Biaxial Loading Research Articles

Study on the Crack Propagation of Stiff-Thin-Film-on-Soft-Substrate Structures under Biaxial Loading.

With the development of flexible electronic technology, lately, there has been an increase in demand for flexible electronic devices based on soft polymer-substrate metal film structures in challenging applications. These soft polymer-substrate metal film structures must tolerate bending, folding, stretching, and even deformation into any shape without failing to be used successfully. As a result, research into the fracture behavior of soft polymer-substrate metal film structures is essential. The purpose of this study was to investigate how fractures develop in Cr film attached to a polyimide (PI) substrate under biaxial stress. A fracture development model was built to determine the fracture propagation law of soft polymer-substrate metal film structures under biaxial stress. Experiments and finite element methods were applied to verify the correctness of the model. The theoretical analysis and finite element simulation results showed that fractures appeared initially at the perimeter of the film and then propagated to the center under biaxial stress. The theoretical and experimental results indicated that the crack propagation direction was related to the ratio of biaxial loading, which became progressively parallel to the direction of small loading as the biaxial loading ratio increased. The theoretical results were in line with the experiment results, which could be used as a preliminary step for further research on the fracture behavior of film-substrate structures.

Biaxial tensile test and meso damage numerical simulation of HTPB propellant

Aiming at the shortcomings of the current research on the mechanical properties of solid propellants under complex stress conditions, an effective cross-shaped test piece configuration and variable-scale biaxial tensile test method are designed in this paper, and the meso-simulation model of propellant is constructed by Micro-CT test and random filling algorithm. Then, based on the Hook-Jeeves method and the cohesive force model, the mechanical performance parameters of each mesoscopic component were obtained, and finally the damage evolution process of the propellant was numerically simulated. The results show that the stress–strain curve of the propellant under biaxial loading is similar to that of uniaxial stretching, and has obvious rate dependence and stress state dependence. The mechanical properties of the propellant under biaxial tensile loading are significantly lower than those in uniaxial stretching, and the maximum elongation is only 45–85% of that in uniaxial stretching. The fracture process of propellant can be divided into initial linear stage, damage evolution stage and fracture stage. The dewetting phenomenon generally occurs at the interface between the large-sized AP particles and the matrix. With the loading of the load, the pores formed by the dewetting and matrix tearing continue to converge into cracks and expand in the direction perpendicular to the resultant force, and finally fracture. The propellant dehumidifies more easily under high strain rate loading, but the degree of dewetting is lower when the same strain is reached.

A numerical analysis on the behavior of CFRP laminates under biaxial loads

The study of the failure mechanisms of a composite material is essential for the efficient design of structures. The analysis of the effect of transverse biaxial loads, both at micromechanical and macromechanical level, is required for an integral vision of the whole mechanism of damage. In a previous work by the authors a transverse biaxial testing campaign was performed on cruciform specimens; in the present work a FEM model that successfully reproduces the coupons elastic state is presented in order to understand the failure occurrence and to make failure predictions avoiding the complexity of the experimental process.

Experimental study on multi-cellular L-shaped CFST slender columns under biaxial eccentric compression

Multi-cellular L-shaped concrete-filled steel tubular (MCL-CFST) column is an improved L-shaped CFST column, which is composed of multiple rectangular steel tubes welded by U-shaped steel plates and then filled with concrete. The global stability capacity of MCL-CFST slender columns is vital for engineering applications. However, few investigations have been carried out on the stability performance of the MCL-CFST slender columns. This paper mainly focuses on the global stability performance of MCL-CFST slender columns. Firstly, six hinged supported MCL-CFST slender columns were designed and tested under biaxial eccentric loading. The load-displacement curves, failure modes, strain development and second-order effects of MCL-CFST slender columns were reported. Then, a refined finite element (FE) model of the MCL-CFSTs was established and verified by experimental results. Moreover, based on the validated FE model, the effects of eccentricity, column height and sectional dimension on the stability performance of MCL-CFSTs under eccentric loading were investigated, and the bending resistance curves Mx/Mxu-My/Myu in two directions under various parameters were obtained. These results can provide valuable references for engineering practice.

Cyclic stress–strain response and crystal plasticity finite element analysis of AISI 9310 steel in biaxial fatigue loading

AbstractThere are still many gaps in the research on the multiaxial fatigue failure mechanism of the gear shaft. In this paper, cyclic stress–strain response and biaxial fatigue damage characteristics of gear steel AISI 9310 were investigated. The specimens showed obvious cyclic softening characteristics at all phase angles, and the softening rate was directly associated with the initiation and propagation of cracks. The fractographies at different phase angles revealed that the specimens under out‐of‐phase loading suffered fatigue failure caused by a single crack source on the surface, while the fatigue crack under in‐phase loading was gathered together by the propagation of different crack sources. Finally, the established crystal plastic finite element model showed a good prediction of the plastic strain energy density at different phase angles, and the maximum error was 13.03%. Furthermore, a biaxial fatigue life prediction method was proposed, with a maximum error of 39.5%.

A comparative study of invariant-based hyperelastic models for silicone elastomers under biaxial deformation with the virtual fields method

Silicone elastomers have been widely used for biomedical applications. A variety of hyperelastic models have been proposed to describe this type of materials in the past few decades. The assessment of the quality of the proposed models is mostly based on stress–strain data obtained from uniform deformation, but very little work has been done to investigate model performances with heterogeneous deformation fields and full-field characterization methods. In this study, thirteen hyperelastic models are evaluated using the virtual fields method combined with full-field deformation data obtained from biaxial tests. The quality of these models is assessed by their capabilities to predict the mechanical responses of silicone elastomers, and the influences of the first and second invariants on modeling of elastomers are investigated through comparative studies between models. The results indicate that for elastomers under finite biaxial deformation, Yeoh model performs the best among selected models; the first invariant plays an important role in constitutive modeling; the second invariant does not have obvious influence on improving the fitting performance. This study provides a full-field method to calibrate and compare hyperelastic models of silicone elastomers under biaxial loading conditions.

Failure of short carbon-fiber-reinforced PEEK composites under high strain rate biaxial loading

The dynamic failure of short carbon fiber reinforced polyether-ether-ketone (SCFR-PEEK) composites under biaxial stresses was investigated in this paper. Cruciform specimens were loaded with a biaxial split Hopkinson tensile bar system, and a high-speed camera was utilized to record the deformation and failure processes. A nonlinear numerical model calibrated with dynamic uniaxial tests was used to estimate the stress in the cruciform specimen, in conjunction with strain fields from digital image correlation (DIC) of high-speed camera images. The failure of the cruciform specimen initiated inside the gauge section under all dynamic loading cases, and the numerical strain fields are in good agreement with the experimental ones. The dynamic failure envelope under biaxial stresses was successfully obtained, the failure strain decreased and failure stress increased with strain rate noticeably. The testing method developed here is also applicable for dynamic biaxial testing of many other composites.

Effects of biaxial loading path on seismic behavior of T-shaped RC walls

T-shaped RC walls are commonly used to resist horizontal seismic excitations in multiple directions. The differences in the intensity and spectrum characteristics of two translational components of ground motion cause the wall to experience complex biaxial displacement trajectories, resulting in a different seismic response compared to the behavior derived from conventional uniaxial cyclic tests. Thus, to investigate the seismic behavior and coupling mechanism of T-shaped walls subjected to different magnitudes of loading in two orthogonal directions, this study examined five identical T-shaped walls under uniaxial loading along two principal axes and biaxial loading with three represented loading paths. The test results showed that the mechanical behavior in one direction was significantly affected by the loading in the orthogonal direction owing to internal force redistribution and additional stress caused by the biaxial coupling bending, resulting in vertical variation and intersection of their hysteretic curves. Further, the biaxial loading primarily aggravated the cracking and damage of the flange, which accelerated the performance degradation in the flange direction and reduced the effective flange width involved in resisting web direction load. In addition, the biaxial coupling effect was found to be proportional to the area enclosed by the loading path. Thus, the most severe damage and performance degradation were observed under a square path, followed by an eight-shaped path, with the cruciform path exhibiting the least effect. Consequently, based on the results, recommendations for the design of T-shaped walls subjected to biaxial earthquake actions were proposed.

Investigation of Biaxial Properties of CFRP with the Novel-Designed Cruciform Specimens.

The biaxial loading properties of carbon-fiber-reinforced polymer (CFRP) are critical for evaluating the performance of composite structures under the complex stress state. There are currently no standardized specimens for the CFRP biaxial experiments. This work developed a new design criterion for the cruciform specimen coupled with the Hashin criterion. The finite element analysis was conducted to investigate the effect of geometric parameters on the stress distribution in the test area. The embedded continuous laying method (ECLM) was proposed to achieve the thinning of the center of the test region without introducing defects. The manufacturing quality of the cruciform specimens was verified by the ultrasonic C-scanning test. The biaxial test platform consisting of the biaxial loading system, digital image correlation (DIC) system, strain electrical measurement system, and acoustic emission detection system was constructed. The biaxial tensile tests under different biaxial loading ratios were conducted. The results showed that the biaxial failure efficiently occurred in the test area of the cruciform specimens designed and manufactured in this paper. The failure modes and morphology were characterized using macro/microscopic experimental techniques. The biaxial failure envelope was obtained. The results can be used to guide the design of composite structures under biaxial stress.

Effect of simulated axial residual stress and transverse residual stress in welded P92 pipe and plates including plasticity error

The paper deals with the measurement of the residual stresses in P92 welded pipe using the blind hole drilling technique.The post weld heat treatment (PWHT) of P92 welded pipe was also conducted to study their effect on residual stresses .The P92 pipe weld joints were prepared using gas tungsten arc welding process. The residual stress measurement was carried out using the strain gauge rosette that was associated with the plastic deformation of material and stress concentration effect of multi-point cutting tool. The corrective formulation was developed for calculating the corrected value of residual stresses from the experimentally obtained strain value. The Strain gauge response was estimated experimentally using the tensile testing for the uniaxial loading while finite element analysis was performed for biaxial loading. Gas tungsten arc welds joint was prepared for conventional V-groove and narrow groove design.

Does elastic stress modify the equilibrium corner angle?

We consider the influence of elasticity and anisotropic surface energy on the energy-minimizing shape of a two-dimensional void under biaxial loading. In particular, we consider void shapes with corners for which the strain energy density is singular at the corner. The elasticity problem is formulated as a boundary integral equation using complex potentials. By incorporating the asymptotic behavior of the singular elastic fields at corners of the void, we develop a numerical spectral method for determining the stress for a class of arbitrary void shapes and corner angles. We minimize the total energy of surface energy and elastic potential energy using calculus of variations to obtain an Euler-Lagrange equation on the boundary that is coupled to the elastic field. The shape of the void boundary is determined using a numerical spectral method that simultaneously determines the equilibrium void shape and singular elastic fields. Our results show that the precise corner angles that minimize the total energy are not affected by the presence of the singular elastic fields. However, the stress singularity on the void surface at the corner must be balanced by a singularity in the curvature at the corner that effectively changes the macroscopic geometry of the shape and effectively changes the apparent corner angle. These results reconcile the apparent contradiction regarding the effect of elasticity on equilibrium corner angles in the results of Srolovitz and Davis (2001) and Siegel, Miksis and Voorhees (2004), and identify an important nontrivial singular behavior associated with corners on free-boundary elasticity problems.

Parametric study of 3D steel moment connections with built-up box column subjected to biaxial cyclic loads

In this numerical research, the variation of cyclic behavior of beam-to-box column connection was studied. Dimensional and load conditions were parametrically evaluated with the goal of assessing the applicability and use of this biaxial moment connection according to the Seismic Provisions, such as bending strength and rotation capacity, secant and tangent stiffness, dissipated energy and strong column-weak beam relationship. A total of 83 different models of 3D connections were developed using in ANSYS software with the load at the top of the column. Results show a cyclic behavior not controlled by axial load. However, the variations of clear span to depth beam ratio caused degradation of the strength, secant and tangent stiffness as well as in dissipated energy. The 80% of plastic moment of beam and rotation at 4% interstory drift were reached for all models analyzed according to criteria established in AISC 341. Finally, the configurations designed with low levels of axial load are controlled by the design of the web panel zone shear, while configurations designed for high levels of axial load are controlled by the strong column-weak beam criterion. • The hysteretic response curves of the joints with end-plate connections and built-up box column subjected to cyclic loading were plumped. • The beam can concentrate the inelasticity effectively in a wide deformation range. • The behavior exhibited is acceptable for 7 < L/d < 20 ratio. • A numerical prequalification was possible.

Crack coalescence mechanism of flaw pairs under biaxial loading conditions using additively printed models and photoelastic experiments

Revelation of the mechanism of crack coalescence is critical in understanding the failure of solids. However, specifying the mechanism of crack coalescence is challenging because the stress distribution in a complicated fracture system is complex. A visualization method using 3D printing models and photoelastic techniques was introduced to directly reveal and quantify the evolution of stress concentration at the flaw tips of flaw pairs under different biaxial loading schemes. The results indicate that the evolution of shear stress concentration at the flaw tips along the dip angle of the flaw plays a primary role in crack initiation from the flaw tips. A synchronous loading scheme significantly constrains the development of shear stress concentration at flaw tips; thus, cracks can rarely initiate. In an asynchronous loading condition, shear cracks are primarily observed emerging from the flaw tips due to the variation of shear stress concentration on the flaw tips. The propagation of shear cracks is the main cause of crack coalescence in the bridging region. This phenomenon is more significant in the scenario of a positive bridging angle.

Influence of additional static stresses on biaxial low-cycle fatigue of 2024 aluminum alloy

In this paper, a previously developed modification of the Sainz model of multiaxial fatigue is reduced to an invariant form. Model constants were determined for different sets of setup experiments. It was supposed to introduce an additional summand to account for the phase shift between loading modes. The model is used to describe the fatigue behavior of the D16T aluminum alloy. Low-cycle fatigue tests under biaxial loading conditions are presented, with one mode changing cyclically and the other mode remaining constant in magnitude throughout the test. The results of cyclic durability prediction by the modified model provide good convergence.

Single shot quantitative polarized light imaging system for rapid planar biaxial testing of soft tissues.

Quantitative Polarized Light Imaging (QPLI) is an established technique used to compute the orientation of collagen fibers based on their birefringence. QPLI systems typically require rotating linear polarizers to obtain sufficient data to estimate orientation, which limits acquisition speeds and is not ideal for its application to mechanical testing. In this paper, we present a QPLI system designed with no moving parts; a single shot technique which is ideal to characterize collagen fiber orientation and kinematics during mechanical testing. Our single shot QPLI system (ssQPLI) sorts polarized light into four linear polarization states that are collected simultaneously by four cameras. The ssQPLI system was validated using samples with known orientation and retardation, and we demonstrate its use with planar biaxial testing of mouse skin. The ssQPLI system was accurate with a mean orientation error of 1.35° ± 1.58°. Skin samples were tested with multiple loading protocols and in each case the mean orientation of the collagen network reoriented to align in the direction of primary loading as expected. In summary, the ssQPLI system is effective at quantifying collagen fiber organization, and, when combined with mechanical testing, can rapidly provide pixel-wise measures of fiber orientation during biaxial loading.

Variation of Fracture Toughness with Biaxial Load and T-Stress under Mode I Condition

The effect of a biaxial load on brittle fractures of solids under predominantly elastic deformation and mode I loading conditions is studied in this article. A cross-shaped specimen is used in this work, and the variation of T-stress is achieved by changing the load applied to the arm parallel to the crack. In the tests, under a series of different loads parallel to the crack, a series of load values perpendicular to the crack are obtained, and the stress intensity factor is calculated by FEM (Finite Element Analysis). The test data demonstrate that the apparent fracture toughness of the material varies with the load parallel to the crack and the T-stress, since the T-stress is directly related to the load parallel to the crack. If only the first term of the Williams series solution is used to describe the stress field near the crack tip, the variation of KC is unexplained; therefore, more than one term in the Williams series solutions is used to develop the theory of biaxial effect on solid fracture behavior. The fracture criterion based on this consideration is also used to predict crack instability or crack curving under mode I load conditions. Experimental data are presented and compared with the theory.

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.

Potential Use of Transparent Wood in Spatial Folded Structures

Transparent wood is a relatively new material, the manufacturing starts with removing the lignin from wood veneer and infiltrating the delignified wood by a polymer thereafter. Transparent wood usually proves better mechanical properties than original wood and polymer. The article presents the potential use of transparent wood in bearing structures. The transparent wood could be used as I-beams structures, box beams, trusses, or folded structures. A spatial folded structure was numerically analyzed. Various types of transparent wood or transparent plywood were used. A comparison with commonly used materials, such as glass and other wood-based materials were made. The comparison shows that transparent wood has great potential in the use as a structural material. The plywood made from transparent wood veneer with the alternating direction of wood fibers acts as a laminate and allows a biaxial load transfer, which can be successfully used in a thin plate of the spatial folded structure while maintaining relatively good transparency.

Surface Wrinkling versus Global Buckling Instabilities in Thin Film‐Substrate Systems under Biaxial Loading: Direct 3D Numerical Simulations (Adv. Theory Simul. 9/2022)

Surface Wrinkling versus Global Buckling Instabilities in Thin Film-Substrate Systems In article 2200183, Nikravesh, Ryu and Shen develop a computational strategy to directly simulate complex surface wrinkles and structural buckling of the thin film-compliant substrate structure, covering the entire biaxial loading spectrum and providing mechanistic rationale for the evolution of local wrinkle configurations mediated by global buckling.

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.