Biaxial Cyclic Loading Research Articles

Fatigue cracking simulation based on crack closure effects in Al-based sheet materials subjected to biaxial cyclic loads

Fatigue crack growth experiments have been carried out on cruciform specimens in the range of thickness 1.2–10 mm of Al-based alloys, loaded under constant (regular) and variable (irregular) amplitudes of uniaxial and biaxial loads, including sequences of various overloads. Different cases for crack closure effects are considered because of shear lips development, crack-growth direction re-orientation after multiparameters change of cyclic loads, by examining plastic blunting effect at a crack tip during an overload and interaction effects analyzing the crack retardation length and associated parameters together with their relationships. Crack closure effect because of rotation instability of material mesovolumes under biaxial compression–tension has suggested to analyse semi-elliptical cracks. Under biaxial cyclic loads in the range of load ratio-1.4 < λ < +1.5, and R-ratios from 0.05 to 0.8, for frequency variations ϖ, fatigue striation formation takes place beyond a crack-growth rate close to 4 × 10 −8 m/cycle. The striation spacing and the crack-growth rate increase as the ϕ-angle of the out-of-phase biaxial loads increases (in the range of ϕ from 0° to 180°). Cycle loading parameters must be taken into account in order to describe the crack growth period when using a unified method that involves an equivalent stress intensity factor K e = K I F ( λ , R , ϕ , ϖ ) . The values of F ( λ , R , ϕ , ϖ ) are determined. The calculated crack growth period (predicted using F ( λ , R , ϕ , ϖ ) ) in regular and irregular cases of cyclic loads, including material cracking after overloads, is correlated with the experimental data, and the error is of the order of 15%.

Influence Analysis of Multifactor on LCF Damage of Single Crystal Nickel-Based Superalloy under Multiaxial Non-Proportional Loading

A formula of equivalent strain for FCC single crystal superalloy was derived based on Hill’s yield criterion and was used for design of biaxial tension-torsion strain paths and loading levels of specimens. biaxial tension-torsion non-proportional cyclic loading process for single crystal nickel-based superalloy at the temperature of 680°C and 850°C was simulated by FEM analyzes; and influence degree of factors, such as strain range, strain path angle, tension-torsion loading phase angle, cycle characteristics and temperature etc., to low cycle fatigue damage of single crystal nickel-based superalloy were analyzed by using analysis of variance based on orthogonal experiments. The results show that if Hill’s equivalent stress range is used as a fatigue damage parameter, the factors produce effects on low cycle fatigue damage of single crystal nickel-based superalloy. The factors are listed in the order of significance as followed: temperature, strain range, tension-torsion loading phase angle, strain path angle and axial loading strain ratio.

Micromechanical behavior of granular materials with inherent anisotropy under cyclic loading using 2D DEM

This paper presents the micromechanical behavior of granular materials due to different initial inherent anisotropic conditions during cyclic loading using the discrete element method (DEM). Oval particles were used to model the samples. Three samples, with three different inherent anisotropic conditions based on the particle’s bedding direction, were prepared and subjected to biaxial cyclic loading. The differences in the inherent anisotropic conditions of the samples affect the stress–strain-dilative behavior of granular materials. The width of the stress–strain cyclic loops decreases as the preferred bedding angle changes from vertical to horizontal. Contact fabric evolution is found to be dependent on the inherent anisotropic fabric of the sample during loading and unloading. The fabric anisotropy is dominant for horizontal particle bedding at the end of loading and for vertical particle bedding at the end of unloading. A change in fabric anisotropy is observed only for the first few loading–unloading cycles for the given conditions depicted in the present study.

On the Effects Associated with Control Parameters Delay during Biaxial Cyclic Loading of Engineering Materials

The paper presents experimental results of investigations carried out on the P91 steel and 2024 aluminium alloy under complex stress states due to various combinations of an axial force and twisting moment. An influence of out-of-phase sinusoidal and trapezoidal strain signals on the mechanical behaviour of tested materials was considered. The experiments enabled identification of the second order effects connected with the non-proportional cyclic loadings such as the phase shift between stress and strain signals during the deformation along the circular strain path, and a significant stress drop of the one of loading components applied in the case of deformation enforced by the trapezoidal signals. The experimental programme also contained the tests of monotonic tensile deformation realized simultaneously with delayed torsional cycles. They enabled to observe a drastic variations of the proportional limit and yield point of the materials in the tensile direction. This fact manifests an important material feature which can be applied to the optimal designing of some metal forming processes like an extrusion or forging for example.

Determinist-Probabilistic Concept in Modeling Fatigue Damage Through a Micromechanical Approach

Motivated by a micromechanical determinist-probabilistic model coupled with damage recently developed by the authors, a new generalization is proposed to describe the nonlinear elasto-inelastic cyclic strain-stress behavior of polycrystals notably under biaxial cyclic loading paths. In this context, this generalization considers a compressible and linear anisotropic granular elastic strain behavior coupled with damage. The model is expressed in the framework of the time dependent plasticity for a small strain assumption. It is assumed that a damage variable initiates at the mesoscopic (granular) level where the plastic strain localization phenomenon takes place. The associated thermodynamic force of the damage variable is determined using the concept of total granular energy (elastic and inelastic). The transition of the elastic strain from the single to the polycrystal is modified due to its explicit coupling with damage. Comparisons between predicted and experimental results are conducted describing the low-cycle fatigue behavior of the aluminum alloy 2024 under different complex cyclic loading paths. It is demonstrated that the model has a reasonable ability in describing the cyclic behavior of this alloy. Qualitatively, the model is tested under different cyclic loading paths with stress-controlled condition describing especially the ratcheting behavior of the alloy. In fact, the effects of the applied mean stress on the predicted overall elasto-inelastic behavior and on the fatigue life are carefully studied. It shows the dependence of the fatigue life on the mean stress value.

Fatigue and creep to leak tests of proton exchange membranes using pressure-loaded blisters

Abstract In this study, three commercially available proton exchange membranes (PEMs) are biaxially tested using pressure-loaded blisters to characterize their resistance to gas leakage under either static (creep) or cyclic fatigue loading. The pressurizing medium, air, is directly used for leak detection. These tests are believed to be more relevant to fuel cell applications than quasi-static uniaxial tensile-to-rupture tests because of the use of biaxial cyclic and sustained loading and the use of gas leakage as the failure criterion. They also have advantages over relative humidity cycling test, in which a bare PEM or catalyst coated membrane is clamped with gas diffusion media and flow field plates and subjected to cyclic changes in relative humidity, because of the flexibility in allowing controlled mechanical loading and accelerated testing. Nafion® NRE-211 membranes are tested at three different temperatures and the time–temperature superposition principle is used to construct stress-lifetime master curve. Tested at 90 °C, 2%RH extruded Ion Power® N111-IP membranes have a longer lifetime than Gore™-Select® 57 and Nafion® NRE-211 membranes.

Cyclic Softening Behaviour of a Duplex Stainless Steel

Abstract This second part aims to propose an extension of the bi-phased polycrystalline model shown in a previous contribution [1], in order to simulate the cyclic softening observed in an austenitic-ferritic stainless steel under uniaxial and non-proportional biaxial cyclic loading [2]. Assuming that the cyclic softening for uniaxial and biaxial non-proportional cyclic loading is due to a rearrangement of dislocations in hard (rich in dislocations) and soft (poor in dislocations) zones in ferritic grains [3], the ferritic single crystal law is modified. The new model parameters are identified from TEM observations [3] and by inverse procedure. Finally, the new model is validated for other cyclic loading paths. A good agreement is observed between simulation and experimental data.

A biaxial hysteretic model for a structural system incorporating strength deterioration and pinching phenomena

A biaxial hysteretic model is developed to take into account the commonly observed hysteretic characteristics of strength and stiffness degradation, pinching and biaxial interaction. The concept of zero force point is proposed to develop the biaxial hysteretic model. Two non-linear inelastic springs and one linear elastic spring are connected in parallel to define the cyclic behavior of the proposed biaxial hysteretic model. The proposed biaxial hysteretic model is rate-independent and capable of simulating not only global (such as story shear force versus story drift response of the whole structure) but also the local hysteretic behavior of structural member (such as moment versus curvature or plastic rotation response of a structural element). The biaxial cyclic loading test data of six reinforced concrete columns, which are designed for flexural failure and shear failure, are used to validate the proposed biaxial hysteretic model.

J0407-1-4 押出成型によるラミー麻/PP複合材料の創製と強度評価(バイオマス由来材料の成形加工と特性評価(1))

The purpose of this study is to develop a natural fiber reinforced polymer matrix composite with high strength and stiffness, in order to apply biomass resources for practical use. A MAPP-included polypropylene resin was used as a matrix of the composite, and extruded with 5 and 10 wt% ramie short fibers. In this extrusion the composites were fabricated as a thin sheet, and treated with cyclic loading application to increase the strength and stiffness of the reinforcement. The results show that the composites were improved in tensile strength and Young's modulus after the treatment. Especially, Young's modulus of the composites increases 52% higher at 90° direction after bi-axial cyclic loading treatment. Through this treatment the composites are also improved in strength at bi-axial directions.

Analysis on shear capacity of prestressed concrete spatial connections

Based on experimental results of prestressed concrete spatial connections, nonlinear finite element models were established to analyze the shear capacity of spatial connections and parametric studies were performed using ANSYS. It is found that the shear capacity of spatial connection is influenced by joint hoop, beam prestress, column compressive load, and direction of resultant shear force. The parametric studies also indicate that the shear capacity of spatial connection under biaxial cyclic loading is lower than that of corresponding connections under plane loading. A design formula for calculating the shear capacity of spatial connections is proposed based on the parametric studies and verified by the available test results.

Residual service life of thin-walled structural elements under biaxial cyclic loading

We generalize the energy approach to the evaluation of the residual service life of structural elements under biaxial loading proposed somewhat earlier. On this basis, we construct a mathematical model aimed at the evaluation of the period of subcritical growth of a fatigue crack in the plate subjected to biaxial cyclic loading. The model is used to analyze the influence of the parameters of biaxial cyclic loading on the period of subcritical growth of the fatigue crack.

Elastoplastic finite element analysis and fatigue life prediction for notched specimens under biaxial cyclic loading

An elastoplastic finite element analysis is adopted for thin tubular and notched specimens under biaxial proportional and nonproportional tension-torsion loading at high temperature. Elastoplastic material property is described by the Von Mises yield criterion, the multilinear kinematic hardening rule and uniaxial cyclic stress-strain data under high temperature. Tension-torsion loading with strain controlling is carried out by applying the axial and circular displacement on one end of the specimen in the cylindrical coordinate system. The method is proved suitable by comparison between FEA and experimental results. Then the elastoplastic finite element method is used to the notched specimens. The local cyclic stress-strain responses at notch root are obtained. Fatigue crack initiation life is predicted on the basis of the local stress-strain data with Kandil-Brown-Miller and Smith-Watson-Topper models.

Fatigue behavior of filament‐wound glass fiber reinforced epoxy composite tubes under tension/torsion biaxial loading

AbstractA study of filament‐wound glass fiber/epoxy composite tubes under biaxial fatigue loading is presented. The focus is placed on fatigue lives of tubular specimens under tension/torsion biaxial loading at low cycle up to 100,000 cycles. Filament‐wound glass‐fiber/epoxy tubular specimens with three different lay‐up configurations, namely [±35°]n, [±55°]n, and [±70°]n lay‐ups, are subjected to in‐phase proportional biaxial cyclic loading conditions. The effects of winding angle and biaxiality ratio on the multiaxial fatigue performance of composites are discussed. Specimens are also tested under two cyclic stress ratio: R = 0 and R = −1. The experimental results reveal that both tensile and compressive loading have an influence on the multiaxial fatigue strength, especially for [±35°]n specimens. A damage model proposed in the literature is applied to predict multiaxial fatigue life of filament‐wound composites and the predictions are compared with the experimental results. It is shown that the model is unsuitable for describing the multiaxial fatigue life under different cyclic stress ratios. POLYM. COMPOS. 28:116–123, 2007. © 2007 Society of Plastics Engineers

Determination of an HCF criterion by thermal measurements under biaxial cyclic loading

A probabilistic two-scale model was recently developed to describe high-cycle fatigue (HCF) properties of steels associated with an identification method of the scatter based on thermal measurements. Up to now, this theoretical framework was used for uniaxial load histories. It is proposed to modify the probabilistic two-scale model to account for the effect of a multiaxial and proportional load histories on HCF properties. This modification consists in the introduction of an equivalent activation stress in the process controlling the plasticity kinetics. Thermal measurements are performed under biaxial tension–compression load histories to identify and validate an HCF criterion.

A comparison between two analytical models that approximate notch-root elastic–plastic strain–stress components in two-phase, particle-reinforced, metal matrix composites under multiaxial cyclic loading: experiments

This paper presents the experimental assessment of two simplified models, formulated in a companion paper by the authors, that estimate the elastic–plastic behavior at the notch-root surface of particulate metal matrix composites (PMMCs). The validity of each model is assessed by measuring the notch root strains on circumferentially notched PMMC bars when subjected to a variety of bi-axial cyclic loading paths. The notch root strains are measured using a 3D image correlation system that uses photogrammetric principles and image processing in assessing surface strain fields. Both models are found to be in good agreement with the experimental results in terms of the shape and orientation of the elastic–plastic local shear and axial strains.

Multiple crack fatigue growth modeling by displacement discontinuity method with crack-tip elements

This paper presents a numerical approach for modeling multiple crack fatigue growth in a plane elastic infinite plate. It involves a generation of Bueckner’s principle, a displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author and an extension of Paris’ law to a multiple crack problem under mixed-mode loading. Because of an intrinsic feature of the boundary element method, a general multiple crack growth problem can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modeled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. Fatigue growth modeling of an inclined crack in an infinite plate under biaxial cyclic loads is taken into account to illustrate the effectiveness of the present numerical approach. As an example, the present numerical approach is used to study the fatigue growth of three parallel cracks with same length under uniaxial cyclic load. Many numerical results are given.

Dislocation Structures of Duplex Stainless Steel in Uniaxial and Biaxial Cyclic Loading

Austenitic-ferritic duplex stainless steel has been subjected to uniaxial and biaxial nonproportional cyclic loading with the same equivalent strain amplitude. The dislocation structures in specimens fatigued to fracture using both types of loadings were studied and compared. Uniaxial cyclic loading, both in austenitic and in ferritic grains, produces simple structures due to activation of predominantly one slip system. Non-proportional cyclic loading results in formation of cell and wall structures and thus in higher stress response of the material.

Biaxial cyclic deformation of an epoxy resin: Experiments and constitutive modeling

Biaxial (proportional and non-proportional) cyclic tests were conducted on thin-walled tubular specimens to investigate deformation behavior of an epoxy resin, Epon 826/Epi-Cure Curing Agent 9551. The focus was placed on the biaxial stress-strain response and their dependency on the load control mode, stress or strain range and loading path. Experimental results indicated that under strain-controlled equi-biaxial (proportional) cyclic loading, mean stress relaxation occurred in both axial and hoop directions, whereas under stress-controlled equi-biaxial cyclic loading, ratcheting strains accumulated in both principal directions. Under strain- or stress-controlled non-proportional cyclic loading, anisotropy in stress-strain responses was induced in both axial and hoop directions, and the axial and hoop hysteresis loops rotated in opposite directions. This was particularly evident at high stress or strain levels. The experimental results were further used to evaluate the predictive capabilities of a nonlinear viscoelastic constitutive model. Qualitative and quantitative comparison with the test data indicated a good agreement in predicting the complex stress-strain response under biaxial cyclic loading with various loading paths, applied stress or strain ranges and loading control modes.

BEHAVIOUR OF U-SHAPED WALLS SUBJECTED TO UNIAXIAL AND BIAXIAL CYCLIC LATERAL LOADING

This paper presents the results of an experimental and numerical investigation on the behaviour of U-shaped walls subjected to lateral uniaxial and biaxial cyclic loading. The test specimens have been sized and detailed according to EC8 code. The tests aimed at studying the behaviour of a full scale U-shaped wall in uniaxial and biaxial bending and shear, and compared the alternative design requirements of two versions of ECS. A 3D multilayer thin shell finite element formulation, incorporating a concrete model with a smeared cracking capability, was used to simulate the experimental behaviour of this specimen. Comparison between numerical and experimental results shows that the model is capable of predicting with acceptable accuracy the most important characteristics of the measured global and local response. Based on the findings of both experimental and numerical results, some additional recommendations for design and analysis have resulted.

On the use of nominal stresses to predict the fatigue strength of welded joints under biaxial cyclic loading

ABSTRACTIn this paper, the modified Wöhler curve method proposed by Susmel and Lazzarin is employed to predict the fatigue life of welded connections subjected to biaxial cyclic loading. This criterion is reformulated here in order not to take into account the mean stress effect, as suggested by several design codes (at least when welded connections are not completely stress relieved). The accuracy of the proposed method in fatigue lifetime estimation was evaluated by using a number of data sets taken from the literature. The modified Wöhler curve method was applied in terms of nominal stresses and was calibrated using the uniaxial and torsional fatigue curve determined by reanalysing the experimental data, as well as using the standard fatigue curves of the Eurocode 3. The proposed approach was seen to be successful, giving multiaxial fatigue life predictions located within the widest scatter band related either to uniaxial or to torsional data, independently of both out‐of‐phase angle and load ratio value. Finally, the accuracy of the modified Wöhler curve method was compared to the one obtained by applying the procedure suggested by the Eurocode 3: the proposed criterion is demonstrated to be much more accurate and reliable than the standard one.