Biaxial Cyclic Loading Research Articles

Monotonic and cyclic lateral loading of piles in low- to medium-density chalk

Offshore and other structures often rely on driven piles to carry lateral loads. However, there is currently no established design method to cover lateral loading at chalk sites, which are widespread across Northwest Europe. This paper reports monotonic and cyclic lateral load tests on highly instrumented 508 mm and 1220 mm diameter. open steel piles driven at a well-characterised chalk test site in Kent, UK, for a recent joint industry project that developed new benchmark datasets and analyses, supported by high-quality testing. The ultimate lateral pressures mobilised in the chalk are shown to be relatively low compared to its uniaxial compressive strengths (UCS) due to pile-driving damage, natural fracturing, local yielding and brittleness. Significant gaps opened between the piles and chalk during loading, that led to a substantially softer response on unloading and subsequent reloading, as well as marked axial capacity losses. Reaction curves extracted from the field measurements and applied in a one-dimensional numerical model perform well in reproducing the monotonic lateral tests. As with piles driven in other materials, one-way cyclic lateral loading led to permanent displacement accumulation and stiffness changes that were linked to the cyclic loading parameters. Both effects were more marked under biaxial cyclic lateral loading.

Experimental investigation on mechanical behavior of silane‐modified polyurethane sealant under biaxial cyclic loading

AbstractThe biaxial tension–tension cyclic loading experiments were conducted on the cruciform specimens prepared using a silane‐modified polyurethane sealant to investigate their mechanical behavior. The finite element method was employed to validate the mechanical behavior of cruciform specimens under the biaxial cyclic loading conditions. It is shown that the highest stress concentration is in the central region of the cruciform specimens, indicating that the shape design of the specimen is suitable for the biaxial tension–tension cyclic tests. Additionally, the effects of loading path, mean stress, and stress amplitude on ratcheting strain and dissipated energy were analyzed through the experimental data. The experimental results demonstrated that the loading path had an influence on the mechanical behavior of the cruciform specimen. The additional ratcheting strain caused by the non‐proportional loading path was found to be loading path dependent of the adhesive. Moreover, the mean stress and stress amplitude greatly affected the strain response curves of the specimen under biaxial cyclic loading. The ratcheting strain and dissipated energy increased with increasing mean stress and stress amplitude; nevertheless, stress amplitude had more influence on the mechanical behavior than the mean stress.

Effect of biaxial cyclic loading path on the mechanical and microstructure properties of articular cartilage

Cyclic loading stimulation has the potential to change both the mechanical properties and microstructure of cartilage, subsequently damaging the articular cartilage and contributing to joint osteoarthritis. This study focuses on investigating the behavior of knee articular cartilage under biaxial cyclic loading and analyzing the associated microstructural changes at the ultrastructural level. We studied the in-plane biaxial cyclic loading behavior of cartilage with a particular emphasis on understanding the effects of loading paths, taking into consideration the complex loading conditions encountered during daily activities. The experimental results reveal a clear influence of the constraints in the Y-direction (orthogonal direction) on the strain evolution in the X-direction. Furthermore, the variation in orthogonal stress corresponding to the loading path significantly impacts the biaxial mean strain of the test sample. To be specific, the uniaxial path, characterized by no constraints in the Y-direction, demonstrates the highest mean strain of 25.08 ± 0.88% in the X-direction, while the proportional path exhibits the lowest mean strain (10.77 ± 0.49%) in the X-direction due to the Y-direction's largest stress constraint. We explored the effects of stress amplitude and peak stress holding time on mean strain under a square path. Our observations indicate that the mean strain of cartilage increases with the higher stress amplitude or the longer peak stress holding time. Additionally, we analyzed the collagen fibril networks before and after biaxial cyclic loading to reveal the intrinsic deformation mechanism. The rearrangement of collagen fibril networks is closely associated with the stress state of cartilage, where higher stress levels lead to more severe fibril damage.

Numerical assessment of the cyclic behaviour of structural steel members subjected to biaxial bending

AbstractIn recent decades, there has been extensive research on the behaviour of steel structures under seismic actions. While the monotonic behaviour of steel elements subjected to uniaxial bending is well understood, there is still a need to investigate the cyclic behaviour and energy dissipation capacity, especially in relation to metal elements subjected to biaxial bending. This is of paramount interest for seismic analysis and performance assessment of steel buildings. Modelling and damage assessment criteria derived for members subjected to uniaxial bending may not be entirely appropriate for the seismic analysis of buildings composed of structural steel members subjected to biaxial bending. Therefore, this research aims to investigate the behaviour of steel members subjected to biaxial cyclic bending and compare it to behaviour under uniaxial loading conditions. To this end, detailed 3D finite element analyses are conducted to examine the effects of bidirectional lateral cyclic loading on the hysteretic response of steel members under different uniaxial and biaxial lateral displacement‐controlled load paths. The numerical results presented in this paper provide an insight into the influence of biaxial loading on the behaviour of steel members in terms of backbone curves and deformation capacity, and indicate that biaxial cyclic loading paths can significantly affect the rotation capacity of steel elements.

Temperature‐dependent mechanical performance of Nafion® 212 proton exchange membrane under uniaxial and biaxial loading

AbstractThe degradation of proton exchange membranes (PEMs) can significantly affect the structural integrity and lifetime of fuel cells. This study investigates the effects of temperature, peak load, initial strain, and loading modes on the mechanical properties of Nafion® 212 PEM using an in‐situ biaxial testing system. The findings indicate that membrane creeping is positively correlated with temperature and peak loads. The stress relaxation rate increases with the increase of initial strain, and an increase in temperature also leads to an apparent decrease in the anti‐relaxation properties of Nafion® 212 membrane. Additionally, the mechanical properties of low‐cycle fatigue at various temperatures were explored under biaxial cyclic loading conditions. When the temperature is fixed, the membrane strain increases and gradually stabilizes with the rise of fatigue cycles. With an increase in temperature, the strain increases at a greater rate. The phase difference increases with temperature growth, and the “hysteresis” phenomenon of the strain becomes more pronounced, resulting in greater energy loss. These results provide valuable insights into the mechanical behavior of Nafion® 212 PEM under different conditions. And can inform the design and optimization of fuel cell systems and contribute to the development of more robust and durable PEM materials.

Numerical analytical method of predicting the durability of fibrous composite materials under conditions of biaxial cyclic loading

A combined numerical-analytical method for predicting the durability of fibrous composite materials under conditions of biaxial cyclic loading is proposed. The model of nonlinear elastic behavior of random composites is used. The mechanics problem of determining the stress-strain state in the matrix and fibers is solved within the framework of the physically nonlinear theory of elasticity with the use of numerical methods. To predict the durability of an anisotropic composite in the macro volume, the matrices strengthening effect were used. The method of determining the equivalent stress used for asymmetric two-dimensional loading is considered. The influence of the average stress on the fatigue characteristics of the matrix with nonlinear strengthening is shown. Examples are given that illustrate the importance of the mutual influence of nonlinear elastic and anisotropic properties of the composite on the redistribution of stresses in the fibers and the matrix. As a practical result, we can note the possibility of predicting the long-term strength of the material when the field of cyclic stresses is determined in the vicinity of the inclusions. For a detailed analysis of local stress fields and specification of the type of complex load in structural elements, a numerical analysis was performed using finite element programs for a single, forming cell in the context of random homogenization.

Calculations of biaxial fatigue limits with models using the experimental crack direction

Several models from the literature were used to predict the fatigue limit in notched components subjected to biaxial cyclic loading. The predictions of these models are based on the elastic stresses along a line which is considered to be representative of the crack direction in its initial part. The line used in the models changes considerably. For one of the studied models, the line direction corresponds to Mode I, while for another it is Mode II, and for the other two models considered the direction is between Mode I and Mode II. However, quite naturally, the experimental crack direction is unique. In recent years, a study of experimental fatigue limits and crack directions in its initial part for three materials was carried out in hollow cylindrical specimens with a circular hole subjected to cyclic axial, torsional and in-phase biaxial loading. The directions of the cracks that were measured experimentally are on average similar for the three materials and close to Mode I. The analysed models give, in general, good predictions of the experimental fatigue limits, although they use directions that are completely different and that they too differ markedly from the experimentally found ones. The predictions of the models using, in a forced way, the measured experimental directions are good in most cases, which reveals a surprising insensitivity of these models to the main hypotheses on which their own formulations are based.

Numerical investigation on the ultimate strength behaviour and assessment of continuous hull plate under combined biaxial cyclic loads and lateral pressure

The ultimate strength of continuous hull plate under combined biaxial cyclic loads and lateral pressure is investigated in the present paper by using nonlinear finite element method. Geometric nonlinearity due to large deflection and material nonlinearity induced by kinematic hardening and isotropic hardening are both accounted for. A parametric study is designed and completed to examine the longitudinal ultimate compressive strength behaviours in the cycles on the basis of a large number of load-shortening curves. Effects of series of parameters especially the plate slenderness ratio, transverse cyclic compression, lateral pressure and cycle number are analyzed with details. It is found that the strength characteristic and collapse mode are highly affected by the coupling influence of the mentioned factors as well material behaviours. A dimensionless unified formulation as a function of the decisive factors is empirically proposed to accurately assess the ultimate strength of continuous hull plate in various cycles.

Behavior of double skin composite core wall subject to biaxial cyclic loads

This study performed a biaxial cyclic test on scaled double skin composite (DSC) core wall. The core wall consisted of two C-shaped DSC shear walls and steel coupling beams (SCBs) connecting the walls. In particular, seismic behavior of the core wall subject to reversed biaxial cyclic load was investigated. The failure mode of the core wall mainly included its local buckling of steel faceplate, fracture of vertical butt welds, fracture of side plate, and concrete crushing at the corners of walls. The lateral shear resistance in its two directions was mutually coupled. Once loaded in one direction, lateral shear resistance in other direction compromised. Due to energy dissipation of SCBs in their Y-direction, hysteresis loop for Y-directional loading was fuller than that for X-directional loading, and equivalent damping ratio of X-direction was 31.91% greater than that of Y-direction at ultimate point. Their initial stiffness in X-direction without SCBs configuration was the highest, and ductility coefficient of X- and Y-directions was relatively close, within 4.63–5.47%. The strain distribution curves along DSC shear wall bottoms of core wall before its peak resistance showed plane section assumption was valid under biaxial lateral load. In particular, DSC core wall high-rise buildings were promoted in this study.

Fatigue Strength Estimation of Ductile Cast Irons Containing Solidification Defects

The goal of the present paper is to discuss the accuracy and reliability of a procedure for the fatigue strength estimation of defective metals by considering some experimental data available in the literature. In particular, the fatigue behaviour of three ductile cast irons (DCIs) containing solidification defects (i.e., micro-shrinkage porosity) is simulated through the above a procedure, based on the joined application of the area-parameter model and the Carpinteri et al. multiaxial fatigue criterion. The fatigue strength of such DCIs subjected to both uniaxial (rotating bending or torsion) and biaxial (combined tension and torsion) cyclic loading is evaluated and compared with the experimental results.

Seismic performance of flanged RC walls under biaxial cyclic loading

Flanged RC walls are frequently utilized to provide strength and stiffness in two horizontal directions, yet the coupling of the bidirectional horizontal components of ground motion are bound to have large impact on the seismic response of flanged walls. However, few data exist characterizing the performance of flanged walls subjected to biaxial cyclic loading. Aiming to provide an insight into the influence of the biaxial coupling effect on the seismic behavior of flanged RC walls, three T-shaped and two L-shaped walls were tested under uniaxial and biaxial loading. Subsequently, a finite element model was employed for parametric studies and generating numerical data for a detailed comparison of the seismic performance of the flanged walls under uniaxial and biaxial loading. The results showed that the coupling of alternating loadings in orthogonal directions intensified the cracking and damage of flanged walls, resulting in the reduction of the bearing and deformation capacities, an increase in the proportion of flexural deformation in the plastic hinge area, acceleration of the energy dissipation process, and a more significant shear lag effect as opposed to uniaxial loading. Furthermore, the damage aggravation as well as reduction in seismic performance of L-shaped wall due to the biaxial coupling effect were more obvious than that of T-shaped wall. Based on the test and numerical results, the reduction of the ultimate inter-story drift ratio caused by biaxial loading was quantified through statistical analysis and the derived reduction factors can provide reference for the performance-based seismic design and anti-collapse design of flanged RC walls under multi-dimensional seismic action.

Parametric study of 3D steel moment connections with built-up box column subjected to biaxial cyclic loads

In this numerical research, the variation of cyclic behavior of beam-to-box column connection was studied. Dimensional and load conditions were parametrically evaluated with the goal of assessing the applicability and use of this biaxial moment connection according to the Seismic Provisions, such as bending strength and rotation capacity, secant and tangent stiffness, dissipated energy and strong column-weak beam relationship. A total of 83 different models of 3D connections were developed using in ANSYS software with the load at the top of the column. Results show a cyclic behavior not controlled by axial load. However, the variations of clear span to depth beam ratio caused degradation of the strength, secant and tangent stiffness as well as in dissipated energy. The 80% of plastic moment of beam and rotation at 4% interstory drift were reached for all models analyzed according to criteria established in AISC 341. Finally, the configurations designed with low levels of axial load are controlled by the design of the web panel zone shear, while configurations designed for high levels of axial load are controlled by the strong column-weak beam criterion. • The hysteretic response curves of the joints with end-plate connections and built-up box column subjected to cyclic loading were plumped. • The beam can concentrate the inelasticity effectively in a wide deformation range. • The behavior exhibited is acceptable for 7 < L/d < 20 ratio. • A numerical prequalification was possible.

Analysis of biaxial fatigue limit models for cases with circular notches

This work shows an analysis of several models of multiaxial fatigue for notches: Navarro-Rios’ model, which analyses the interaction between the crack and its associated plastic zone with the material microstructural barriers, and three models that combine a critical volume method for notches with a critical plane model for multiaxial fatigue in unnotched solids. Specifically, the application of these models for the prediction of the fatigue limit for a plate with a circular hole subjected to axial, shear and in-phase biaxial cyclic loading is studied. The effects of two parameters are analysed: the radius of the hole and the relationship between the torsional and axial fatigue limits. For all the analysed models, cases are observed in which an increase in the hole radius produces an increase in the predicted fatigue limit, that is, the evolution of the fatigue limit with an increasing hole radius is not always monotonically decreasing, as would be expected. These effects, which we have called “humps” because of their appearance on the prediction graphs, mainly occur in shear loading. No humps were observed in the studied experimental results, but the number of available experimental results is too small to assure this tendency. The results shown in the work indicate that a greater knowledge of the physics of multiaxial fatigue in notches is necessary to achieve models that are capable of providing increasingly accurate predictions.

Biaxial Cyclic Loading of Woven Fabrics

For the purpose of this paper, investigations were carried out on specifically designed fabrics with different structural parameters. The biaxial cyclic loading of fabrics and its consequences were investigated. The weave structures with the smallest weave units (plain weave, basket weave 2/2, rib weave 1/1 (2+2) and rib weave 2/2 (1+1) with the same warp and weft density (24 ends/cm and 24 picks/cm) were selected. Biaxial cyclic loadings of fabrics were performed on a newly developed patented device. The influence of the low level of cyclic loadings of fabrics on the change of tensile properties in warp and weft direction was investigated. The results showed that the low level of biaxial cyclic loading can lead to a permanent linear deformation of fabrics. Despite the fact that the forces that cyclically strain the fabric in two directions amount to 10% of the breaking elongation, after a certain number of cycles there is an irreversible deformation and reduction of breaking forces, but sometimes they can result in an increase in breaking forces. It was found that the tensile elongation of fabrics is affected both by thread crimping and by the structural properties of fabrics resulting from changes in the weave.

Predictive model for bidirectional shear strength of reinforced concrete columns subjected to biaxial cyclic loading

Corner columns are subjected to bidirectional lateral loading in three-dimensional framed structures during seismic events, which can deteriorate their shear strength. The majority of the design codes do not consider the effect of biaxial lateral loading in the calculation of the column shear strength, and hence an accurate formulation that can predict the bidirectional shear strength is still lacking. Gene Expression Programming (GEP) was used in this research to predict the bidirectional shear strength of columns subjected to biaxial cyclic loads based on a database collected from different experimental studies found in the literature. Based on the previous experimental studies, it is found that the biaxial shear strength of RC columns are predominantly controlled by the column axial load, cross-sectional area of the columns, column shear reinforcement area, concrete compressive strength, and the height of the column. These parameters were used to develop the GEP models in this research. The models were statistically evaluated in order to ensure their applicability, and then they were compared to the ACI-318 formulation of the uniaxial shear strength. The R2 value obtained using the ACI-318 formulations is low compared to that obtained using the GEP models, where the R2 value obtained using the ACI formulation is 0.35, and that obtained using the first and second GEP models are 0.87 and 0.73, respectively. This confirms that the GEP models are more fitting to the experimental results compared to the ACI-318 formulation.

Cyclic Damage Accumulation in the Femoral Constructs Made With Cephalomedullary Nails

Background: The purpose of this study was to evaluate the risk of peri-prosthetic fracture of constructs made with cephalomedullary (CM) long and short nails. The nails were made with titanium alloy (Ti-6Al-4V) and stainless steel (SS 316L).Methods: Biomechanical evaluation of CM nail constructs was carried out with regard to post-primary healing to determine the risk of peri-implant/peri-prosthetic fractures. Therefore, this research comprised of, non-fractured, twenty-eight pairs of cadaveric femora that were randomized and implanted with four types of fixation CM nails resulting in four groups. These constructs were cyclically tested in bi-axial mode for up to 30,000 cycles. All the samples were then loaded to failure to measure failure loads. Three frameworks were carried out through this investigation, Michaelis–Menten, phenomenological, and probabilistic Monte Carlo simulation to model and predict damage accumulation.Findings: Damage accumulation resulting from bi-axial cyclic loading in terms of construct stiffness was represented by Michaelis–Menten equation, and the statistical analysis demonstrated that one model can explain the damage accumulation during cyclic load for all four groups of constructs (P > 0.05). A two-stage stiffness drop was observed. The short stainless steel had a significantly higher average damage (0.94) than the short titanium nails (0.90, P < 0.05). Long titanium nail group did not differ substantially from the short stainless steel nails (P > 0.05). Results showed gender had a significant effect on load to failure in both torsional and bending tests (P < 0.05 and P < 0.001, respectively).Interpretation: Kaplan–Meier survival analysis supports the use of short titanium CM nail. We recommend that clinical decisions should take age and gender into consideration in the selection of implants.

Fatigue behaviour assessment of additive manufactured Ti-6Al-4V by means of a critical plane criterion

In the present paper, the fatigue behaviour of AM Ti-6Al-4V specimens under both uniaxial and biaxial cyclic loading is theoretically examined. In particular, fatigue tests available in the literature are simulated by means of a critical plane-based fatigue criterion proposed in the past by Carpinteri et al. The accuracy of the criterion is evaluated by comparing the theoretical results in terms of fatigue life with the experimental ones. Fatigue life is computed by using an equivalent strain amplitude (also named fatigue damage parameter) together with the tensile Manson-Coffin curve.

Fatigue strength evaluation and lifetime estimation for ductile cast irons under multiaxial loading

The goal of the present research is to theoretically estimate both fatigue strength and lifetime of Ductile Cast Iron (DCI) smooth specimens under uniaxial and biaxial cyclic loading. To such an aim, a critical plane-based multiaxial fatigue criterion formulated in terms of stresses is hereafter applied to several experimental fatigue data available in the technical literature, related to both infinite and finite life tests. The theoretical results (in terms of fatigue strength and fatigue life) are compared with the experimental ones and, for finite life fatigue tests, also with those derived through the Crossland criterion.

Paper Review of “Fatigue surface crack growth behavior in flat plate and out-of-plane gusset-welded joints under biaxial cyclic loads with different phases”

Paper Review of “Fatigue surface crack growth behavior in flat plate and out-of-plane gusset-welded joints under biaxial cyclic loads with different phases”

Determination of the Non-Proportional Cyclic Hardening Coefficient Sensitive to the Loading Amplitude

The research on determination of sensitivity of metal materials to non-proportional cyclic loading and the accompanying effects is analyzed. The indirect methods for determining the coefficient of non-proportional cyclic hardening of materials based on simple experiments are considered. A comparative analysis of methods for predicting non-proportional cyclic hardening for out-of-phase with a 90°displacement of biaxial cyclic loading with strain control is performed. It is shown that methods that use only the parameters of the stress–strain curve of materials are less effective, since they do not take into account the effect of cyclic loading amplitude on non-proportional hardening, which is quite significant for metals and alloys with face-centered cubic microstructure. Analysis of experimental data obtained at cyclic non-proportional deformation of stainless and carbon steels, aluminum and titanium alloys showed that the coefficient of non-proportional cyclic hardening varies depending on the loading amplitude. For most of the studied materials with face-centered cubic structure, there is a tendency to increase this hardening coefficient with increasing amplitude of cyclic loading and to its stability or slight decrease for metals with volume-centered cubic structure. Based on the behavior of the vast majority of materials, a logarithmic functional dependence is chosen to take into account the effect of the strain amplitude on the non-proportional cyclic hardening. A modification of the key parameter for determining mentioned hardening is proposed, taking into account both the characteristics of the stress–strain curve and the dimensionless value of the cyclic strain amplitude. It is shown that its use allows one to obtain a better correlation of experimental data with the approximation dependence proposed earlier by the author. The results of determining the coefficients of non-proportional cyclic hardening due to the improved approach meet the requirements of engineering use.