Biaxial Loading Research Articles

Postbuckling behavior of two-dimensional decagonal quasicrystal plates under biaxial compression

Two-dimensional (2D) decagonal quasicrystal (QC) plates are analyzed for their postbuckling behaviors when subjected to biaxial compressive loads in this research. The analysis using a combination of the first-order shear deformation theory (FSDT) along with von Kármán’s nonlinear equations of motion, while also accounting for the initial geometric imperfections. The governing equations for the QC plate are obtained through the application of the Hamiltonian variational principle, and the postbuckling equilibrium path for the four-sided plate with simply support is calculated using a two-step perturbation technique. The quasiperiodic structure and phonon-phason coupling in 2D decagonal QCs play a crucial role in determining their mechanical behavior. The numerical analysis explores the effects of geometric shape, phonon-phason coupling constants, initial geometric imperfections, and compressive forces on the postbuckling characteristics of the plates. Numerical simulations validate the theoretical model, demonstrating its accuracy. The application of FSDT, von Kármán theory, and the two-step perturbation method to QC plates, considering the complex interactions involving the phason field unique to quasicrystals, provides new insights into the intricate mechanical responses of QC plates under postbuckling conditions.

Ultimate strength of welded aluminium stiffened panels under combined biaxial and lateral loads: A numerical investigation

The number and size of aluminium non-monohull ships have been steadily increasing over time. This raises growing concerns regarding their structural strength, especially considering the adverse effects of the heat-affected-zone (HAZ) on welding connections in aluminium structures. This paper investigates the ultimate strength of welded aluminium stiffened panels under combined biaxial compressive loads and lateral pressure through the application of numerical simulations. Altogether 360 cases are simulated with varied panel lengths, welding patterns and load combinations. The results are presented and discussed with respect to force end-shortening curves, failure modes and ultimate strength. Influences of the combined loads and HAZ effects are summarized. The numerical results are compared to two commonly used design methods in the marine industry, the International Association of Classification Societies (IACS) rule and the Panel Ultimate Limit States (PULS) approach. Their applicability to welded aluminium stiffened panels is discussed, and modifications are suggested with respect to the transverse loads, lateral pressure, and HAZ effects.

Yield locus and texture evolution of AA7475-T761 aluminum alloy under planar biaxial loading: An experimental and analytical study

AA7475 aluminum alloy is used as a structural material in aerospace and automobile applications where complex loading conditions are applicable. The material properties under multi-axial loading are recommended for efficient component design. Hence, the mechanical behaviour of AA7475-T761 aluminium alloy was investigated through planar biaxial tensile tests. The yield locus evolution and plastic strain direction were measured at higher plastic strain values (up to 7 %) at various load ratios. The yield loci were constructed and compared with existing yield criteria. Yld2000–2d yield criterion demonstrated accurate predictions with a deviation of approximately 1 %, highlighting its effectiveness in capturing the yield behavior of AA7475. Microstructure analysis using Electron Backscatter Diffraction (EBSD) was conducted to understand the misorientation evolution under the multi-axial loading. Bulk-texture analysis was performed using X-ray diffraction method. Texture analysis revealed that uniaxial deformation favoured the development of Cube and Inverse-Copper textures, while biaxial deformation yielded split Inverse-Goss texture formation. Fractography study shows very different fracture surfaces of biaxial samples compared to uniaxial samples. Overall, this study contributes to a comprehensive understanding of the yield behavior, microstructure, and texture evolution of AA7475-T761 aluminium alloy under different loading conditions at very large strains.

Experimental investigation on the fatigue life and damage mechanism of plain weave composites under biaxial tension–torsion combined fatigue loading

In this paper, the fatigue life and damage mechanism of plain weave composites under biaxial tension–torsion combined fatigue loading (TTF) are experimentally investigated. A biaxial TTF loading spectrum is designed to consider different fatigue frequencies and amplitudes, and an automated multi-module loading method with synchronized acquisition of the digital image correlation (DIC) and the testing machine is proposed. A comprehensive analysis of the experimental results, including fatigue lives, strain distribution, temperature variation, stiffness degradation, and typical damage morphologies at different fatigue cycles, has been conducted by utilizing DIC, infrared thermography (IRT) and computed tomography (CT). It is observed that the superimposed torsional fatigue load results in a rapid reduction in fatigue lives of plain weave composites, accompanied by more significant residual strain, energy dissipation, temperature rise and stiffness degradation. Particularly, the superimposed torsional fatigue loads mainly promote matrix cracking and debonding around the fiber/matrix interfaces, which then accelerates the damage initiations and accumulations of fiber yarns, ultimately leading to a rapid reduction in TTF fatigue lives. This study can provide valuable references for the design and safe application of plain weave composites under TTF loading.

The Influence of the Interface on the Micromechanical Behavior of Unidirectional Fiber-Reinforced Ceramic Matrix Composites: An Analysis Based on the Periodic Symmetric Boundary Conditions

The long-term periodicity and uncontrollable interface properties during the preparation process for silicon carbide fiber reinforced silicon carbide-based composites (SiCf/SiC CMC) make it difficult to thoroughly investigate their mechanical damage behavior under complex loading conditions. To delve deeper into the influence of the interface strength and toughness on the mechanical response of microscopic representative volume element (RVE) models under complex loading conditions, in this work, based on numerical simulation methods, a microscale representative volume element (RVE) with periodic symmetric boundary conditions for the material is constructed. The phase-field fracture theory and cohesive zone model are coupled to capture the brittle cracking of the matrix and the debonding behavior at the fiber/matrix interface. Simulation analysis is conducted for tensile, compressive, and shear loading as well as combined loading, and the validity of the model is verified based on the Chamis theory. Further investigation is conducted into the mechanical response behavior of the microscale RVE model under complex loading conditions in relation to the interface strength and interface toughness. The results indicate that under uniaxial loading, increasing the interface strength leads to a tighter bond between the fiber and matrix, suppressing crack initiation and propagation, and significantly increasing the material’s fracture strength. However, compared to the transverse compressive strength, increasing the interface strength does not continuously enhance the strength under other loading conditions. Meanwhile, under the condition of strong interface strength of 400 MPa, an increase in the interface toughness significantly increases the transverse compressive strength of the material. When it increases from 2 J/m2 to 20 J/m2, the transverse compressive strength increases by 28.49%. Under biaxial combined loading, increasing the interface strength significantly widens the failure envelope space under σ2-τ23 combined loading; with the transition from transverse compressive stress to tensile stress, the transverse shear strength shows a trend of first increasing and then decreasing, and when the ratio of transverse shear displacement to transverse tensile/compressive displacement is −1, it reaches the maximum. This study provides strong numerical support for the investigation of the interface properties and mechanical behavior of SiCf/SiC composites under complex loading conditions, offering important references for engineering design and material performance optimization.

Toughening of intrinsically brittle materials by inserting arrays of voids

The aim of the current paper is to find optimum arrangements of voids that are able to catch and trap all possible cracks that might originate from a free surface. The idea is to investigate whether it is possible to apply this crack trapping mechanism to enhance the fracture toughness of intrinsically brittle materials. In doing so, the void volume shall be as small as possible. The investigation applies the crack trajectory interpolation (CTI) method, which is a new, computationally efficient approach to approximate crack trajectories near a single void or stiff particle. Under the assumption of linear superposition, the CTI-method is extended to predict the crack trajectories near arrangements of voids. This is done for uniaxial and biaxial loading conditions. The investigation shows that a symmetrical arrangement of voids should be avoided, since cracks near the symmetry line can bypass the array. Staggered void arrangements provide better conditions for crack trapping. By using elliptical voids with an aspect ratio of 2 instead of circular voids, it is possible to achieve a higher crack trapping efficiency and a lower void volume. A damage-based approach is used to determine the improvements in fracture toughness due to crack trapping for various void arrangements. The Python code of the CTI method is presented in the Appendix of this work.

Investigation of the mechanical response of recovered geogrids under repeated loading

This study investigates the mechanical response and performance of biaxial polypropylene geogrid specimens cyclic loading. This work assesses the influence of embedment depths and subgrade strengths on the of geogrids. The experimental program involved subjecting the geogrid specimens to 100 repeated tensile loading cycles at four distinct load targets: 20%, 40%, 60%, and 80% of the geogrid ultimate tensile strength. The analysis focused evaluating the effects of preloading factors such as California Bearing Ratio (CBR) values, embedment depth, and the response to cyclic testing. Results show trends in stiffness reduction and changes in damping ratio with increased number of cycles. A comparative analysis was conducted with a control specimen from the same batch, highlighting the difference in mechanical response attributed to precycling variables. The findings indicate that the overall mechanical behavior of recovered geogrids is comparably consistent with new geogrids. However, variations in strain and stiffness reduction were observed among the recovered specimens, suggesting a pattern of yielding before failure. The findings suggest a minimal effect of embedment depth on the damping ratio at lower CBR. Overall, it was found that precycling and subgrade conditions have minimal effect on the mechanical response of the recovered specimens when tested in isolation.

Experiments on Low–Cycle Ductile Damage and Failure Under Biaxial Loading Conditions

BackgroundThe damage and failure behavior of ductile metals depends on the stress state as well as on the loading history. Biaxial experiments with suitable specimens can be used to targeted generate different loading conditions, thus allowing the investigation of a wide variety of load cycles with different stress states.ObjectiveIn the biaxial experiments with the newly presented HC-specimen cyclic shear loads are superimposed by various constant compressive and tensile loads. Buckling during compressive loading in both axes is avoided by an additional newly introduced downholder.MethodsThe strain fields at the surfaces of the biaxial specimens are evaluated by digital image correlation (DIC), and after failure the corresponding fracture surfaces are analyzed by scanning electron microscopy (SEM). Associated numerical simulations employing the presented material model provide information on the current stress states.ResultsThe introduced downholder successfully prevents buckling during compressive loading. The strain fields detect a clear influence of the shear direction and a tensile superposition of the cyclic shear load leads to more brittle and a compressive superposition to more ductile behavior. The accompanying numerical calculations reveal the associated, different stress states.ConclusionsThe new experimental program with biaxially loaded specimens for the investigation of damage and failure behavior under cyclic loading enables the targeted examination of a wide variety of load cycles and is thus suitable for the comprehensive analysis of these phenomena.

Modeling dynamic crack growth in quasicrystals: Unraveling the role of phonon–phason coupling

In this work, we employed the phase-field fracture (PFF) model for dynamic brittle fracture in quasicrystals (QCs). The dynamic PFF formulation is derived using both elastodynamics and elasto-hydrodynamic theory. The temporal discretization is achieved using an implicit generalized-α method, which is unconditionally stable for a particular choice of constants. The model incorporates two distinct crack driving forces: (a) the contribution of elastic strain energy from both phonon and phason fields and (b) the contribution solely from the elastic energy associated with the phonon field. To validate the implementation of QCs, we have conducted benchmarking against recent results in the literature, particularly in the context of quasi-static loading. We addressed various paradigmatic case studies to demonstrate the dynamic crack nucleation and propagation in planar 2D decagonal QCs, with a primary emphasis on understanding the interplay between phonon and phason fields. Phason walls, representing low-energy crack paths resulting from atomic rearrangements, play a significant role in crack propagation by introducing an additional energy component. Notably, increasing the phonon–phason coupling constant expedites both crack initiation and propagation. Furthermore, variations in the phonon–phason coupling parameter result in different crack trajectories, observed in both uniaxial and biaxial loading scenarios. The developed code can be downloaded from https://github.com/Hirshikesh/Quasicrystal.git.

The experimental and numerical investigation of fracture behaviour in PMMA notched specimens under biaxial loading conditions – Tension with torsion

This paper presents the results of experimental fracture test of flat PMMA specimens under biaxial loading condition tension with torsion (proportional). The specimens were made in two thicknesses: 5 and 15 mm and were weakened with V-type edge notches with different root radii: 0.5; 2 and 10 mm. Thanks to the ARAMIS 3D 4 M non-contact vision system, measurement of the elongation and twist angle were recorded. During experimental part all of the deformation processes were observed using PHANTOM cameras. Obtained records made it possible to precisely indicate the moment of crack initiation (tensile force and torsional moment values). Using the microscopic observations the location of crack initiations were determined. Results obtained for biaxial loading were compared with those obtained for uniaxial tension and torsion. Based on experimental data the numerical calculation with FEM were carried out. The principal stress and plastic strain distribution under critical load, were obtained. The points of occurrence of stress maxima and plastic strain were indicated, which were taken as potential crack initiation sites. On the basis of the stress and plastic strain values measured at the critical points, a stress–strain fracture criterion was formulated, which was then positively verified. Additionally, new form of stress–strain fracture criterion was proposed. The bilinear form of the fracture criterion can be successfully used to predict fracture in PMMA flat specimens, regardless of the notch root radius, type of load or element thickness.

New test rig for biaxial and plane strain states on uniaxial testing machines

The increasing interest in hydrogen technology and storage systems has also significant influence on material characterization. Storage solutions such as cryo-compressed hydrogen (CcH2) or compressed gaseous hydrogen (CGH2) use high pressure to improve the energy density. The pressurized hydrogen is stored in a pressure vessel. This leads to various strain states in the vessel, which are difficult to reproduce with standard testing equipment, such as a uniaxial testing machine. This contribution presents a new test rig for uniaxial testing machines that is able to generate a biaxial load on a cruciform specimen. A hinged structure converts the uniaxial load into a biaxial load. Different attachments allow both equi-biaxial and plane strain states. In addition, the test rig provides access to both sides of the specimen, extending the possibilities for testing under load, such as optical measurement, specimen cooling or permeability measurement. Finally, experiments show the functionality of the test rig and the desired strain states in the specimen.

Biaxial Tensile Testing of Cruciform Samples to Determine the Impact of Pre-Strain on the Forming Limit Diagram of Aluminum Alloy 5052 through Finite Element Simulation

The present work focuses on the effect of pre-strain on the forming limit curves (FLCs) of aluminium alloy 5052 sheet of 2.5 mm thickness using cruciform samples. To identify the effect of pre-strain on the FLC, the finite element simulations are performed on cruciform samples. The cruciform samples are deformed to a small level of pre-strain in different strain paths. Thereafter, the further deformation under the various strain paths to measure the effect of pre-strain on the forming limits are carried out. Pre-strain in uniaxial, plane strain and biaxial loading conditions are considered in this work. For each case, i.e., uniaxial, plane strain and biaxial conditions two pre-strain conditions are considered. The cruciform samples are carefully thinned in the central region to promote development of large plastic strains there and eventually to neck and fail. The output obtained through simulations are presented in terms of forming limit curves for various strain paths.

The Fracture Evolution Mechanism of Tunnels with Different Cross-Sections under Biaxial Loading

Biaxial compression tests based on an elliptical tunnel were conducted to study the failure characteristics and the meso-crack evolution mechanism of tunnels with different cross-sections constructed in sandstone. The progressive crack propagation process around the elliptical tunnel was investigated using a real-time digital image correlation (DIC) system. Numerical simulations were performed on egg-shaped, U-shaped, and straight-walled arched tunnels based on the mesoscopic parameters of the elliptical tunnel and following the principle of an equal cross-sectional area. The meso-crack evolution and stress conditions of the four types of tunnels were compared. The results show that (1) fractures around an elliptical tunnel were mainly distributed at the end of the long axis and mainly induce slabbing failure, and the failure mode is similar to a V-shaped notch; (2) strain localization is an important characteristic of rock fracturing, which forebodes the initiation, propagation, and coalescence paths of macro-cracks; and (3) the peak loads of tunnels with egg-shaped, U-shaped, and straight-walled arched cross-sections are 98.76%, 97.56%, and 90.57% that of an elliptical cross-section. The elliptical cross-section shows the optimal bearing capacity.

Study on the biaxial mechanical behavior of steel fiber reinforced recycled aggregate concrete

Steel fiber reinforced recycled aggregate concrete (SFRAC) was proposed considering the enhancement of mechanical properties by incorporating steel fibers and the reduction of environmental impacts and cost due to the addition of recycled aggregates. To better understand the mechanical properties of SFRAC under biaxial compression and its failure criteria, 150 SFRAC specimens were prepared with different replacement ratios of recycled coarse aggregate (50%, 75%, 100%) and volume fractions of steel fibers (0%, 0.6%, 1.2%, 1.8%). In addition, various stress ratios were considered in the biaxial compression test (σ1:σ2=0:1.0, 0.2:1.0, 0.5:1.0, 0.7:1.0, 1.0:1.0). The results indicated that the failure of SFRAC was observed as columnar and splitting modes depending on the biaxial stress ratio. The impacts of the considered variables on the biaxial peak strength were studied. The increasing volume fraction of steel fibers tended to improve the biaxial peak strength of SFRAC within a threshold beyond which the impact was negative. Similarly, the biaxial strength of most SFRAC samples showed a pessimum effect when the biaxial loading stress ratio was higher than 0.7, though they were still higher than the uniaxial compressive strength. A failure criterion for SFRAC under biaxial compression loading is proposed, in which four parameters are included. The calculations are in good agreement with the experimental results.

Analytical solution to stress intensity factors of cracks on both sides of a triangular hole in an infinite plate

This paper presents an analytical solution for determining the stress intensity factors (SIFs) of double-sided cracks emanating from a triangular hole in an infinite plate. A conformal function is introduced, which can be applied to these cracks, and the SIFs are analytically derived using the Muskhelishvili method. By combining the Schwarz-Christoffel integral with the conformal transformation for cracks originating from circular holes, a mapping function for the cracked triangular hole is presented. The accuracy of the SIF at the single right-sided crack of the triangular hole is validated using finite element method (FEM) and compared with existing references. This study investigates the influence of biaxial loading factors and lengths of cracks on SIFs. The SIF of the hole-edge crack is related to the structure from which the crack emanates. This analytical approach provides a reliable solution for calculating SIFs of double-sided cracks emanating from a triangular hole.

Critical Failure Characteristics of a Straight-Walled Arched Tunnel Constructed in Sandstone under Biaxial Loading

To characterize the failure of rock mass surrounding underground tunnels, biaxial compression tests were conducted on a real sandstone model with a straight-walled arched hole. The acoustic emission (AE) system and digital image correlation (DIC) optical inspection equipment were used to investigate the crack evolution process and failure precursors of the tunnel. A two-dimensional particle flow code (PFC2D) was used to conduct numerical simulations on the sample, so as to investigate the mesoscopic failure mechanism of rock mass. The results show that the failure of the single tunnel constructed in sandstone occurs mainly in the walls on both sides (between the spandrels and arch feet), showing slabbing failure characteristics and a certain abruptness. The crack initiation in sandstone in early stage is not obvious, and the crack propagation in rock mass is rapid when acoustic emissions are enhanced. The small increments in the AE count and amplitude and the continuous reduction in the b-value can be used as precursors for the failure of rock mass. When the height–span ratio is 0.8 and 1.0, the stress distribution around the chamber is more uniform, and when the height–span ratio is greater than 1.0, the stress is mainly concentrated in the vault and arch bottom. In the PFC simulations, tensile fractures firstly initiate in the middle of walls and at the arch feet, arcuate fracture concentration zones are then formed, in which shear fractures appear and a few particles spall from the surfaces. When approaching the ultimate bearing capacity, rock masses on both sides of the tunnel are fractured over large areas, and the slender coalesced fractured zone develops to the deep part of rock mass, causing failure of the sample.

Mechanical Behavior of Lithium-Ion Battery Separators under Uniaxial and Biaxial Loading Conditions.

The mechanical integrity of two commercially available lithium-ion battery separators was investigated under uniaxial and biaxial loading conditions. Two dry-processed microporous films with polypropylene (PP)/polyethylene (PE)/polypropylene (PP) compositions were studied: Celgard H2010 Trilayer and Celgard Q20S1HX Ceramic-Coated Trilayer. The uniaxial tests were carried out along the machine direction (MD), transverse direction (TD), and diagonal direction (DD). In order to generate a state of in-plane biaxial tension, a pneumatic bulge test setup was prioritized over the commonly performed punch test in an attempt to eliminate the effects of contact friction. The biaxial flow stress-strain behavior of the membranes was deduced via the Panknin-Kruglov method coupled with a 3D Digital Image Correlation (DIC) technique. The findings demonstrate a high degree of in-plane anisotropy in both membranes. The ceramic coating was found to negatively affect the mechanical performance of the trilayer microporous separator, compromising its strength and stretchability, while preserving its failure mode. Derived from experimentally calibrated constitutive models, a finite element model was developed using the explicit solver OpenRadioss. The numerical model was capable of predicting the biaxial deformation of the semicrystalline membranes up until failure, showing a fairly good correlation with the experimental observations.

Marginal integrity in minimally invasive molar resin composite restorations: Impact of polymerization shrinkage

ObjectivesThis study utilized non-linear finite element (FE) models to explore polymerization shrinkage and its impact on marginal integrity in molars following both selective caries removal (SCR) and conventional treatment. Specifically, we performed 2D in silico simulations to study residual stresses post-resin polymerization shrinkage and their influence on the marginal integrity of various restoration types. MethodsInitially, FE models were developed based on a cohesive zone framework to simulate crack propagation along the bonded interfaces between restoration and tooth structure in SCR-treated molars with class I and class II restorations. The modeled resin composite restorations first underwent polymerization shrinkage and were then subjected to various occlusal loading conditions. Stress magnitudes and distributions were identified to evaluate the margin integrity and predict the mechanism and location of interfacial failure. Results and discussionThe FE models computed polymerization shrinkage stresses of less than 1 MPa, exerting a minor influence on the composite/tooth interface. Occlusal loading, however, significantly impacted the load-bearing capacity of the composite/tooth (c/t) interface, potentially jeopardizing the restoration integrity. Especially under bi-axial occlusal loading, interfacial debonding occurred in the vertical cavity walls of the class I restorations, increasing the risk of failure. Notably, SCR-treated teeth exhibited better margin integrity than restored teeth after complete caries removal (NCR).These findings provide valuable insights into the mechanical behavior of SCR-treated teeth under different loading conditions and highlight the importance of considering the load scenarios that may lead to failure at the c/t interface. By investigating the factors influencing crack initiation and delamination, this novel research contributes to the optimization of restorative treatments and aids in the design of more resilient dental restorations.

Analysis of Experimental Biaxial Surface Wrinkling Pattern Based on Direct 3D Numerical Simulation.

This paper presents a direct 3D numerical simulation of biaxial surface wrinkling of thin metal film on a compliant substrate. The selected compliant substrate is a commercial Scotch tape on which a gold metal thin film has been transferred by using low adhesion between the thin metal film and polyimide substrate. Compared with the previous fabrication of a cylindrical thin-film wrinkling pattern, an undulated wrinkling pattern has been implemented by increasing the width of the thin metal film in order to create biaxial straining in the thin film. To understand the wrinkling behavior due to biaxial loading, a simple direct numerical simulation based on material imperfections defined in the compliant substrate has been conducted. Through modeling and simulation, it was found that the wrinkling mode is determined by the biaxiality ratio (BR), the ratio between transversal strain and longitudinal strain. Depending on the BR, the wrinkling mode belongs to one of the cylindrical, undulated (or herringbone), checkerboard, or labyrinth modes as a function of applied strain. The cylindrical wrinkling is dominant at the input of BR less than 0.5, while the undulated (or herringbone) ones become dominant just after the onset of the wrinkling pattern at BR greater than 0.9. Through the comparison of the wrinkling patterns between simulation and experiment, the applied BR of the fabricated thin film has been successfully estimated.

Three-dimensional elastoplastic post-buckling analysis of porous FG plates resting on Winkler/Pasternak foundation using meshless RRKPM

This paper presents a three-dimensional (3D) analysis of the elastoplastic post-buckling behavior of porous functionally graded (FG) plates resting on Winkler/Pasternak foundations under uniaxial and biaxial in-plane loadings using an enhanced meshless approach. The principle of virtual work is used to derive the governing equations, and 3D nonlinear Green–Lagrange strains are considered. Plastic deformation is modeled employing the Prandtl–Reuss flow law and the isotropic hardening von Mises criterion. A novel meshless radial basis reproducing kernel particle approach is used to obtain the discretized system of equations. The Newton–Raphson method, coupled with the arc-length technique, is used to compute post-buckling paths of porous FG plates. Numerical assessments show that post-buckling paths are significantly influenced by porosity parameter, porosity distribution, foundation parameters, material gradient, plate thickness, loading ratio, and boundary conditions (BCs).