Biaxial Loading Research Articles

Optimization of a cruciform specimen for fatigue crack growth under in and out-of-phase in-plane biaxial loading conditions

Mixed-mode loading conditions are present in different mechanical components. Understanding the influence of in-plane biaxial loading paths parameters allows for fatigue crack growth (FCG) prediction and component fatigue life assessment. Cruciform specimens are used to simulate these conditions, but large specimen dimensions are required in order to keep crack propagation unaffected by specimen geometry. This article describes the procedure used to optimize a new cruciform specimen geometry, with small dimensions. Having identified the specimen arms fillet as a major source of crack growth interference, this effect was kept to a minimum, while using arm slots with different widths and lengths. Individual slot dimensions were optimized using a Direct MultiSearch (DMS) algorithm, minimizing the stress intensity factor (SIF) difference between the optimal specimen and an infinite plate. FCG on the optimized specimen was simulated under in and out-of-phase loading conditions. Due to crack closure effects, fatigue propagation under fully out-of-phase loading is less sensitive to specimen geometry. Therefore, the final geometry was chosen considering the required biaxial loading ratio under in-phase loading.

Biaxial cyclic behavior of bolted end-plate connection to I-column reformed by box-plates

In the research study, different 3D joint concepts of a frame formed by an I-column subjected to the biaxial cyclic load were simulated. Non-linear finite element models using the Ansys software were developed to evaluate the biaxial cyclic behaviors of the joints. After verification via five existing experimental tested beam-to-column connections, six different representative finite element models of the joints, including a 3D corner joint, two 3D edge joints, and two 3D interior joints with the biaxial cyclic load as well as a 2D corner joint as a base specimen with uniaxial cyclic load, were established with and without under axial compression force on the column. A newly developed weak-axis connection detail was implemented to connect the beam to the weak-axis of the column. Two box-plates parallel to the web of the column connected between the flange tips of the I-shaped column were used to reform the region of the I-column corresponding to the beam connection. The four-bolted unstiffened end-plate connection specified in AISC 358-16 was used as the beam-to-column connection in both the strong-axis and the weak-axis directions of the I-shaped column. The results indicate that biaxial loading causes a loss of strength in the early loading cycles compared to uniaxial loading. The strong-axis connection of the 3D corner joint has less ultimate connection rotation and a greater value of rotational stiffness than that of the 2D corner. Moreover, all the connections of the joints possessed good hysteretic curves satisfying the limits given in the ANSI/AISC 341-16. Axial compression force on the column reduced performance parameters of the connections such as plastic rotation capacity, energy dissipation ability, and hysteretic equivalent viscous damping ratio. By the way, the weak-axis connections of the joints are acceptable to consider as partially restrained connections, while the strong-axis connections are fully-restrained.

A hyperelastic-damage model based on the strain invariants

We develop a unified framework to describe the hyperelastic and damage behaviors of soft materials. The free energy density consists of both the crosslinked part of Langevin chains and the entanglement part described by a tube model. The micro–macro transition is obtained by using the averaging value over a microsphere. Consequently, the free energy density only depends on the strain invariants. The damage mechanism is then incorporated via the network alteration theory for the crosslinked part, while the deformation can also induce dilation of the tube and subsequent a decrease in the modulus for the entangled part. The hyperelastic model captures the Mooney Rivlin plot with a first decrease in the small deformation regime and then an increase in the large deformation region. The hyperelastic model can also accurately reproduce the stress–strain relationships in the uniaxial and biaxial loading conditions for various elastomer systems. The damage model can describe the stress response of filled rubbers in uniaxial and biaxial loading conditions, which shows a considerable improvement compared with the damage model without the entanglement effect. Since the model only depends on the strain invariants, the model can be easily implemented into the commercial finite element software Abaqus through a UHYPER. The finite element model can accurately reproduce the experimentally measured strain distribution of filled rubbers with complex geometry in the loading process. These results clearly show that the hyperelastic-damage model developed in this work has strong potentials to predict the mechanical responses of soft materials for practical applications.

Impact of physiological loads of arterial wall on nucleus deformation in endothelial cells: A computational study

IntroductionComputational modeling can enhance the understanding of cell mechanics. To achieve this, finite element models of endothelial cells were proposed with shapes mimicking their natural state inside the endothelium within the cardiovascular system. Implementing the recently proposed bendo-tensegrity concept, these models consider flexural (buckling) as well as tensional/compressional behavior of microtubules and also incorporate the waviness of intermediate filaments. Materials and methodsFour different models were created (flat and domed hexagons, both regular and elongated in the direction of blood flow) and loaded by biaxial deformation, blood pressure, and shear load from blood flow – natural physiological conditions of the arterial endothelium – aiming to investigate the “in situ” mechanical response of the cell. ResultsThe impact of individual components of loads on the nucleus deformation (more specifically on the first principal strain) potentially influencing mechanotransduction was investigated and the role of the cytoskeleton and its constituents in the mechanical response of the endothelial cell was assessed. The results show (i) the impact of pulsating blood pressure on cyclic deformations of the nucleus, which increase substantially with decreasing axial pre-stretch of the cell, (ii) the importance of relatively low shear stresses in the cell response and nucleus deformation. ConclusionNot only the pulsatile blood pressure but also the wall shear stress may induce significant deformation of the nucleus and thus trigger remodelation processes in endothelial cells.

Examination of Toughening Mechanisms of Zirconia Fabricated by Spark Plasma Sintering Methods

Ceramics/ metal functionally graded materials (FGMs) have been attracting much attention as composite materials that are intended for application to high-temperature structures. This study fucuses on toughening of ceramics and their matrix composites, which are building blocks of the FGMs. Partially stabilized zirconia (PSZ) with toughening additives such as Ni particles, Inconel fibers, SiC particles, SiC whiskers and a-alumina (Al2O3) particles were fabricated by spark plasma sintering (SPS). Toughening mechanisms were investigated based on their micro and macro-scale mechanical properties and microstructures. Disk bending tests, producing balanced biaxial loading conditions, were conducted probing bending strength at macro scales, while Vickers hardness tests were carried out to estimate fracture toughness and examine toughening mechanisms at micro scales. The results demonstrated that toughness of ZrO2 increased by adding Ni particles, Inconel fibers and Al2O3 particles. Addition of Al2O3 particles highly enhanced disk bending strength and deformability.

An integrated UAV photogrammetry-discrete element investigation of jointed Triassic sandstone near Sydney, Australia

Over the last decade, UAV Structure-from-Motion photogrammetry and digital rock mass mapping tools have been rapidly adopted into geotechnical engineering practice. As computing power has increased, numerical models and remote sensing methods have become more sophisticated, and much research has been applied to the development of digital rock mass classification and data collection methods. This investigation presents a case study of UAV photogrammetry mapping, discrete fracture network analysis and discrete element method modelling of jointed sandstone exposed in coastal cliffs and wave-cut platforms near Sydney, Australia. The aim of the study is to investigate a selection of digital mapping and numerical modelling approaches for rock mass geomechanical characterisation. A cohesive workflow is presented for UAV photogrammetry survey, discontinuity mapping, simulation of rock mass scale laboratory tests, and 3D DFN simulations of roof reinforcement in a large-span road tunnel.Digital discontinuity mapping is undertaken using two different software tools, and results are compared with historical conventional mapping. A novel GIS-based workflow is demonstrated to interrogate the mapping data, using a cellular grid approach to measure fracture intensity and fracture network connectivity. The discontinuity statistics are used as inputs to a series of 3D discrete element method numerical UCS, triaxial, and biaxial load tests that investigate the rock mass anisotropy and the impact of confining stress on rock mass shear strength, stiffness, and failure mechanisms. Next, the mapping data are applied to DFN simulations of a 31 m span tunnel, based on upcoming proposed road tunnels in Sydney. The tunnel simulations show how predicted displacements in the tunnel roof are proportional to fracture intensity.

On the influence of different in-plane biaxial loading conditions over FCG lives

In-plane biaxial loading conditions have a strong influence over fatigue crack growth trajectories and lives. Under equal and proportional loadings on both axes, pure mode I propagation occurs. Mixed mode conditions were simulated using different biaxial load ratios, and mode II propagation can be introduced when different loading phases or mean load values are used. Using an automatic algorithm, different in-phase and out-of-phase loading conditions were simulated in a cruciform specimen. Fatigue life is proportional to initial notch angle β, but inversely proportional to the load phase shift ϕ. The present results increase mixed mode fatigue crack propagation understanding.

Analysis of biaxial proportional low-cycle fatigue crack propagation for hull inclined-crack plate based on accumulative plasticity

Fracture failures of ship plates subjected to in-plane biaxial low-cycle fatigue loading are generally the coupling result of accumulative plasticity and biaxial low-cycle fatigue damage. A biaxial low-cycle fatigue crack growth analysis of hull structure that accounts for the accumulative plasticity effect can be more suitable for the actual evaluation of the overall fracture performance of the hull structure in severe sea conditions. An analytical model of biaxial low-cycle fatigue crack propagation with a control parameter for ∆CTOD is presented for hull inclined-crack plate. A test was conducted for cruciform specimens made of Q235 steel with an inclined crack to validate the presented analysis. The biaxial accumulative plasticity behavior and the effects of biaxiality and stress ratios were investigated. The results of this study reveal a strong dependence of biaxial low-cycle fatigue crack propagation on biaxial accumulated plasticity.

Experimental and Numerical Investigation of High-Temperature Multi-Axial Fatigue

Abstract Gas turbines and aircraft engines are dominated by cyclic operating modes with fatigue-related loads. This may result in the acceleration of damage development on the components. Critical components of turbine blades and disks are exposed to cyclic thermal and mechanical multi-axial fatigue. In this work, planar-biaxial low-cycle-fatigue (LCF) tests are conducted using cruciform specimens at different test temperatures. The influence on the deformation and lifetime behavior of the nickel-base disk alloy Inconel 718 is investigated at selected cyclic proportional loading cases, namely, shear and equi-biaxial. The calculation of the stress and strain distribution of the cruciform specimens from the experimental data is difficult to obtain due to complex geometry and temperature gradients. Therefore, there is a need for finite element (FE) Simulations. A viscoplastic material model is considered to simulate the material behavior subjected to uniaxial and the selected planar-biaxial loading conditions. At first, uniaxial simulation results are compared with the uniaxial experiment results for both batches of IN718. Then, the same material parameters are used for simulating the biaxial loading cases. The prediction of FE simulation results is in good agreement with the experimental LCF test for both shear and equi-biaxial loadings. The equivalent stress amplitude results of the biaxial simulation are compared with the uniaxial results. Furthermore, the lifetime is calculated based on the stabilized cycle from the simulation and by using Crossland and Sines multi-axial stress-based approaches. The Crossland model predicts fatigue life significantly better than the Sines model. Finally, the simulated lifetime results are compared with the experimental lifetime.

AE Monitoring of Damage in Flexible Solar Cells under Biaxial Loading

Microdamage initiation and accumulation processes in flexible solar cells under biaxial tensile loading were monitored by acoustic emission (AE) technique. Furthermore, the contribution to the degradation of power generation performance was evaluated using lock-in thermography (LT). Comparing the results of uniaxial with biaxial tensile tests, it was shown that the strains at the onset of the degradation in the maximum power Pmax and the short circuit current Isc were equivalent for both tests. Whereas the open circuit voltage Voc decreased at lower strain in the biaxial test than the uniaxial. Furthermore, it was also observed that the cracks near the current collection holes were perpendicular to the tensile direction in the uniaxial, whereas in the biaxial, the cracks were radial from the current collection holes. Consequently, the fundamental knowledge on the characterization of durability of flexible solar cells, such as the prediction of degradation was obtained.

Numerical analysis of damage and fracture in steel sheets undergoing non-proportional loading paths

The paper deals with the numerical analysis of damage and fracture mechanisms in steel sheets. Newly developed H-specimens are taken from thin sheets and are tested under different biaxial loading conditions. Results of numerical simulations of a series of biaxial experiments are presented showing also the effect of non-proportional loading paths on inelastic deformation behavior and on damage processes. In this context, an anisotropic continuum damage model is presented based on yield and damage conditions as well as evolution laws for plastic and damage strain rates. Different stress-state-dependent branches of the damage criteria are taken into account corresponding to various damage and failure processes on the micro-scale depending on the stress triaxiality and the Lode parameter. Experiments with the biaxially loaded H-specimen have been performed. Results for proportional and corresponding non-proportional loading histories are discussed. During the experiments strain fields in critical regions of the specimens are analyzed by digital image correlation (DIC) technique. Numerical simulations of the experiments have been performed and numerical results are compared with experimental data. Furthermore, based on the numerical analysis evolution of stress variables is examined and stress distributions in critical specimens areas are detected allowing prediction of stress-state-dependent damage and fracture mechanisms. The numerical results also demonstrate the efficiency of the experimental program and the new specimens geometries covering stress states in the shear-tension regime as well as the effect of the loading histories on inelastic deformation and damage behavior in steel sheets.

Characterization of surface properties of thin film composite (TFC) membranes under various loading conditions

The performance of membranes relies on their surface characteristics which degrade due to complex loading during operation. Available studies examine surface properties under uniaxial loading, and limited, if none, are available under various loading conditions. We assess the surface integrity of thin film composite membranes under static and dynamic uniaxial and biaxial loading using contact angle, atomic force microscopy, and scanning electron microscopy measurements by examining surface hydrophilicity and morphology. We demonstrate the limitations of uniaxial tests in assessing the surface properties. Damage of the polyamide layer was observed at dynamic load levels much below the expected static rupture load.

Correction factors for in-plane shear strength and stiffness testing of flat angle-ply composite laminates with high Poisson’s ratios

In this paper, a method to obtain correction factors for in-plane shear properties in fibre-reinforced polymers with high Poisson’s ratio under biaxial load conditions and at high loads is presented. Experimental testing shows the deviations from classical laminate theory for such cases. The transverse deformation ratio is a general form of Poisson’s ratio and, for a ±45° angle-ply laminate, increases with strain. This effect is shown to exist for long and short test specimens, where significant biaxiality in the stress state is present. Reasons for this include fibre rotation at higher loads in tensile load conditions, and matrix plasticity and damage initiation. Test results show that the expanded formulas compensate errors in shear strength calculation of angle-ply laminates which arise from using nominal parameters with standard formulas. The results are also applicable to structures under biaxial load and when transverse contraction is inhibited, e.g. in shear panels. Further potential uses are in the presence of high shear strains and to detect the onset of damage under shear loading.

Cubic b-splines to perform topology optimization with buckling load on carbon fiber nano reinforced simply supported cross ply laminated composite square plates using inverse buckling formulation

Composite laminates are widely used in several civil engineering structures. Composite laminates are used in bridges, aircraft, and construction because of their light weight and high strength. The study on the behavior of these laminates is very important now. The main focus of this research is to propose a new method to perform topology optimization of nano-reinforced composite laminates carrying buckling loads. The goal is to present the optimal layout of the material, stress distribution at the optimal state, buckling load factors at the optimal state, and most importantly, the deformed profile of the composite laminate at the optimal state. The elastic stiffness matrix and the geometric stiffness matrix can be used to determine the buckling load. The reason for taking the reciprocal of the buckling load is that during optimization, the number of elements that are not participating in carrying the load increases, and hence the stress carried by these elements is minimal. Hence, we have considered the inverse value of the buckling load factor. The design domain is modelled using cubic b-splines. Higher-order shear deformation theory is used, and isogeometric analysis is performed to determine the buckling load. The deformed profile of the plate at the optimal state, the optimal layout of the material, stress distribution, buckling load factors, and the corresponding mode shapes are given as well. Only carbon fiber nano-reinforced, cross-ply square plates with a simple support structure have been considered. Three different types of loading conditions, namely uniaxial compressive loading, bi-axial compressive loading, and pure shear loading, are considered. Coding is done in MatLab®, and the buckling load factors are determined. Several examples from the literature are considered with different moduli ratios, laminae, and span to thickness ratios, and the non-dimensional buckling load is determined for each. The results obtained are in good agreement with those given in the literature.

Load Distribution Optimization Method for Fatigue Test of Full-scale Structure of Biaxial Resonant Wind Turbine Blade

Wind turbine blade is the key component of wind turbine to realize wind energy capture, so it is necessary to verify the rationality of blade structure design through full-scale structural fatigue test. In order to improve the test accuracy and efficiency, this paper proposes to establish the dynamic analysis model of the multi-degree of freedom system of the tested blade by using the finite beam element to realize the calculation method of the load amplitude of the biaxial fatigue test and integrate the dynamic analysis model and the target load calculation method into the particle swarm optimization algorithm to realize the optimization of the load distribution of the biaxial resonant full-size structure fatigue test. Through the design of a biaxial resonant loading scheme of 2.5MW-52.5m wind turbine blades, the results show that this method can quickly and accurately adjust the optimization parameters such as the position of the exciter and the motion quality of the exciter in the flapwise and edgewise on the premise that the fatigue cumulative damage caused by the test load is not less than the cumulative damage of the target load.

Analysis of biaxial proportional low-cycle fatigue and biaxial accumulative plasticity of hull inclined-crack plate

Fracture induced failure of plates in hull structures subjected to in-plane biaxial low-cycle fatigue loading are generally a combination of accumulative plasticity and biaxial low-cycle fatigue damage. A biaxial low-cycle fatigue crack growth analysis of a hull structure that accounts for the accumulative plasticity effect can be suitable for the actual evaluation of the overall fracture induced failure of the hull structure in severe sea conditions. An analytical model of biaxial low-cycle fatigue crack propagation with a control parameter for the J integral was presented for hull inclined-crack plate. The test was conducted for cruciform specimens made of Q235 steel with an inclined crack to validate the presented analysis. The biaxial accumulative plasticity behaviour and the effects of the biaxiality and stress ratios were investigated by numerical analysis. The results of this study reveal a strong dependence of biaxial low-cycle fatigue crack propagation on biaxial accumulated plasticity.

Mechanical Behavior of Reactive Powder Concrete Subjected to Biaxial Loading

To investigate the biaxial mechanical characteristics of reactive powder concrete (RPC), RPC plate specimens and bone‐shaped specimens were tested under compression‐compression and compression‐tension loadings, respectively. The strengths and strains of the specimens were recorded, and the crack patterns and failure modes in various stress states were examined. Based on the test data, the characteristics of biaxial strength were analyzed, and a biaxial failure criterion was established. The characteristics of major stress‐strain curves and failure modes in different biaxial stress states were determined. The results show that the ratio between the biaxial compression strength and the uniaxial compression strength was 1.44–1.58 for RPC. When the stress ratio under compression‐tension was −0.05, the tensile strength decreased by 48%. Under compression‐compression, the proportional limit of RPC was about 95%, and its peak strain was high. Under compression‐tension, as the compressive stress increased, the elastic modulus decreased, and the peak strain in the tensile direction increased. When the RPC specimens were under compression‐compression, the failure mode of RPC was splitting failure. Under compression‐tension, the failure mode changed from single‐crack tensile failure to multicrack compressive failure with increasing confining stress.

Propagation of notch fatigue cracks on maraging steel under biaxial conditions

The current work aims at characterizing the fatigue behaviour of an additively manufactured maraging steel. This is a class of high-strength steels widely used in aircracft, aerospace, offshore and military industries thanks to its good performance in terms of strength, toughness, ductility, dimensional stability and weldability. Fabrication of such steel via laser-beam powder bed fusion (additive manufacturing) makes it an excellent candidate for producing prosthetic parts because of its properties, offering a reduction in manufacturing material consumption, labor and machining time. The study is focused on the multiaxial behaviour of the steel, given the wide range of loads often existing in biomedical components. To this end, different critical plane methods are used to predict the fatigue life and the cracking orientation under several biaxial loading scenarios. Thickness effects were also evaluated. Cylindrical specimens were used and these were fabricated in the vertical orientation on the base plate, using a linear printing system equipped with a Nd:YAG fibre laser. The building strategy comprised the deposition of 40 μm thick layers at a scan speed of 80 mm/s. The results are useful to understand the predominant failure mode and the type of critical plane method that is most convenient for such material.

Seismic Performance and Mechanical Mechanism of Steel‐Enhanced Damping Concrete Core Wall with Concealed Steel Plate Bracings under Oblique Loading

This article focuses on the seismic performance and mechanical mechanisms of core walls under biaxial earthquakes. Through the oblique loading test (biaxial loading test) on one 1/6 scale steel‐enhanced damping concrete core wall with steel plate bracings, the failure patterns, the load‐bearing capacities, the yield mechanisms, and the strain distributions, etc. were investigated. Comparisons were made with the available test results of the authors’ previously unidirectional tested core walls and the tests completed by other scholars. The oblique tested core walls exhibited lower initial stiffness, but higher yield displacements, loading capacities, and ultimate displacements. A much more serious damage was also found in the wall limbs of oblique tested core walls by comparing with the unidirectional test core walls. Then finite element analysis (FEA) was also carried out to study the axial compression ratio (n), coupling beam span‐depth ratio (l/h) on the stress distributions, and effective width of the end wall limbs (be). From the analysis results, it can be indicated that l/h affects much the stress distributions of oblique test core wall, which would be in eccentric force states if the coupling beam span‐depth ratio was small, while the axial compression ratio does not affect the stress distributions dramatically. be varies with loading steps, the minimum value (be, min) of which increases with the decrease of l/h, and be, min will grow along with n.

Prediction of Failure Envelope of Calcified Aneurysmatic Tissue

The abdominal aortic aneurysm (AAA) may have a varying degree of calcification where calcium particles are found in different geometrical configurations. The impact of calcification on the failure of aneurysms is not very clear as literature shows contradictory results. This work is dedicated to investigating the impact of calcification on the failure strength of an aneurysmatic wall using micromechanical finite element simulations. A Representative Volume Elements (RVE) consisting of circular and elliptical particles are generated with different volume fractions, which is further extruded in the thickness direction. A two-fibre model is used for modeling anisotropic tissues. Calcium particles are assumed to be elastic. An anisotropic phase-field model is employed to model the failure in the tissue. A unique set of representative material parameters as well as phase-field parameters, like critical fracture energies for isotropic and anisotropic parts, are determined by fitting the model to experimental data, available in the literature. Finite element simulations are being performed on RVEs to generate a failure envelope of the calcified tissues under bi-axial loading conditions. This study will help in better understanding and better prediction of failure in aneurysms.