Biaxial Loading Conditions Research Articles

Experimental Bi-axial tensile tests of spinal meningeal tissues and constitutive models comparison

Introduction This study aims at identifying mechanical characteristics under bi-axial loading conditions of extracted swine pia mater (PM) and dura and arachnoid complex (DAC). Methods 59 porcine spinal samples have been tested on a bi-axial experimental device with a pre-load of 0.01 N and a displacement rate of 0.05 mm·s−1. Post-processing analysis included an elastic modulus, as well as constitutive model identification for Ogden model, reduced Gasser Ogden Holzapfel (GOH) model, anisotropic GOH model, transverse isotropic and anisotropic Gasser models as well as a Mooney-Rivlin model including fiber strengthening for PM. Additionally, micro-structure of the tissue was investigated using a bi-photon microscopy. Results Linear elastic moduli of 108 ± 40 MPa were found for DAC longitudinal direction, 53 ± 32 MPa for DAC circumferential direction, with a significant difference between directions (p < 0.001). PM presented significantly higher longitudinal than circumferential elastic moduli (26 ± 13 MPa vs 13 ± 9 MPa, p < 0.001). Transversely isotropic and anisotropic Gasser models were the most suited models for DAC (r2 = 0.99 and RMSE:0.4 and 0.3 MPa) and PM (r2 = 1 and RMSE:0.06 and 0.07 MPa) modelling. Conclusion This work provides reference values for further quasi-static bi-axial studies, and is the first for PM. Collagen structures observed by two photon microscopy confirmed the use of anisotropic Gasser model for PM and the existence of fenestration. The results from anisotropic Gasser model analysis depicted the best fit to experimental data as per this protocol. Further investigations are required to allow the use of meningeal tissue mechanical behaviour in finite element modelling with respect to physiological applications. Statement of significanceThis study is the first to present biaxial tensile test of pia mater as well as constitutive model comparisons for dura and arachnoid complex tissue based on such tests. Collagen structures observed by semi-quantitative analysis of two photon microscopy confirmed the use of anisotropic Gasser model for pia mater and existence of fenestration. While clear identification of fibre population was not possible in DAC, results from anisotropic Gasser model depicted better fitting on experimental data as per this protocol. Bi-axial mechanical testing allows quasi-static characterization under conditions closer to the physiological context and the results presented could be used for further simulations of physiology. Indeed, the inclusion of meningeal tissue in finite element models will allow more accurate and reliable numerical simulations.

Investigation on in-plane and out-of-plane constraint effects for plates with I-II mixed mode cracks under biaxial compressive loading

Crack sizes, geometrical configurations of specimens and structures, as well as loading conditions have significant effect on in-plane and out-of-plane constraint effects. Safety assessment with constraint effects can effectively improve the accuracy. There are prominent discrepancies between compressive fracture and tensile fracture. Most of engineering structures are usually under biaxial loading conditions, so that the influence of biaxial compressive loading on fracture analysis with constraint effects is worth paying attention. The size effect factor (relative crack length a/W, thickness to width ratio t/W and crack inclination angle β) and load factor (lateral pressure coefficient λ) of central cracked plate (CCP) specimens with I-II mixed mode crack on constraint effects under biaxial compressive loading have been investigated through theoretical analysis and finite element analysis. In-plane non-singular T-stress (T11) and its components (Tx, Ty, and Txy), out-of-plane non-singular T-stress (T33), out-of-plane constraint parameter Tz and stress triaxiality factor h have been adopted to quantify constraint effects. It demonstrates that λ has remarkable influence on SIF, T11 and T33 under biaxial compressive loading. The effect of higher a/W (long cracks) on B11 is more noticeable when I-II mixed mode crack is closer to pure mode II crack or pure mode I crack. The proportion of shear fracture increases under biaxial compression with λ. With the increase of β, B33 decreases sharply and then increases rapidly with higher λ. Tz can directly reflect stress states and adequately describe the loss of out-of-plane constraint. The stress state of crack tip is more likely to asymptotic plane-strain condition ahead of crack tip under compression. There are crucial differences in variation range and tendency of Tz subjected to biaxial tensile and biaxial compressive loading. Moreover, Tz is insensitive to λ. Stress triaxiality factor h can illustrate in-plane and out-of-plane constraint effects including size effect and load factor (sensitive to a/W, t/W, β and λ), especially can be adopted as a unified constraint parameter for long cracks under biaxial compressive loading. The in-plane T-stress components can be directly calculated by T11 under biaxial compression. The empirical equations of KII and T11 containing size effect and load factor simultaneously are effective and convenient for applications.

Molecular dynamics simulation of plastic deformation in polyethylene under uniaxial and biaxial tension

Plastic deformation of polyethylene in uniaxial and biaxial loading conditions is studied using molecular dynamics simulation. Effects of tensile strain rates from 1 × 105 to 1 × 109 s−1, and mass density in the range of 0.923–0.926 g/cm3 on mechanical behaviour and microstructure evolution are examined. Two biaxial tensile deformation modes are considered. One is through simultaneous stretching in both the x and y directions and the other sequential stretching, firstly in the x-direction and then in the y-direction while strain in the x-direction remains constant. Tangent modulus and yield stress that are determined using the stress–strain curves from the molecular dynamics simulation show a strong dependence on the deformation mode, strain rate and mass density, and all are in good agreement with results from the experimental testing, including fracture behaviour which is ductile at a low strain rate but brittle at a high strain rate. Furthermore, the study suggests that the stress–strain curves under uniaxial tension and simultaneous biaxial tension at a relatively low strain rate contain four distinguishable regions, for elastic, yield, strain softening and strain hardening, respectively, whereas under sequential biaxial tension, stress increases monotonically with the increase of strain, without noticeable yielding, strain softening or strain hardening behaviour. The molecular dynamics simulation also suggests that an increase in the strain rate enhances the possibility of cavitation. Under simultaneous biaxial tension, with the strain rate increasing from 1 × 106 to 1 × 109 s−1, the molecular dynamics simulation shows that polyethylene failure changes from a local to a global phenomenon, accompanied by a decrease of the void size and increase of uniformity in the void distribution. Under sequential biaxial tension, on the other hand, the density of the cavities is clearly reduced.

Hybrid hierarchical homogenization theory for unidirectional CNTs-coated fuzzy fiber composites undergoing inelastic deformations

A new hybrid homogenization approach is proposed for simulating the homogenized and local response of unidirectional fuzzy fiber nanocomposites undergoing inelastic deformations. Fuzzy fiber composites are hierarchical reinforcing structures where the fibers coated with radially aligned carbon nanotubes (CNTs) are embedded in the matrix. In this spirit, the fuzzy fiber composites are modeled as a three-scale medium. At the microscale, the CNTs-reinforced matrix is homogenized as nanocomposite interphase (NCP) attached to the main fiber via the asymptotic expansion homogenization (AEH). At the mesoscale, an intermediate equivalent fiber that substitutes for the NCP and the main fiber is constructed using the composite cylinder assemblage (CCA) and the transformation field analysis (TFA) techniques. At the macroscale, homogenization of the equivalent fiber and the surrounding matrix is handled by AEH which yields the effective response of the whole fuzzy fiber composites. The new technique facilitates accurate and efficient studies of the inelastic deformation mechanisms of periodic fuzzy fiber arrays with single or multiple inclusions under biaxial and triaxial loading conditions, eliminating exhausting interphase mesh discretizations encountered in the classical full-field homogenization. An added advantage is that the proposed theory captures the fiber-fiber interaction neglected in the classical CCA-TFA, an issue that leads to the exceptionally stiff post-yielding stress-strain response common in the mean-field micromechanics approaches.

Understanding the effect of anisotropy in composite materials on the performance of cruciform specimens

The anisotropic nature of fibre-reinforced composite materials is often not accounted for during the design process of composite cruciform specimens. Here, the response of cruciform specimens depends on both - the layup configuration and the variations in the biaxial loading conditions. This work studies the effect of anisotropy in composite materials on the uniformity of the developed multi-axial stress state in cruciform specimens. For that, a combination of 3D finite element and analytical models are used to analyze the behaviour of 12 different cruciform specimen geometries consisting of different layups and subjected to different biaxial loading conditions. In this study, it is shown how the shape of the gauge zone, the shape of the corners formed by the adjacent arms and the presence of slots in the arms can be used to design cruciform specimens with uniform stress states in the gauge zone, while accounting for the varying anisotropy.

A micromechanics-based model for visco-super-elastic hydrogel-based nanocomposites

This article presents a micromechanics-based model that constitutively relates internal network physics of hydrogel-based nanocomposites with their visco-super-elastic mechanics. The model is based on the Eshelby inclusion theory combined to the concept of cubic material volume to take into account the effective role of inorganic nanoparticles on the finite-strain response of hydrogels. Dynamic bonds between hydrogel chains and nanoparticles allow to describe the impressive time-dependent properties of hydrogel-based nanocomposites such as rate-dependent extreme stretchability, strong hysteresis upon stretching-retraction and room temperature self-healing facility. The model is compared to a few available experimental data of a variety of hydrogel-nanofiller material systems in terms of stress-strain response till failure, hysteresis, continuous relaxation and self-healing. The effects on the hydrogel behavior of loading conditions (strain rate and strain level) and internal network structures (due to variations in reinforcing elements and cross-linker amounts) are examined. The micromechanical model simulations are found in excellent agreement with experimental observations showing the relevance of the proposed approach. The mechanisms of nanofillers reinforcement and failure are discussed with respect to the model. The room temperature self-healing characteristics of hydrogel systems are discussed in connection to loading history and nanostructure. To further illustrate the model capabilities, the behavior of hydrogel systems is finally treated under different biaxial loading conditions.

Strength evaluation of continuous curvilinear variable stiffness panels with circular cutouts under biaxial normal loading and off-design conditions

Continuous curvilinear variable stiffness (CCVS) design is explored to improve strength of panels with cutouts compared to straight-fiber laminates. All possible biaxial loading combinations and several force ratios are investigated. A total of 40 optimization problems (40 loading conditions) are solved using a surrogate-based genetic algorithm. CCVS designs provide at least 50% improvement in failure load for all loading conditions over a quasi-isotropic laminate, the baseline. Under off-design conditions, some CCVS designs outperform the baseline for all loading conditions by an average of 52% and 44%, respectively, for a plate with a small and a large hole.

Determination of theoretical stress concentration factor for circular/elliptical holes with reinforcement using analytical, finite element method and artificial neural network techniques

Machine parts always work under different types of stresses or loading conditions. The sudden dimensional changes lead to sudden increase in stress on the critical section of the machine parts. This state is defined as stress concentration factor (SCF). The strength of the machine part decreases on the located point at maximum stress. In this study, SCFs of circular/elliptical holes with bead reinforcement in an infinite panel under uniaxial and biaxial stresses were modeled, simulated, calculated and verified using analytical, finite element analysis (FEA) and artificial neural networks (ANN) techniques. This study presents a new model for predicting SCF for panels using artificial intelligence techniques under uniaxial and biaxial loading conditions. Theoretical SCF (Kt) values for different shapes and loading conditions have been compiled and graphical forms of these experimental results were published by Peterson (Peterson’s stress concentration factors, 3rd edn. Wiley, Hoboken, 2007). There is a need to convert these curves into a numerical data set to be used in machine part design easily. Theoretical SCF (Kt) was obtained from the Peterson’s charts in numerical form according to dimensional parameter ratios using high-accuracy graphical computer software. Using these dimensional parameter ratios, a parametric finite element model (FEM) was created. Uniaxial and biaxial boundary conditions were applied to the FEM model. Mesh optimization was accomplished to the parametric FEM model. Mesh formation is compatible with the model according to dimensional sizes and ratios. Mesh optimization was provided to element size and per unit volume. Numerical and FEA results were tested, approved and confirmed with Peterson’s original data using statistical methods. A code was created for the improvement of the ANN model in the Matlab ANN Toolbox Editor. Different ANN model variations were tested and the best-performing ANN model was determined among the tried models. Numerical, FEA and ANN model results were compared and confirmed with one another. The developed model provides an easy method to predict and calculate the stress in defining the Kt according to dimensional ratios and applied loading states (uniaxial/biaxial).

A micromechanics-based model for deformation-induced damage and failure in elastomeric media

In order to predict damage and failure in elastomeric media, a new physically-based model based upon a multiscale approach is proposed. The behavior of polymer chains is described by means of statistic mechanics, in which the stretchability and detachability of the internal bonds are introduced to account for the enthalpy contribution to chain elasticity and the time-dependent stochastic process of chain scission, respectively. The complex but inevitable coupling effect between the chain conformation change and the bond length change is addressed in a rigorous approach, and the bond rupture is treated as an energy activation process that is related to the thermal oscillation and stimulated by the chain stretch. The micro-macro transition is realized with a non-affine microsphere-based strategy where the length variability of polymer chains is considered statistically, as well as its evolution with the loading histories. The model is firstly used to discuss some history-dependent features (Mullins effect and monotonic biaxial failure) of rubbers in relation to damage accumulation due to progressive chain scission events. The efficiency of the model is then critically discussed by comparisons with a few illustrative experiments of different rubbery media under high thermal environmental and thermal aging effects. To illustrate further the predictive capability of the model, the failure of rubbers is finally treated under a wide range of biaxial loading conditions.

Mixed-mode crack growth simulation in aviation engine compressor disk

This study focuses on a mixed mode crack growth analysis of an aviation gas turbine engine (GTE) compressor disk based on simulation principles. The operation damages occur via inclined surface cracks in a “dovetail type” disk-and-blade attachment. Based on the sizes and configuration of this attachment, three geometries for simulation models of the GTE compressor disk are proposed. The biaxial loading conditions of the simulation models are determined and numerically verified to reproduce the stress-strain state in critical zones of the compressor disk during operation. To determine the elastic-plastic fracture mechanical parameters, a 3D full-size finite element method (FEM) analysis is conducted for the GTE compressor disk and simulation models, based on operating loading conditions. As a result, the distributions of the new mixed-mode fracture resistance parameters in the form of equivalent elastic and plastic stress intensity factors along the crack front in the disk-and-blade dovetail-type attachment are applied to the experimental uniaxial and biaxial data for crack growth rate interpretation. The possibility of using the proposed simulation principles for an assessment of the structural integrity of GTE rotating disks is discussed.

Experimental study on grain failure of lightweight expanded clay aggregate under uniaxial and biaxial load conditions

This paper presents a fairly comprehensive experimental study on the failure stresses of LECA grains, with diameters ranging from 12 to 20 mm. With that purpose, more than 700 LECA grains were driven to failure under uniaxial and biaxial load conditions by applying forces using a standard PLT apparatus and an additional tool able to exert horizontal forces, specially designed and manufactured for this investigation. The whole equipment allows controlling and measuring the value of the forces applied on two perpendicular axes while the test is running.The results were analyzed by a probabilistic approach using Weibull distributions with the octahedral shear stress as failure criterion. Additionally, the average diameter, sphericity and weight density of all the grains failed were determined to correlate them with their octahedral shear stress at failure.Based on the results, a new model is proposed that allows estimating the failure stress according to a Weibull distribution that depends on grain diameter and weight density.

The effect of residual stress on mixed‐mode crack propagation behaviour in friction stir welded 7075‐T6 aluminium alloy panel under biaxial loading

AbstractThe effect of residual stress on mixed‐mode crack propagation behaviour in friction stir welded (FSW) 7075‐T6 panel under biaxial loading was investigated. Stress intensity factors (KI and KII) were used to study the effects of residual stress on crack behaviours with five different biaxial loading ratios. It was observed that residual stress has a considerable effect on the mixed‐mode crack growth. In most cases, the crack deviation from the initial crack is mainly affected by residual stress at the beginning of crack propagation. The variation of crack path is strongly linked with the residual stress as well as the biaxial loading ratio. In addition, KI and KII are susceptible to residual stress under biaxial loading conditions. Residual stresses contribute to a higher proportion of KII compared with that of KI. KI and KII in the retreating side are more affected by the residual stress.

Failure analysis of boron/glass hybrid laminates under biaxial tension

Designing modern composite structures requires sound understanding about the deformation and failure behavior of the combined materials. Hybridization of glass–epoxy layers into boron-epoxy has the potential to reduce the cost of the structure, nevertheless the failure behavior has not been established especially under biaxial loading condition. Therefore, this paper aims to perform simulation and analyze the failure behavior of boron/glass hybrid composite laminates under biaxial tension. The first stage of the work focused on replicating established experimental work on composite laminates made of boron-epoxy under biaxial tension. Prior to that, mesh convergence analysis and numerical validation has been performed. Finally, finite element simulation was performed to investigate the effect of hybridization of glass–epoxy layers into boron-epoxy under biaxial tension. Three lamination schemes, [0/90]s, [0/±45/90]s and [0/±45]s, where glass–epoxy was added either at the skin or core of the hybrid laminates were modelled and loads constituting the failure of each lamination scheme, were determined. The built-in function for failure analysis and Maximum Stress Theory, available in ANSYS software were employed. Based on the results, it could be observed that there is significant difference between boron laminates and its hybrid laminates failure behavior. Moreover, it is also simulated that the hybrid laminate could withstand more load compared to the original boron-epoxy laminates. Based on these findings, it can be concluded that the current study is useful and has provided significant knowledge about understanding the behavior of boron/glass hybrid composite laminates under biaxial tension.

Dynamic and quasistatic interlaminar shear strength of carbon fiber laminate under bi-axial loading conditions

Cubic shaped specimens with different angles between layer orientation and loading surface were tested quasistatically and dynamically. We found, that shear strength is slightly dependent on the compression load when the angle between layer orientation and load direction is in the range 30-60 degrees and increases 2 times at the angle 750. Material is strain rate sensitive but the behavior of the shear strength is the same at the high strain rates. transversal direction.

Elastic Buckling Response of a Composite Panel Stiffened Around Cutouts

Perforated composite panels are widely used in many engineering applications as subcomponents of complex structures including aircraft, ships, and other transport vehicles. In many of these applications, the primary objective of using the panel is to resist buckling. In this present study, a finite element analysis is performed adopting popular commercial software code Ansys on the buckling behavior of a simply supported quasi-isotropic symmetric composite panel with central circular cutouts, reinforced with stiffeners on both sides of the cutouts under uniaxial, biaxial and combined loading conditions. The main objective is to achieve the elastic buckling response of the perforated composite panels considering some important aspects of the stiffener as follows: (1) effect of the presence of reinforcement, (2) effect of stiffener area, (3) effect of stiffener thickness, (4) effect of stiffener material and (5) effect of fiber orientation angle. It is observed that reinforcement can significantly improve the critical buckling load of a panel, which is already reduced due to cutouts. Then, increasing the area of the stiffener does not have a major impact on the buckling stability of the panels. However, increasing the thickness can play a crucial role to strengthen the buckling stability. Finally, it is found that in comparison to aluminum and titanium alloys, epoxy-carbon is more practical as a stiffener material with correct fiber orientation angle (90°), considering the low weight increment and higher buckling achievability.

Mechanical properties of warp-knitted metal mesh fabric under biaxial tension loading

In this study, warp-knitted metal mesh fabric was used as the research object, and its mechanical loading behavior under uniaxial and biaxial stress loading states was studied. The relationship and connection between the effective elastic modulus of its anisotropic structure was studied with different loading angles of stress as variables. The results showed that there were differences in the mechanical properties and effective elastic modulus under these loading angles, and there was a linear relationship between the effective elastic modulus of the metal mesh with the same warp-knitted structure under different directions of stress, which will provide a theoretical basis for broadening its application in the field of anchor spray support, flexible wearable electronic devices, satellite antennas, water filter walls and other applications.

Buckling analysis of functionally graded materials by dynamic approach

Laminated composites exhibit difference in the mechanical properties at the interface between two materials resulting in stress concentration. This may lead to damages in the form of delamination, matrix cracking and adhesive bond separation. Functionally Graded Materials (FGM) are formed by gradual variation of two or more material over a particular volume, thereby overcomes these issues. Buckling problems of FGM plates are usually solved by static approach. In some cases, particularly non-uniform loading and geometric discontinuity, the stress concentration usually occurs. In such cases, the solution to the buckling problem by dynamic approach is most suitable. In the dynamic approach, the natural frequencies are calculated by applying in-plane loads. As the intensity of the in-plane load increases, the frequency of the material decreases and finally becomes zero at the onset of buckling. The load at which the natural frequency becomes zero that load is called a buckling load. In this investigation, the vibration and buckling characteristics of FGM panels subjected to uniaxial and biaxial loading conditions have been studied by using the finite element method (F.E.M). In the Finite element (FE) formulation, the effective material properties of FGM plates are assumed to vary in the thickness direction according to the power-law distribution of volume fraction of the constituents. The plate is modelled by using 8-noded serendipity element by incorporating the effect of transverse shear deformation and rotary inertia. The effect of different parameters such as volume fraction index (n), the thickness of the panel (h) and boundary condition of the plate are considered to study the buckling behaviour of the FGM plate under uniaxial loading conditions.

Experimental and FEA analysis of high-performance concrete column under biaxial loading

In this work, the analysis of the long column loaded biaxially using high performance concrete is carried out. Total four numbers of high performance concrete columns are casted and then tested with biaxial load using loading frame. The compressive strength of the concrete used in columns is from 60 MPa and 80 MPa. After successfully casting of long columns using high performance concrete with 60 MPa and 80 MPa is cured for 28 days. For HPC, the average compressive strength achieved is 67 MPa and 86 MPa for 60 MPa and 80 MPa grades respectively. Biaxially loaded HPC columns at eccentricity of 10% and 20% for 60 Mpa and 80 Mpa grade is studied. The applied loads are in the range of 800 kN to 950 kN to assess the deflection of HPC long columns at different eccentricities. The experimental and FEA analysis was carried out to assess the performance of columns. From experimental and FEA analysis, it was seen that as eccentricity increases the deflection of HPC columns increases. The maximum deflection observed for 80 MPa grade HPC long column with 20% eccentricity. It was seen that, deflections observed for biaxial loading conditions for these fabricated columns are in allowable limits. It was also observed that, load carrying capacity developed in 60 MPa and 80 MPa grade HPC long column is greater than value given in codes.

The Effects of Nonproportional Biaxial Loading Paths on Ductile Fracture Initiation: A Void Growth Analysis

Abstract The effects of nonproportional biaxial loading paths on ductile fracture initiation toughness are studied in this article. To this end, the growth of a cylindrical void (hole) located in front of a mode I plane strain crack has been studied using large-deformation finite element analysis. A specific microstructural feature of a steel alloy was thoroughly studied by having a single void positioned at a fixed distance from the crack tip and void that was equal to 10 times the diameter of the void. In particular, the nonproportional biaxial loading path effects on the crack tip blunting, void growth, ligament reduction, and near-tip stress fields are investigated computationally. Under small-scale yielding conditions, one proportional loading and two nonproportional loading paths are applied to the modified boundary layer models, covering both low-constraint (negative T-stress) and high-constraint (positive T-stress) crack tip conditions. We have observed that the nonproportional load paths have a marked effect on the void growth, crack tip blunting, and the resulting ligament reduction. By applying the simple criteria for the coalescence of the crack tip and void, the ductile fracture initiation toughness is estimated. It is shown that the ductile fracture toughness is dependent on loading paths and constraint conditions (the T-stress ratios). Compared with the proportional biaxial loading case, different load sequences of the biaxial loads will result in either an increase or a decrease the fracture initiation toughness. This effect is particularly significant for specimen geometry with low-constraint conditions (i.e., negative T-stress ratios). Results from this study are of relevance to ductile fracture assessment of components or structures, such as pressure vessels that operate under nonproportional biaxial loading conditions.

On the fracture characteristics of advanced high strength steels during hydraulic bulge test

The advanced high strength steels (AHSS) are well recognized for their high-strength-to-weight ratio combined with good shock absorption properties. Moreover, these steels are also known for their complex forming and fracture characteristics. This study is aimed at investigating the fracture behavior of AHSS sheets under the influence of an equal-biaxial state of stress. The work was conducted on two important AHSS sheets – (i) DP980 and (ii) TRIP1180. A hydraulic bulge test was performed to cause the fracture under biaxial loading condition. The strains near the pole of the bulge specimens were measured using the digital image correlation technique. A detailed micro- and macro-scale characterization was performed to examine the fracture aspects of both sheets. The results clearly indicated the occurrence of shear localization during fracture. Moreover, the likely sources of micro-crack initiation were also revealed. Apart from fracture characterization, a comprehensive finite element study was done using appropriate constitutive equations. Finally, a simple fracture criterion was applied to predict the onset of fracture for both steels.