Uniaxial Ratcheting Research Articles

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.

Uniaxial ratcheting behaviors of Zircaloy-4 tubes at 400 °C

A series of uniaxial tensile, incremental cyclic and uniaxial ratcheting tests were conducted at 400°C on Zr-4 tubes to investigate the mechanical behaviors under various loading conditions. The experimental results show that this material features cyclic softening at room temperature (RT), and cyclic stable and hardening at 400°C. Uniaxial ratcheting strain increases with the increase of mean stress and stress amplitude, and decrease with the increase of loading rate. Loading history has significant influence on the uniaxial ratcheting behavior. Lower stress level after a loading history with higher stress level leads to the shakedown of ratcheting. Higher loading rate after a loading history with lower loading rate brings down the ratcheting strain rate. The sequence of stress rate appears to have no effects on the final ratcheting strain accumulation. The ratcheting strain is sensitive to temperature, and the higher temperature leads to less ratcheting under same normalized stress (σ‾=σ/σ0.2).

An experimental study on uniaxial ratcheting of polycarbonate polymers with different molecular weights

The uniaxial ratcheting was experimentally observed on the polycarbonate (PC) polymers with different molecular weights (i.e., PC-7030PJ and PC-7020PJ) at room temperature. The effects of mean stress, stress amplitude, stress rate and peak hold-time on the ratcheting were observed. The results show that obvious ratcheting deformation occurs in the two prescribed polycarbonate polymers subjected to the stress-controlled cyclic loading; and the ratcheting strain accumulates cyclically in the direction of non-zero mean stress. The ratcheting greatly depends on the mean stress and stress amplitude, and the ratcheting strain increases more rapidly as the mean stress and stress amplitude increase. The ratcheting of two prescribed polycarbonate polymers is also significantly time-dependent, the ratcheting strains observed in the load cases with longer peak hold-time and at lower stress rate are larger than that with shorter peak hold-time and at higher stress rate. More importantly, a comparison of the ratcheting of two prescribed polycarbonate polymers shows that, at room temperature, the ratcheting of the polycarbonate polymer with a larger molecular weight (i.e., PC-7030PJ) is more remarkable than that with a smaller one (i.e., PC-7020PJ).

A Noncyclic Method for Determination of Accumulated Strain in Stainless Steel 304 Pressure Vessels

Experimental results of uniaxial ratcheting tests for stainless steel 304 (SS304) under stress-controlled condition at room temperature showed that the elastic domain defined in this paper expands with accumulation of plastic strain. Both ratcheting strain and viscoplastic strain rates reduce with the increase of elastic domain, and the total strain will be saturated finally. If the saturated strain and corresponded peak stress of different experimental results under the stress ratio R ≥ 0 are plotted, a curve demonstrating the material shakedown states of SS304 can be constituted. Using this curve, the accumulated strain in a pressure vessel subjected to cyclic internal pressure can be determined by only an elastic-plastic analysis, and without the cycle-by-cycle analysis. Meanwhile, a physical experiment of a thin-walled pressure vessel subjected to cyclic internal pressure has been carried out to verify the feasibility and effectiveness of this noncyclic method. By comparison, the accumulated strains evaluated by the noncyclic method agreed well with those obtained from the experiments. The noncyclic method is simpler and more practical than the cycle-by-cycle method for engineering design.

Experimental studies on the uniaxial ratchetting of polycarbonate polymer at different temperatures

A series of uniaxial stress-controlled cyclic tests were carried out at different temperatures to investigate the uniaxial ratchetting of polycarbonate (PC) and its time-dependent behavior. The cyclic tests were conducted with a constant peak stress, various valley stresses and at four prescribed temperatures (i.e., 0, 30, 60 and 90°C). The effects of applied valley stress and ambient temperature on the uniaxial ratchetting of the PC are discussed. From the experimental observations, it is concluded that the ratchetting of the PC depends greatly on the test temperature; both the ratchetting strain and ratchetting strain rate increase with increase of test temperature. The effect of different valley stresses on the ratchetting is also dependent on the test temperatures, and fatigue rupture occurs in the load cases with negative valley stresses and at higher temperatures.

EFFECTS OF TANGENT OPERATORS ON PREDICTION ACCURACY OF MESO-MECHANICAL CONSTITUTIVE MODEL OF ELASTO-PLASTIC COMPOSITES

With a newly developed homogenization cyclic constitutive model of particle reinforced metal matrix composites [Guo et al. (2011)], the effects of tangent operators, i.e., continuum and algorithmic tangent operators [defined by Doghri and Ouaar (2003)] on the accuracy of the developed meso-mechanical constitutive model to predict the monotonic tensile and uniaxial ratchetting deformations of SiC P /6061 Al composites were investigated in this work. The predictions were obtained by the developed model with the choices of different tangent operators and various magnitudes of load increments. Comparison of prediction accuracy and necessary error analysis on the results obtained by different tangent operators were conducted. It is shown that: the stress or strain difference in each load increment and produced by using different tangent operators will accumulate step by step; accurate prediction should be obtained by employing a load increment small enough, especially when the algorithmic tangent operator is used in predicting the uniaxial ratchetting of the composites.

Analysis of uniaxial ratcheting behavior and cyclic mean stress relaxation of a duplex stainless steel

The growing presence of a non-conventional stainless steel like a super duplex grade S32750 requires clarification of the structural responses to cyclic loading. This study attempted to characterize the uniaxial ratcheting behavior and the cyclic mean stress relaxation of S32750 super duplex stainless steel which had cyclic hardening characteristics under strain-controlled cyclic loading. A constitutive model capable of simulating the uniaxial ratcheting response and the mean stress relaxation was developed in the framework of rate-independent plasticity theory. Verification of the proposed constitutive model was achieved by simulating uniaxial strain- and stress-controlled cyclic loading tests including cyclic mean stress relaxation and comparing the predicted results with the experimental measurements. The influences of mean stress level, stress amplitude and loading history on the uniaxial ratcheting behavior as well as the effects of mean strain and strain amplitude on the mean stress relaxation was further examined through the verified constitutive model.

Uniaxial ratchetting of extruded AZ31 magnesium alloy: Effect of mean stress

The uniaxial ratchetting of extruded AZ31 magnesium alloy was investigated in the cyclic tests with different mean stresses and at room temperature. The prescribed mean stresses and corresponding stress amplitudes were chosen to make the different plastic deformation mechanisms such as dislocation slipping, twinning and detwinning occur individually or simultaneously during the cyclic deformation of the AZ31 magnesium alloy with a hexagonal close packed crystal structure, and then the effect of mean stress on the uniaxial ratchetting of the magnesium alloy was discussed. It is seen that ratchetting occurs in the AZ31 magnesium alloy during the stress-controlled cyclic loading, but different evolution features are observed in the uniaxial ratchetting tests with different mean stresses. Different ratchetting behaviors are determined by the different deformation mechanisms of extruded AZ31 magnesium alloy occurring in the tensile and compressive parts of cyclic loading. A sigmoidal stress–strain hysteresis loop of the magnesium alloy presented in the cyclic tension–compression tests with some suitable mean stresses and stress amplitudes is caused by the twinning/detwinning deformation mechanism, which should be reasonably considered in constructing a cyclic constitutive model to describe the uniaxial ratchetting of magnesium alloys.

On Constitutive Models for Ratcheting of a High Strength Rail Steel

The ratcheting behaviour of a hypereutectoid high strength rail steel with carbon content of 0.85% was experimentally studied under both uniaxial and bi-axial cyclic loadings recently by the authors. To numerically simulate the multiaxial ratcheting behaviour of the rail steel, the Abaqus built-in Lemaitre-Chaboche model was applied first in current study. Following Abaqus documentation, the material data for the Lemaitre-Chaboche model were calibrated from the uniaxial loading test results. Comparing with experimental data, the Lemaitre-Chaboche model with the calibrated data provides overpredictions for the ratcheting responses of the rail steel under both uniaxial and bi-axial loadings. After that, a modified cyclic plasticity model with a coupling multiaxial parameter in the isotropic and kinematic hardening rules was applied for the material. The material data for this modified model were calibrated from both uniaxial and bi-axial loading tests. Comparison between the simulated results and the experimental data show that this modified cyclic plasticity model has the capacity to simulate both uniaxial and multiaxial ratcheting behaviour of the hypereutectoid rail steel with an acceptable accuracy.

Macroscopic and microscopic investigations on uniaxial ratchetting of two-phase Ti–6Al–4V alloy

The uniaxial ratchetting of Ti–6Al–4V alloy with two phases (i.e., primary hexagonal close packed (HCP) α and secondary body-centered cubic (BCC) β phases) was investigated by macroscopic and microscopic experiments at room temperature. Firstly, the effects of cyclic softening/hardening feature, applied mean stress and stress amplitude on the uniaxial ratchetting of the alloy were discussed. The macroscopic investigation of Ti–6Al–4V alloy presents obvious strain-amplitude-dependent cyclic softening, as well as a three-staged evolution curve with regard to the ratchetting strain rate. The ratchetting depends greatly on the applied mean stress and stress amplitude while the ratchetting strain increases with the increasing applied mean stress and stress amplitude. Then, the evolution of dislocation patterns and deformation twinning during the uniaxial ratchetting of two-phase Ti–6Al–4V alloy were observed using transmission electron microscopy (TEM). The microscopic observation shows that deformation twinning occurs in the primary α phase and its amount increases gradually during the uniaxial ratchetting. Simultaneously, the planar dislocation evolves from discrete lines to some dislocation nets and parallel lines with the increasing number of cycles. The deformation twinning in the primary α phase is one of main contributions to the uniaxial ratchetting of Ti–6Al–4V alloy, and should be considered in the construction of corresponding constitutive model.

A finite viscoelastic–plastic model for describing the uniaxial ratchetting of soft biological tissues

In this paper, a phenomenological constitutive model is constructed to describe the uniaxial ratchetting (i.e., the cyclic accumulation of inelastic deformation) of soft biological tissues in the framework of finite viscoelastic-plasticity. The model is derived from a polyconvex elastic free energy function and addresses the anisotropy of cyclic deformation of the tissues by means of structural tensors. Ratchetting is considered by the evolution of internal variables, and its time-dependence is described by introducing a pseudo-potential function. Accordingly, all the evolution equations are formulated from the dissipation inequality. In numerical examples, the uniaxial monotonic stress–strain responses and ratchetting of some soft biological tissues, such as porcine skin, coronary artery layers and human knee ligaments and tendons, are predicted by the proposed model in the range of finite deformation. It is seen that the predicted monotonic stress–strain responses and uniaxial ratchetting obtained at various loading rates and in various loading directions are in good agreement with the corresponding experimental results.

Crystal plasticity based constitutive model for uniaxial ratchetting of polycrystalline magnesium alloy

In the framework of crystal plasticity, a constitutive model is constructed to describe the uniaxial ratchetting of polycrystalline magnesium alloy at room temperature. At the scale of single crystal, three kinds of slip systems, i.e., basal〈a〉, prismatic〈a〉and pyramidal〈c+a〉slip systems and one kind of twinning system, i.e., tension twinning system, are introduced into the model. New orientations of slip systems in the twinned region of single crystal are obtained by rotating the original ones, and then a rotation tensor is used in the proposed model. Evolution equations of dislocation slipping and twinning deformation are obtained in the form of power-law. Also, the residual twinning and its accumulation during the cyclic loading are considered in the proposed model. Finally, an explicit scale-transition rule is adopted to extend the proposed single crystal constitutive model to the polycrystalline version. The capability of the proposed model to describe the uniaxial ratchetting of the polycrystalline magnesium alloy is verified by comparing the predictions with corresponding experimental results. More predictions of the ratchetting of magnesium single crystal and polycrystalline alloys are also discussed by the proposed model.

Uniaxial ratcheting behavior of sintered nanosilver joint for electronic packaging

Uniaxial ratcheting behavior and the fatigue life of sintered nanosilver joint were investigated at room temperature. All tests were carried out under stress-controlled mode. Force–displacement data were recorded during the entire fatigue lifespan by a non-contact displacement detecting system. Effects of stress amplitude, mean stress, stress rate, and stress ratio on the uniaxial ratcheting behavior of the sintered nanosilver joint were discussed. Stress-life (S–N) curves of the sintered joints were also obtained. The Smith–Watson–Topper (SWT) model, the Gerber model and the modified Goodman model, all of which took effect of mean stress into consideration, were compared for predicting the fatigue life of the sintered joint. Both the ratcheting strain and its rate increased with increasing stress amplitude or mean stress. The increase in stress amplitude and mean stress both reduced the fatigue life of the sintered joint, while the fatigue life prolonged with the increase in stress rate and stress ratio. The modified Goodman model predicted the fatigue life of the sintered joints well.

A plastic shakedown constitutive curve based on uniaxial ratcheting behavior of 304 stainless steel at room temperature

ABSTRACTOn the basis of the Bauschinger effect, a relationship between the elastic space defined in this study and the accumulated plastic strain is measured in uniaxial ratcheting tests of 304 stainless steel at room temperature. According to this relationship, a new model of uniaxial ratcheting is established and used to simulate uniaxial ratcheting behavior. The results of simulation agree well with the experimental results. These results demonstrate that the relationship between the elastic space and the accumulated plastic strain plays an important role in uniaxial ratcheting simulation. Furthermore, by taking into account the interaction of ratcheting and viscoplasticity, the relationships among elastic space, accumulated plastic strain and loading cases are discussed. It can be seen that, when the stress ratio R of valley stress versus peak stress is not less than zero, the accumulated plastic strain is a function of the peak stress. So, a constitutive curve is obtained to describe the stable states of plastic shakedown for 304 stainless steel material under the stress ratio R ≥ 0. It can be used to determine the accumulated plastic strain of engineering structures under cyclic loading only by an elastic–plastic analysis.

Uniaxial ratcheting behavior of hygrothermal aging anisotropic conductive adhesive film

A series of uniaxial ratcheting experiments on anisotropic conductive adhesive film (ACF) were conducted under stress-control at elevated temperature using a DMA-Q800. The ratcheting behavior of ACF specimens with different hygrothermal aging times was investigated at room temperature and 120 °C. The effects of loading rate, mean stress and stress amplitude on the ratcheting behavior of unaged and aged specimens were compared. The results show that the ratcheting strains of aged specimens are smaller than those of unaged specimens under the same experimental conditions. The cycling stability of aged specimens is increased by hygrothermal aging. At room temperature, with the increase of aging time, the ratcheting strains of aged specimens increase with hygrothermal aging time when it is less than or equal to 96 h but, however, decrease when it exceeds 96 h. At 120 °C the ratcheting strains of ACF only decrease with the increase of hygrothermal aging time. Additionally, the effects of loading rate, mean stress and stress amplitude on the ratcheting behavior of unaged and aged ACF are different and their effects are weakened by hygrothermal aging.

Constitutive modeling for the anisotropic uniaxial ratcheting behavior of Zircaloy-4 alloy at room temperature

A series of monotonic tensile, compressive and uniaxial ratcheting tests are conducted at room temperature on Zircaloy-4 (Zr-4) tubes to investigate the mechanical behaviors under various loading conditions. The experimental results show that the ratcheting strain is sensitive to mean stress, stress amplitude and mean stress direction. It is found that the material features anisotropy both in monotonic tests and uniaxial ratcheting tests with different mean stress directions. The difference of mechanical properties under tensile and compressive loading, especially the yield stress, is believed to contribute to the anisotropic ratcheting behavior of the material. In order to describe the anisotropic nature of the uniaxial ratcheting behavior of Zr-4, an anisotropic Ohno–Wang (OW) constitutive model introducing an initial back stress is developed. The results predicted show reasonable agreement with the experimental data.

Development and Application of a High-Thrust Voice Coil Motor

A Voice Coil Motor (VCM) for precise positioning with high output force was designed. The stability and heat dissipation of VCM were analyzed. The performance of VCM was also compared with that of the same type VCM produced by SMAC. Uniaxial ratcheting behavior of solder wire (Sn63/Pb37) was studied by uniaxial cyclic stress controlled tension deformation tests,to verify the VCM systematically.

Stress-based fatigue life prediction models for AZ31B magnesium alloy under single-step and multi-step asymmetric stress-controlled cyclic loadings

The uniaxial ratcheting and low-cycle fatigue failure behaviors of the hot-rolled AZ31B magnesium alloy are studied by the asymmetric cyclic stress-controlled experiments at room temperature. The effects of loading histories with the variable mean stress, stress amplitude and stress rate on the ratcheting respond and fatigue life of the studied magnesium alloy are discussed. Considering the combined effects of ratcheting damage and fatigue damage on the material failure, the stress-based fatigue life prediction models are developed to evaluate the low-cycle fatigue life under the single-step and multi-step cyclic loadings. Results show that (1) the prior stress cycling with high mean stress or stress amplitude restrains the ratcheting strain in the subsequent cycling with low mean stress or stress amplitude. (2) Due to the rate-independent property of the studied material at room temperature, the effects of the loading history with variable stress rate on the ratcheting behavior are not obvious. (3) The comparisons between the measured and predicted results confirm that the developed model can give an accurate estimate of the low-cycle fatigue life for the hot-rolled AZ31B magnesium alloy under the single-step and multi-step asymmetric stress-controlled cyclic loadings.

Effects of pre-strain on uniaxial ratcheting and fatigue failure of Z2CN18.10 austenitic stainless steel

Effects of both tensile and compressive pre-strain on cyclic deformation of Z2CN18.10 austenitic stainless steel under stress cycling with mean stress are studied. As compared to as-received material, ratcheting strain of subsequent stress cycling decreases with increasing tensile pre-strain (TP) level. Lower level of compressive pre-strain (CP) is found to accelerate ratcheting strain accumulation while higher level of CP retards the accumulation. Tensile pre-straining is beneficial to ratcheting–fatigue life while compressive pre-straining is detrimental. A modified fatigue model to address the effect of pre-straining is proposed to predict the fatigue lives of the stress cycling tests with mean stress.

Uniaxial ratcheting and fatigue failure behaviors of hot-rolled AZ31B magnesium alloy under asymmetrical cyclic stress-controlled loadings

Uniaxial ratcheting and low-cycle fatigue failure behaviors of the hot-rolled AZ31B magnesium alloy are studied by uniaxial asymmetrical cyclic stress-controlled experiments at room temperature. The effects of mean stress, stress amplitude and stress rate on the uniaxial ratcheting response and ratcheting life of the studied magnesium alloy are analyzed. The microscopic observations near fracture surface are carried out. In addition, a fatigue parameter is introduced to describe the ratcheting damage and fatigue damage processes, and a new model is established to describe the relationship between the linear density of twins and the fatigue parameter. Results show that (1) the mean stress and stress amplitude has a great influence on the ratcheting strain and fatigue failure life. When the mean stress or stress amplitude is increased, the ratcheting strain and its rate rapidly increase. So, the fatigue failure life is reduced. (2) The increase of mean stress and stress amplitude can accelerate the generation of twins, which decreases the fatigue resistance and increases the ratcheting strain. However, the stress rate has little effect on the twinning. So, the effects of stress rate on ratcheting and low-cycle fatigue failure behaviors are not obvious under the tested conditions. This is because the studied magnesium alloy shows highly rate-independent property at room temperature within the tested strain rate range. (3) The established model can accurately describe the relationship between the linear density of twins and the fatigue parameter. Furthermore, the threshold fatigue parameter for twinning is found.