Biaxial Ratcheting Research Articles

In‐plane biaxial ratcheting effect and low‐cycle fatigue behavior of CP‐Ti based on DIC method

AbstractIn‐plane biaxial fatigue tests of commercial pure titanium (CP‐Ti) were performed to investigate the effects of load ratio and phase shift on fatigue and ratcheting behavior. The results show that with the decrease of load ratio or the increase of phase shift, biaxial ratcheting strain effect is more significant, leading to the deterioration of fatigue resistance. Analysis of the crack morphology and fracture characteristic reveals that the crack propagation path becomes complex and the fracture morphology changes due to the enhanced non‐proportional hardening effect. Finally, current multiaxial life prediction models are evaluated to compare the applicability in the biaxial fatigue life prediction.

Biaxial ratcheting analysis based on real behaviors of subsequent yield surface

To develop a plastic constitutive equation for general plastic deformation analysis, it is useful to confirm that the constitutive equation is viable for analyzing mechanical ratcheting in which a small strain accumulates along with cyclic loading. Many constitutive models and analyses on mechanical ratcheting have been proposed. However, most models do not consider distortion and rotation of the subsequent yield surface observed in the process of ratcheting deformations. In this study, behaviors of both the subsequent yield surface and the ratcheting deformations have been experimentally evaluated for the initially isotropic metals of SUS316FR stainless steel, 6-4 brass and S25C mild steel, which were subjected to biaxial mechanical ratcheting. Simulation analysis of biaxial ratcheting was conducted based on real behaviors of the subsequent yield surfaces such as swing rotation, translation, and distortion observed in ratcheting, and the two-surface hardening rule. The reliability of the proposed plastic constitutive model was verified by comparing the numerical results with the corresponding experimental results.

Uniaxial and biaxial ratcheting behavior of pressurized AISI 316L pipe under cyclic loading: Experiment and simulation

Ratcheting defined as the progressive accumulation of plastic strain occurring during cyclic loading in the presence of the mean stress is one of the most prevalent failure modes in engineering structures. Experimental studies were conducted to characterize the uniaxial and biaxial ratcheting responses of an AISI 316L pipe. Experimental results show that an obvious cyclic hardening occurs in the AISI 316L pipe under uniaxial strain loading. Uniaxial ratcheting rate obtained from the axial cyclic experiment reaches a quasi-steady rate after a certain number of loading cycles. Moreover, using a designed four-point bending experimental setup, different axial stress amplitudes in the presence of the constant hoop stress were considered to characterize the biaxial ratcheting response of the material. The ratcheting strain and ratcheting strain rate in the hoop direction increase with increasing axial stress amplitudes under the constant hoop stress. To simulate the uniaxial and biaxial ratcheting behavior of the AISI 316L pipe, the Chaboche nonlinear kinematic hardening model was used. Using the Particle Swarm Optimization (PSO) technique, parameters of the Chaboche model were identified efficiently from the monotonic response of a cold-worked sample. The elastic limit of the material was measured using a very careful quasi-static cyclic compression experiment. The procedure to calibrate the material parameters for the Chaboche model and finite element simulation results were validated well with experimental data for the AISI 316L pipe. It is shown that the Chaboche model with the suitably-calibrated parameters from the experimental study can be applied to rigorously predict the ratcheting behavior of the AISI 316L pipe under cyclic uniaxial and biaxial loading conditions.

Evaluation of Sensitivity and Calibration of the Chaboche Kinematic Hardening Model Parameters for Numerical Ratcheting Simulation

Ratcheting failure of materials and structures subjected to low cycle fatigue in the presence of significant mean stress is of great interest to researchers. In this experimental and numerical study, the response of 316L stainless steel samples was observed in symmetric strain control uniaxial test followed by post-stabilized monotonic test, uniaxial and biaxial ratcheting tests, in order to determine the Chaboche model parameters and to evaluate ratcheting prediction using finite element analysis. The critical elastic limit was initially obtained from incremental uniaxial cyclic tests. The Chaboche parameters were subsequently extracted from experimental hysteresis and post-stabilized monotonic stress plastic-strain curves using two optimization technics, namely, the Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). The two optimization methods were compared for efficiency, in terms of time and accuracy. The PSO method presented higher efficient results and was subsequently used to derive the parameters from hysteresis and post-stabilized monotonic curves. Different values (by definition) of elastic limit were also used. The Finite Element commercial software ANSYS was utilized with the Chaboche model to predict the uniaxial and biaxial ratcheting behavior of 316L stainless steel pipe. The comparison between experimental and the numerical simulation demonstrates that adopting post-stabilized monotonic curve rather than hysteresis curve and with accurate elastic limit obtained from incremental loading test improves ratcheting prediction significantly.

Uniaxial and biaxial ratcheting behavior of ultra-high molecular weight polyethylene

Experimental studies were conducted to investigate the uniaxial and biaxial ratcheting behaviors of Ultra-high molecular weight polyethylene (UHMWPE). The effects of stress amplitude, stress rate and hydroxyapatite content on uniaxial ratcheting behavior were studied firstly. It is found that the ratcheting strain and its rate increase as stress amplitude increases. However, the ratcheting strain and its rate decrease with rising of stress rate. Meanwhile, it is found that the ratcheting strain decreases with increase of hydroxyapatite content. The ratcheting strain rates with different hydroxyapatite contents are not obviously different. The modified ratcheting strain accumulative model was constructed to predict the uniaxial ratcheting behavior of UHMWPE with different stress amplitudes, stress rates and hydroxyapatite contents. It is seen that the predictions agree with the experimental results very well. The effects of different loading paths on biaxial ratcheting behavior of UHMWPE were studied. Both ratcheting strain and ratcheting strain rate are strongly influenced by the loading path. It is found that the uniaxial loading path gives the highest ratcheting strain and its rate while the proportional loading path gives the lowest ratcheting strain and its rate.

Particle swarm optimization procedure in determining parameters in Chaboche kinematic hardening model to assess ratcheting under uniaxial and biaxial loading cycles

AbstractAs parameters in Chaboche model are difficult to be determined from experimental data, a single objective particle swarm optimization procedure was employed to obtain them. Hysteresis loop and uniaxial and biaxial ratcheting simulations were conducted to validate the determined models. Chaboche models determined by particle swarm optimization give more accurate simulation of ratcheting compared with the model determined by trial and error method. Chaboche models containing different backstress components were studied. Models determined considering uniaxial ratcheting can only predict uniaxial ratcheting precisely, while giving very bad simulation of biaxial ratcheting. The linear hardening rule in the N3L1 model clearly decreases the rate of the accumulation of ratcheting strain, and the N3L1 model gives the best simulations. For biaxial ratcheting, the fourth backstress component can decrease the rate of the accumulation apparently, while it has a little influence on prediction of uniaxial ratcheting.

Fatigue Life Evaluation for Cu-Solder Joint Showing Biaxial Ratchetting Deformation under Simulated HALT Loading Condition

Fatigue Life Evaluation for Cu-Solder Joint Showing Biaxial Ratchetting Deformation under Simulated HALT Loading Condition

212 Biaxial Ratchetting Deformation of Cu-Solder Joint Specimen Considering Thermal Cyclic and Vibration Loading Condition

212 Biaxial Ratchetting Deformation of Cu-Solder Joint Specimen Considering Thermal Cyclic and Vibration Loading Condition

Biaxial Ratchetting Deformation of Solders Considering Halt Conditions

Recently, Halt (Highly accelerated limit test) is widely employed for evaluation of reliability of electronic products. Halt condition is quite severe. The tested products are subjected to mechanical impacts, thermal shock, and vibration at same time. However, there has not been a reasonable and accurate evaluation method for Halt yet. To construct an accurate evaluation method of Halt, basic deformation mechanism of parts of the electronic products should be clarified from both experimental and theoretical points of view. In this paper, focusing on solder joints of circuit boards of electronic products, ratchetting deformation, especially, biaxial ratchetting deformation of solder joints is revealed from both experimentally and theoretically. The authors have already conducted biaxial ratchetting test combining axial and torsional cyclic loading using a tubular specimen of Type 304 stainless steel. However, as for solders, it is difficult to make tubular specimen. Since size of the solder joints is micron, a small size joint specimen of copper tube and solder is employed in this paper. First, to confirm the quality of the joint specimen such as boundary between copper and solder, both the tensile and cyclic loading tests are conducted at several temperatures using Sn-3Ag-0.5Cu. The basic characteristic of tensile and fatigue failure is obtained from these tests. After the confirmation of the accuracy of the joint specimen, biaxial ratchetting tests are conducted superposing the tensile load on cyclic torsion. The biaxial ratchetting tests are conducted using a biaxial loading testing machine developed for the joint specimens of solder and copper.

Influence of mean stress and stress amplitude on uniaxial and biaxial ratcheting of ST52 steel and its prediction by the AbdelKarim–Ohno model

The paper presents a new type of experiment focused on investigation of the influence of mean stress and stress amplitude on steady state ratcheting realized in ST52 steel at the Technical University of Ostrava. Therefore, a new cyclic plasticity model based on the AbdelKarim–Ohno kinematic hardening rule, Jiang–Sehitoglu memory surface, and modified Calloch isotropic hardening rule is described. The model allows correct description of the stress–strain behavior of ST52 steel, including ratcheting, non-Masing behavior, and cyclic hardening under proportional as well as non-proportional loading. The model was implemented in the commercial FE code ANSYS using a Fortran subroutine. The results of all simulations focusing on the uniaxial and biaxial ratcheting prediction correspond with experiments very well. The AbdelKarim–Ohno nonlinear kinematic hardening rule in its original form gives an accurate prediction of ratcheting even for the non-proportional loading, when the additional hardening is correctly described by the isotropic hardening rule.

In-plane biaxial ratcheting behavior of PVDF UF membrane

A series of in-plane biaxial cyclic tests were conducted to investigate the biaxial ratcheting behavior of polyvinylidene fluoride (PVDF) ultrafiltration (UF) membranes via cruciform shaped specimens. A tailored biaxial cyclic testing system and an integrated non-contact displacement detecting system were used. The effects of stress amplitude, mean stress, stress rate and constant stress in the Y-direction on ratcheting behavior of PVDF UF membranes in the X-direction were studied. It was found that the ratcheting strain increases more rapidly as stress amplitude and mean stress become larger. However, the ratcheting strain and its rate decreased with increasing the stress rate or the constant stress in the Y-direction. Furthermore, the biaxial ratcheting tests were carried out on PVDF UF membrane with water immersion. It was found that the water immersion environment significantly accelerated the accumulation of ratcheting strain and its rate.

Modelling of biaxial ratcheting behaviour of ultrahigh-molecular-weight polyethylene with viscoplasticity theory based on overstress for polymers

Biaxial ratcheting behaviour of ultrahigh-molecular-weight polyethylene (UHMWPE) has been modelled using the viscoplasticity theory based on overstress for polymers (VBOP) with the modified Chaboche kinematic hardening rule. Investigated loading condition is: axial strain-controlled cyclic loading of thin-walled tubular specimen in the presence of constant pressure. To improve the circumferential strain ratcheting response of UHMWPE, changes designed to account for kinematic hardening and tangent modulus effects are proposed. Numerical results are compared with previously obtained experimental data. It is shown that modified tangent modulus improves the model responses. The biaxial ratcheting behaviour of UHMWPE is modelled quantitatively with VBOP. © 2015 Society of Chemical Industry

Uniaxial and Biaxial Ratcheting of ST52 Steel under Variable Amplitude Loading – Experiments and Modeling

The paper shows results of experiments focused on the influence of loading frequency on ratcheting as well as interesting results obtained from uniaxial tests and biaxial tests with rectangular and circular loading paths under variable amplitude loading realized on the ST 52 steel at the VŠB-Technical University of Ostrava. The model based on the AbdelKarim-Ohno kinematic hardening rule and Calloch isotropic hardening rule was used for stress-strain behavior description in finite element analysis using commercial software Ansys. The material model was implemented into the FE code using a fortran subroutine. Results of simulations containing ratcheting and cyclic hardening effects correspond with experiments very well.

Biaxial Ratcheting of Ultra High Molecular Weight Polyethylene: Experiments and Constitutive Modeling

Abstract Responses of ultra-high molecular weight polyethylene (UHMWPE) under biaxial cyclic loading were investigated through systematically conducting experiments. Biaxial experiments on UHMWPE tubular specimens were conducted first by prescribing a steady internal pressure followed by a symmetric axial-strain controlled cycle. The steady internal pressure induced a steady nominal circumferential stress, which under the application of the axial strain-controlled cycle, induced circumferential strain ratcheting in the UHMWPE tubular specimens. Experimentally observed ratcheting responses of UHMWPE under biaxial cyclic loading was simulated using one of the unified state variable theories, the viscoplasticity theory based on overstress for polymers (VBOP). To improve the circumferential strain ratcheting simulation of the VBOP model, the Chaboche kinematic hardening rule was implemented in the model. The simulation of the VBOP model with the classical kinematic hardening model was also carried out to demonstrate the current state of the modeling for UHMWPE. Improvement of the circumferential strain ratcheting simulation by the modified VBOP model is demonstrated; however, simulations also indicate that further model modification will be needed.

Material parameter optimisation of Ohno-Wang kinematic hardening model using multi objective genetic algorithm

Ohno-Wang hardening model is an advanced constitutive model to evaluate the cyclic plasticity behaviour of material. This model has capability to simulate uniaxial and biaxial ratcheting response of the material. But, it is required to determine large number of material parameters from several experimental responses in order to simulate this phenomenon. Material parameters for constitutive models are generally determined manually through trial and error approach which is tedious and less accurate. Due to arbitrariness and complexity of cyclic loading, advanced constitutive material models become non-linear and multimodal in functional and parameter space. To overcome this problem, an automated parameter optimisation approach using genetic algorithm has been proposed in the present work to identify Ohno-Wang material parameters of 304LN, stainless steel for uniaxial simulation. Optimisation by this approach has improved the model prediction in uniaxial low cycle and ratcheting fatigue simulations after comparison with the experimental response.

Modeling of unixial and biaxial ratcheting of austenitic steel using Chaboche model

This paper is devoted to the study of the role of identification data base on the prediction of the cyclic behavior of the 304 L stainless steel on ambient temperature. The identification is done using the Chaboche constitutive model. The investigations have been performed with reference to both unixial and biaxial experimental data, strain controlled tests, ratchet tests, ratchet tests after a strain controlled strain tests. Results were reported in graphs representing the effect of the optimized parameters on the prediction of the behavior of the material. The parameters of the Chaboche model have been calculated from the curve of a unixial strain controlled test. Then they were optimized using different data base on ZéBuLoN. The simulation obtained by optimized parameters gives a good representation of stabilised loop in the way it is done with the simulated test. Ratchet was also well predicted in the case of optimization done with all tests considered in the simulation. In this paper it has been demonstrated that the optimization using different data bases have a big impact on the cyclic results and ratchet results.

Multiaxial ratcheting with advanced kinematic and directional distortional hardening rules

Ratcheting is defined as the accumulation of plastic strains during cyclic plastic loading. Modeling this behavior is extremely difficult because any small error in plastic strain during a single cycle will add to become a large error after many cycles. As is typical with metals, most constitutive models use the associative flow rule which states that the plastic strain increment is in the direction normal to the yield surface. When the associative flow rule is used, it is important to have the shape of the yield surface modeled accurately because small deviations in shape may result in large deviations in the normal to the yield surface and thus the plastic strain increment in multi-axial loading. During cyclic plastic loading these deviations will accumulate and may result in large errors to predicted strains.This paper compares the bi-axial ratcheting simulations of two classes of plasticity models. The first class of models consists of the classical von Mises model with various kinematic hardening (KH) rules. The second class of models introduce directional distortional hardening (DDH) in addition to these various kinematic hardening rules. Directional distortion describes the formation of a region of high curvature on the yield surface approximately in the direction of loading and a region of flattened curvature approximately in the opposite direction. Results indicate that the addition of directional distortional hardening improves ratcheting predictions, particularly under biaxial stress controlled loading, over kinematic hardening alone.

Ratcheting and wrinkling of tubes due to axial cycling under internal pressure: Part II analysis

Part I presented a set of experiments in which pressurized tubes were cycled axially under stress control about a compressive mean stress. This loading history causes biaxial ratcheting involving compressive axial strain and expansion of the diameter of the tube. The compressive strain in turn induces the initiation and growth of axisymmetric wrinkles. Persistent cycling resulted in localization of the wrinkles and collapse. In Part II the problem is first modeled as a shell with initial axisymmetric imperfections while the biaxial ratcheting of the material is modeled using the Dafalias–Popov two-surface nonlinear kinematic hardening model. It is demonstrated that when suitably calibrated this modeling framework reproduces the prevalent ratcheting deformations and the evolution of wrinkling including the conditions at collapse accurately for all experiments. The calibrated model is then used to evaluate the ratcheting behavior of pipes under thermal-pressure cyclic loading histories experienced by axially restrained pipelines.

Ratcheting and wrinkling of tubes due to axial cycling under internal pressure: Part I experiments

Under compression, pressurized tubes thick enough to deform plastically buckle into an axisymmetric wrinkling mode. The wrinkle amplitude is initially small but with persistent compression grows inducing a gradual reduction in axial rigidity and eventually causing a limit load instability, which is followed by collapse. The onset of buckling and collapse can be separated by a strain level of a few percent. This work investigates whether a tube that develops small-amplitude wrinkles can be subsequently collapsed by persistent axial cycling. Part I presents the results from a set of experiments on super-duplex tubes with D/ t of 28.5 loaded as follows. A tube is pressurized and then compressed into the plastic range to a level that initiates wrinkling. It is then cycled under stress control about a compressive mean stress while the pressure is kept constant. The combined loads cause simultaneous ratcheting in the hoop and axial directions as well as a gradual growth of the wrinkles. At some stage the amplitude of the wrinkles starts to grow exponentially with the number of cycles N leading to localization and collapse. The rate of ratcheting and the number of cycles to collapse depend on the initial compressive pre-strain, the internal pressure, and the stress cycle parameters all of which were varied sufficiently to generate an adequate data base. Interestingly, in all cases collapse was found to occur when the accumulated average strain reached the value at which the tube localizes under monotonic compression. A shell model coupled to a specially calibrated plasticity model that can reproduce the biaxial ratcheting exhibited in the problem are presented in Part II. The model is first evaluated by comparison to the experiments and then used to study parametrically cyclic loading histories seen in buried pipelines.

Effect of elastic modulus variation during plastic deformation on uniaxial and multiaxial ratchetting simulations

In order to identify different variables that affect ratchetting simulations, variation of elastic modulus during loading and unloading is considered and discussed based on the experimental observations which pointed out by Morestin and Boivin, 1996, Ishikawa, 1997, Cleveland and Ghosh, 2002, Zhou et al. (2005) and recently by Khan et al., 2009a, Khan et al., 2009b, Khan et al., 2009c. Then the effect of such variation on simulations is scrutinized from the theoretical point of view by considering simulations of ratchetting experiments conducted on stainless steel 304L by Hassan et al. (2008) using the well-known Armstrong–Frederick model. It is shown that, using two different values for the elastic modulus during loading and unloading could have a significant effect on simulations of uniaxial ratchetting. On the other hand, such significant effect hardly occurs in the case of simulations of biaxial ratchetting experiments under consideration. The importance of such findings is that the excessive ratchetting over-prediction resulting from any specific kinematic hardening rule is expected to decrease significantly by taking into consideration this effect. In this case, modeling of kinematic hardening rules could necessitate more attention and reconsideration.