In-plane Tensile Tests Research Articles

Extension of the GISSMO fracture model for thin-walled structures under combined tensile and bending loads

Ductile fracture prediction for thin-walled structures requires computationally efficient simulation tools able to approximately represent the key effects that occur on the sub-thickness scale. Unfortunately, classical shell elements, typically used to model deformation and failure of thin components, are inherently in a state of plane stress and therefore unable to capture the through-thickness stress distribution. This is consequential considering recent studies that demonstrated the differences between fracture in bending vs. in-plane tension. A laterally constrained thin metal plate under in-plane tension is likely to fracture under significantly lower plastic strain than the same plate under bending (with fracture initiating on the tensile side), even though both these conditions are examples of plane strain tension. Under in-plane tension fracture is preceded by a through-thickness neck, and therefore higher stress triaxiality than in the case of plane strain bending, where necking is absent. To account for these differences, we propose an extension of the GISSMO model, which relies on a simple fracture criterion based on stress-dependent fracture strain defined by the user (i.e. fracture locus). The fracture strain is typically determined experimentally using a combination of in-plane tensile tests under varying degree of lateral constraint and shear tests. The proposed extension involves defining a separate fracture locus for bending, also determined experimentally using bending tests. Fracture occurs when the equivalent plastic strain reaches its critical level represented by interpolation between the two bounding cases, i.e. bending and in-plane tension, with a bending index Ω used as an interpolation parameter.

Bending behaviors of carbon fiber composite honeycomb cores with various in-plane stiffness

Designing curved surfaces with a traditional straight-walled honeycomb is challenging due to its excessive in-plane stiffness, making it prone to fracturing during bending. The research motivation is overcoming the flexibility limitation of conventional straight-wall honeycombs with the new curved-wall design. Moreover, the three-dimensional failure mechanism map based on the theoretical models is expected to contribute to the design of a carbon fiber composite curved-wall honeycomb. This paper outlines the fabrication process using a modified co-curing method. It also includes theoretical models developed to examine the effect of the center angle of curved walls on the honeycomb’s in-plane stiffness and bending behavior. In-plane tensile and three-point bending tests were conducted to verify the theoretical modes. Finite element model was created to study the stress distribution and damage degree. The study is also aimed at examining the load-bearing capacity of sandwich beams with curved-wall honeycomb cores. A three-dimensional failure mechanism map shows how the failure modes of sandwich structures are affected by the center angle of the curved walls. The study offers a new approach to designing carbon fiber composite honeycombs with flexible bending deformation and high load-bearing capacity. These honeycombs could potentially be used in lightweight launch-vehicle shell structures.

Characterisation and damage modelling of oxide/oxide composites considering temperature dependence

Continuous fibre reinforced ceramic matrix composites (CMCs) are increasingly being employed in safety critical applications. As a result, their use in these applications requires the adoption of appropriate design methodologies that are able to consider their complex non-linear mechanical behaviour. In this paper, a simple but robust formulation for continuum damage model, thermodynamically consistent and written under plane stress condition, is proposed for a laminated 2D woven composite material. This model is implemented via the Classical Laminate Theory (CLT) extended to non-linear behaviour to predict the behaviour of different stacking sequences. In-plane tensile tests were performed on an oxide/oxide composite up to 1000 °C to fully identify the model. The procedure is described and used on tests at room temperature before being extended higher temperature tests. Finally, the law and its coupling with the CLT are validated by means of tests on quasi-isotropic and cross-ply laminates at different temperatures.

A novel mechanical attachment for biaxial tensile test: Application to formability evaluation for DP590 at different temperatures

A novel mechanical attachment for conducting in-plane biaxial tensile test is provided in this paper. In this attachment, the conversion of force from an external actuator into two pairs of orthogonal forces is achieved by specially designed trapezoidal blocks. By using trapezoidal blocks with different inclination angles, biaxial tensile tests of six different tensile ratios can be performed. A heating device is designed for the attachment to conduct thermal biaxial tensile tests. The heating device adopts a combination of the induction heating technology and the conduction heating method. With the developed mechanical attachment and the heating device, the forming limit curves (FLC) of DP590 sheets at ambient temperature, 300 °C, 400 °C and 500 °C are determined using biaxial tensile tests. A classical Nakazima test procedure at ambient temperature is carried out to establish a reference FLC for the material, and the reference FLC is further used to evaluate the results from biaxial tensile tests. Furthermore, an anisotropic GTN model based on Yld2000-3d yield criterion is calibrated by inverse identification procedures and applied to predict the localized necking and fracture for DP590 sheets under biaxial tensions.

Prediction and characterization of forming limits at necking from shear to equi-biaxial loading using the biaxial tensile testing method: Feasibility study and application to AA6061-T4

Determination of forming limit curve (FLC) over a wide range of strain paths can provide a more thorough understanding of sheet metal formability. In this work, for the first time, in-plane biaxial tensile tests employing two distinct cruciform specimens are performed to construct the FLC of AA6061-T4 sheets from shear to equi-biaxial stretching. Four different necking detection methods are investigated in a FE (finite element) procedure to find proper ones for the defined specimens. This procedure consists of the FE modeling of the biaxial tensile test and the Marciniak test. An anisotropic Gurson-Tvergaard-Needleman (GTN) plasticity model based on Hill’48 yield function is calibrated and implemented in simulations to reproduce the anisotropic plasticity and failure behavior of AA6061-T4 sheets. Then, the selected necking detection methods are applied to the biaxial tensile test to experimentally identify the limit strains at necking. The results show that considering two distinct cruciform specimens is an effective solution for the biaxial tensile test to determine the FLC covering a wider range of strain paths. The predicted FLCs show good agreement with the experiments, indicating that the numerical biaxial tensile test combined with the anisotropic GTN plasticity model is an efficient tool for predicting sheet metal formability.

Asphalt shingle modeling and parameter estimation under short period loading condition

Asphalt shingles are one of the major sources of insurance damage claims after a hailstorm. The mechanical behavior of asphalt shingles needs to be thoroughly investigated to evaluate their hail resistance performance. In this study, tensile tests are conducted on the asphalt shingles samples and one of the important components of asphalt shingles - the fiberglass base mat. The elastic moduli of samples cut from different orientations vary. The simplified representative volume element (RVE) model of asphalt shingle is developed, and its constituent material properties are estimated through optimization to ensure the simulation results match the experimental results. To investigate the effectiveness of modeling asphalt shingles as an orthotropic material, the developed asphalt shingle RVE model is used to estimate the effective orthotropic material model properties and the in-plane tensile tests simulation results can reasonably match the experimental results. Meanwhile, the effect of fiber volume ratio and constituent material properties on the asphalt shingle moduli are further investigated based on the asphalt shingle RVE model.

Fusion-bonding performance of short and continuous carbon fiber synergistic reinforced composites using fused filament fabrication

In this work, short and short continuous fiber synergistic reinforced composites (S-CFRPCs) were successfully fabricated by fused filament fabrication. The influences of short fiber content on the filament bonding properties were evaluated through short beam shear (SBS) and in-plane tensile shear tests. The data showed an increasing and then decreasing trends of interlaminar shear strength (ILSS) and in-plane shear strengths of S-CFRPCs specimens as short fiber content rose from 0 wt% to 10 wt%. Specimens with a short fiber content of 5% displayed higher load carrying capacities and significant fusion-bonding performances, with approximately 41% and 80% increase in ILSS and in-plane shear strength when compared to 0% specimen, respectively. The fracture surfaces of tested S-CFRPCs specimens indicated fiber pull-out and resin fracture as dominant bonding failure models. The use of proper amounts of short fibers effectively improved the fusion-bonding of S-CFRPCs. In sum, these findings look promising for future design of strong and tough composite structures.

Designing a Cruciform Specimen via Topology and Shape Optimisations under Equal Biaxial Tension Using Elastic Simulations.

Stress uniformity within the gauge zone of a cruciform specimen significantly affects materials’ in-plane biaxial mechanical properties in material testing. The stress uniformity depends on the load transmission of the cruciform specimen from the fixtures to the gauge zone. Previous studies failed to alter the nature of the load transmission of the geometric features using parametric optimisations. To improve stress uniformity in the gauge zone, we optimised the cross-arms to design a centre-reduced cruciform specimen with topology and shape optimisations. The simulations show that the optimised specimen obtains significantly less stress variation and range in the gauge zone than the optimised specimen under different observed areas, directions, and load ratios of von Mises, S11, S22, and S12. In the quantified gauge zone, a more uniform stress distribution could be generated by optimizing specimen geometry, whose value should be estimated indirectly each time through simulations. We found that topology and shape optimisations could markedly improve stress uniformity in the gauge zone, and stress concentration at the cross-arms intersection. We first optimised the cruciform specimen structure by combining topology and shape optimisations, which provided a cost-effective way to improve stress uniformity in the gauge zone and reduce stress concentration at the cross-arms intersection, helping obtain reliable data to perform large strains in the in-plane biaxial tensile test.

Concurrent multiscale modeling of in-plane micro-damage evaluation in Z-pinned composite laminates

Most of the unit cell models for Z-pinned composite laminates (ZCL) are mesoscopic in scale, where the fiber reinforced zone is modeled as homogeneous but without detailed characterization and failure analysis of the fibers and matrix. This paper proposes a new concurrent multiscale unit cell model to investigate the in-plane micro-damage evolution of ZCL. The novelty worth mentioning is the proposed element-based method to generate random microbuckling spatial fibers in the fiber reinforced zone, where the microbuckling is caused by fiber waviness and fiber crimp, and then the mesh of fiber, Z-pin, matrix, and the interface between Z-pin and matrix is regenerated. In-plane tensile tests (ASTM D3039) are conducted for verification. There is good agreement between experiment and simulation, only with deviations of −0.97% and 2.69% for tensile modulus and fracture initiation stress, respectively. The research indicates that in-plane micro-damage initiates from the interface between Z-pin and matrix. The stress concentration and higher local fiber volume fraction, caused by the microbuckling spatial fibers clustered near the Z-pin, play a major role in the evolution of interface damage, crack initiation and growth.

U-Type Honeycomb Based on Super-Elastic Shape-Memory Alloy for One-Dimensional Large Wing Morphing

Flexible skin is an important part of morphing wings, which must comply with the altered geometry during wing morphing. Especially for some applications of one-dimensional large morphing wing such as chord-change, flexible skin is demanded to be capable of large deformation. In this paper, we present a U-type honeycomb structure of shape-memory alloy (SMA) for flexible skin that can undergo large deformation owing to the super-elastic Nickel Titanium (NiTi)-SMA, and the mechanical properties are studied by numerical and experimental methods. In the stage of linear elasticity, U-type honeycomb structure is analyzed theoretically based on the virtual work principle, and its mechanical behavior in the stage of large deformation is studied by finite element method with considering geometric and material nonlinearity. In-plane tensile tests and out-of-plane load-bearing tests are performed, and the experimental results agree well with the numerical results. The experimental results have proved that the U-type honeycomb structure based on NiTi-SMA has large deformation capability, of which the recoverable global strain can reach at least 60%, and has great potential in the application of morphing wings.

Prediction of strength and fatigue life for 2D plain-woven high-alumina fiber reinforced alumina matrix composites under a complex in-plane stress state

This paper presents a strength criterion and fatigue life prediction method for 2D braided alumina matrix composites under a complex in-plane stress state. The static strength of the material was obtained by in-plane tensile, compression, and pure shear tests. Considering the difference between tensile and compressive properties of materials and the influence mechanism of in-plane tensile and shear coupling on material strength, a revised Hoffman strength theory was proposed. The predicted off-axis tensile strength is consistent with the test results, and the deviation is not more than 10%. Tensile fatigue tests were carried out with the off-axis angle θ=0°, 15°, 30°, 45°, the stress ratio R=0.1, and frequency f=10 Hz. The test results show that the fatigue life decreases with the increase of off-axis angle. Due to the in-plane shear stress component, the fatigue failure is gradually changed from fiber-dominated to fiber-matrix dominated mode. Based on a combination of the uniaxial tensile fatigue life curve, the Broutman-Sahu residual strength model, which is used to characterize the variation of the residual strength with the fatigue cycles, and the modified Hoffman strength theory, the paper proposes a fatigue life prediction model under complex in-plane loading conditions. The fatigue shear damage factor is defined to characterize the effect of the normal and shear stress interaction on fatigue life. The fatigue life prediction model is used to predict the fatigue life of specimens in the off-axis tensile fatigue tests. The predicted result agrees with the test result, and the deviation is within the 1-time life span. The results indicate that the proposed fatigue life prediction model can be used to predict the fatigue life of 2D braided alumina matrix composites under the complex in-plane stress condition with the given stress ratio, temperature, and fatigue load frequency.

In-plane and out-of-plane characterization of a 3D angle interlock textile composite

The present work focuses on the characterization of the in-plane and out-of-plane behavior of a three-dimensional angle-interlock woven composite. In-plane tensile and compression tests, short beam shear tests and through-the-thickness compressive tests were carried out to assess the mechanical behavior of the composite material. The results are presented in terms of stress–strain responses, elastic moduli, failure strains and strengths. In addition, the material elastic properties were measured using an ultrasonic method. Results are compared with the values of the elastic properties determined by mechanical testing. A good correlation is observed which demonstrates the pertinence of this technique to measure in particular the through-thickness elastic properties of the material.

In-plane shear tensile characteristics of polyester composites: Effects of sunlight exposition

This work focusses on the analysis of in-plane shear tensile test carried out on samples aged by UV–Visible light. The tendency of in-plane shear properties with exposure time fits to a decreasing exponential curve. Different thermosetting polyester resins, curing temperatures profiles, and fibreglass fabrics are employed for this study. The type of resin and curing temperature influence on elastic modulus and shear strength of composite. The ageing degree varies between 14% and 25%, depending on shear property and the composition.

Edge strength of core drilled and waterjet cut holes in architectural glass

In structural glass design, an often-applied connection is a bolted connection subjected to in-plane tensile loads. Traditionally, the hole in the glass pane is manufactured by core drilling and conical edge finishing. An alternative method is by waterjet cutting the holes, resulting in cylindrically shaped holes. This research compares the edge strength of core drilled and waterjet cut holes. It focuses on in-plane tensile tests and consists of an experimental part in combination with a numerical part. In the in-plane tensile tests, peak stresses occur perpendicular to the load direction. These stresses are found to be higher for waterjet cut holes (+ 13%) compared to core drilled holes. As a result, the characteristic ultimate load is lower for waterjet cut holes (− 16%). Furthermore, the influence of thermally toughening the glass is found to be more favourable for the characteristic ultimate load of specimens containing core drilled holes than it is for waterjet cut holes. Next to that, it was found that the ultimate load linearly increases with the panel thickness. Eccentric loading, caused by insufficient bushing material or rotation of the bolt, only slightly decreases the ultimate load, provided that no hard contact between bolt and glass occurs. In addition, coaxial double ring tests were performed in the hole area, showing that waterjet cut holes result in larger stresses near the hole edge than core drilled holes. Furthermore, waterjet cut holes are found not to be perfectly round, while drilled holes are. This un-roundness negatively influences the ultimate load and the stresses in the glass; the larger the extent of un-roundness, the higher the stresses and the lower the ultimate load. Also, the orientation of the un-round hole is of influence on the stresses and ultimate load for the tensile test. It is concluded that waterjet cut holes result in lower characteristic ultimate loads and higher stresses. Due to the different edge finishing, the ultimate load still is lower compared to core drilled holes, even if the waterjet cut holes are perfectly round.

A comparative study of a quasi 3D woven composite with UD and 2D woven laminates

To develop a composite with high in-plane properties and sufficient delamination resistance, a quasi-three-dimensional (Q3D) woven composite has been designed. In Q3D, some yarns in each layer are woven into those in the adjacent layers and form a 3D interlocking network. This study examines the performance of a carbon fiber/SC-15 epoxy triaxial Q3D [(0°/60°/−60°)4] composite. For comparison, a [0°/60°/−60°]4 composite laminate with unidirectional (UD) plies and a [0°/60°/−60°]4 laminate with two-dimensional woven (2DW) layers were fabricated using the same carbon fiber and epoxy system. The in-plane tensile, interlaminar fracture, and low-velocity impact tests were performed for all three types of composites. The results show that the Q3D composite has the in-plane tensile modulus and strength comparable to that of UD and 2DW composites, but offers a higher resistance to interlaminar crack propagation and impact damage. This work provides insights into the influences of fiber structures on composite properties and performances.

In-plane and out-of-plane tensile behaviour of single-layer graphene sheets: a new interatomic potential

This paper compares simple interatomic potentials for carbon nanostructures with hexagonal lattice, by investigating the in-plane and the out-of-plane tensile behaviour of single-layer graphene sheets. Attention is given both to potentials already considered in the literature and to a new one, which we call the damped DREIDING potential, in which damping functions are added to the DREIDING potential. For each potential, a calibration of its parameters and a focus on its performance are carried out in the in-plane context, by comparison with ab initio results of the rigidities and of the tensile limit properties, under periodic conditions. In addition, the damped DREIDING potential is used to perform in-plane tensile tests on both pristine and perforated single-layer graphene sheets of finite size. In the out-of-plane context, the calibration from ab initio results is only possible with reference to the rigidity. For the damped DREIDING potential, a sensitivity analysis, applied to a nanoindentation problem, on a pristine single-layer graphene sheet of finite size is provided. In doing so, a narrow range of value of the force needed to remove an atom from a sheet is given.

Elastic-plastic model for the mechanical properties of paperboard as a function of moisture

Abstract To verify a linear relation between normalized mechanical property and moisture ratio, in-plane tensile tests were performed on four types of paperboard from different manufacturers. Tensile properties were normalized with respect to the property at standard climate (50 % RH, 23 °C). Short-span Compression Tests were also performed to investigate if the relation was linear also for in-plane compression. The tests were performed at different relative humidity (20, 50, 70 and 90 % RH) but with constant temperature (23 °C) in MD and CD, respectively. The linear relation was confirmed for the normalized mechanical properties investigated. In fact, when also the moisture ratio was normalized with the standard climate, all paperboards coincided along the same line. Therefore, each mechanical property could be expressed as a linear function of moisture ratio and two parameters. Moreover, an in-plane bilinear elastic-plastic material model was suggested, based on four parameters: strength, stiffness, yield strength and hardening modulus, where all parameters could be expressed as linear functions of moisture ratio. The model could predict the elastic-plastic behavior for any moisture content from the two parameters in the linear relations and the mechanical properties at standard climate.

A study on ratio and linearity of strain path in in-plane biaxial tensile test for formability evaluation

In-plane biaxial tensile test is an alternative to determine the forming limit diagram (FLD) for evaluating the formability of metal sheets, in which cruciform specimens are deformed under the plane stress condition. Given that strong dependence of an FLD on both the strain state and the strain path, it is critical to realise the deformations under various proportional strain paths in the in-plane biaxial tensile test. In this study, three different stretching modes in a previously developed planar biaxial tensile rig, called stretching model-I, stretching model-II and stretching model-III, were applied to deform one type of cruciform specimen for AA5754 under an expected strain state of the equi-biaxial tension, the plane-strain tension and the uniaxial tension, respectively. The digital image correlation (DIC) technique was adopted for strain field measurement. By analysing the ratio and the linearity of the strain paths in the different zones within the gauge area of the cruciform specimens, it was found that, by using the stretching mode-I, the equi-biaxial strain state was obtained only in the central zone, and the corresponding strain path is linear. The plane-strain states were not achieved in any zones within the gauge area by using the stretching mode-II, and the corresponding strain paths are nonlinear. By using the stretching mode-III, the fracture occurred in a zone within the gauge area where the strain state is uniaxial and the corresponding strain path is linear, while the strain state in the central zone is close to the pure shear and the strain path is nonlinear.

Effect Of Temperature And Strain Rate On The Plastic Anisotropic Behavior Characterized By A Single Biaxial Tensile Test

The heterogeneous strain field measured by digital image correlation in the central gauge area of a cruciform specimen permits to characterize the plastic anisotropic behavior of metallic sheets with a unique specimen [1]. Indeed, minor and major strains measured along several paths show a wide range of strain states, from uniaxial to equi-biaxial stress state. Thanks to the recording of forces along the two loading directions and to the strain field measurement, an identification of complex anisotropic yield criteria (like Bron and Besson criterion) is possible by inverse procedure. Then, a unique test is sufficient to evaluate the anisotropic behavior of the sheet. The aim of this work is to evaluate the effect of temperature and strain rate on the anisotropic behavior of AA6061 sheet. For this purpose, a biaxial device equipped with four hydraulic cylinders and accumulators (applied speed until 200mm/s), and with an air flow generator (applied temperature up to 160°C) is used to perform in-plane biaxial tensile tests for different conditions of strain rate and temperature. Numerical simulations of the equi-biaxial tensile test are then performed for these different experimental conditions. The numerical simulations are based on a FE model of the cruciform specimen including temperature and strain rate hardening dependencies while the Bron and Besson yield criterion has been calibrated only at room temperature and under quasi-static conditions. Finally, agreement between experimental and numerical evolutions of principal strains and strain paths ratios along three specific profiles is compared and the relevance of using only one experimental condition (room temperature and quasi-static strain rate) to calibrate the yield criterion is discussed.

On Phenomenological Failure Loci of Metals under Constant Stress States of Combined Tension and Shear: Issues of Coaxiality and Non-Uniqueness

The present study investigates how the choice of characterization test and the composition of the stress state in terms of tension and shear can produce a non-unique failure locus in terms of stress triaxiality under plane stress conditions. Stress states that are composed of tensile and simple shear loadings result in a loss of proportionality between the cumulative strain and stress such that the principal frames become non-coaxial despite a constant stress triaxiality. Consequently, it is shown that the conventional interpretation of a failure locus in plane stress is based upon an implicit assumption of proportional coaxial loading. The use of simple shear tests along with traditional in-plane tensile tests for fracture characterization is only one “path” that can be taken in terms of the stress triaxiality, which may produce a bifurcation at uniaxial tension while the tension–torsion path does not. In general, the failure locus in terms of the equivalent strain is a failure surface and must consider the composition of the stress state that produces a given triaxiality. A comprehensive review of phenomenological fracture loci within a modified Mohr-Coulomb (MMC) framework is performed to highlight how the choice of stress states obtained using different characterization tests can change the apparent fracture locus of a material. The finite strain solutions for the work conjugate equivalent strain are derived for various loading paths that produce the same stress triaxiality. It is then shown that accounting for non-coaxiality leads to equivalent failure strains that are even higher than previously reported in tension–torsion tests within the literature. The equivalent plastic strains integrated from finite-element simulations are work-conjugate by definition. The equivalent strains estimated from the cumulative principal strains using DIC strain measurement depend upon a coaxial or non-coaxial assumption. Finally, an analytical solution for the onset of diffuse necking that accounts for the stabilizing influence of shear loading against a tensile instability is considered. Even under plane stress conditions, a failure surface arises in terms of the equivalent strain at necking, the stress triaxiality, and the severity of shear loading.