Ratcheting Strain Research Articles

Experimental Studies on Deformation Behaviors of Rubbery Materials under Cyclic Loading

Macroscopic cyclic tension-unloading experiments are conducted to investigate the cyclic deformation behaviors of CB filled vulcanized hydrogenated nitrile butadiene rubber at room temperature. In the load-controlled cyclic tension-unloading tests, remarkable ratchetting occurs, and the effects of the level and rate of cyclic loading on the ratchetting are also investigated. The ratcheting strain increases with the increasing mean stress and stress amplitude, and more obvious ratchetting is observed in the cyclic test with load-hold or at lower loading rate. In the displacement-controlled cyclic tension-unloading tests, the responding peak stress of the H-NBR decreases continuously, but the residual strain increases with the increasing number of cycles. Furthermore, the zero-stress hold at the end of cyclic test demonstrates that the residual strain will be recovered partially, which implies that the residual strain of the H-NBR after cyclic test consists of the reversible and irreversible parts.

Cyclic tensile response of Mo-27 at% Re and Mo-0.3 at% Si solid solution alloys

Stress-controlled uniaxial cyclic tensile tests were conducted on binary Mo-27at% Re and Mo-0.3at% Si solid solutions as a function of temperature and compared against the previously reported cyclic response of pure Mo. The Mo-27at% Re alloy with a recrystallized grain size of ~30µm was evaluated in the temperature range 25°C–800°C at R=0.1 and stress range that was 80% of the ultimate tensile strength (UTS); a peak in fatigue life was observed between 300°C and 500°C. The decrease in fatigue life at the higher temperatures of 700°C and 800°C is attributed to dynamic strain aging. Transmission electron microscopy of the cyclically-deformed alloy revealed parallel bands of dislocation at room temperature that transitioned to a uniform cell structure at 500°C and back to orthogonal planar arrays at 800°C. The as-extruded Mo-0.3at% Si alloy was evaluated from 25°C to 1200°C and showed superior fatigue life and ratcheting strain resistance as compared to pure Mo and the Mo-27at% Re alloy (within the temperature range where data were available for comparison). The superior resistance is attributed to the high density of dislocations within the material in this mostly unrecrystallized state rather than Si in solid solution. Above 800°C, the ratcheting strain increases and fatigue life decreases rapidly with increasing temperature and is associated with dynamic recovery.

Time-Dependent Uniaxial Ratchetting of Ultrahigh Molecular Weight Polyethylene Polymer: Viscoelastic–Viscoplastic Constitutive Model

Uniaxial tension–unloading recovery, creep-recovery, and stress-controlled cyclic tests are first performed to investigate the recoverable viscoelasticity and irrecoverable viscoplasticity (including the uniaxial ratchetting) of ultrahigh molecular weight polyethylene (UHMWPE) polymer at room temperature. The results show that obvious time-dependent ratchetting occurs in the asymmetrical stress-controlled cyclic tension–compression and tension–tension tests of the UHMWPE, and total ratchetting strain consists of both recoverable viscoelastic and irrecoverable viscoplastic parts. Based on the experimental observation, a new viscoelastic–viscoplastic constitutive model is proposed to describe the time-dependent ratchetting of the UHMWPE. In the proposed model, the viscoplastic strain is set to be contributed simultaneously by the unified viscoplastic and creep ones. Meanwhile, a memory surface is introduced into the viscoelastic model to improve the description to the shapes of stress–strain hysteresis loops. Finally, the proposed model is verified by comparing the predictions with the corresponding experimental results of the UHMWPE. It is clearly demonstrated that the proposed model predicts the creep, viscoelastic recovery, and uniaxial time-dependent ratchetting of the UHMWPE well.

Evaluation of AF type cyclic plasticity models in ratcheting simulation of pressurized elbow pipes under reversed bending

The ratcheting behavior was studied experimentally for Z2CND18.12N elbow piping under cyclic bending and steady internal pressure. Dozens of cyclic plasticity models for structural ratcheting responses simulations were used in the paper. The four models, namely, Bilinear (BKH), Multilinear (MKIN/KINH), Chaboche (CH3), were already available in the ANSYS finite element package. Advanced cyclic plasticity models, such as, modified Chaboche (CH4), Ohno-Wang, modified Ohno-Wang, Abdel Karim-Ohno and modified Abdel Karim-Ohno, were implemented into ANSYS for simulating the experimental responses. Results from the experimental and simulation studies were presented in order to demonstrate the state of structural ratcheting response simulation by these models. None of the models evaluated perform satisfactorily in simulating circumferential strain ratcheting response. Further, improvement in cyclic plasticity modeling and incorporation of material and structural features, like time-dependent, temperature-dependent, non-proportional, dynamic strain aging, residual stresses and anisotropy of materials in the analysis would be essential for advancement of low-cycle fatigue simulations of structures.

A kinematic hardening rule to investigate the impact of loading path and direction on ratcheting response of steel alloys

The present study investigates ratcheting response of 304, 1045, 1026 and 1018 steel samples undergoing butterfly loading paths with different loading sequences/ directions through the newly developed kinematic hardening rule of Ahmadzadeh–Varvani (A-V). Components of backstress unity vector and the normal vector to the yield surface in the dynamic recovery of the model account for loading non-proportionality. The MaCaulay brackets 〈dɛ¯p·a¯/|a¯|〉 enable the hardening rule to track different directions under multiaxial stress cycles. Coefficient γ2 controls the rate of ratcheting and is regulated by term (2−n¯.a¯/|a¯|) to further lower the ratcheting strain curve. Term 〈n¯.a¯/|a¯|〉1/2 in the dynamic recovery prevents ratcheting plastic shakedown as stress cycles progress. Constant γ2 introduces a gradual decrease in the magnitude of (a¯−b¯) as the stress cycles advances. The movement of tensor b¯ with the initial value of zero follows backstress (a¯)exponentially over stress cycles. The difference in the magnitudes of b¯ and a¯ curves in butterfly down BFD (forward) and butterfly up BFU (reverse) histories verifies the loading path accountability through the dynamic recovery in the A-V model. This difference is initially large and as the number of cycles increases, term (a¯−b¯) decays and then stays constant and unchanged. History BFD with higher magnitude of term (a¯−b¯) possessed higher ratcheting as compared with BFU history. The predicted ratcheting curves through the A-V model consistently agreed with experimental data obtained under different loading paths and directions.

Uniaxial fatigue behavior of Cu-Nb micro-composite conductor, Part II: Modeling and simulation

A damage-coupled constitutive model has been built to predict the ratcheting effect and fatigue life of Cu-Nb micro-composite conductor under different loading conditions. The model is rate-independent and has no isotropic hardening effect according to the experiments reported in Part I. The Abdel-Karim-Ohno model (Abdel-Karim and Ohno, 2000) is improved for a better description of the ratcheting effect. Two damage factors Dt and Da are respectively defined to be related to the ratcheting strain and accumulative plastic strain. The damage factor Dt is coupled to the model to reflect the stress reduction. On the contrary, the damage factor Da is not coupled to the model but still calculated to decide the failure of the conductor. Accordingly, there are three failure criteria for different peak stress levels without considering the ratcheting strain above 5%. When the peak stress is above 758.5MPa, the failure is decided by the peak stress being equal to the tensile stress corresponding to the ratcheting strain. When the peak stress is between 650MPa and 758.5MPa, the failure is caused by the competition between the ratcheting strain and Da whose critical values are respectively 5% and 0.065. When the peak stress is below 650MPa, failure happens due to Da>0.065. As a result, the simulated ratcheting effect is more or less overestimated for some loading conditions, which leads to certain deviation between the predicted and experimental fatigue life. Nevertheless, the precision is still reasonable with the fatigue life ranging from 102 to 105 which is large enough for a further analysis of the fatigue behavior of pulsed magnets where the conductor is applied.

Non-proportionally multiaxial cyclic deformation of AZ31 magnesium alloy: Experimental observations

The non-proportionally multiaxial cyclic deformation of extruded AZ31 magnesium alloy with a hexagonal close-packed (HCP) crystal structure is investigated at room temperature by performing the strain- and stress-controlled axial-torsional cyclic tests with different loading paths and using thin-walled tubular specimens. The cyclic hardening/softening and multiaxial ratchetting of the AZ31 alloy are discussed. The AZ31 alloy shows significant cyclic hardening in both axial and torsional stress-strain responses. An additional softening occurs in the axial response, while an additional hardening presents in the torsional one under the multiaxial (i.e., combined axial-torsional) cyclic loading conditions. The multiaxial ratchetting mainly occurs in the direction of non-zero mean stress, and the ratchetting strain greatly depends on the shapes of multiaxial loading paths. The traditional equivalent stress-strain responses cannot reasonably characterize the multiaxial cyclic ones of the AZ31 alloy, since different mechanisms of plastic deformation are involved in the axial and torsional deformations. The axial and torsional stress-strain responses should be discussed separately.

A constitutive hardening model of coupled plastic deformation and martensitic transformation in steels

The article presents a constitutive model aimed at simulation of martensitic transformation induced by stress and plastic strain coupled with the hardening process in austenitic steels. The yield and transformation conditions are assumed to depend on back stresses evolving during plastic deformation and transformation processes. Their interaction affects essentially the hardening rate of a material. The thermodynamic background is reviewed and applied with both free energy and dissipation functions used in derivation of the rules of flow, hardening and transformation kinetics. The constitutive model parameters are specified and next the simulation of strain hardening for monotonic and cyclic loading is presented for the cases of uniaxial tension-compression and for combined tension-torsion deformation programs. The effect of strain ratcheting is analyzed for the cases of uniaxial and combined loading. It is shown that the transformation process is shown to essentially reduce the ratcheting strain.

Relaxation of contact pressure and self-loosening in dynamic bolted joints

Bolted joints are widely used in a variety of engineering applications where they are dynamically loaded with frequencies of vibration spread over a wide spectrum with the same general effects. When under dynamic loading, bolted joints can become loose due to a loss in clamping pressure in the joints. This vibrational loosening sometimes can cause serious problems, and in some cases can lead to fatal consequences if it remains undetected. Non-intrusive ultrasonic and image processing techniques were simultaneously used to investigate the relaxation of contact pressure and loosening of bolted joints subjected to cyclic shear loading. Three critical areas, the contact interface of the bolted component, the bolt length and the rotation of the bolt head, were monitored during loosening of the joints. The results show that loosening of bolted joints can be grouped into three stages: very rapid, rapid, and gradual loosening. The earliest stage of the loosening of bolted joints is characterised by cyclic strain ratcheting–loosening of the bolted joint during vibration without rotation of the bolt head. The higher the rate of relaxation at this early stage, the lower is the resistance of the bolted joint to vibration-induced loosening. Both the dynamic shear load and an additional constant shear load in another direction were observed to affect the rate of loosening, and at this early stage, a rise in the magnitude of the additional constant shear load increases the rate of loosening. Furthermore, the contact pressure distribution affects the rate of loosening at the bolted joint interface, as loosening increases away from area of high contact pressure.

A Screening Method for Prevention of Ratcheting Strain Derived From Movement of Temperature Distribution

In this paper, we simplify the existing method and propose a screening method to prevent thermal ratcheting strain in the design of practical components. The proposed method consists of two steps to prevent the continuous accumulation of ratcheting strain. The first step is to determine whether all points through the wall thickness are in the plastic state. This is based on an equivalent membrane stress, which comprises the primary stress and the secondary membrane stress. When the equivalent stress exceeds the yield strength in some regions of the cylinder, the axial lengths of these regions are measured for the second step. The second step is to determine whether the accumulation of the plastic strain saturates. For this purpose, we define the screening criteria for the length of the area with full section yield state. When this length is sufficiently small, residual stress is generated in the direction opposite to the plastic deformation direction. As a result of residual stress, further accumulation of the plastic deformation is suppressed, and finally shakedown occurs. To validate the proposed method, we performed a set of elastoplastic finite element method (FEM) analyses, with the assumption of elastic perfectly plastic material. Not only did we investigate about the effect of the axial length of the area with full section yield state but also we investigated about effects of spatial distribution of temperature, existence of primary stress, and radius thickness ratio.

Effect of local wall thinning on ratcheting behavior of pressurized 90<sup>°</sup> elbow pipe under reversed bending using finite element analysis

Ratcheting deformation of pressurized Z2CND18.12N stainless steel 90° elbow pipe with local wall thinning subjected to constant internal pressure and reversed bending was studied using finite element analysis. Chen-Jiao-Kim (CJK) kinematic hardening model, which was used to simulate ratcheting behavior of pressurized 90° elbow pipe with local wall thinning at extrados, flanks and intrados, was implemented into finite element software ANSYS. The local wall thinning was located at extrados, flanks and intrados of 90° elbow pipe, whose geometry was rectangular cross-section. The effect of depth, axial length and circumferential angle of local wall thinning at extrados, flanks and intrados on the ratcheting behaviors of 90° elbow pipe were studied in this paper. Threedimensional elastic-plastic analysis with Chen-Jiao-Kim (CJK) kinematic hardening model was carried out to evaluate structural ratcheting behaviors. The results indicated that ratcheting strain was generated mainly along the hoop direction, while axial ratcheting strain was relatively small.

Study on ratcheting effect of pressurized straight pipe with local wall thinning using finite element analysis

Ratcheting deformation is studied on straight pipe made of Z2CND18.12 N stainless steel with local wall thinning subjected to constant internal pressure and reversed bending using finite element analysis. The local wall thinning is located at the center of straight pipe, whose geometry is rectangular cross-section. The effect of depth, axial length and circumferential length on the ratcheting behavior of straight pipe is studied in this paper. Three-dimensional elastic-plastic analyses with ANSYS employed Chen–Jiao–Kim (CJK) kinematic hardening model is carried out to evaluate structural ratcheting behaviors. Results indicate that ratcheting strain is along the center of straight pipe extending to the two ends. The ratcheting strain occurs mainly at hoop direction. Axial ratcheting strain is relatively small. The effects of the depth, axial length and circumferential length of local wall thinning on the ratcheting response are discussed by CJK model.

Effect of micro-cavities on different plastic zones at the fatigue crack tip of a compact tension specimen

Knowledge of cyclic plastic deformation response at the fatigue crack tip is crucial to understand the nature of cyclic damage acting on the crack tip. Interaction between crack and defect is equally important to understand the cyclic damage progression at crack tip; however isotropic hardening model was adopted in all existing literatures. Isotropic hardening model is suitable to model only the monotonic plastic zone and unable to model the cyclic/reverse plastic zone. Kinematic hardening model is suitable to model the key cyclic plastic deformation responses like Bauschinger effect, ratcheting, and mean stress relaxation. A non-linear kinematic hardening (Chaboche) model is used in this present investigation to represent the material’s cyclic stress–strain response accurately.Effect of micro-cavity positions (angle and distance from crack tip) and sizes on plastic zones near a crack tip is investigated in this study by two dimensional plane strain finite element model of a compact tension specimen. It is observed that the size and shape of the monotonic and cyclic plastic zones are affected by position and size of the micro-cavity. During asymmetric loading condition, the ratcheting strain accumulation direction is also affected by the position of micro-cavity.

Cycle symmetrization, asymmetrical behaviour and ratchetting during low cycle fatigue of high temperature alloys

Strain-controlled (low-cycle fatigue type) experiments were performed on 12 different high temperature alloys (ferritic, austenitic, superalloys, single-crystal material, a directionally solidified alloy and two titanium alloys) in the range 550–950°C. Symmetrical cycling conditions were suddenly changed to offset strain cycling at the same strain range, but in the tension or compression direction. Up to 50 cycles were allowed to determine the subsequent approach to symmetrical stress limits for each material (elastoplastic shakedown). Comparison is made with limited reported tests and related load-control tests involving strain ratchetting . Shakedown behaviour is shown to depend both on the path of approach, defined by stress–strain properties, but overall trends of stress versus cycle plots are best made by assuming an effective strain range which is less than the imposed experimental strain range.

Ratcheting fatigue behaviour of Al-7075 T6 alloy: Influence of stress parameters

The use of aluminium and aluminium based alloys are increasing rapidly on account of its high formability, good thermal and electrical conductivity, high strength and lightness. Aluminium alloys are extensively used in aerospace, automobile, marine and space research industries and are also put into structural applications where chances of fatigue damage cannot be ruled out. In the current work, it is intended to study the ratcheting fatigue behavior of 7075-T6 aluminium alloy at room temperature. This Al alloy is potentially used in aviation, marine and automotive components as well as in bicycle parts, rock mounting equipment and parts of ammunition where there is every chance of failure of the parts due to deformation caused by ratcheting. Ratcheting is the process of accruement of plastic stain produced when a component is subjected to asymmetric cyclic loading under the influence of low cycle fatigue. To accomplish the requirements of the projected research, stress-controlled cyclic loading experiments were done using a ±250 kN servo-hydraulic universal testing machine (Instron: 8800R). The effect of stress parameters such as mean stress and stress amplitude were investigated on the ratcheting behavior of the selected aluminium alloy. It was observed that, ratcheting strain increased with increase in the value of stress amplitude at any constant mean stress while a saturation in strain accumulation attained in the investigated material after around 10-20 cycles, under all test conditions. The analyses of hysteresis loop generated during cyclic loading indicate that the material exhibits cyclic hardening in the initial fifty cycles which gets softened in further loading up to about 70-80 cycles and finally attains a steady state. The increase in the ratcheting strain value with stress parameters happens owing to increased deformation domain during cycling. The cyclic hardening accompanied by softening is correlated with characteristic precipitation features of the investigated Al 7075 alloy.

Temperature‐dependent uniaxial ratchetting of ultra‐high molecular weight polyethylene

AbstractUniaxial stress‐controlled cyclic tests were performed on the ultra‐high molecular weight polyethylene (UHMWPE) polymer at different temperatures. The effects of stress level, stress rate, peak/valley stress hold and loading history on the ratchetting of the UHMWPE were discussed at different temperatures, and the temperature‐dependence of ratchetting was addressed. It is concluded from the experimental observations that the ratchetting of the UHMWPE depends greatly on the test temperature, and the ratchetting strain increases with the increasing temperature from −20 to 37 °C, but decreases when the temperature is equal to or higher than 60 °C in some cases. The ratchetting is also time‐dependent and increases with the increase of peak stress hold time and the decrease of stress rate. The ratchetting presents apparent loading history dependence, and previous cyclic history with higher stress level remarkably restrains the occurrence of ratchetting in the subsequent cyclic loading cases with lower stress levels, but previous cyclic history with lower stress level hardly influences the ratchetting in the subsequent cyclic loading cases with higher stress levels.

In situ near‐tip normal strain evolution of a growing fatigue crack

AbstractNormal strains near a growing fatigue crack have been studied in situ using the Digital Image Correlation technique in a compact tension specimen of stainless steel 316L under tension–tension cyclic loading. An error analysis of the measured displacements and strains has been carried out, and the results show that the precisions of displacements and strains in the direction perpendicular to the crack plane and ahead of the crack are better than those parallel to the crack plane and in the wake of the crack. The errors in the measured displacements are in the range of 0.06 to 0.1 µm and between 0.2% and 0.4% for the measured strains, the latter are well below the critical strain at the onset of crack growth about 8%. Strain ratchetting was found ahead of the growing fatigue crack tip, albeit very close to the crack tip.

Experimental observation on multiaxial ratchetting of polycarbonate polymer at room temperature

Multiaxial stress-controlled and mixed stress-strain-controlled cyclic tests were carried out to investigate the multiaxial ratchetting of polycarbonate (PC) polymer at room temperature. The effects of applied mean stress, stress amplitude, loading rate, loading path and loading history on the ratchetting are discussed. The results show that the multiaxial ratchetting mainly occurs in the direction of non-zero mean stress. In the multiaxial stress-controlled cases, the ratchetting strain increases with increasing mean stress and stress amplitude and decreasing stress rate. Different values of ratchetting strain were obtained in the multiaxial cyclic tests with seven different loading paths, and prior cyclic loading with higher stress level resulted in decreased ratchetting in the subsequent cyclic loading with lower stress level. In the multiaxial mixed stress-strain-controlled tests, the ratchetting increased with increasing axial (or equivalent shear) stress and torsional-angle (or axial-displacement) amplitude and decreasing applied deformation rate.

Fatigue life assessment of adhesive joints based on ratchetting strain evolution

ABSTRACTIn this article, experimental tests have been performed in order to examine the behavior of double-lap adhesive joints under constant amplitude fatigue loading and then a fatigue damage model was proposed based on ratchetting strain as a damage parameter. This parameter was employed in this study since it is feasible to be measured during the operational life of structures without interruptions and in a nondestructive manner. The predictions produced by the proposed model revealed acceptable agreements with the experimental data. Afterward, an alternative form of the F–N curve was obtained, which can be used to establish the design allowables.

Ratcheting Strain Accumulation Due to Asymmetric Cyclic Loading of Zircaloy-2 at Room Temperature

Asymmetric stress cycling leads to accumulation of plastic strain which is called as ratcheting strain. The problem is generally associated with nuclear fuel cladding materials used in nuclear power plants and in pressurized pipe lines. In the present investigation asymmetric stress controlled fatigue tests were conducted with three different parameters namely, mean stress, stress amplitude and stress rate (keeping two parameter constant and varying third parameter) to see the plastic strain accumulation and its effect on fatigue life of Zircaloy-2 at room temperature. The tests were conducted with mean stress varying from 80 to 150 MPa, stress amplitude varying from 270 to 340 MPa and stress rate varying from 30 to 750 MPa/s respectively. The experimental outcomes show that with increase in mean stress and stress amplitude, the ratcheting strain accumulation increases with reduction in fatigue life. However, increase in stress rate leads to improvement in fatigue life of the material due to small ratcheting strain accumulation. Cyclic softening is observed during initial cycles for lower values of mean stress and stress amplitude and cyclic hardening is predominant for higher values of mean stress and stress amplitude. However, cyclic hardening is observed with increase in stress rate.