Biaxial Tensile Loading Research Articles

Two-pheromone Ant Colony Optimization to design dispersed laminates for aeronautical structural applications

The objective of the present study is to find out the effect of using non-conventional fiber orientations (orientations not limited to 0^o, +/-45^o and 90^o) to improve the composite material response. The Ant Colony Algorithm is used to optimize the stacking sequence for biaxial tension and compression loading condition under strength constraints. Moreover, a modified algorithm (two-pheromone algorithm) is used to design a fully dispersed laminate. Results show that dispersed laminates can improve the critical buckling load by up to 8% for the biaxial compression loading case. With respect to the biaxial tensile loading condition, the results show that the matrix cracking failure index can be decreased up to 100% and the fiber tensile failure index can be decreased by 40% using the two pheromone formulation.

Study on Anisotropic Mechanical Behavior at near Pre-Crack for AZ31B Sheet under Biaxial Stress

In this study, a biaxial tensile test of cruciform specimens containing centre notch was conducted in order to clarify the deformation behavior near the crack tip at the early stages of crack initiation when objected to a biaxial stress state. Results show that the hardness and stress value within the deformed zone increased with increase in the loading ratio. Observation of the microstructure reveals that the deformation is dominated by basal slip under equal biaxial tensile loading. The asymmetrical biaxial tensile loading generates deformation twins near the crack tip. These results indicate that existing deformation twins contribute to higher hardness, and there is obvious anisotropism in the vicinity of crack tip under asymmetrical biaxial tensile loading.

位相差を有する二軸繰り返し載荷条件下における疲労亀裂伝播挙動

Fatigue crack propagation under biaxial tensile loading containing phase differences is highlighted in this study. Ships and offshore structures are subjected to many types of loading, e.g. wave induced forces, gravity, and inertia forces. Generally, these loadings have different axial components with different phases. However, the structural integrities of structures and vessels are evaluated according to design codes based on theoretical and experimental investigations under a uniaxial loading condition. Most of these codes are based on the S-N curves approach. An approach that does not use S-N curves has been favored by researchers, with the fracture mechanics approach preferred for evaluating the fatigue life of structures. An advanced fracture mechanics approach was developed based on the Re-tensile Plastic zone Generating (RPG) stress criterion for fatigue crack propagation. In this study, fatigue crack propagation tests under biaxial loading with four different phase conditions and two different loading components are performed and the effect of the phase difference under biaxial loading is evaluated. The authors present a numerical simulation method of fatigue crack propagation based on the RPG stress criterion under different biaxial loading phase conditions and the validity of the proposed method is confirmed by comparing the estimated fatigue crack propagation histories with measured data.

Prediction of Matrix Failure in Fibre Reinforced Polymer Composites

Recent development has enabled fibre and matrix failure in a fibre reinforced composite material to be predicted separately. Matrix yield/failure prediction is based on a Von Mises strain and first strain invariant criteria. Alternative matrix failure criteria for enhanced prediction accuracy are discussed in this paper. The proposed failure envelope formed with basic failure criteria intersects with uniaxial compression, pure shear and uniaxial tensile test data points smoothly. For failure of typical neat resin, significant improvement of prediction accuracy compared with measured material data is demonstrated. For a unit cell with a fibre and surrounding matrix with typical material properties, a FEM analysis indicates a significant improvement in prediction accuracy in the pure shear load case and a marginal improvement in the biaxial tensile load case. This paper also provided a preliminary discussion about the issues when material nonlinearity of the matrix material is involved.

109 応力軟化を考慮した異方性超弾性モデルによる競泳水着の数値シミュレーションに関する研究(OS9 オーガナイズドセッション《計算力学と数値シミュレーション》)

The purpose of this study is development of a newly design method for competitive swimwear by numerical simulation. The method is able to visualize the stress distribution applied to swimwear in motion. The swimwear consists of well-stretched chemical fabric. The fabric has a properly similar to rubber. Thus, the fabric was regarded as hyperelasticity. Also, the fabric has stress-softening and anisotropic characteristic which depends on the directions of warp and weft yarn. The mechanical properties were evaluated by biaxial tensile loading test. From the results, the anisotropic hyperelastic model considering stress-softening was constructed and introduced the numerical simulation. The model is able to adjust the axial and shear stiffness individually. Therefore, a newly design method for competitive swimwear by numerical simulation was proposed.

Material modeling of AZ31 Mg sheet considering variation of r-values and asymmetry of the yield locus

A commercial AZ31 magnesium alloy sheet was tested under uniaxial tension/compression loading and proportional biaxial tensile loading using cruciform specimens. Plastic work contours and directions of the plastic strain rates were determined over a range of equivalent plastic strain, 0.001 ≤ ε 0 p ≤ 0.008 , to quantitatively determine the elastic–plastic deformation behavior. The shape of the work contours changed with plastic strain and the r -values increased with plastic strain. The measured work contours and directions of plastic strain rates were compared with those predicted using selected yield functions in the first quadrant of the stress space. A recently proposed yield function, CPB2006 [O. Cazacu, B. Plunkett, F. Barlat, Int. J. Plast. 22 (2006) 1171–1194] was also evaluated to account for the asymmetry of the yield locus with consideration of the uniaxial compression test data. The standard deviation between the measured and calculated data for the work contours and the directions of plastic strain rates were calculated, allowing the validity of these yield functions to be evaluated. The CPB2006 yield criterion with an exponent of 3 provided a fairly accurate description of the anisotropy and asymmetry of the work contours for the AZ31 sheet.

An analytical model for the buckling of plates under mixed boundary conditions

An analytical approach for the buckling analysis of rectangular plates under mixed boundary conditions is presented. In order to solve the partial differential equation governing the problem at hand a method of separation of variables is here adopted, by introducing the displacement field as a result of the scalar product of two vectors which combine prescribed and unknown scalar functions. By following this strategy, exact buckling solutions for a wide class of problems, in which mixed boundary conditions can be assigned relaxing some usual constraints, are determined, and buckling load of plates, where biaxial tensile and compressive loads are applied in presence of piecewise clamped and partially supported sides, obtained analytically. Several cases of engineering interest are finally analyzed, and comparisons of the theoretical outcomes with literature data and Finite Element-based numerical results are also shown, in order to highlight the effectiveness of the proposed strategy.

Study on Deformation Performance of PVC Membrane Materials under Biaxial Cyclic Tensile Loads

This article presents the mechanical properties of PVC coated fabrics under biaxial cyclic tensile loads. Tests of PVC at five load ratios in the warp and weft directions, which are 0:1, 1:2, 1:1, 2:1 and 1:0 respectively, were carried out, and tensile performances of the samples under biaxial tensile loads were analyzed. The test results show that the PVC membrane is highly nonlinear and orthotropic under biaxial tensile loads. With the increase of loading cycles, the total residual strain is nearly unchangeable and the hysteresis curve becomes stable. Slope of warp curve is larger than weft curves, and the weft loop area is greater than the warp one with the same load ratio. The generalized poisson ratio changes due to variations of the load ratio (R). when R<1, the experimental values and theoretical values of the generalized poisson's ratio are negative. When R≥1, generalized poisson's ratios tend to be constant, When the load ratio are 0:1 and 1:0, the curves become straight lines.

On the thermomechanical behavior of two-dimensional foam/metal joints with shear-deformable adherends: Model validation with FE analysis

The stress distributions in metal/adhesive/foam planar joints subjected to biaxial tensile load and thermal load was investigated through a semi-analytical model. The shear deformation of adherends was accounted for according to a linear law in order to obtain closed-form solutions. For the model validation, a comparative study with a finite element (FE) simulation was carried out. A 2D behavior of stress fields is observed due especially to the Poisson's ratio effects and the biaxial nature of loads. The through thickness shear stresses are comparable to normal stresses; therefore, the adherend shear deformation must be accounted for correct failure prediction. According to the comparison with FE results, the normal stress distributions at any location in the foam and the shear stresses in the foam regions close to the adhesive surface can be well predicted by the proposed model. The through thickness shear stresses, however, showed to vary according to a cubic law rather than a linear law.

Numerical analysis of competitive swimwear using finite element method

The purpose of this study is development of a new design method for competitive swimwear by numerical simulation. Biaxial tensile loading tests were conducted to obtain the mechanical characteristics of competitive swimwear. The fabrics of competitive swimwear consist of chemical fiber. Therefore, the fabrics show anisotropic characteristics that depend on the fiber orientation angle. From biaxial tensile loading test results, the fabric has orthotropy and the stiffness of the fabric shows the graph like the two polygonal lines along with the increase of stretch. An anisotropic hyperelastic model was applied to the reproduction of mechanical characteristics of swimwear. The anisotropic hyperelastic model in this paper is able to adjust the axial and shear stiffness individually. The material parameters of the anisotropic hyperelastic model for the finite element simulation were determined from biaxial tensile loading test results. And then, finite element simulation of tensile loading tests was conducted to show the applicability of our design method to competitive swimwear. In finite element analysis, the bias of deformation and stress distribution by the anisotropy were reproduced. It is important to design the pressure given by stretch of competitive swimwear from the two viewpoints, the exercise performance and the burden to the heart function. We estimated the pressure caused by wearing competitive swimwear against the human body using a simple cylinder model.

Deformation analysis of 2/2 twill weave fabrics

Biaxial tensile loading processes in 2/2 twill weave fabrics are studied. The performed calculations are based on the theory of biaxial deformation of woven materials with account of their geometry and mechanical characteristics of the warp and weft threads/yarns. Numerical procedures are proposed, in order to solve the resolving system of equations which allows for yarn compressibility in transversal directions. The effectiveness of numerical algorithms is demonstrated by comparison of predicted results and the experimental data.

Local fibre reinforcement of holes in composite multilayered plates

For various technical reasons, cutouts such as holes in thin-walled structures are inevitable and are of significant technical relevance. Unfortunately holes lead to an undesired stress concentration at the hole vicinity and a reduced strength of the structure. Therefore in practice a local reinforcement in the form of a ring is usually applied around the hole. The increasing requirements for modern structures in terms of low weight and high strength lead to the question of an optimal reinforcement design. The present paper addresses the new but well-approved techniques of the use of curved fibre format to determine the aforementioned optimal design of the reinforcement. The optimization of cutouts in laminated composite plates under bi-axial tensile loading conditions has been investigated using two approaches: the finite element and the Rayleigh–Ritz method. The used methodology implemented successfully theoretical results based on the complex potential theory. For the considered problems, the proposed methods were shown to successfully produce a constant objective function around the hole boundary under biaxial loading. The optimal reinforcement of holes in laminated composite plates illustrated that the optimum depends on the degree of orthotropy. Significant reduction of stress concentrations were demonstrated. The results obtained illustrate the necessity and usefulness of the applied optimization procedure.

Amorphous carbon interlayers for gold on elastomer stretchable conductors

Gold on polydimethylsiloxane (PDMS) stretchable conductors were prepared using a novel approach by interlacing an hydrogenated amorphous carbon (a-C : H) layer between the deposited metal layer and the elastomer. AFM analysis of the a-C : H film surface before gold deposition shows nanoscale buckling, the corresponding increase in specific surface area corresponds to a strain compensation for the first 4–6% of bi-axial tensile loading. Without this interlayer, the deposited gold films show much smaller and uni-directional ripples as well as more cracks and delaminations. With a-C : H interlayer, the initial electrical resistivity of the metal film decreases markedly (280-fold decrease to 8 × 10−6 Ω cm). This is not due to conduction within the carbon interlayer; both a-C : H/PDMS and PDMS substrates are electrically insulating. Upon cyclic tensile loading, both films become more resistive, but return to their initial state after 20 tensile cycles up to 60% strain. Profiling experiments using secondary ion mass spectroscopy and x-ray photoelectron spectroscopy indicate that the a-C : H layer intermixes with the PDMS, resulting in a graded layer of decreasing stiffness. We believe that both this graded layer and the surface buckling contribute to the observed improvement in the electrical performance of these stretchable conductors.

Correlation between crystallographic orientation and mechanical response in a three-dimensional β-Ti microstructure

Abstract

FEM Analysis and Verification of Stress Intensity Factor of Dugdale Model in Silicon Steel Plate under Biaxial Tensile Load

A plate containing a central crack and subjected to biaxial stresses has been studied by a finite element method using ANSYS. The stress intensity factor was calculated using displacement extrapolation method and Dugdal model. From the results, it was found that the stress intensity factors increased with the increasing load ratio. There was good agreement between experimental and theoretical results.

A Comparison of Uniaxial and Biaxial Mechanical Properties of the Annulus Fibrosus: A Porcine Model

The annulus fibrosus of the intervertebral disk experiences multidirectional tension in vivo, yet the majority of mechanical property testing has been uniaxial. Therefore, our understanding of how this complex multilayered tissue responds to loading may be deficient. This study aimed to determine the mechanical properties of porcine annular samples under uniaxial and biaxial tensile loading. Two-layer annulus samples were isolated from porcine disks from four locations: anterior superficial, anterior deep, posterior superficial, and posterior deep. These tissues were then subjected to three deformation conditions each to a maximal stretch ratio of 1.23: uniaxial, constrained uniaxial, and biaxial. Uniaxial deformation was applied in the circumferential direction, while biaxial deformation was applied simultaneously in the circumferential and compressive directions. Constrained uniaxial consisted of a stretch ratio of 1.23 in the circumferential direction while holding the tissue stationary in the axial direction. The maximal stress and stress-stretch ratio (S-S) moduli determined from the biaxial tests were significantly higher than those observed during both the uniaxial tests (maximal stress, 97.1% higher during biaxial; p=0.002; S-S moduli, 117.9% higher during biaxial; p=0.0004) and the constrained uniaxial tests (maximal stress, 46.8% higher during biaxial; S-S moduli, 82.9% higher during biaxial). These findings suggest that the annulus is subjected to higher stresses in vivo when under multidirectional tension.

Microstructure evaluation and crack initiation crack for AZ31 sheet under biaxial stress

In this study, a biaxial tensile test of cruciform specimens containing centre notch was conducted with a miniature biaxial tensile test system in order to clarify the deformation behavior near the crack tip at the early stages of crack initiation when objected to a biaxial stress state. Stress distributions were determined by X-ray diffraction stress measurement, and the crack initiation angle was predicted by modified Dugdale model. The microstructure evolutions were investigated by the electron backscatter diffraction technique. The deformation twins were formed at the biaxial tensile test due to the creation of a large stress field near the crack-tip region. The formation region of deformation twins became small with the equiaxial tension due to the lower stress concentration. Observation of the microstructure reveals that the deformation is dominated by basal slip under equal biaxial tensile loading. The asymmetrical biaxial tensile loading generates deformation twins near the crack tip. These results indicate that deformation twinning in the vicinity of crack tip is more significant in predicting the initial crack growth.

In situ observation of crack nuclei in poly-granular graphite under ring-on-ring equi-biaxial and flexural loading

Fracture tests of graphite are known to exhibit sensitivity to stress state, such as a difference between their flexural and tensile strengths. Bi-axial tensile and flexural loading are representative of the stress states in some regions of graphite components in nuclear fission reactors, where loading develops from fast neutron irradiation-induced dimensional change and thermal strains. Study of the behaviour of the inherent defects that determine strength variability requires in situ observation of crack nucleation. To this end, digital image correlation can be used to monitor the evolution of displacement fields and hence the cracks on the surface of large samples whilst under load. In this study, a ring-on-ring flexural test setup was developed to apply equi-biaxial tensile stress to large disc specimens of graphite along with the conventional four-point-bend test. A 17% reduction in mean flexural strength was observed for the equi-biaxial loading, relative to uniaxial loading. DIC was used to characterise the observed fracture nuclei. Linear elastic fracture mechanics analysis was shown to be inadequate to explain the strength reduction. It is suggested that fictitious crack models, originally developed to simulate the behaviour of concrete structures, can be utilised to explain the behaviour.

Calculation of Stress Intensity Factor under Mixed Mode Biaxial Tensile Load by Photoelastic Hybrid Method

In this study, the photoelastic experiment hybrid method was introduced and applied to the fracture problems of the isotropic polycarbonate plate with a central crack under the uniaxial and equibiaxial tensile load. The influences of equibiaxial tensile load on the isochromatic fringes and stress fields, stress intensity factors near the mixed mode crack-tip were investigated. As the results, without relation to the inclined angle of crack, the asymmetric isochromatic fringes around the crack propagation line under uniaxial tensile load has become symmetric and the slope of isochromatic fringe loop has inclined toward crack surface when an equal lateral tensile load was added. Furthermore, the distribution of all stress components have changed from asymmetric shape to symmetric shape, and only the range of compressive stress of σχ/σ0 have changed as compared with the mode I condition under unaxial load with β = 0°. When an equal lateral tensile load was added to uniaxial load, the value of stress intensity factors are little changed when β = 0° but the values of KI /K0 are increased and KII /K0 are become zero, that is, mode I situation when β = 15°~45°.

On the Tensile Experiments of the Woven Membrane Materials under Bi-Axial Loads

As a kind of flexible fabric reinforced composites, the woven membrane materials suffer from the bi-axial tensile loads in the application of the lightweight structures. Therefore, the experiments under bi-axial tensile loads are essential for the acquaintance of the mechanical characters of the membrane materials. This paper has summarized thoroughly the details of the bi-axial tensile tests, especially the in-plane cruciform tests. The aspects include the shape and configuration of the cruciform sample, the practice of the applied stresses and the testing of the strains in the two axial directions. It could be expected to be the reference for the establishment of the testing standard of the bi-axial tensile experiment for the membrane materials.