbows reported elsewhere. The constitutive relations of the material model follow the context of von Mises cyclic elasto-plasticity, and the hardening models are implemented in a user subroutine, developed by the authors, which employs a robust numerical integration scheme, and is inserted in a general-purpose finite element software. The three hardening models are evaluated in terms of their ability to predict the strain range at critical locations, and in particular, strain accumulation over the load cycles, a phenomenon called “ratcheting.” The overall good comparison between numerical and experimental results demonstrates that the proposed numerical methodology can be used for simulating accurately the mechanical response of pipe elbows under severe inelastic repeated loading. Finally, this paper highlights some limitations of conventional hardening rules in simulating multi-axial material ratcheting.

Ratcheting Prediction at the Notch Root of Steel Samples Over Asymmetric Loading Cycles

Abstract The present study intends to evaluate local ratcheting and stress relaxation of medium carbon steel samples under various asymmetric load levels by means of two kinematic hardening rules of Chaboche (CH) and Ahmadzadeh-Varvani (A-V). The Neuber's rule was coupled with the hardening rules to predict ratcheting and stress relaxation at the vicinity of the notch root. Stress-strain hysteresis loops generated by the CH and A-V models were employed to simultaneously control ratcheting progress over stress cycles and stress relaxation at notch root while strain range kept constant in each cycle. The higher cyclic load levels applied at the notch root accelerated shakedown over smaller number of cycles and resulted in lower relaxation rate. The larger notch diameter of 9 mm on the other hand induced lower stress concentration and smaller plastic zone at the notch root promoting ratcheting progress with less materials constraint over loading cycles compared with notch diameter d = 3 mm. Predicted ratcheting results through the A-V and CH models as coupled with the Neuber's rule were found in good agreements with the experimental data. The choice of the A-V and CH hardening rules in assessing ratcheting of materials was attributed to the number of terms/coefficients and complexity of their frameworks and computational time/central processing unit (CPU) required to run a ratcheting program.

A Crystal-Plasticity Cyclic Constitutive Model for the Ratchetting of Polycrystalline Material Considering Dislocation Substructures

A crystal-plasticity cyclic constitutive model of polycrystalline material considering intra-granular heterogeneous dislocation substructures, in terms of three dislocation categories: mobile dislocations, immobile dislocations in the cell interiors and in the cell walls, is proposed based on the existing microscopic and macroscopic experimental results. The multiplication, annihilation, rearrangement and immobilization of dislocations on each slip system are taken as the basic evolutionary mechanism of the three dislocation categories, and the cross-slip of screw dislocations is viewed as the dynamic recovery mechanism at room temperature. The slip resistance associated with the isotropic hardening rule results from the interactions of dislocations on the slip systems. Meanwhile, a modified nonlinear kinematic hardening rule and a rate-dependent flow rule at the slip system level are employed to improve the predictive capability of the model for ratchetting deformation. The predictive ability of the developed model to uniaxial and multiaxial ratchetting in macroscopic scale is verified by comparing with the experimental results of polycrystalline 316L stainless steel. The ratchetting in intra-granular scale which is obviously dependent on the crystallographic orientation and stress levels can be reasonably predicted by the proposed model.

Limited Versus Unlimited Strain Accumulation Due to Ratcheting Mechanisms

After distinguishing material ratcheting and structural ratcheting, different phenomena related to structural ratcheting are gathered. Ratcheting of elastic–plastic structures observed with stationary position of loads is distinguished from ratcheting with moving loads. Both categories are illustrated by examples. The effect of evolution laws for the internal variables describing kinematic hardening on the accumulation of strain due to a ratcheting mechanism, and whether the ratcheting mechanism ceases with the number of cycles so that the accumulated strains are limited, is discussed. Some conditions are shown, under which the Chaboche model can lead to shakedown. Scenarios where shakedown is guaranteed at every load level, or where it may or may not occur at a specific load level, or where it definitely cannot occur at any load level, are distinguished. Correspondingly, the usefulness of shakedown analyses, which are searching for maximum load factors assuring shakedown, or direct (or simplified) methods to obtain postshakedown quantities by avoiding incremental cyclic analyses is discussed.

Ratcheting assessment of visco-plastic alloys at ambient temperature by means of the A-V and O-W hardening rule frameworks

The present study evaluates ratcheting response of samples made of Z2CND18.12N Steel, Zircaloy-4, and 63Sn37Pb solder alloys subjected to asymmetric stress cycles with different stress levels and rates by means of the Ohno-Wang (O-W) and Ahmadzadeh-Varvani (A-V) isotropic-kinematic hardening rules. The framework of hardening rules was constructed on the basis of visco-plasticity constitutive equation to account for the effects of stress rate and time-dependency over ratcheting progress. Elements of visco-plasticity were adopted in the hardening rules on the basis of Chaboche's formulation to evaluate stress rate dependent ratcheting of materials at room temperature. The predicted ratcheting curves and stress-strain hysteresis loops on the basis of the O-W and A-V frameworks have compared with those of experimentally obtained. The A-V framework resulted in consistent ratcheting curves and hysteresis loops and better agreement with experimental data than the O-W framework at various stress ratios.

Ratcheting behavior of UHMWPE reinforced by carbon nanofibers (CNF) and hydroxyapatite (HA): Experiment and simulation

Uniaxial tensile tests were performed to investigate the mechanical properties of the ultra-high molecular weight polyethylene (UHMWPE) with different modification conditions. It was found that the different modification conditions have great influence on the mechanical properties of the UHMWPE. Subsequently, the uniaxial ratcheting behaviors of the UHMWPE/CNF and UHMWPE/HA composite materials were observed under the stress-controlled cyclic tensile condition at room temperature. The dependence of uniaxial ratcheting of composite materials on the mean stress, stress amplitude, stress rate and nano-material content was investigated. The results show that the ratcheting strain and its rate of the two composite materials increase as the mean stress and stress amplitude increase, however, the ratcheting strain and its rate decrease with the increase of the stress rate and nano-material content. Furthermore, it is found that the ratcheting strain of the UHMWPE/HA composite material is more remarkable than that of the UHMWPE/CNF composite material. A new viscoplastic constitutive model is proposed to describe the ratcheting behavior of the UHMWPE composite materials. In this model, a new viscosity function and modified kinematic hardening law were employed. Comparison of simulation and experimental results shows that the simulations are in good agreement with the experimental results.

A unified material model to predict ratcheting response in head-hardened rail steel due to non-uniform hardness distributions

The non-uniform hardness distribution, metallurgy and ratchetting behaviour of head-hardened Australian rail steel (AS60 HH) are studied. In a bid to extrapolate material properties across the rail head continuum, a unified material model of the rail head has been developed, in which only the hardness of the material is variable. This simplification is shown to enable the material model to reasonably describe ratchetting behaviour across the rail head for heat-treated pearlitic steels. Finally, homogeneous material ratchetting models are used to study the evolution of plastic strain deformation under realistic rail-wheel contact conditions. The results show that non-uniform material properties may compromise ratcheting response with wear progression, thus impacting lifetime of AS60 HH rail steel and re-railing frequency.

A two-rod testing approach for understanding ratcheting in structures

In a national project, with the aim to develop a robust method for structural verification of pressure equipment subjected to ratcheting, a two-rod test approach is developed. Two testing machines, with one specimen in each, are controlled in such way that a constant primary load and a cyclic secondary load are applied on the specimens. The ferritic steel P265 and the austenitic steel 316L are tested for a number of load combinations. Test results show that ratcheting is produced in all tests. As expected, the amount of ratcheting increases with the load level. At the start of a two-rod test, structural ratcheting dominates over material ratcheting. Depending on the load level and combination of primary load and cyclic secondary load, material ratcheting might eventually become more important.Based on results from tensile testing and fully-reversed strain controlled cycling, five different constitutive models are calibrated. The possibility to simulate the response of the conducted experiments with the different models is investigated. The most advanced model investigated, i.e. the nonlinear kinematic Chaboche model, does not necessarily give the best predictions. Up to a strain level of 5%, i.e. the criterion in ASME NB-3228.4, the bi-linear model best predicts the experiments.Recommendations for how ratcheting in structures subjected to cyclic plastic deformation can be predicted by numerical simulation are given.

Plastic ratchetting of railhead material in the vicinity of insulated rail joints with wheel and thermal loads

A detailed finite element analysis (FEA) was carried out to present a stress analysis of an insulated rail joint IRJ considering a wheel load on the IRJ producing stresses above the shakedown limit of the rail material. A 5mm endpost thickness is considered at the discontinuity in the rail steel which is required to form the 6 bolt IRJ. In addition, an axial pressure load of 165MPa was also considered on the rail faces at the discontinuity in the form of compression (buckling) and tension (pull-apart). A modified Hertzian contact pressure distribution is considered in this simulation. 100 cycles of dynamic wheel load of 174kN were applied to the rail top materials in the vicinity of the IRJ.Residual stress and plastic strain, equivalent plastic strain and permanent deformation of railhead material in the vicinity of IRJ are presented. The strain data depict damage of endpost materials and ratchetting failure of rail ends due to vertical wheel load and axial thermal load. The ratchetting failure modes follow the established trend of decay in the ratchetting rate in successive wheel load cycles. The size of the plastic zone in the railhead materials is also identified.

Use of a Two-Rod Approach for Understanding Ratcheting in Structures

In a national project, with the aim to develop a robust method for structural verification of pressure equipment subjected to ratcheting, a two-rod test approach is developed. Two testing machines, with one specimen in each, are controlled in such way that a constant primary load and a cyclic secondary load are applied on the specimens. The ferritic steel P265 and the austenitic steel 316L are tested for a number of load combinations. Test results show that ratcheting is produced in all tests. As expected, the amount of ratcheting increases with the load level. At the start of a two-rod test, structural ratcheting dominates over material ratcheting. Depending on the load level and combination of primary load and cyclic secondary load, material ratcheting might eventually become more important.Based on results from tensile testing and fully-reversed strain controlled cycling, five different constitutive models are calibrated. The possibility to simulate the response of the conducted experiments with the different models is investigated. The most advanced model investigated, i.e. the nonlinear kinematic Chaboche model, does not necessarily give the best predictions. Up to a strain level of 5%, i.e. the criterion in ASME NB-3228.4, the bi-linear model best predicts the experiments.Recommendations for how ratcheting in structures subjected to cyclic plastic deformation can be predicted by numerical simulation are given.

Cyclic Plasticity Analysis of the Coke Drum under Moving Axial Temperature Front

Experiments of uniaxial tension and ratcheting of material of coke tower 15 Cr Mo R are carried out under 20 ℃, 200 ℃, 300 ℃, and 400 ℃. The ratcheting strain of the material is predicted by OW-II model, which could predict the stable ratcheting strain rate of the material well. The transient temperature field under oil-feeding and water quenching are numerically simulated with the help of dynamic coordinate system method, which yields the axial temperature difference and its characteristic value for the simplified characteristic temperature load to be used in the cyclic plastic analysis of coke drum. According to the cyclic plastic analysis of coke drum cycled between oil-feeding and water quenching, the bottom alignment of temperature difference ranges produces much ratchet strain rate. In addition, the co-existence of cyclic internal pressure would increase the ratcheting strain of the structure. By parametric study, the ratchet boundary is determined for the temperature gradient under oil-feeding and water quenching. It indicates that, when temperature difference range of water quenching is smaller, the ratchet boundaries would be influenced much more by the cyclic internal pressure.

Thermal Ratcheting of Solder-Bonded Layered Plates

The cyclic growth and recovery of warpage were observed in experiments on Si/solder/Cu layered plates subjected to cyclic thermal loading [1]. In the present study, the experiments were analyzed using representative material models for the solder and Cu layers in finite element analysis. The warpage growth/recovery behavior observed was reproduced well in the analysis using the Armstrong-Frederick and Ohno-Wang models for the solder and Cu layers, respectively. Material ratcheting due to non-proportional cyclic loading was found to happen in the solder layer as a consequence of the CTE mismatch, while material ratcheting due to proportional cyclic loading occurred in the Cu layer as a result of the significant temperature dependence of viscoplasticity in the solder layer.

Ratchetting of railhead material of insulated rail joints (IRJs) with reference to endpost thickness

Insulated rail joints (IRJs) are the most important structural link in a railway track for electrical signal purposes. Because of the presence of the discontinuity in the rail material at IRJs, problems with maintaining rail/track geometric requirements and much increased dynamic wheel load effects on IRJs result. Material degradation and damage to the rail ends at the discontinuity therefore occur. A few studies have been carried out to address this issue globally. A local stress and damage analysis is essential to study the material behaviour of the rail ends with an appropriate elasto-plastic material model. For cyclic loading, a kinematic hardening material model alone is not enough to predict ratchetting damage, plastic deformation and initiation of rolling contact fatigue (RCF) defects at the rail ends of IRJs.In this paper, a three-dimensional (3D) finite element analysis (FEA) is carried out to study the distribution of stresses and strains in the vicinity of the IRJs using modified Hertzian Contact Theory (HCT). A solid rail model with a 10mm thick fibreglass insulating endpost filling the rail discontinuity is considered and two beam elements are connected to the solid rail model by equation constraints. A 5mm fibreglass endpost is also considered for comparison purposes. A combination of nonlinear kinematic and isotropic hardening material models is considered in the simulation. A local stress analysis model, called sub-modelling, is incorporated to capture degradation of materials accurately and to obtain ratchetting damage of the endpost material of the IRJ. It also captures the decay of the ratchetting rate. The effects of cyclic wheel loads on the IRJ are also presented. The analysis indicates that material degradation occurs progressively due to the loading spectra. Simulation results also present the IRJs mechanical behaviour with response to endpost thicknesses for enhancing better geometric design of IRJs.

A fatigue damage indicator parameter for P91 chromium‐molybdenum alloy steel and fatigue pre‐damaged P54T carbon steel

ABSTRACTTwo grades of structural steel were subjected to fully reversible, constant stress amplitude cyclic loading. The local strain response of the material was measured and recorded during the test, with the applied testing technique enabling the monitoring of hysteresis loop variation for the narrowest cross‐section of the hourglass specimen. Changes in hysteresis loop width, representing the local inelastic response of the material, were recorded in order to monitor the density of structural imperfections. Material ratcheting behaviour was observed as changes in the mean strain for selected load cycles. Ratcheting was attributed to local deformation of the material in the vicinity of imperfections such as voids or inclusions, as well as deformation induced by the propagation of microcracks. Definitions of a damage indicator parameter and damage parameter were proposed. The fatigue behaviour of the two investigated grades of steel was finally illustrated in the form of damage curves for different stress amplitudes and for undamaged and fatigue pre‐damaged material.

A numerical approach for predicting shakedown limit in ratcheting behavior of materials

Studying the ratcheting and shakedown behavior of materials under cyclic loading is significant for controlling structural deformation and improving the service lifetime of materials. In this study, cyclic loading tests were performed on DH36 steel at room temperature under various conditions while evaluating the effects of the loading waveform, the loading rate and the stress ratio to reveal the material characteristics of ratcheting and shakedown behavior and to provide an experimental basis for proposing and implementing a numerical method that predicts the shakedown limit in this type of cyclic plastic behavior. A numerical analysis method using the plastic deformation energy as a shakedown criterion was proposed based on the energy dissipation phenomena observed in the tests. The method was then applied to two classic examples of shakedown analysis by computation and was compared with related results from the literature to evaluate its effectiveness and reliability. This method provides a new approach for the numerical analysis of the material shakedown limit.