Off-axis Tension Tests Research Articles

Comparing the in-plane shear moduli of cardboard measured by flexural vibration, torsional vibration, static torsion, off-axis vibration, and off-axis tension tests

Abstract Flexural vibration (FV), torsional vibration (TV), static torsion (ST), longitudinal vibration (OAV), and tension (OAT) of 45° off-axis tests of flat pieces of cardboards were analyzed to determine the in-plane shear modulus (IPSM) using samples of various widths. The analyses were performed with simulations using the finite element method (FEM) for models with and without lamination and physical experiments using cardboard samples. For the FV, TV, and ST tests, the IPSM was calculated using binary search (BS) and linear regression (LR). The FEM results suggest that the IPSM values obtained from the TV and ST test simulations were affected by lamination. In contrast, the effect of lamination was not clear in the FV, OAV, and OAT test simulations. The coefficient of variation obtained from the FV experiments was often larger than that obtained from other tests. Despite this variation, the FV test is more attractive than the other tests because the experiments could be performed easily, and the effect of lamination could be reduced.

X-ray microtomography observation of interfacial debonding in CFRP under combined loading

One of the remaining challenges for advancing the theoretical mechanics of composite materials is to describe the relationship between interfacial debonding and the mechanical properties of composites. The fiber/matrix interfacial debonding of model composites caused by combined loading has been observed by in-situ X-ray radiography and post-mortem X-ray computed tomography (CT) in this paper. Off-axis tension (fiber axis lying at 30°, 45°, 60° or 90° with respect to the loading direction) tests have been performed on carbon fiber reinforced polymer (CFRP) cruciform specimens using an in-situ loading rig. The morphological characteristics of the cracks at the interface and in the matrix are recorded. Based on our observations, the difference between interfacial debonding caused by normal tension and tangential shear stresses and their cooperative actions in composites under combined loading have been studied. This research can give insights into interfacial debonding in composites and help to build an accurate micro-mechanical model.

Modeling 3D transverse elasto-plastic damage of unidirectional fiber-reinforced polymer composites using a smeared crack approach

This work presents a novel formulation of a 3D smeared crack model for unidirectional fiber-reinforced polymer composites based on a stress invariant approach for transverse yielding and failure initiation, and on a continuum damage approach. This formulation is developed to facilitate the implementation in an implicit solver, increasing solution robustness and computational efficiency in quasi-static and long duration analyses. The performance of the model is evaluated using monotonic and non-monotonic damage evolution, verified with single element tests to demonstrate the consistency of the proposed formulation. Additional benchmark examples regarding off-axis tension and compression tests are simulated and compared with the experimental results, showing good agreement for the plastic response, failure load and failure strain.

Membrane behavior of uni- and bidirectional non-crimp fabrics in off-axis-tension tests

The production of high-performance composite parts with non-crimp fabrics (NCFs) requires a profound understanding of the material’s behavior during draping to prevent forming defects such as wrinkling and gapping. Simulation methods can be used to model the complex material behavior of NCFs and predict their deformation during the draping process. However, NCFs do not intrinsically deform under pure shear like most woven fabrics, but often under superimposed shear, transverse tension and in-plane roving compaction. Therefore, non-standard characterization methods have to be applied besides typical picture frame tests or bias-extension tests. Off-axis-tension tests (OATs) utilize a simple setup to characterize a fabric’s membrane behavior under different ratios of superimposed shear, transverse tension and in-plane compaction. OATs at three different bias angles (30^circ , 45^circ and 60^circ ) are conducted to investigate a unidirectional and a bidirectional NCF. A method is presented to measure the fiber curvatures in addition to the occurring strains. The investigations reveal a relatively symmetrical, shear-dominated behavior with limited roving slippage for the Biax-NCF. The behavior of the UD-NCF strongly depends on the stitching load during tests and is characterized by an asymmetric shear behavior as well as significant roving slippage. The off-axis-tension test results can be used as the basis for the development and validation of new simulation methods to model the complex membrane behavior of NCFs.

Strength properties of unidirectional laminated engineered bamboo boards under off-axis tension and compression tests

The strength properties of 30-mm unidirectional laminated engineered bamboo boards under off-axis tension and compression tests at seven different loading directions were studied in this research. The different failure modes, stress-displacement curves, and the corresponding full-field surface strain field measured through the digital image correlation (DIC) method were reported. The probability plots of off-axis strength values and the estimated characteristic strength values were given. Based on the original test data, the strength criteria based on Tsai and Wu theory was developed for the engineered bamboo panels studied herein. The values of strength tensors Fi and Fij were estimated based on the test results, which can be used to accurately model engineered bamboo products under complex stress conditions such as joint or notch regions. The characteristic off-axis strength values based on the Hankinson's formula given by the current standards are suggested to be further calibrated for design applications.

Digital Image Correlation Analysis of Strain Fields in Fibre-Reinforced Polymer–Matrix Composite under ±45° Off-Axis Tensile Testing

This study presents an experimental investigation of an in-plane shear of a glass lamina composite using a ±45° off-axis tension test. Typically, the shear stress curve, shear modulus, and in-plane shear strength for composite lamina-type materials are identified. Previous research indicated that a loading rate affects the strength of this composite. This study extends the existing literature by utilising a non-contact optical digital image correlation (DIC) method to measure strain distribution during the test. Two cross-head displacement rates were examined. The obtained strain maps reveal an uneven distribution resembling fabric texture. As the deformation progresses, the differences in the strain pattern increase. Subsequently, a quantitative analysis of the differences between regions with extreme (minimum and maximum) strain values and regions with average values was conducted. Based on these measurements, shear stress–strain curves, indicating variations in their courses, were constructed. These differences may reach several percent and may influence the analysis of numerical simulations. The DIC results were validated using strain gauge measurements, a commonly utilised method in this test. It was demonstrated that the location of the strain gauge installation impacts the results. During the tests, the occurrence of multiple microcracks in the resin was observed, which can contribute to the nonlinearity observed in the shear stress–shear strain curve.

Off-Axis Tension Behaviour of Unidirectional PEEK/AS4 Thermoplastic Composites

An experimental method for non-standard off-axis tension tests of unidirectional composites is developed. A new oblique end-tab is designed to eliminate stress concentration and in-plane bending moment induced by off-axis tension loading. Finite element analysis and experiments on Polyetheretherketone (PEEK)/AS4 unidirectional thermoplastic composites (CFRTP) were conducted to evaluate the effectiveness of the proposed testing method. Simulation and test results demonstrate that the use of oblique end-tabs eradicates stress concentration and bending movements. The digital image correlation (DIC) method was used to help investigate the full-field tension/shear coupling deformation response of the off-axis specimen. Test results show significant nonlinear behaviour and inhomogeneous strain distribution under tension/shear combined stresses. A fractographic study was carried out to study the damage mechanisms under a tension/shear combined stress state. Specimens with 30°, 45° and 60° off-axis angles, fail in tension/shear mixed failure mode. Fracture surface morphology indicates that matrix plastic deformation and ductile drawing under tension/shear coupled stress state induced the nonlinear stress-strain response.

Material parameters of European spruce for tensile–shear fracture modeling

In this work, we present the results from an experimental campaign on solid and glued laminated timber made of European spruce (Picea abies) with 10.5mm or 45mm thick lamellas. We conducted off-axis tension and compression tests, shear block test, and compact tension test. The main purpose of the study was to obtain a consistent set of material parameters suitable for the calibration of a material model capable of capturing complex timber behavior, i.e. both linear and non-linear response together with respective fracture pattern, under various combinations of tension, shear, and compression. Elastic parameters and strengths parallel and perpendicular to the grain were retrieved from off-axis tension and compression tests. The traction–separation relation and fracture energy for the crack parallel to the grain was obtained by inverse analysis of compact tension test. The results capture the complexity of timber fracture and provide data for numerical simulations.

Investigation of the Membrane Behavior of UD-NCF in Macroscopic Forming Simulations

Unidirectional non-crimp fabrics (UD-NCF) provide an exceptionally high lightweight potentialcompared to other dry fabrics. However, their defect-free formability is limited compared towoven or biaxial fabrics due to their susceptibility to draping effects like wrinkling, gapping andfiber waviness. To predict these local effects and the global forming behavior efficiently, macroscopicmodelling approaches require the consideration of the mesoscopic material structure. A very detailedmacroscopic approach was proposed by Schirmaier et al. [1] and its prediction accuracy validatedwith qualitative and quantitative comparisons to component forming results. However, the approachcouples several deformation modes and therefore requires a very high number of inversely determinedmaterial parameters. In the present work a new macroscopic forming model for the membrane behaviorof UD-NCF is introduced based on superimposed shear, transverse tensile and perpendicular to thecarbon fiber tows oriented compressive strains. The model is parametrized with experimental resultsof different off-axis-tension-tests (OATs) (30°, 45° and 60°) and compared to the model proposed bySchirmaier et al. [1]. The results of the new membrane model agree well with the experimental andsimulative results in large areas, while utilizing a significantly reduced number of material parameters.However, some limitations are identified due to the reduced complexity of the model.

Mechanical response and damage mechanism of 2D woven SiCf/SiC ceramic matrix composites under tension-shear coupling load

The macroscopic mechanical behavior and coupling damage mechanism of 2D woven SiCf/SiC ceramic matrix composites (CMC) prepared by chemical vapor infiltration (CVI) process under tension-shear coupling load were experimentally analyzed. At macroscale, the uniaxial tension, uniaxial shear and off-axis tension tests were completed and the results were compared. The tensile modulus and proportional limit have no significant difference with the increase of off-axis angle, while failure strength decreases by 22.3% compared the 45° tensile (165.4 MPa) with the 0° tensile (212.8 MPa). Based on the strain-difference analysis, the coupling damage effect of SiCf/SiC-CMC was characterized. At microscale, the main damage types of SiCf/SiC-CMC during loading were analyzed by scanning electron microscope (SEM), and the corresponding laws between micro damage development and macro mechanical behavior under different loading conditions were revealed by cluster analysis of acoustic emission (AE) signals. The test results show that the micro damage caused by tensile and shear stress components promote each other. The macro mechanical behavior of SiCf/SiC-CMC under complex loading is controlled by basic micro damage forms such as matrix cracking, interface debonding and fiber fracture. The tension-shear coupling load affects the evolution process of the basic damage forms, and then change the macro properties of SiCf/SiC-CMC.

Mechanical analysis of fiber-reinforced plastics using an elastoplastic-damage constitutive equation considering asymmetric material behavior

Mechanical modeling of fiber-reinforced plastics to predict nonlinear mechanical behavior along the off-axis direction is very complex due to tension–compression asymmetry. This study aimed aims to develop a generalized constitutive model for different types of unidirectional and woven composites, considering tension–compression asymmetry in various deformation ranges from elastic to plastic, and finally to failure. To capture the asymmetry effectively, a new multivariable plastic model was proposed with additional dilatational components and different elastic moduli for tension and compression. Finally, asymmetric failure criteria and a damage evolution law were introduced for strength prediction. The proposed model was implemented in a finite element analysis software via a user material subroutine, and experimentally validated in terms of off-axis tension and compression tests in various loading directions. The experimental results were accurately predicted using a multi-parameter plastic model in this study compared to previous other models with few parameters.

Comparison of the shear behavior in graphite-epoxy composites evaluated by means of biaxial test and off-axis tension test

Abstract Characterization of shear behavior in composite materials remains a not fully solved problem. In the last fifty years, many different approaches have been proposed to solve this problem (rail shear, thin-walled tube torsion, off-axis tensile, ±45° tensile, Arcan, Iosipescu, asymmetric four-point bend, plate twist, v-notched rail shear, off-axis flexural, and shear frame), although none of these approaches have achieved an unquestionable solution. For this reason, proposals of alternative methods and comparison between different experimental techniques are of interest. In the present work, the use of cruciform samples with the fiber oriented at 45° with respect to the load directions, and subjected to tension-compression (creating a pure shear stress state at the central part of the samples), is studied. The experimental results of the cruciform samples have been compared with the off-axis tests (with the fiber at 10°) for the same material (AS4/8552), finding a good agreement between the shear experimental curves, especially at the initial part of the curve, where the shear modulus is calculated. Nevertheless, the shear strength value obtained by means of the cruciform specimen has shown to be significantly lower than that obtained using the off-axis test. A Finite Element numerical model of the cruciform specimen has been developed to analyze the stress field of the samples. Numerical results have shown that there is a central area of the cruciform specimens where a pure and uniform shear stress state is developed, which is suitable for the evaluation of the shear constitutive law of the material. It has been observed that there is a (σ 22) stress concentration in the transition between the straight and curved parts of the boundary geometry of the samples, which explain some premature failures of the samples. This premature failure could be avoided with tabs extended up to the beginning of the central part of the sample.

Experimental and numerical investigation of progressive damage and failure behavior for 2.5D woven alumina fiber/silica matrix composites under a complex in-plane stress state

The focus of this work is to characterize the progressive damage and failure behavior of 2.5D woven alumina fiber reinforced silica ceramic matrix thin composite specimen under a planar tension-shear stress state. The tensile and shear stress–strain diagrams in the principal material coordinate system were obtained using the off-axis tension test with the digital image correlation technique. A mesoscale finite element model of the composite material was developed within the framework of continuum damage mechanics. The thickness effect on the macroscopic mechanical response was considered by removing the periodic boundary conditions along the thickness direction. The macroscopic stress–strain response given by the numerical model was validated by the experimental results. The interaction of the planar biaxial tension and shear stresses was taken into account in the model, quantified using a shear contribution coefficient in the modified 3D Hashin failure criterion. The results from the damage evolution analysis indicate that the linear tensile stress–strain response with a brittle fracture characteristic for the on-axis tension specimen is governed by the axial fiber bundle. The nonlinear tensile stress–strain response with the significantly reduced ultimate stress under biaxial tension and shear stress state results from multiple damages with evolution in both axial and transverse fiber bundles. Both the effective tensile modulus and the ultimate tensile strength increase with increasing the thickness of the specimen due to the increase of the fiber volume fraction. The strengthening induced by the size effect is less significant for the specimen under biaxial tension and shear stress state than that for the on-axis tension specimen owing to the involvement of shear response dominated by the matrix of the material. The results of this study provide new insight into the failure of 2.5D woven ceramic-based composite material, which contributes to the optimal design of the reusable thermal protection system structure.

Dynamic shear strength evaluation of CFRP using off-axis tension test: theoretical and experimental studies

Shear strength evaluation in composites is still a problem that has not been fully solved. Dynamic shear strength evaluation is even more complicated. In present work, failure theories are used to determine the range of fiber orientations in which the evaluation of shear strength is feasible. The symmetrical laminate is used to eliminate coupled shear strain to improve measurement accuracy. Three different fiber orientation laminates are chosen for quasi-static tension test. And a combination of experimental and numerical method is carried out for high strain rate tests. The results show that the fiber orientation of ± 15° is suitable for evaluating the dynamic shear strength of CFRP (Carbon Fiber Reinforced Polymer). This study is of great significance to dynamic shear strength evaluation method of continuous fiber reinforced composites considering strain rate effect.

Effects of fabric architectures on mechanical and damage behaviors in carbon/epoxy woven composites under multiaxial stress states

The mechanical properties and damage evolutions of carbon/epoxy woven fabric composites with three different fabric architectures, including one plain weave and two twill weave patterns, are experimentally investigated under multiaxial stress states. In particular, the effects of weave patterns are investigated by monotonic and cyclic off-axis tension tests. Both elastic modulus and strength degrade remarkably with increasing off-axis loading angle, while Poisson's ratio is much higher than that measured from on-axis tests and increases with loading strain gradually. Different fabric architectures show limited effects on the modulus and strength under multiaxial stress states, and they are well predicted by transformation equation and Tsai-Wu failure criteria, respectively. However, significantly different failure behaviors are observed in three fabric composites, and microstructure observation shows that fabric architecture affects the stress concentration and the damage development. Smaller crimp ratio and compacted structure postpone the damage development but result in more abrupt failure under multiaxial stress states.

Premature failures in standard test specimens with composite materials induced by stress singularities in adhesive joints

This work presents three examples of standard test configurations, involving composite materials, where the presence of stress singularities induced by adhesive joints causes premature failures leading to underestimated strength values. Slight modifications of the local geometry, removing or reducing, in these critical points, the order of the stress singularities, have shown to give higher experimental failure loads, with almost double failure loads in the most striking cases.The three examples analyzed in the present work are: a) the tensile and shear strength determination of a bimaterial interface, b) the off-axis tension test, for the intralaminar shear strength of unidirectional long fibre composite materials and c) the compression test of thick composite laminates. In two of the three cases, the premature failure occurs at the corner where the tab (which is necessary for the grip jaw faces of the testing machine) is bonded to the composite laminate, while in the third one the failure occurs at the bimaterial interface of the two materials, all of them involving an adhesively bonded joint and corner configurations with stress singularities.With the use of a semi-analytical tool, developed by the authors, to calculate the order of stress singularities, slight and very local geometrical modifications have been successfully carried out to eliminate the stress singularity configuration. After the modifications, higher failure loads have been obtained in the tests carried out.The major outcome of the present work is the role that the singular stresses play in the premature failure of standard tests involving adhesive bonding. A correlation between the removal of the singularity stress configuration in critical parts of the samples and a higher experimental failure load, in all studied cases, has been clearly shown.

On the optimal choice of fibre orientation angle in off-axis tensile test using oblique end-tabs: Theoretical and experimental studies

Shear strength evaluation in composite materials still remains a not fully solved problem. One of most promising proposals to characterise a material in shear by means of a simple tensile test is the off-axis tension test with oblique end-tabs whose inclination coincides with that of the longitudinal isodisplacement lines. This end-tab configuration presents an essential difficulty since the tab angle depends on the material properties including the shear modulus G12, which is one of the values to be obtained from off-axis tension tests.In the present work, the study of the most suitable fibre orientation for the performance of off-axis tests under an oblique tabs configuration has been addressed. An analytical study on the dependence of the tab angle ϕ on both the fibre orientation θ and the material properties E11, E22, ν12 and G12 has been carried out, the quotient G12/E11 being identified as the parameter that controls the evolution of the tab angle.The influence of deviations in the tab angle on the stress state near the corners of specimen has been analysed by means of a novel study of the nominal singular stress state at these points. The results of this study show that negative deviations in the angle of the tabs contribute to decrease the severity of the stress state at the corner, whereas positive deviations contribute to increase the order of the stress singularity. Additionally, the range of fibre orientations in which the evaluation of shear strength S is feasible has been determined, i.e., the effect of σ12 in the failure is clearly dominant versus the effect of the rest of the stress-state components.In the experimental part of this work, four different fibre orientation angles (5°, 10°, 15° and 20°) have been considered to perform the off-axis tension test under oblique end-tabs configuration. The experimental results of these tests show that only for 10° fibre orientation angle the majority of specimens fail at the central zone under a uniform stress state. Finally, for a fibre orientation angle θ = 10°, specimens with induced positive deviations in tab angle of +3° and +7° have been tested, it being observed that all the failures appears at the end of specimens.On the basis of both theoretic and experimental results, the optimal fibre orientation angle to use in the tests is θ = 10°. The tab angle must be evaluated on the basis of an estimation of the material properties (quotient G12/E11), it being recommendable, in case of ignoring the value of G12, to use a tab angle lesser than the theoretical value to avoid positive deviations.

Elastic anisotropy of dual-phase steels with varying martensite content

The elastic anisotropy of 5 cold-rolled steel sheets typical of automotive applications is probed experimentally and the results are represented using orthotropic elasticity. The steels have an increasing volume fraction of martensite, ranging from zero to over 90%. This leads to different strength and ductility for each of the 5 steels, with the strongest being 5.8 times so over the weakest, but only 0.11 times as ductile. The elastic properties measured are the Young's modulus and Poisson's ratio at 15° increments from the rolling direction of the sheets. These properties are measured by uniaxial tension and pure-bending experiments, respectively, instrumented with electrical-resistance strain-gages. The recorded responses are repeatable and, well within the limit of elastic deformations, linear. Both properties are found to have orientational dependence. The variation of the Young's modulus is the opposite of that of Poisson's ratio. In addition, the dual-phase (ferritic-martensitic) steels exhibit the opposite trends than the single-phase (purely ferritic) one. These experiments are then compared to the results of orthotropic elasticity. Under plane-stress, this material model depends on 4 material parameters. This simple model represents all of the experiments very well, indicating that the elastic anisotropy stems from the rolling-induced microstructure and, for the dual-phase steels, the presence of the second, reinforcing phase. Furthermore, the model allows the quantification of extension-shear coupling when these orthotropic materials are loaded off-axis to the material orientations. This coupling was found to be limited, so that the off-axis tension tests are indeed close to the uniaxial stress state. One of the material parameters needed is the in-plane shear modulus, which poses challenges in its determination for the present thin sheets. Despite the mild anisotropy found in these materials, assuming the isotropic value for the shear modulus deteriorates the predictions significantly. This work demonstrates that single- and dual-phase steels indeed behave elastically as orthotropic materials, as expected on theoretical grounds based on their pre-processing by rolling. The results of this work can be used to introduce elastic anisotropy in sheet metal forming simulations intending to predict springback, with only a limited number of experiments needed for calibrating the model for a given material.

Evaluation of a modified Iosipescu shear test method for determining the shear properties of clear wood

A modified Iosipescu shear test method is proposed as an alternative for measuring the shear properties of clear wood. The method adopts four-point asymmetric loading procedure in the Iosipescu shear test but with the loading positions shifted to the neutral axis of the specimen. The original V-notched specimen is replaced by a combination of polyvinyl chloride blocks at two ends and a bow-tie-shaped wood specimen in the middle to provide a better stress pattern at failure. The measured shear strength and shear moduli are compared with results from compression test and off-axis tension test. Finite element analysis is also carried out to study the stress distribution in the wood specimen. Results show that the new shear test setup can provide close-to pure shear stress state in the specimen yielding better estimates of the shear properties of wood. The shear strength obtained by the new test setup is slightly lower than that from the off-axis tensile test which is probably due to the relatively thick specimen chosen in this study.

The shear behaviour of pine wood in the Arcan test with the digital image correlation

The Arcan shear test is used together with the digital image correlation to study the shear stress-strain relationship for pine wood in the symmetry plane LR . The relationship of shearing perpendicular to the grain direction is shown by the straight line below the proportional limit and the nonlinear curve beyond it describing hardening up to the ultimate limit. Subsequent failure modes are shown during the load increase. Additionally, some results of the off-axis tension tests, as well as the uniaxial tension tests, with the mechanical and electric resistance strain gauges are presented to determine and compare the shear modulus from both methods of testing.