Biaxial Loading Conditions Research Articles

Crack path and fracture surface analysis of ultrasonic fatigue testing under multiaxial loadings

Ultrasonic fatigue testing machines and related research are continuously growing. They allow researchers to study fatigue in a time and energy reliable manner, fatigue strength and fracture mechanics between 10E06 to 10E10 cycles, the established Very High Cycle Fatigue (VHCF) regime. Almost all published research to date was conducted under uniaxial tension–compression, pure torsion or bending loading under ultrasonic fatigue testing. The interest in multiaxial ultrasonic testing for VHCF has begun to evolve from the increasing available knowledge surrounding uniaxial fatigue in VHCF. Tension-Torsion and in-plane biaxial ultrasonic fatigue tests were first reached by adapting the tension–compression ultrasonic setup. The present work focuses on the crack path, critical initiation angle, fracture surface analysis and evaluation of different specimens, that failed under different biaxial loading conditions under ultrasonic fatigue. Specimens were specially designed and machined to function under ultrasonic fatigue machines resonance concept. Three different biaxial loading paths were carried out, in-phase tension–torsion and tension–tension, and out-of-phase tension–compression. Crack initiation, crack path and crack surface morphologies were analyzed by optic microscope and scanning electron microscope. Experimental results were analyzed and discussed; conclusions concerning these types of failures under ultrasonic testing regime are drawn.

Effect of biochemical attack on the mechanical performance of used concrete sewer pipes

The structural response and failure mechanisms of 35 used concrete sewer pipes are investigated by means of a combined experimental–numerical approach, whereby specific attention focuses on determining the effect by biochemical attack. Accordingly, the degree of degradation of the inner and outer surfaces of the pipes is carefully analysed by visual inspection, and subsequently categorized in 6 different surface condition classes. The type and degree of biochemical attack are determined by respectively performing X-ray diffraction analyses and phenolphthalein tests. The sewer pipes, which vary in age, size and geometry, are subjected to biaxial loading conditions in a full-scale test set-up. The experiments show that the material degradation of relatively old sewer pipes can be considerable, and for a large part may be attributed to the process of biogenic sulphide corrosion. This process typically induces a weak, corroded layer at the inside of the pipe, which is characterized by the appearance of exposed granulates and porous mortar between the granulates. The experimental failure responses of the used sewer pipes are compared against numerical results obtained from detailed Finite Element Method (FEM) simulations. The failure response of each sewer pipe type is well predicted by the FEM model if the negligible mechanical properties of the biogenic sulphide corrosion layer at the inside of the pipe are accounted for in the simulations. The relatively low concrete tensile strength of old sewer pipes and the reduced effective wall thickness due to biogenic sulphide corrosion cause that the ultimate bearing strength and structural stiffness of these pipes may be more than a factor of two lower than those of completely new sewer pipes. The results of the present work provide a scientific basis for the decision-making process on sewer rehabilitation and replacement, in particular by revealing and quantifying the influence on the structural bearing strength by biogenic sulphide corrosion. • Structural response and failure mechanisms of 35 used concrete sewer pipes are investigated via a combined experimental–numerical approach. • Effect of biochemical attack on bearing strength is quantified. • Mechanical collapse of sewer pipes is characterized by the development of 4 failure cracks. • Results provide a scientific basis for decision-making process on sewer rehabilitation and replacement.

Multiaxial Damage Ratio Strength Criteria for Fiber-Reinforced Concrete

Based on the damage ratio strength theory, a dimensionless damage ratio strength criterion for fiber-reinforced concrete (FRC) under true triaxial stress states was established under the assumption of small strains. Based on the experimental data of steel fiber–reinforced concrete (SFRC), polypropylene fiber–reinforced concrete (PFRC), hybrid fiber–reinforced concrete (HFRC), and steel fiber–reinforced high-performance lightweight concrete (SFRHLC), parameters for the damage ratio criterion were recommended. The damage ratio values were verified by SFRC experimental results under uniaxial, biaxial, and triaxial loading conditions, and the damage ratio values of SFRC under uniaxial tension, uniaxial compression, and biaxial equal compression stress conditions were compared with those of plain concrete. The true triaxial damage ratio strength criterion can be reduced to the conventional triaxial criterion and biaxial criterion, and the corresponding simplified strength criteria were proposed. The proposed dimensionless six-parameter criterion agrees well with the experimental results of the aforementioned materials for true triaxial, conventional triaxial, and biaxial loading conditions. Compared with the strength criteria in other studies, the proposed criterion can accurately represent the strength characteristics of FRC.

Improvement of scarf repair patch shape for composite aircraft structures

ABSTRACT Scarf patching is the preferred technique for repairing physically damaged aircraft composite structures. The commonly used patch design is a circular conical frustum with a 3°optimized scarf angle. However, for this repair patch design the volume of material removed from the repaired composite panel can be quite large. This paper examines the effects of the different parameters on the stress state in the patch adhesive, such as ply orientation, stacking sequence, ply thickness and scarf angle. It explores an adaptive design of the repair patch for orthotropic materials and composite laminates, using 3D Finite Element Analysis. The design optimization approach is based on the evaluation of a Failure Criterion Index (FCI) and the minimization of its Relative Standard Deviation (RSD). An optimized scarf shape, which takes into account biaxial tensile loading conditions, fiber direction, and stacking sequence, is an elliptical conical frustum that induces a variable scarf angle along the sweeping angle. This design showed that less parent material is removed than that of the circular shape (decreased by up to 41%) and that the shear stress dispersion in the adhesive was significantly reduced (RSD decreased by up to 18%). The optimization method and the improved shapes are presented and discussed with respect to the influencing parameters.

Damage ratio strength criterion for cast iron

According to the assumption of small strains and total strain decomposition of cast iron, the expressions of the inelastic principal strain rate and relative energy dissipation rate of cast iron are derived, and the parameters of the tensile and compressive damage ratio of cast iron in the inelastic phase are proposed. Based on the least energy consumption principle, combined with the above expressions and parameters, the damage ratio strength criterion for cast iron under biaxial stress states is established. The damage ratio variable expression of the cast iron damage ratio strength criterion considering the effect of Lode angle is proposed. Furthermore, the values of the damage ratio variable are verified by the experimental stress–strain curves of cast iron under uniaxial stress states. By comparing the predicted values to 104 experimental data points of cast iron specimens, the failure envelopes of the proposed criterion can represent the failure behavior of cast iron under biaxial loading conditions. To facilitate the practical application in engineering, the further simplified expression of the four-parameter damage ratio strength criterion for cast iron under biaxial stress states is suggested and those empirical parameters are recommended. Compared with some main strength criteria, the simplified criterion is in better agreement with the experimental results under every stress state.

Mechanical responses of L450 steel under biaxial loading in the presence of the stress discontinuity

The Lüders plateau behaviour is a phenomenon of stress discontinuity associated with strain localisation which can affect the fracture behaviour of mild steel subjected to plastic strains. Together with experimental studies of biaxial loading tests with digital image correlation (DIC), this work considers the effect of stress discontinuity on the mechanical behaviour of L450 steel subjected to biaxial loading, using the so-called “up-down-up” (UDU) constitutive model in finite element analyses (FEA) of cruciform specimens. The softening modulus of the UDU model and the stress ratio were found to significantly affect the simulated evolution of the Lüders band. A method has been proposed to use appropriate UDU parameters which capture the characters of the Lüders bands in biaxial loading conditions. Based on the selected parameters, the formation of the Lüders bands illustrated in the stress distribution and the Lüders plateau in the force-displacement were studied over the full range of the loading ratio under biaxial loading conditions.

A DFT investigation on the mechanical and structural properties of halogen- and metal-adsorbed silicene nanosheets

Herein, the effects of halogen and metal atomic adsorption on the mechanical and structural characteristics of silicene are studied using density functional theory (DFT) calculations. Cl, Br, Au, Ca, Ga, Li, and Na atoms are selected as the adsorption atoms. Moreover, the phonon dispersion and electron localization function are investigated to show the stability of considered nanostructures and to visualize the bonding properties, respectively. It is shown that the adsorption leads to decreasing the elastic and bulk moduli of some structures, while it increases them in some other structures. It is seen that except for Ca-adsorbed nanosheet, both the elastic and bulk moduli of all other structures decrease after adsorption. Furthermore, the isotropic behavior of all the studied nanosheets is indicated. The plastic behavior is also analyzed. It is revealed that the second critical strain of all nanosheets, except for SiBr and SiCl, decreases under uniaxial loading. However, under biaxial loading conditions, the second critical strain of Au-, Ca-, and Ga-adsorbed structures decreases, while in other structures (SiBr, SiCl, SiLi, and SiNa) the adsorption increases the yield strain.

Responses of Pre-Holed Granite under Coupled Biaxial Loading and Unloading Stress Condition

Underground excavation is a necessary process for constructing mines, tunnels and depots in granite rock mass. In this study, the numerical granite specimens were established by the discrete element method and confirmed by laboratory experiments in order to investigate the peak stress, cracking development and failure properties of pre-holed granite under coupled biaxial loading and unloading conditions. The results show that, for the specimens containing D-type and square holes, the peak biaxial unloading strengths first decrease, then increase and finally decrease as the inclination angles of the holes increase. For the specimens with elliptical holes, the peak biaxial unloading strengths first decrease and then increase with the increases in the inclination angles of the holes. The biaxial unloading strengths of specimens containing elliptical, circular, D-type and square holes decrease in that order. The cracks initially appear near the crossover points between the X-type shear fracturing plane and the pre-hole in the center and gradually expand along the X-type shear direction, which indicates that the failure of pre-holed granite is primarily shear failure. When the overall length of cracks expanding along the X-type shear direction extends to the size of the pre-hole in the center, the failure of the pre-holed specimen occurs. When the existing pre-hole in the center of the granite specimen extends to connect with the shear slip in the vicinity of the hole, this triggers overall failure.

Fatigue Crack Growth Behavior of CP-Ti Cruciform Specimens with Mixed Mode I-II Crack under Biaxial Loading.

Investigations on the fatigue crack growth of commercial pure titanium are carried out with cruciform specimens under different biaxial load ratios (λ = 0, 0.5, and 1) and crack inclination angles (β = 90°, 60°, and 45°) in this paper. Based on the finite element results, the modified solution of stress intensity factors KI and KII for cruciform specimens containing mixed mode I-II crack is obtained by considering crack size, biaxial load ratio, and crack inclination angles. The experimental results show that the maximum tangential stress criterion is fit for the prediction of crack initiation angles for mixed model I-II crack under uniaxial or biaxial loading condition. When the biaxial load ratio increases, the crack propagation angle becomes smaller, and so does the fatigue crack growth rate of mode I crack or mixed mode I-II crack. Based on an equivalent stress intensity factor, a new valid stress intensity factor is proposed to better describe the biaxial fatigue crack growth behavior, which can demonstrate the contribution of mode I and mode II of stress intensity factor.

Inverse identification of large strain plasticity using the hydraulic bulge-test and full-field measurements

The hydraulic bulge test (HBT) is an important experimental technique to identify the properties of materials and, in particular, metals. One of the main advantages of such technique, in testing metals, is the possibility of reaching high levels of deformation before fracture. Moreover it allows the investigation of a biaxial loading condition. A hemispherical test can be performed using mechanical punches or the hydraulic pressure of a fluid. When hydraulic pressure is used, the test is not affected by friction. The hydraulic bulge test (HBT) is therefore a very efficient method to evaluate the properties of metals at large strains. Usually, the outcome of the HBT is the hardening curve in the equi-biaxial stress state that occurs at the top of the dome, during the expansion. In this paper a different approach is proposed, where the full-field displacement field obtained with stereo-DIC is used in an inverse identification scheme. The finite strain theory is used to map the stress and strain in the reference configuration so that the problem can be reduced to a 2D plane stress case. The method was first validated using a numerical model of the HBT and then applied on a real test performed on a BH340 steel.

Adaptive affine homogenization method for Visco-hyperelastic composites with imperfect interface

Despite intense research on homogenization methods, it is a still challenging task to predict the nonlinear mechanical responses of visco-hyperelastic particle-reinforced composites. In this work, we propose an adaptive affine method, a novel mean-field homogenization method designed to ensure the consistency of the accumulated strain state and the concentration tensor, and apply the method to predict the mechanical responses of the composites in the large strain regime under uniaxial, cyclic, and biaxial loading conditions. Our method is also extended to predict the mechanical response in the presence of interfacial imperfections described by linear cohesive traction-separation laws. The analytic predictions are validated against finite element analyses of representative volume elements. We believe that our adaptive affine method can be extended to model various nonlinear responses of load-bearing composites including the effects of (visco)plasticity and finite deformation.

Static and fatigue behavior of a carbon‐fiber SMC‐R composite under combined tensile and shear stresses

AbstractRandomly oriented short fiber reinforced sheet molding compound composites (SMC‐R) are among the most commonly used composites for automotive and many non‐automotive structural applications. Many studies have reported the static and fatigue properties of SMC‐R composites under uniaxial stress conditions. However, there are many applications in which they may be subjected to biaxial stress conditions and their biaxial properties have not been reported in literature. The current study considers the static and fatigue characteristics of a randomly oriented carbon fiber SMC‐R under both uniaxial and biaxial loading conditions with various combinations of tensile and shear stresses. A butterfly shaped Arcan specimen was used to conduct the biaxial stress tests. Since both static strength and fatigue life data exhibited significant variability, statistical analysis was conducted using Weibull distribution to analyse the variations in these properties of the material. In biaxial conditions in which a shear stress is imposed along with a tensile stress, the tensile strength of the material decreases with increasing shear stress. A failure envelope drawn based on von Mises equation shows reasonable agreement with the experimental results. As a percentage of the static strength, the fatigue strengths at 1 million cycles in tension and combined equal tension and shear are significantly higher than the fatigue strength in pure shear.

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.

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.

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.

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.

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.

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.

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.

Evaluation of Hoffman and Xia plasticity models against bi-axial tension experiments of planar fiber network materials

The anisotropic properties and pressure sensitivity are intrinsic features of the constitutive response of fiber network materials. Although advanced models have been developed to simulate the complex response of fibrous materials, the lack of comparative studies may lead to a dubiety regarding the selection of a suitable method. In this study, the pressure-sensitive Hoffman yield criterion and the Xia model are implemented for the plane stress case to simulate the mechanical response under a bi-axial loading state. The performance of both models is experimentally assessed by comparison to bi-axial tests on cruciform-shaped specimens loaded in different directions with respect to the material principal directions. The comparison with the experimentally measured forces shows the ability of the Hoffman model as well as the Xia model with shape parameter k≤2 to adequately predict the material response. However, this study demonstrates that the Xia model consistently presents a stiffer bi-axial response when k≥3 compared to the Hoffman model. This result highlights the importance of calibrating the shape parameter k for the Xia model using a bi-axial test, which can be a cumbersome task. Also, for the same tension-compression response, the Hill criterion as a special case of the Hoffman model presents a good ability to simulate the mechanical response of the material for bi-axial conditions. Furthermore, in terms of stability criteria, the Xia model is unconditionally convex while the convexity of the Hoffman model is a function of the orthotropic plastic matrix. This study not only assesses the prediction capabilities of the two models, but also gives an insight into the selection of an appropriate constitutive model for material characterization and simulation of fibrous materials. The UMAT implementations of both models which are not available in commercial software and the calibration tool of the Xia model are shared with open-source along with this work.