Biaxial Loading Research Articles

Mechanical Behaviour of 7075-T6 Aluminium Alloy: Integrating Digital Image Correlation and Finite Element Analysis for Uniaxial and Biaxial Load Scenarios

The objective of this study is to investigate the mechanical properties of 7075-T6 Aluminium (Al) alloy under both uniaxial and biaxial loads. The study will be conducted using a combination of experimental and numerical methods. The experimental method used is the digital image correlation (DIC) technique, which was utilized to capture the deformation and strain fields of the material specimen under tensile test. A tensile machine was employed to apply uniaxial and biaxial loads on the sample. The strain and deformation distribution of the results was generated on the DIC and correlated software. The numerical method involved the use of a commercial finite element software to create a finite element model and simulate the mechanical behaviour of the material under the same loading conditions. The results obtained from the experimental and numerical methods were compared to validate the accuracy of the numerical model. The outcomes demonstrated that under uniaxial loading, localized necking and fracture were observed, while biaxial loading resulted in shear deformation and fracture. This research contributes to the development of more accurate models for predicting the mechanical behaviour of the model samples under different loading conditions.

Asymmetric deformation and failure behavior of roadway subjected to different principal stress based on biaxial tests

The magnitude and direction of stress will affect the failure of roadway. The impact of stress magnitude and direction on roadway failure was investigated using a rock failure system equipped with true triaxial loading, acoustic emission (AE), and digital image correlation (DIC) technologies. The system allowed for the simulation of rock sample failures under various three-dimensional stress conditions, while real-time monitoring was conducted using a high-precision microseismic system. By prefabricating rectangular holes at different angles in sandstone specimens, roadways under different stress effects in engineering can be simulated. Biaxial loading tests were then performed on these prefabricated sandstone cube specimens to observe external fracture characteristics and internal fracture information using acoustic emission equipment. The peak strength of samples with holes is approximately 38–56% of that of intact samples. In the early and middle loading stages, the strain on the surface is on the order of 10-3. In the later loading stage, the strain on the surface is on the order of 10-2. The findings indicate that roadway failure primarily involves local particle ejection, fragment spalling, large-scale particle ejection, plate crack buckling, and eventual failure. The ultimate failure mode varies based on stress deflection angles: with no included angle, the roadway exhibits a ’V’ shaped failure zone on both sides, predominantly experiencing tensile failure. At included angles of 30°, 45°, and 60° between stress and roadway axis, the roadway displays a “—” failure pattern along the diagonal, characterized by a combination of tension and shear failure. The extension angle of the“—” failure zone varies depending on the stress deflection angle. At a 90° included angle, the roadway shows a ’V’ shaped failure in the roof and floor, primarily undergoing tensile failure. Real-time monitoring of the strain field evolution around the roadway during failure using DIC method revealed valuable insights. AE events at different deflection angles reflect the progression of micro cracks in the specimen, showing a strong correlation with macro failure. The research outcomes elucidate the mechanisms behind various forms of roadway failure induced by stress deflection and shed light on the failure mechanism at different stress deflection angles.

Failure criterion and compressive constitutive model of seawater concrete incorporating coral aggregate subjected to biaxial loading

Failure criterion and compressive constitutive model of seawater concrete incorporating coral aggregate subjected to biaxial loading

Effects of transverse loading on the ultimate strength prediction of stiffened panels under biaxial loads: Potential improvements to the IACS rule formulation

The current International Association of Classification Societies (IACS) rule for designing stiffened panels was found in Wang et al. (2024) to conservatively predict the ultimate strength of panels when transverse loads predominate. This conservatism arises from the overestimation of bending moments acting on stiffeners by directly applying the beam analogy in both longitudinal and transverse directions in the rule formulation when evaluating stiffener yielding.To address this issue, this paper applies the orthotropic plate theory to calculate bending moments experienced by the stiffeners of panels under biaxial loads. Orthotropic properties are derived from equivalent sectional areas and moments of inertia. The predicted bending moments are validated through comparisons with numerical simulations. The effects of boundary conditions and deflection patterns with varying numbers of half-waves are discussed. Based on the analytical results, a modification of the IACS rule formulation is proposed by introducing a correction factor to account for transverse loading effects in the bending moment calculations. The factor is a function of the ratio between longitudinal and transverse loading.The modified IACS rule formulation is verified through numerical simulations of aluminium panels using ABAQUS and comparisons with results from existing literature on steel stiffened panels under various biaxial loading conditions. The modified rule formulation shows improved accuracy in predicting the ultimate strength of stiffened panels, particularly in cases with dominating transverse loads. The modified IACS rule formulation can be useful for more reliable and cost-effective design of ships and offshore structures.

Numerical analysis of failure mechanics of concrete under true dynamic triaxial loading using a four-phase meso-model

In the present paper, the failure mechanics of concrete under true triaxial dynamic loading is investigated. A four-phase concrete meso-model is developed. The meso-model consists of aggregate, mortar, interfacial transition zone (ITZ) and macropores. A finite element (FE) model of a split Hopkinson pressure bar is also created to apply true triaxial dynamic loading. The development of cracks in concrete is presented for the uniaxial, biaxial and triaxial loading cases. The presence of local discontinuity is modelled, and its effect on the failure of concrete is extensively investigated and discussed. In the last, the effect of aggregate distribution is also analysed. It is found that the internal structure of concrete changes the stress distribution from true triaxial to compression or extension triaxial, which is the prime cause of internal cracking.

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.

Small fatigue crack behavior of CP-Ti in thin-walled cruciform specimens under biaxial loading

This study investigates the small fatigue crack propagation behavior of commercially pure titanium (CP-Ti) using thin-walled cruciform specimens under in-plane biaxial loading, considering the effects of biaxial ratio and phase angle. Increasing phase angle results in more secondary cracks merging with main cracks perpendicular to the rolling direction (RD) and transverse direction (TD), a phenomenon attributed to the rise in shear stress that accelerates main crack growth. Higher loading biaxiality or a lower phase angle leads to decreased crack propagation rates and increased biaxial fatigue life. Electron backscatter diffraction (EBSD) analysis reveals that when the maximum normal stress aligns with the RD, prismatic slip primarily governs crack propagation, thereby accelerating crack propagation rates. Conversely, alignment with the TD reduces prismatic slip activity and crack propagation rates. Under equi-biaxial loading, prismatic slip activity decreases further, and crack propagation is dominated by multiple slip and twinning, consequently resulting in the slowest propagation rates. Additionally, a higher proportion of prismatic slip under high phase angle also accelerates crack propagation. Finally, incorporating Findley equivalent stress into the Chapetti model, which considers the crack length-dependent threshold effect, a highly accurate biaxial small fatigue crack propagation rate model is proposed.

Statistical Modeling and Probable Calculation of the Strength of Materials with Random Distribution of Surface Defects

Based on the solutions of deterministic fracture mechanics and the methods of probability theory, the algorithm for calculating the probabilistic strength characteristics of plate elements of structures with an arbitrary stochastic distribution of surface defects is outlined. On the plate surface, there are uniformly distributed cracks that do not interact with each other, the plane of which is normal to the surface, and the depth is much less than its length on the surface. The cracks’ depth and angle of orientation are random values, and their joint distribution density is specified. Plates made of this material are under the influence of biaxial loading. The probability of failure, along with the mean value, the dispersion, and the variation coefficient of the plate’s strength, taking into account the surface defects under different types of stress, were determined. Their dependence on the type of loading, the size of the plate, and the surface structural heterogeneity of the material were studied graphically. Joint consideration of the influence of the interrelated properties of real materials, such as defectiveness and stochasticity, on strength and fracture, opens up new opportunities in creating a theory of strength and fracture of deformable solids.

Smeared fixed crack model for quasi-static and dynamic biaxial flexural response analysis of aluminosilicate glass plates

Glass materials are extensively used in load-bearing structures and impact-resistant components because of their distinctive physical and chemical properties. Accurate predictions and assessment of the mechanical responses of glass structures are crucial for structural design and reliability analysis. In this study, quasi-static and dynamic ball-on-ring (BOR) biaxial flexural tests are conducted on aluminosilicate glass. The smeared fixed crack model is calibrated for deformation and failure analyses. First, the model parameters are calibrated carefully, particularly for different failure criteria. Both the deformation field and fracture modes agree well with the experimental observations during the quasi-static tests. For the low-velocity impact biaxial flexural loading condition, three different numerical techniques, namely the initial scaling tensile strength criterion, non-local approach with energy criterion, and rate-dependent failure stress criterion, are implemented in the numerical models for dynamic failure analysis. Finally, the proposed smeared fixed crack model is compared with the widely used Johnson Holmquist Ⅱ (JH-2) model and demonstrates advantages for low-velocity impact response analysis of glass structures.

Stochastic fracture analysis of orthotropic cracked plate using extended isogeometric analysis (XIGA) subjected to uniaxial & biaxial mechanical loading

Stochastic fracture analysis of orthotropic cracked plate using extended isogeometric analysis (XIGA) subjected to uniaxial & biaxial mechanical loading

النموذج الرياضي المقارب لدراسة سلوك انبعاج صفيحة فولاذية

A mathematical study was conducted to investigate the buckling of isotropic steel plates using instability theories. The First-Order Shear Deformation Theory (FSDT) and Higher-Order Shear Deformation Theory (HSDT) were employed to account for shear effects. These latter theories were adopted because they consider shear deformation with high precision, unlike classical theories that neglect this important action. The equilibrium equations, derived from Hamilton's principle, were used, and Navier-type solutions were preferred to calculate buckling loads under uniaxial or biaxial loading. Parametric variations and different buckling modes were investigated, and the results showed excellent agreement with existing references. The main objective of this study in civil engineering is to continuously find mathematical formulations to solve plate buckling problems with extreme accuracy and to predict buckling behavior in simulations, mimicking what happens to metallic structures. Keywords: Plate Buckling-Elastic Instability-Isotropic Metal Plate-First-Order Shear Deformation Theory (FSDT)-Higher-Order Shear Deformation Theory (HSDT).

Dynamic Strength and Fragmentation of Highly Oriented Ti3SiC2 under Multiaxial Compression

MAX phases are distinguished by their unique kink band formation, a distinct deformation mechanism in layered materials. This study explores the influence of global grain orientation c-axis, strain rate, and stress state on the compressive response of highly oriented Ti3SiC2 through experimental methods. A Kolsky (or split-Hopkinson) bar is employed to evaluate the dynamic compressive response under uniaxial and biaxial (planar confinement) conditions under 102s-1 strain rate. Macroscopic ultra-high-speed visualization during loading and microscopic post-mortem fractography reveal that confinement states significantly impact both macroscopic failure patterns and microscopic fracture mechanisms. Notably, biaxial loading with dynamic load edge-on to the grains and 80MPa planar confinement along the layers resulted in the highest dynamic compressive strength observed (1636±136MPa), a 66% increase compared to the unconfined uniaxial dynamic condition. The planar confinement appears to delay crack propagation and enhance inelastic deformation.

Experimental and numerical investigation on rock fracturing and fragmentation under coupled static pressure and blasting

The blasting technique is widely adopted to break rock in civil and mining engineering, and its operation is generally subjected to static pressure due to tectonic and gravitational stresses. In the present study, the rock fracturing and fragmentation under coupled static pressure (uniaxial pressure and confining pressure) and blasting are experimentally and numerically investigated. First, 11 blast tests with 100-mm cubic red sandstone samples are carried out based on a biaxial loading system. Then, the blast-produced rock fragmentation in blast testing is numerically modeled using finite element method with LS-DYNA, and the explosion pressure attenuation and fracture evolution in rock samples are numerically reproduced. The simulated rock fragmentation data are obtained by image processing in ImageJ, and the fragment size distribution of red sandstone under combined static stress and blasting is characterized using Weibull distribution. Accordingly, the effects of uniaxial pressure and confining pressure on blast-created rock fragmentation are quantitatively compared and analyzed, and the corresponding mechanisms are discussed and revealed. The current findings indicate that the static pressure plays a role in increasing blast-induced compressive stress and reducing tensile stress in both radial and hoop directions and thus results in a decrease in the length and number of fractures propagating vertically to the direction of applied pressure, further leading to the creation of coarser fragmentation. Blasting under confining pressure produces larger fragments than that under uniaxial pressure. The average fragment size increases quickly at first and then increases slowly with the increase of static stress, which can be well characterized using a logarithm equation. Based on current findings, increasing the free surface is crucial in practical blasting to improve rock fragmentation performance under blasting.

Capturing sclera anisotropy using direct collagen fiber models. Linking microstructure to macroscopic mechanical properties.

Because of the crucial role of collagen fibers on soft tissue mechanics, there is great interest in techniques to incorporate them in computational models. Recently we introduced a direct fiber modeling approach for sclera based on representing the long-interwoven fibers. Our method differs from the conventional continuum approach to modeling sclera that homogenizes the fibers and describes them as statistical distributions for each element. At large scale our method captured gross collagen fiber bundle architecture from histology and experimental intraocular pressure-induced deformations. At small scale, a direct fiber model of a sclera sample reproduced equi-biaxial experimental behavior from the literature. In this study our goal was a much more challenging task for the direct fiber modeling: to capture specimen-specific 3D fiber architecture and anisotropic mechanics of four sclera samples tested under equibiaxial and four non-equibiaxial loadings. Samples of sclera from three eyes were isolated and tested in five biaxial loadings following an approach previously reported. Using microstructural architecture from polarized light microscopy we then created specimen-specific direct fiber models. Model fiber orientations agreed well with the histological information (adjusted R2's>0.89). Through an inverse-fitting process we determined model characteristics, including specimen-specific fiber mechanical properties to match equibiaxial loading. Interestingly, the equibiaxial properties also reproduced all the non-equibiaxial behaviors. These results indicate that the direct fiber modeling method naturally accounted for tissue anisotropy within its fiber structure. Direct fiber modeling is therefore a promising approach to understand how macroscopic behavior arises from microstructure.

In-plane biaxial fatigue life prediction model for high-cycle fatigue under synchronous sinusoidal loading

The unique advantage of in-plane biaxial loading is no rotation of the maximum principal stress during cyclic loading, which has a distinct effect on fatigue life. This study aims to propose a life prediction model for in-plane biaxial fatigue encompassing both in-phase and out-of-phase conditions. For synchronous sinusoidal loadings, an equivalent stress expression is derived using the integral method, accounting for the influences of shear and normal stresses across all planes. The equivalent stress is then compared to a reversed uniaxial constant amplitude loading to predict fatigue life. To validate and compare the model, in-phase and out-of-phase in-plane biaxial fatigue experiments were conducted using 24 nickel-based superalloy cruciform specimens at temperatures of 420℃, 550℃, and 600℃. The results show that the proposed model is superior to conventional stress-invariant based models, with most results staying within the ± 2 error bands. Using the proposed model, the effects of mean tensile stress, biaxiality and phase shift are discussed. Additionally, a novel non-proportional factor is introduced to enhance multiaxial fatigue life prediction by distinctly separating the effects of principal stress and its directional variations.

A new approach on constitutive modeling for quasi-brittle materials under multiaxial loading

Abstract This work introduces a new method for expanding unidimensional models to predict material behavior under multiaxial loading. The concept of six-dimensional mechanical space is adopted, and in each basis direction of the space, there is one fiber-bundle model (FBM), so these six FBMs are independent amongst one another but follow the same damage evolution rule. Under triaxial loading, these FBMs have different stress and strain states, so six corresponding damage variables have different values. The anisotropic damage is thus represented by the six damage variables. When it is under uniaxial loading, the six-dimensional space reduces to one-dimensional space, so the proposed model can be calibrated using uniaxial loading test data, and the calibrated model can predict the material behavior under multiaxial loading conditions. Biaxial loading and triaxial loading test data are used to verify the proposed model, and parametric analyses are performed to analyze model predictions under different loading conditions. It shows that model predictions agree well with the test data and are consistent with experimental observations.

Crack Growth Patterns of Aluminum Tubular Specimens Subjected to Cyclic Tensile Loads

This study presents a detailed analysis of a fatigue test campaign in order to identify different crack patterns. It was conducted on 6061-T6 aluminum tubular specimens featuring an internal diameter of 10 mm and different thicknesses (2, 3 and 4 mm). These specimens were subjected to cyclic tensile loads with a load ratio of R = 0.1, utilizing a sinusoidal load function at a frequency of 3 Hz. The investigation examines the crack growth rates, the stress intensity factor, and the final and intermediate fracture zones by applying overloads in some cases. The differences with two-dimensional specimens and the importance of this study for the interpretation of results with biaxial loading states are highlighted. The different states of crack growth detected are analyzed using artificial vision techniques. The differences between the exterior and interior faces of the specimen are revealed, and a series of states prior to the formation of the radial crack front expected in these specimens are identified.

Quantum Effect Enables Large Elastocaloric Effect in Monolayer MoSi2N4${\rm MoSi}_2{\rm N}_4$ and Graphene

AbstractLow‐dimensional materials with outstanding heat conductivity and elastocaloric effect (eCE) are significant for environmentally friendly and energy‐efficient nano refrigerators. However, most of elastocaloric materials with first/second‐order phase transition suffer from hysteresis loss. Herein, an emerging monolayer is theoretically demonstrated as a promising candidate, which exhibits no hysteresis loss enabled by reversible elastic response, as well as large eCE and high eC strength enabled by quantum effect (QE). Considering the remarkable influence of QE and thermo‐mechanical coupling (TMC) in the monolayer limit, the adiabatic temperature change () is evaluate by incorporating QE and TMC. Molecular dynamics simulation significantly underestimates , whereas method with QE slightly overestimates when compared to method with QE+TMC. At 300 K, of is –(11–42) K under biaxial tensile forces of 26–84 nN. The elastocaloric coefficients are –(0.3–0.9) , comparable to that of armchair carbon nanotubes. A large eCE ( around 15 K under a biaxial tensile load of 35 nN) is also revealed for graphene by incorporating QE and TMC. This study proposes a more comprehensive method for quantitatively predicting eCE in 2D materials by including QE and TMC, offering a theoretical guideline for refrigerating materials in the monolayer limit.

A physics-informed machine learning model for global-local stress prediction of open holes with finite-width effects in composite structures

Fast and accurate methods are required to predict stresses in the vicinity of open and closed holes in composite structures, especially in a global-local modelling context as applied during the design of airframe structures. Fast analytical solutions for infinite-width anisotropic plates with open holes do not consider finite-width effects. Heuristic methods and semi-analytical solutions can be used to towards addressing such effects. To improve the accuracy and speed of these respective methods, we use machine learning (ML) methods trained on high-fidelity finite element analyses to make finite-width corrections. However, such methods require large amounts of training data to reduce errors to satisfactory levels. Therefore, in this study, the fusion of analytical solutions with machine learning is performed. We develop an analytical solution-informed ML model that is as fast as an analytical solution and superior in accuracy to analytical solutions with heuristic finite-width scaling. Our informed ML model offers accuracies equal to analytical solutions for the infinite-width case, and it is capable for use in a global-local modelling context, under uniaxial and biaxial loading. Our informed ML model outperforms prediction accuracy across all cases compared to uninformed ML models and requires a significantly lower size training dataset size.

Stress relaxation assessment of high-temperature bolts under combined biaxial loads: Theory and simulation

Estimating bolt stress within high-temperature bolted connection systems is crucial for determining bolt preload and assessing bolt assembly integrity. This work proposes a theoretical model for estimating high-temperature bolt load under combined tension, bending, torque, and shear loads, considering the characteristics of bolt stress distribution and relaxation. To assess the model's accuracy, finite element analysis was employed to examine the impact of various creep parameters and load combinations on bolt stress relaxation. The results indicate that the introduction of bending moments, torque, and shear loads accelerates axial stress relaxation in bolts. Under a high-temperature load for 300,000 h, the stress relaxation predicted by the theoretical model aligns well with the results from finite element analysis.