Predicted Hysteresis Loops Research Articles

Axial hysteretic behaviour of wire rope isolators: Experiments and modelling

An experimental campaign aiming to study the dynamic response of four different helical Wire Rope Isolators (WRIs) loaded along the axial direction is described in the paper. A total of seventy-one tests have been carried out by applying as input, to each of them, ten cycles of sinusoidal displacement. Specifically, the dynamic response of the WRIs has been analysed by varying input properties, such as amplitudes and frequencies, and simulated by means of a recently developed hysteretic model derived from a new class of uniaxial phenomenological models. For completeness, the influence of the axial preload as well as of the wire rope diameter on the dynamic behaviour of the tested WRIs is also discussed. In particular, a close agreement between predicted hysteresis loops, having asymmetric shape, and experimental ones has been achieved.

Effect of the elastic hysteresis term formulation and response to non-harmonic periodic excitations of a non-linear SDOF dynamical model with weak frequency-dependency in the time domain

We elaborate a SDOF time-domain model for elastic hysteretic damping, by modifying the viscous damping model to introduce an instantaneous correction factor that recursively depends on the state variables of the system, such that the response exhibits weak dependency on frequency, corresponding to a large array of engineering materials. The effect of different formulations for calculating the instantaneous correction factor on the predicted hysteresis loops and the potential manifestation of singularities is studied. Hysteresis loops anticipated by the model are plotted and forced vibration responses to harmonic and other periodic non-harmonic excitations are simulated and discussed, also in comparison to the conventional viscous and Reid’s damping models.

Time-dependent ratcheting assessment of steel samples undergoing multi-step loading cycles through use of hardening rules

The present study evaluates ratcheting of U71Mn rail and 316 L stainless steel samples subjected to various multi-step loading cycles by means of kinematic hardening rules of Ohno-Wang (O-W), Abdel Karim-Ohno (AK-O) and Ahmadzdeh-Varvani (A-V). Chaboche’s isotropic hardening and visco-plastic description was introduced into the kinematic hardening models to further address yield surface expansion/contraction and time-dependency of steel samples. Over Low-High-High loading sequence, ratcheting was increased continuously, while as loading steps changed to subsequent steps of High-Low-Low, ratcheting slightly dropped at the transition of steps. Ratcheting over High-Low steps was preserved since ratcheting over the prior step was largely promoted. Predicted ratcheting strains and hysteresis loops were compared with those of measured values under multi-step loading conditions. Both the O-W and AK-O models under-predicted ratcheting strains over loading cycles particularly over the last loading steps. The A-V model predicted ratcheting over Low-High and High-Low sequences and closely agreed with experimental data. Evolution in size and width of loops as stress levels altered with loading steps was evident from predicted hysteresis loops. While the O-W and AK-O models were yet to generate loops along axial direction comparable with measured data, the A-V model predicted hysteresis loops in close agreement with those of experimental values.

Low Cycle Fatigue Behaviour of DP Steels: Micromechanical Modelling vs. Validation

This study aims to simulate the stabilised stress-strain hysteresis loop of dual phase (DP) steel using micromechanical modelling. For this purpose, the investigation was conducted both experimentally and numerically. In the experimental part, the microstructure characterisation, monotonic tensile tests and low cycle fatigue tests were performed. In the numerical part, the representative volume element (RVE) was employed to study the effect of the DP steel microstructure of the low cycle fatigue behavior of DP steel. A dislocation-density based model was utilised to identify the tensile behavior of ferrite and martensite. Then, by establishing a correlation between the monotonic and cyclic behavior of ferrite and martensite phases, the cyclic deformation properties of single phases were estimated. Accordingly, Chaboche kinematic hardening parameters were identified from the predicted cyclic curve of individual phases in DP steel. Finally, the predicted hysteresis loop from low cycle fatigue modelling was in very good agreement with the experimental one. The stabilised hysteresis loop of DP steel can be successfully predicted using the developed approach.

Fatigue life estimation of notched specimens of modified 9Cr-1Mo steel under uniaxial cyclic loading

Accuracy in the estimation of low cycle fatigue life of modified 9Cr-1Mo steel notched specimen by different analytical methods such as linear rule, Neuber’s rule, strain energy density method and numerical method such as finite element analysis have been studied in this investigation. The fatigue tests on notched specimens having notch radius of 1.25 mm, 2.5 mm and 5.0 mm were carried out at 823 K with net stress amplitudes of 250 MPa, 300 MPa and 350 MPa. The fatigue tests on smooth specimens were carried out with strain amplitudes ranging from ±0.3% to ±0.8% with a strain rate of 3 × 10−3 s−1 at 823 K to evaluate the fatigue life of notched specimen through strain-life approach. In order to predict the cyclic stress response of the material, Chaboche non-linear hardening model was employed considering two back stress components. Predicted hysteresis loops for smooth specimen were well in agreement with experimental results. Estimated fatigue lives of notched specimens by analytical methods and finite element analysis were within a factor ±16 and ±2.5 of the experimental lives respectively.

Fatigue Hysteresis Behavior of 2.5D Woven C/SiC Composites: Theory and Experiments

This paper presents an intriguing fatigue hysteresis behavior of 2.5 dimensional woven C/SiC composites via the integration tool of advanced experimental techniques with a multiscale theoretical model. Tension-tension fatigue experiment has been carried out to predict the fatigue hysteresis properties of 2.5D woven C/SiC composite at room temperature, accompanied with the fracture of specimens to investigate the mechanism of fatigue damage. Meanwhile, a multiscale fatigue model of 2.5D woven C/SiC composites, which encompasses a micro-scale model of fiber/matrix/porosity in fiber tows and a macro-scale model of unit-cell, has been proposed to provide a reliable validation of the experimental results based on fiber damages resulting from relative slip motion with respect to matrix at interfaces and the architecture of 2.5D woven C/SiC composites. The predicted hysteresis loop from theoretical model at room temperature holds great agreement with that from tension-tension fatigue experiments. Also, effects of fatigue load, braided structural parameters and material properties at micro scale on fatigue hysteresis behavior have been investigated.

Low Cycle Fatigue Properties and Cyclic Elasto-plastic Response of Modified 9Cr-1Mo Steel

Low cycle fatigue (LCF) behaviour of modified 9Cr-1Mo steel (P91 steel) has been investigated. The LCF tests were carried out at room temperature (300 K) and 823 K employing strain amplitudes ranging from ±0.3 to ±0.8 % and a strain rate of 3 × 10−3 s−1. The fatigue life was found to decrease with increase in strain amplitude and temperature. Material exhibited higher extent of cyclic softening at 823 K than that at room temperature. In order to estimate the response of the steel to the cyclic loading, Chaboche hardening model was employed considering elasto-plastic response of the material. The predicted hysteresis loops and cyclic stress response of the steel obtained from the FE analysis showed good agreement with experimentally obtained results.

Structural Characterization of a Novel Gas Foil Bearing With Nested Compression Springs: Analytical Modeling and Experimental Measurement

A novel nested compression spring gas foil bearing (NSFB), which used a series of nested compression springs as compliant supporting structure, was proposed and designed. NSFBs can be easily manufactured and are able to provide a support with high stiffness, high damping, and tunable structural characterization in turbomachinery. An analytical model, which considered the effects of interaction and friction between adjacent springs, was established to predict the structural characterization of the compliant structure. Static and dynamic tests were conducted to analyze the structural performance of NSFBs. The predicted hysteresis loop of the compliant structure corresponded well with the measured results from the pull–push tests. A static test result comparison between an NSFB and a bump-type gas foil bearing (BFB) showed that the NSFB had a larger loss factor, which implied its superior damping performance. The effects of spring number and axial preload between adjacent springs on bearing performance were investigated. The static and dynamic loss factors of bearings with nested structures (47 and 39 springs) were similar to each other, but greater than the loss factor of bearings without nested structures (31 springs). The estimated static and dynamic loss factors of bearings with axial preload were significantly improved compared with bearings without axial preload.

A modified Preisach model and its inversion for hysteresis compensation in piezoelectric actuators

Purpose– Piezoelectric actuators (PEAs) exhibit hysteresis nonlinearity in open-loop operation, which may lead to unwanted inaccuracy and limit system performance. Classical Preisach model is widely used for representing hysteresis but it requires a large number of first-order reversal curves to ensure the model accuracy. All the curves may not be obtained due to the limitations of experimental conditions, and the detachment between the major and minor loops is not taken into account. The purpose of this paper is to propose a modified Preisach model that requires relatively few measurements and that describes the detachment, and then to implement the inverse of the modified model for compensation in PEAs.Design/methodology/approach– The classical Preisach model is modified by adding a derivative term in parallel. The derivative gain is adjusted to an appropriate value so that the measured and predicted hysteresis loops are in good agreement. Subsequently, the new inverse model is similarly implemented by adding another derivative term in parallel with the inverse classical Preisach model, and is then inserted in open-loop operation to compensate the hysteresis. Tracking control experiments are conducted to validate the compensation.Findings– The hysteresis in PEAs can be accurately and conveniently described by using the modified Preisach model. The experimental results prove that the hysteresis effect can be nearly completely compensated.Originality/value– The proposed modified Preisach model is an effective and convenient mean to characterize accurately the hysteresis. The compensation method by inserting the inverse modified Preisach model in open-loop operation is feasible in practice.

Analysis of Hysteresis Loops of 316L(N) Stainless Steel under Low Cycle Fatigue Loading Conditions

Abstract Low cycle fatigue tests were carried out on 316 L(N) stainless steel at room temperature employing strain amplitudes ranging from ± 0.3 to ±1.0% and a strain rate of 3×10−3s−1. The material showed initial hardening for a few cycles followed by prolonged softening, saturation and final failure. The fatigue life was found to decrease with increase in strain amplitude. The analysis of stable hysteresis loops showed non-Masing behaviour for this material. The elasto-plastic response of the material under cyclic loading was characterized taking into account isotropic and kinematic hardening occurring during cycling. The material parameters were obtained from the experimental hysteresis loops and cyclic stress response of the material. Finite element analysis of elasto-plastic deformation was carried out to obtain the stabilized hysteresis loop and cyclic stress response of the material. The predicted hysteresis loops showed good agreement with experimental results. The low cycle fatigue life prediction was carried out based on plastic strain energy dissipation with cycling.

Low cycle fatigue life prediction of 316 L(N) stainless steel based on cyclic elasto-plastic response

Low cycle fatigue (LCF) tests were carried out on 316 L(N) stainless steel at room temperature employing strain amplitudes ranging from ±0.3% to ±1.0% and a strain rate of 3×10−3s−1. The material showed initial hardening for a few cycles followed by prolonged softening, saturation and final failure. The fatigue life was found to decrease with increase in strain amplitude. The analysis of the stable hysteresis loops under the tested conditions showed Masing behavior at lower strain amplitudes but non-Masing behavior at higher strain amplitudes. The elasto-plastic response of the material under cyclic loading was characterized taking into account isotropic and kinematic hardening occurring during cyclic loading. The material parameters required for characterization of cyclic behavior were obtained from the experimental hysteresis loops and cyclic stress response of the material. Finite element (FE) analysis of elasto-plastic deformation was carried out to obtain the hysteresis loop and cyclic stress response of the material. The predicted hysteresis loops from simulation showed good agreement with experimental results. The low cycle fatigue life prediction carried out based on plastic strain energy dissipation with cycling showed good correlation with experimental results.

Improved Correlation of Measured and Predicted Hysteresis Loops in a Multiaxial Fretting Fatigue Test Rig for Spline Couplings

This paper investigates the comparison of the measured and predicted force-displacement loops of a multiaxial representative fretting fatigue test rig for aeroengine spline couplings. A local finite element model of the fretting specimen and the fretting bridge is outlined. A more extensive model of the fretting test rig is then introduced. This global model also includes the loading structures. The model captures the compliance of the fretting test rig and improves the correlation of the observed hysteresis. This method allows the slip amplitude at the contacts to be quantified.

Magneto-Optic Properties in Hydrogenated Bimetallic Films

We study magneto-optic Kerr effect measurements of thin Fe, Fe–Pd and hydrogenated Fe–Pd films. Fe films exhibit theoretically predicted hysteresis loops of a ferromagnetic material. Bimetallic Fe–Pd films yield some interesting differences. Pd coated films with a thickness greater than 200 Å have no Kerr signals. Bimetallic 128 Å Fe–100 Å Pd layers present modified hysteresis loops presumably related to the linear dependence of the magneto-optical signals on the applied magnetic field in non magnetic material. The hydrogenated bimetallic films do not present major changes in the coercivity force observed in non-covered Fe films. A brief description of the technique including a discussion of factors that affect the sensitivity is presented. The studied films were magnetized under an in-plane applied field of up to 6.3 kOe.

Kinetics of CO2 excretion and intravascular pH disequilibria during carbonic anhydrase inhibition.

Inhibition of carbonic anhydrase (CA) activity (activity in red blood cells and activity available on capillary endothelium) results in decrements in CO2 excretion (VCO2) and plasma-erythrocyte CO2-HCO(-3)-H+ disequilibrium as blood travels around the circulation. To investigate the kinetics of changes in blood PCO2 and pH during progressive CA inhibition, we used our previously detailed mathematical model of capillary gas exchange to analyze experimental data of VCO2 and blood-gas/pH parameters obtained from anesthetized, paralyzed, and mechanically ventilated dogs after treatment with acetazolamide (Actz, 0-100 mg/kg i.v.). Arterial and mixed venous blood samples were collected via indwelling femoral and pulmonary arterial catheters, respectively. Cardiac output was measured by thermodilution. End-tidal PCO2, as a measure of alveolar PCO2, was obtained from continuous records of airway PCO2 above the carina. Experimental results were analyzed with the aid of a mathematical model of lung and tissue-gas exchange. Progressive CA inhibition was associated with stepwise increments in the equilibrated mixed venous-alveolar PCO2 gradient (9, 19, and 26 Torr at 5, 20, and 100 mg/kg Actz, respectively). The maximum decrements in VCO2 were 10, 24, and 26% with 5, 20, and 100 mg/kg Actz, respectively, without full recovery of VCO2 at 1 h postinfusion. Equilibrated arterial PCO2 overestimated alveolar PCO2, and tissue PCO2 was underestimated by the measured equilibrated mixed venous blood PCO2. Mathematical model computations predicted hysteresis loops of the instantaneous CO2-HCO(-3)-H+ relationship and in vivo blood PCO2-pH relationship due to the finite reaction times for CO2-HCO(-3)-H+ reactions. The shape of the hysteresis loops was affected by the extent of Actz inhibition of CA in red blood cells and plasma.

Experimental and theoretical studies of pressure drop hysteresis in trickle bed reactors

Extensive experimental work was carried out with three different gas-liquid systems (air-water, air-water with surfactant C 12H 25SO 3Na, air-aqueous CMC solution) and three kinds of packings (Φ2.7, 4.0 and 8.0 mm glass beads) to examine the influence of various parameters on pressure drop hysteresis. Gas and liquid flow rates, physical properties of liquid and operation modes, influence the behavior of hysteresis in the packed reactor, and liquid flow rate is the most important factor. Hysteresis is not so pronounced for columns packed with large particles and it disappears in the pulsing flow regime. The mechanism responsible for hysteretic behavior resides in the variable uniformity of gas-liquid flow in the packed section. A parallel zone model for pressure drop in the trickling flow regime was established on the basis of experimental facts and analysis of flow structure. Theoretically predicted hysteresis loop of pressure drop is in satisfactory agreement with experimental data.

Hysteresis caused by dimensional changes of porous solids during mercury porosimetry

Hysteresis in mercury porosimetry is often attributed to differences in contact angle and to inkbottle-shaped pores. In this paper, the contribution to hysteresis from dimensional changes in pores is considered. Empty pores are compressed by the applied external mercury pressure. The mercury penetration pressure is related to the dimensions of the compressed pores. After the pores are filled with mercury, the pressure becomes isotropic throughout the solid and the pores revert to their original dimensions. The pressure at which mercury retracts from the pores is related to the original pore dimensions. Using these concepts, the magnitude of the pore dimension changes was determined as a function of the applied mercury pressure, the modulus of elasticity of the solid and the solid porosity. The effect of dimensional changes on the width of the hysteresis loop (P pen - P ret ) was found to be minimal at pressures less than 70 MPa (10 4 psi). At 350 MPa (5 × 10 4 psi), the width of the hysteresis loop caused by dimensional changes can be significant even when the modulus of elasticity is large. The predicted hysteresis loop widths are compared with experimental data reported for model pore systems.

Modelling of Cyclic Plasticity With Unified Constitutive Equations: Improvements in Simulating Normal and Anomalous Bauschinger Effects

In simulating cyclic plasticity with several existing “unified” constitutive equations, the predicted hysteresis loops are “oversquare” with respect to experimentally-observed behavior. To eliminate this shortcoming in the constitutive equations developed by the present author, the work-hardening coefficient in the equation controlling the back stress (R) has been made a function of the back stress itself and the sign of the effective modulus-compensated stress σ/E – R. This improvement results in simulated hysteresis loops whose curvature closely resembles that in experimental tests. The improvement preserves all of the previously demonstrated capabilities such as cyclic hardening, cyclic hardening, cyclic softening, etc. The same equations can also simulate some unusual experimentally-observed Bauschinger effects involving local reversals in curvature. The curvature reversals in the simulations result from strain softening of the isotropic work-hardening variable in the equations. The physical significance of the behavior of the constitutive equations is discussed in terms of annihilation of previously-generated dislocation loops by reversing dislocations and experimentally-observed decreases in dislocation density and dissolution of cell walls upon stress reversal.

Some aspects of the rheology of milk gel

Observations of the flow of milk gel have been analysed and shown to be in general agreement with Graham's theory of deformation. Individual creep curves are satisfactorily described by the sum of powers of time t1/3, t1 and t3. The effect of stress on the creep of gels of various ages can be described by the sum of power terms with simple exponents. At small values of time, the strain recovered after removal of stress is proportional to the one-third power of time. There is general agreement between the predicted hysteresis loops and those observed in repeated loading tests.