Failure envelope under biaxial tensile loading for chopped glass-reinforced polyester composites

In this paper we present the biaxial failure curve of a chopped glass-reinforced polyester composite. The curve has been obtained combining the results of experimental tests with the results of numerical simulations developed by means of the Finite Element Method. The experimental tests have been performed applying perpendicular loads to cruciform specimens. Then, taking into account the numerical results, we have constructed the failure envelope in the tensile–tensile quadrant. Moreover we propose to modify the cruciform geometry to obtain, varying the widths of the loaded arms and the tapered central zone, points of the failure curve in which the two components of the plane stress tensor are different.     

Characterisation of material properties for draping of dry woven composite material

Three test methods, uniaxial bias extension, biaxial and picture frame tests are used to characterise the shear behaviour of dry woven fabric during draping. The deformation of the bias extension and biaxial specimens is measured from images of a central gauge section. The forces applied to the material are resolved into forces along and parallel to the tow directions. The deformation of the material in the bias extension and biaxial tests is found to behave in a manner which is reasonably well described by a pin-jointed net analysis. There is negligible change in the shear resistance of the material during biaxial loading, while a slight increase in shear resistance is observed in the picture frame tests. Microscopic examination of the tow architecture [Compos Sci Technol 63 (2003) 99], which shows a significantly smaller crimp amplitude for picture frame tests than for the bias extension and biaxial tests, supports the suggestion raised by Harrison et al. [Proceedings of the 10th European Conference on Composite Materials, 2002], that the increase in resistance in the picture frame tests is associated with an increase in tow cross-over force generated by large loads along the tows.     

Ultimate fracture capacity of pressurised pipes with defects - Comparisons of large scale testing and numerical simulations

In this paper results from large scale 4-point bending tests of pipe-segments are compared with numerical analyses using LINK_pipe. The experiments were carried out as a part of the joint industry project Fracture Control - Offshore Pipelines. The comparisons between large scale testing of pipelines and numerical analyses also address the effect of biaxial loading on the strain capacity. The defect is positioned on the tension side of the pipe when applying the load. A parametric study on changing the nominal wall thickness of the pipe is carried out. Due to variation in the yield stress, a parametric study to see the effect of this variation was also performed. The results demonstrate that ductile crack growth and biaxial loading are important elements in fracture assessment procedures for pipelines.     

Biaxial buckling analysis of double-orthotropic microplate-systems including in-plane magnetic field based on strain gradient theory

Background/purposeThis paper deals with analysis of biaxial buckling behavior of double-orthotropic microplate system including in-plane magnetic field, using strain gradient theory.MethodsTwo Kirchhoff microplates are coupled by an internal elastic medium and also are limited to the external Pasternak elastic foundation. Utilizing the principle of total potential energy, the equilibrium equations of motion for three cases (out-of-phase buckling, in-phase buckling and buckling with a plate) are acquired. In this study, we assumed boundary conditions of all the edges are simply supported. In order to get exact solution for buckling load of system, Navier approach which satisfies the simply supported boundary conditions is applied.ResultsVariations of the buckling load of double-microplate system subjected to biaxial compression corresponding to various values of the thickness, length scale parameter, magnetic field, stiffness of internal and external elastic medium, aspect ratio, shear stiffness of the Pasternak foundation and biaxial compression ratio are investigated. Furthermore, influence of higher modes on buckling load is shown. By comparing the numerical results, it is found that dimensionless buckling load ratio for in-phase mode is more than those of out of phase and one microplate fixed. Also it is shown that the value of buckling load ratio reduces, when non-dimensional length scale parameter increases.ConclusionHowever, we found when properties of plate are orthotropic the buckling load ratio is more than isotropic state. Also, by considering the effect of magnetic field, non-dimensional buckling load ratio reduces.     

Non-linear finite element analysis of inserts in composite sandwich structures

In aeronautics, sandwich structures are widely used for secondary structures like flaps, landing gear doors or commercial equipment. The technologies used to join these kinds of structures are numerous: direct bonding or joining, tapered areas, T-joints, etc. The most common is certainly the use of local reinforcement called an insert. The insert technologies are numerous and this study focuses on high load bearing capacity inserts. They were made with a resin moulded in the Nomex™ sandwich core. Such structures are still designed mainly empirically and the lack of efficient numerical models remains a problem. In this study, pull-out tests were conducted on a representative sample and the non-linearities and the types of failure were analysed. Core shear bucking, failures of the potting and perforation of the composites skins are the main modes of failure. For each mode, local experimental and numerical analysis was carried out that led to the identification of the independent non-linear behaviour of each component. Including the results in a global non-linear finite element model gave good prediction of the failure scenario and an acceptable correlation with the tests.     

基于双轴拉伸试验的飞艇蒙皮材料非线性分析

飞艇蒙皮为多功能层压织物材料,力学行为呈现复杂的非线性,合理表征其非线性的力学模型对飞艇结构设计与分析至关重要。本文对飞艇蒙皮材料试件进行了7个应力比双轴拉伸试验,基于正交异性材料模型,采用应变残差平方和最小方法计算弹性常数,建立线性力学模型;根据试验数据建立应力弹性常数响应面,建立以应力为变量的完整三次式非线性力学模型。并根据此力学模型建立飞艇蒙皮材料有限元分析模型,通过数值模拟七种应力比下的双轴拉伸试验,分析结果的应力分布和分缝位移与试验现象一致。将分析得到的应力-应变曲线与试验结果进行对比,两者能很好的吻合,表明非线性力学模型及分析方法适用于飞艇结构分析。     

Ultraschallbasierte in situ Vorspannkraftermittlung an Schrauben ohne Referenzmessung im nicht verspannten Zustand durch Kombination von Longitudinal- und Transversalwellen

Ultrasonic based bolt preload evaluation is commonly performed using the mono-wave method. This method works by measuring the time of flight of longitudinal waves. Here, a reference measurement in the unloaded condition is necessary for each bolt. In this publication the longitudinal wave is complemented by another type of ultrasonic wave - the transverse wave. This method does not require a reference measurement in the unloaded condition for each bolt. Moreover, an analytic method for determining the bolt-specific K-value is introduced, which is needed for the ultrasonic bolt preload determination. The analytically calculated K-values are compared with experimental K-values from tensile tests. The influence of material, bolt property class and surface protection system were determined with cylindrical specimens. In component tests, the bolt preload was evaluated using the bi-wave method, a possible influence of the bolt assembly method was investigated and the results were interpreted regarding their accuracy.     

Some applications of Burzyński yield condition in metal plasticity

The classical J₂ plasticity theory is widely used to describe the plastic response of metallic materials. However, this theory does not provide satisfactory predictions for materials which exhibit pressure-sensitive yielding or plastic dilatancy. Another difficulty is the difference between the values of yield stresses in tension and compression for isotropic materials, the so-called strength differential effect (SD), leading to the asymmetry of the elastic range. The Burzyński yield condition, proposed in 1928, can be used to overcome some of these problems. In this paper an implicit integration of the elasto-plastic constitutive equations for the paraboloid case of Burzyński’s yield condition is formulated. Also, the tangent operator consistent with the integration algorithm was developed and is presented. The proposed model was implemented in a commercial Finite Element code and different kinds of tests reported in the literature were simulated. The comparison between the numerical and experimental results shows that the plasticity theory with the paraboloid case of Burzyński’s yield condition describes adequately the strength differential effect, which is present in many kinds of materials significant for recent applications.     

Simulating damage and delamination in fibre metal laminate joints using a three-dimensional damage model with cohesive elements and damage regularisation

This paper investigates the capability of a three-dimensional finite element model with damaging material behaviour, cohesive elements and damage regularisation to simulate complex damage patterns in fibre metal laminate (FML) joints. The model incorporates a three-dimensional continuum damage mechanics approach for the composite plies, a plasticity model for the aluminium layers, and a delamination model between layers. A nonlocal averaging scheme is implemented to mitigate the mesh sensitivity that occurs with strain-softening material models. Bearing stress-strain responses and variations in stiffness are calculated, and damage progression is described in detail for all plies and interfaces. Microscopy and stress-strain data from a parallel series of experimental tests are presented, and damage and failure phenomena observed in the tests are compared with the model. Generally, good agreement between model and tests was achieved but certain limitations of the numerical model were observed and are discussed. The combined numerical and experimental information provide a detailed understanding of the failure sequence of FML joints.     

Pull out of FRP reinforcement from masonry pillars: Experimental and numerical results

In this paper, debonding phenomena between carbon fiber reinforced polymer (CFRP) strips and masonry support were investigated on the basis of single-lap shear tests, considering different dimensions of the bond length. To capture the post-peak response of the CFRP–masonry joint, the slip between the support and the reinforcement strip was controlled using a clip gauge positioned at the end of the reinforcement. The tests were simulated by means of a finite element model able to capture the post-peak snap-back behavior due to the failure process. The numerical model is based on zero-thickness interface elements and on a proper non-linear cohesive law. The comparison between experimental and numerical results was performed in terms of overall response, measured by both the machine stroke and the clip gauge positioned at the free end of the reinforcement. The cases of effective bond length greater and lesser than the minimum anchorage length, suggested by the CNR Italian recommendation, were considered.     

An analysis of fracture under biaxial loading using the non-singular T-stress

Finite element analysis using a two-dimensional modified-boundary-layer approach was used to model the effects of biaxial loading on crack tip stress fields. Loadings were applied corresponding to an elastic KI field, non-singular T-stress and a biaxial stress. For through-thickness cracks the T-stress inherent in the specimen geometry is augmented by the external biaxial stress. For surface-notched specimens the biaxial stress acts out of the crack plane. This effect was modelled with generalized plane strain elements. Results were analysed using the Anderson-Dodds approach for cleavage and the Beremin model in the ductile regime. Biaxial loading is predicted to have a large effect on the toughness of a through-thickness crack but little effect on a surface crack. Experimental results from a previous series of large-scale biaxial fracture tests are generally consistent with these predictions.     

Reduction of the stress concentration factor in a homogeneous panel with hole by using a functionally graded layer

This work aims at understanding the effect of a radially heterogeneous layer around the hole in a homogeneous plate on the stress concentration factor. The problem concerns a single hole in a plate under different far-field in-plane loading conditions. By assuming a radial power law variation of Young’s modulus and constant value for Poisson’s ratio, the governing differential equations for plane stress conditions, and general in-plane loading conditions are studied. The elastic solutions are obtained in closed form and, in order to describe localized interface damage between the ring and the plate, two different interface conditions (perfectly bonded and frictionless contact) are studied. The formulae for the stress concentration factors are explicitly given for uniaxial, biaxial and shear in-plane loading conditions and comparisons with interface hoop stress values are performed. The solutions are investigated to understand the role played by the geometric and graded constitutive parameters. The results are validated with numerical finite element simulations in which some simplified hypotheses assumed in the analytical model, are relaxed to explore the range of validity of the elastic solution presented. In this way the results obtained are useful in tailoring the parameters for specific applications.     

Characterising and modelling variability of tow orientation in engineering fabrics and textile composites

Variability of tow orientation is unavoidable for biaxial engineering fabrics and their composites. Since the mechanical behaviour of these materials is strongly dependent on the fibre direction, variability should be considered and modelled as exactly as possible for more realistic estimation of their forming and infusion behaviour and their final composite mechanical properties. In this study, a numerical code, ‘VariFab’, has been written to model realistic full-field variability of the tow directions across flat sheets of biaxial engineering fabrics and woven textile composites. The algorithm is based on pin-jointed net kinematics and can produce a mesh of arbitrary perimeter shape, suitable for subsequent computational analysis such as finite element forming simulations. While the shear angle in each element is varied, the side-length of all unit cells within the mesh is constant. This simplification ensures that spurious tensile stresses are not generated during deformation of the mesh during forming simulations. Variability is controlled using six parameters that can take on arbitrary values within certain ranges, allowing flexibility in mesh generation. The distribution of tow angles within a pre-consolidated glass–polypropylene composite and self-reinforced polypropylene and glass fabrics has been characterised over various length scales. Reproduction of the same statistical variability of tow orientation as in these experiments is successfully achieved by combining the VariFab code with a simple genetic algorithm.     

Mechanical behavior of glass/epoxy tubes under combined static loading. Part II: Validation of FEA progressive damage model

Experimental results from a series of biaxial static tests of E-Glass/Epoxy tubular specimens [±45]₂, were compared successfully with numerical predictions from thick shell FE calculations. Stress analysis was performed in a progressive damage sense consisting of layer piece-wise linear elastic behavior, simulating lamina anisotropic non-linear constitutive equations, failure mode-dependent criteria and property degradation strategies. The effect of accurate modeling of non-linear shear stress–strain response, dependent on the plane stress field developed, was proved of great importance for the numerical FEA predictions, concerning macroscopic stress–strain response. Ultimate load prediction was influenced more decisively when degradation strategies for the compressive strength along the fiber direction were considered.     

Failure analysis of fiber-reinforced composite laminates subjected to biaxial loads

A nonlinear constitutive model for a single lamina is proposed for the failure analysis of composite laminates. In the material model, both fiber and matrix are assumed to behave as elastic-plastic and the in-plane shear is assumed to behave nonlinearly with a variable shear parameter. The damage onset for individual lamina is detected by a mixed failure criterion, composed of the Tsai-Wu criterion and the maximum stress criterion. After damage takes place within the lamina, the fiber and in-plane shear are assumed to exhibit brittle behavior, and the matrix is assumed to exhibit degrading behavior. The proposed nonlinear constitutive model is tested against experimental data and good agreement is obtained. Then, numerical analyses are carried out to study the failure behavior of symmetric angle-ply composite laminates and symmetric cross-ply composite laminates subjected to biaxial loads. Finally, the conclusions obtained from the numerical analysis are given.     

A damage gradient model for fatigue life prediction of notched metallic structures under multiaxial random vibrations

In the present paper, a damage gradient model combing the damage concept with the theory of critical distance (TCD) is established to estimate the fatigue lives of notched metallic structures under multiaxial random vibrations. Firstly, a kind of notched metallic structure is designed, and the biaxial random vibration fatigue tests of the notched metallic structures are carried out under different correlation coefficients and phase differences between two vibration axes. Then, the fatigue lives of the notched metallic structures are evaluated utilizing the proposed model with the numerical simulations. Finally, the proposed model is validated by the experiment results of the biaxial random vibration fatigue tests. The comparison results demonstrate that the proposed model can provide fatigue life estimation with high accuracy.     

Electrical resistance-based strain sensing in carbon nanotube/polymer composites under tension: Analytical modeling and experiments

This paper presents an analytical and experimental study on the strain sensing behavior of carbon nanotube (CNT)-based polymer composites. Tensile tests were conducted on CNT/polycarbonate composites and the responses in the electrical resistance were measured during the tests. An analytical model incorporating the electrical tunneling effect due to the matrix material between CNTs was also developed to describe the electrical resistance change as a result of mechanical deformation. The model deals with the inter-nanotube matrix deformation at the micro/nanoscale due to the macroscale deformation of the nanocomposites. A comparison of the analytical predictions and the experimental data showed that the proposed model captures the sensing behavior. In addition, the effect of the micro/nanoscale structures on the strain induced resistance change was discussed to provide useful information for designing CNT-based polymer composites with high strain sensing capability.     

Biaxial shear/tension failure behavior of Spectra single fibers

An experimental study is conducted to develop the biaxial failure surface of single Spectra 100d and Spectra 130d filaments in a torsion-tension environment. The cross-sectional profiles of single fibers are evaluated using scanning electron microscopy and X-ray computed tomography. In efforts to hold the polyethylene single fiber, a pin-gripping method is developed. Effects of pin diameter on failure stress for both Spectra types are characterized. Additionally, the effect of sample gauge length on fiber tensile strength is investigated. Quasi-static experiments are conducted using an MTS servo-hydraulic system to apply tensile loads on pre-twisted single fibers. A tension Kolsky bar is employed to study the biaxial shear/tensile behavior of single fibers at high strain-rates. A decreasing trend of tensile strength with increasing torsional strain is observed for both Spectra 100d and 130d. Furthermore, a torsional pendulum apparatus is used to determine the apparent torsional shear stresses in pre-twisted fibers at various levels of axial loading and a relationship between apparent shear stress and axial stress is developed. Finally, a biaxial shear/tension failure envelope of each fiber type is established.     

Characterisation of mechanical behaviour and damage analysis of 2D woven composites under bending

In this paper, flexural loading of woven carbon fabric-reinforced polymer laminates is studied using a combination of experimental material characterisation, microscopic damage analysis and numerical simulations. Mechanical behaviour of these materials was quantified by carrying out tensile and large-deflection bending tests. A substantial difference was found between the materials' tensile and flexural properties due to a size effect and stress stiffening of thin laminates. A digital image-correlation technique capable of full-field strain-measurement was used to determine in-plane shear properties of the studied materials. Optical microscopy and micro-computed tomography were employed to investigate deformation and damage mechanisms in the specimens fractured in bending. Various damage modes such as matrix cracking, delaminations, tow debonding and fibre fracture were observed in these microstructural studies. A two-dimensional finite-element (FE) model was developed to analyse the onset and propagation of inter-ply delamination and intra-ply fabric fracture as well as their coupling in the fractured specimen. The developed FE model provided a correct prediction of the material's flexural response and successfully simulated the sequence and interaction of damage modes observed experimentally.     

Numerical model for CFRP confined concrete elements subject to monotonic and cyclic loadings

Uniaxial cyclic and monotonic compression tests were carried out on partially and fully wrapped concrete cylinders with Carbon Fibre Reinforced Polymer (CFRP) wet lay-up sheets. The influence of the concrete compressive strength, CFRP stiffness, geometric confinement arrangement and loading type on the compressive behaviour of reinforced concrete column elements of circular cross-section up to their failure was assessed. A uniaxial stress–strain constitutive model is proposed, and the results obtained from the experimental tests were used to calibrate some of the parameters of this model, and to appraise the model performance. This model allows the simulation of reinforced concrete members by using Timoshenko one-dimensional elements, in the context of the finite element method (fibre model). Good agreement was obtained between numerical simulations and experimental results for both monotonic and cyclic loading tests.