Tsai-Wu Failure Criterion Research Articles

In-plane mechanical properties of birch plywood

There is an increasing demand for engineered wood products in modern structures. Birch plywood is promising in structural applications, due to the combined advantages of its superior mechanical properties and the cross lamination configuration. However, the off-axis mechanical properties of birch plywood have not been thoroughly investigated. The aim of this paper is to establish a comprehensive experimental dataset that could serve as the input in the analytical or numerical models to design birch plywood under various load conditions. Specifically, tensile, compressive and shear tests were conducted under five different angles to the face grain, i.e., from 0° (parallel) to 90° (perpendicular) to the face grain, with an interval of 22.5°. The stress–strain relationships, failure modes, strength and elastic properties of birch plywood are highly dependent on the load-to-face-grain angle. The strength and the elastic properties are also predicted by various analytical and empirical models. Parametric analyses are performed to study the influence of the interaction coefficient F12 in Tsai-Wu failure criterion and the Poisson’s ratio νxy in the transformation model on the predicted strength and modulus respectively. Lastly, the possibilities of predicting the on-axis shear modulus based on the off-axis uniaxial tests are discussed in this paper.

Analysis of Multi-Tendon Friction-Based Composite Anchorage Device for CFRP Cables and Its Anchorage Mechanism

Carbon fiber-reinforced polymer (CFRP) cables are anticipated to be employed in larger, longer, and more durable structures in the engineering field. However, its anchorage devices and mechanism should be appropriately developed and improved. At present, mainly relying on the adhesive force, most anchorage devices may lose their efficiency because of adhesive aging and failure or the slip of an individual tendon. A friction-based composite anchorage device with an integrated bearing of inner cone filler (i.e., load transfer media (LTM)) bonding and a single extruding anchor is proposed, and the anchorage mechanism is examined for Φ7 CFRP cables of strength 2400 MPa. Firstly, sufficient conditions for anti-slip failure of CFRP tendons in the anchorage zone are derived by assuming uniform LTM bonding. The obtained results reveal that the smaller inner pore size of the barrel leads to higher efficiency. Additionally, the maximum efficiency depends on the friction coefficient of the contact surface, the inner cone angle of the barrel, and the diameter and quantity of the CFRP tendons. The necessary conditions for the safety of the CFRP tendon anchorage zone are carefully obtained based on the Tsai–Wu failure criterion. It is concluded that the compressive stress of CFRP tendons in the anchorage zone should gradually increase from the load-bearing end to the no-loading end. Additionally, the relations among the anchorage efficiency coefficient and the CFRP tendon diameter d, the anchorage length l, the dip angle of LTM external conical surface α, and the friction angle β are derived based on the equivalent failure principle. The CFRP cables of four specifications (i.e., with Φ12, Φ19, Φ37, and Φ121 tendons) are designed under theoretical guidance, and eight static tests are carried out for more verification studies. The test results indicate that the anchorage efficiency coefficient of designed anchorage devices can be over 90%, and even up to 96.8%. Further, the failure modes are divergent destruction, which verifies the reliability of friction-based anchorage devices and provides a solid theoretical foundation for the design and engineering applications of CFRP cables.

The Formulation of the Quadratic Failure Criterion for Transversely Isotropic Materials: Mathematical and Logical Considerations

The quadratic function of the original Tsai–Wu failure criterion for transversely isotropic materials is re-examined in this paper. According to analytic geometry, two of the troublesome coefficients associated with the interactive terms—one between in-plane direct stresses and one between transverse direct stresses—can be determined based on mathematical and logical considerations. The analysis of the nature of the quadratic failure function in the context of analytic geometry enhances the consistency of the failure criterion based on it. It also reveals useful physical relationships as intrinsic properties of the quadratic failure function. Two clear statements can be drawn as the outcomes of the present investigation. Firstly, to maintain its basic consistency, a failure criterion based on a single quadratic failure function can only accommodate five independent strength properties, viz. the tensile and compressive strengths in the directions along fibres and transverse to fibres, and the in-plane shear strength. Secondly, amongst the three transverse strengths—tensile, compressive and shear—only two are independent.

Analysis of multilayered carbon fiber winding of cryo-compressed hydrogen storage vessel

In order to meet the hydrogen storage requirements of fuel cell vehicles, and improve the storage density of hydrogen, a cryo-compressed hydrogen storage method was proposed. The performance of cryo-compressed hydrogen storage vessel was analyzed in this paper. Based on the classical laminate theory and heat transfer solution, the stress and displacement of carbon fiber were precisely calculated to guarantee the cryo-compressed vessel severing in the cryogenic condition. Subsequently, the Tsai-Wu failure criterion was used to judge the failure of carbon fiber reinforced plastics layers. The stacking sequence, winding angle, comparison of the vessel's performance at room temperature and low temperature were conducted. The numerical results showed that the properties of storage vessel decreased at cryogenic condition, and the thickness of carbon fiber at cryogenic temperature at least increased by 47.06% than that at the room temperature. Mainly influence of low temperature on the cryo-compressed vessel were concentrated on the hoop stress of helical winding and the axial stress of hoop winding. For the vessel design, it is achievable to increase these two parts by using higher strength resin materials.

Effect of Cutout on the Stability and Failure of Laminated Composite Cylindrical Panels Subjected to In-Plane Pulse Loads

In this investigation, the nonlinear dynamic buckling analysis and the failure analysis of laminated composite cylindrical (LCC) panel with different shapes of cutouts under the action of rectangular in-plane pulse loads are performed in the finite element framework. Cross-ply laminates which are balanced symmetric are considered in the investigation. The first ply failure load (FPFL) of the panel is evaluated and checked whether it occurs before the nonlinear dynamic buckling phenomenon considering Tsai–Wu failure criterion. Convergence and validation studies are undertaken, and the results are compared with those from the existing literature. The effects of loading duration, cutout area and cutout geometry on the panel are investigated in detail and results are reported. The results indicate that for the panel with cutout, its dynamic buckling load (DBL), in certain cases, compared to the static buckling load (SBL), can be lower even if the loading duration is half of its first natural period. Additionally, the vibration and the static buckling analyses of the panels are carried out as and when required.

First failure load of sandwich beams under transient loading using a space–time coupled finite element method

We numerically analyze transient plane stress deformations of linearly elastic laminates and sandwich structures by using a coupled space–time finite element method with the weak form of governing equations derived by the least-squares method. The governing equations are written as seven first-order partial differential equations as in the state space formulation, and each variable is approximated by using piece-wise continuous basis functions. The sum of the integral over the problem (space-time) domain of squares of residuals of the governing equations, and initial and boundary conditions is minimized with respect to the nodal values of the seven variables to deduce coupled linear algebraic equations. The developed software is verified by comparing computed results for sample problems with their either analytical or numerical solutions obtained with a commercial software, ABAQUS. Using statistical method and the Tsai–Wu failure criterion, sensitivities of the maximum deflection and the first failure load to beam’s aspect ratio (AR), the facesheet-core thickness ratio (FCTR), and the facesheet-core in-plane and transverse stiffness ratios (FCISR, FCTSR) are elucidated. For sandwich beams with equal FCISR and FCTSR, the results are sensitive to the AR and the FCTR. In general, they strongly depend upon the FCTSR and its interaction with the AR and the FCTR.

Comparative analysis of Basalt/E-Glass/S2-Fibreglass-Carbon fiber reinforced epoxy laminates using finite element method

This paper aims to numerically analyse (using finite element methods) the static loading effects on basalt/E-glass/S2-fibreglass-carbon fibre reinforced epoxy hybrid composites, an alternative to the conventional and expensive pure carbon fibre epoxy composites. Structural properties of few hybrid composites are evaluated through static tests for validation purpose. The composite specimens comprising of four layers of carbon fibre and four layers of either basalt/E-glass/S2-fibreglass combined with LY556 resin in six varying stacking sequences are analysed for failure based on Tsai-Wu failure criteria. Commercial finite element software ANSYS Composite PrepPost (ACP) and ANSYS Mechanical were employed for this study. All specimen dimensions, boundary conditions and loading were adopted as per ASTM Standards. Results and discussion are followed by a significant comparison of static test results between basalt, E-glass, and S2-fibreglass each combined with carbon fibre epoxy. Finally, the optimal stacking sequence was found to be S2 - [02C/±45 M/0M]S. Basalt-carbon hybrids produced superior results in tensile and flexural tests while the brittle glass-carbon hybrids proved to be better in compression and in-plane shear. Laminates with carbon fibre at the outer layers showed improved performance among contemporaries.

NLFEA based design optimization of GFRP strips in partially confined concrete

The present study aims to introduce a nonlinear finite element approach (NLFEA) carried out on repaired concrete members under axially compressive loading. The main objective is to assess the effect of design parameters of FRP stirrups based on various confinement rate. The constitutive materials were modeled according to numerical models embedded in ABAQUS software namely: Concrete Damaged Plasticity model to take into account the nonlinear behavior of compressive and strained concrete, coupled with damage theory to represent the cracks evolution. An orthotropic-elastic model to predict FRP behavior with Tsai-Wu failure criteria is used. Indeed, the proposed approach is validated by experimental models available in the literature. In conclusion, the predicted numerical results for various design of FRP stirrups and damage configurations highlight the promising of used FRP composites in the repair of concrete members in terms of mechanical performances enhancement.

Using the Kriging Response Surface Method for the Estimation of Failure Values of Carbon-Fibre-Epoxy Subsea Composite Flowlines under the Influence of Stochastic Processes

This paper investigates the use of the Kriging response surface method to estimate failure values in carbon-fibre-epoxy composite flow-lines under the influence of stochastic processes. A case study of a 125 mm flow-line was investigated. The maximum stress, Tsai-Wu and Hashin failure criteria was used to assess the burst design under combined loading with axial forces, torsion and bending moments. An extensive set of measured values was generated using Monte Carlo simulation and used as the base case population to which the results from the response surfaces was compared. The response surfaces were evaluated in detail in their ability to reproduce the statistical moments, probability and cumulative distributions and failure values at low probabilities of failure. In addition, the optimisation of the response surface calculation was investigated in terms of reducing the number of input parameters and size of the response surface. Finally, a decision chart that can be used to build a response surface to calculate failures in a carbon fibre-epoxy-composite (CFEC) flow-line was proposed based on the findings obtained. The results show that the response surface method is suitable and can calculate failure values close to that calculated using a large set of measured values. The results from this paper provide an analytical framework for identifying the principal design parameters, response surface generation, and failure prediction for CFEC flow-lines.

Method of Designing a Friction-Based Wedge Anchorage System for High-Strength CFRP Plates.

The cables of high-strength carbon fiber reinforced polymer (CFRP) plates are starting to be applied to large spatial structures. However, their main anchorage systems rely on the adhesive force, which entails risks to their integrity resulting from aging of the binding agent. In this study, a friction-based wedge anchorage system was designed for CFRP plates. The working mechanism of the proposed anchorage system was explored both theoretically and experimentally. The anti-slip mechanism and condition of CFRP plates were formulated so that the equivalent frictional angle of the contact surface between a CFRP plate and wedges must not be smaller than the sum of the dip angle of the wedge external conical surface and the frictional angle between the wedges and barrel. An analysis of the stress distribution in the anchorage zone of the CFRP plate was conducted using the Tsai-Wu failure criterion, which concluded that the compressive stresses should be reduced on the section closer to the load-bearing end of the anchorage system. Furthermore, the anchorage efficiency coefficient was proposed, which depends on stress concentration coefficients, plate thickness, length of anchorage zone, dip angle of wedge external conical surface, and its frictional angle. Then, it was determined that the minimum length of an anchorage zone for the CFRP plates with various specifications should be at least 49 times larger than the CFRP thickness. A finite element analysis and static tensile tests on six specimens were carried out. The experimental results revealed that the anchorage efficiency coefficient of the optimized anchor reached 97.9%.

Effects of Viscoelasticity on the Stress Evolution over the Lifetime of Filament-Wound Composite Flywheel Rotors for Energy Storage

High-velocity and long-lifetime operating conditions of modern high-speed energy storage flywheel rotors may create the necessary conditions for failure modes not included in current quasi-static failure analyses. In the present study, a computational algorithm based on an accepted analytical model was developed to investigate the viscoelastic behavior of carbon fiber reinforced polymer composite flywheel rotors with an aluminum hub assembled via a press-fit. The Tsai-Wu failure criterion was applied to assess failure. Two simulation cases were developed to explore the effects of viscoelasticity on composite flywheel rotors, i.e., a worst-case operating condition and a case akin to realistic flywheel operations. The simulations indicate that viscoelastic effects are likely to reduce peak stresses in the composite rim over time. However, viscoelasticity also affects stresses in the hub and the hub-rim interface in ways that may cause rotor failure. It was further found that charge-discharge cycles of the flywheel energy storage device may create significant fatigue loading conditions. It was therefore concluded that the design of composite flywheel rotors should include viscoelastic and fatigue analyses to ensure safe operation.

FE analysis and experimental validation of mechanical wedge–barrel anchors for CFRP rods

This paper presents a comparative study of the geometrical optimization of mechanical wedge–barrel anchors for prestressed carbon fiber-reinforced polymer (CFRP) rods. Various anchor configurations were simulated using three-dimensional finite-element (FE) models. The FE models were validated using the draw-ins of the wedges, which were measured in static tensile tests. The configurations consisted of a steel barrel and aluminum wedges, taking advantage of the previous anchors. The conical profile of the wedge and barrel in different configurations had either a curve or a constant differential angle. In addition, a series of geometric modifications were introduced to the wedge at the loading using a fillet or cut. The stress concentration on the CFRP rod was evaluated using failure index Fs in the Tsai–Wu failure criterion for composite materials. The results of the FE simulations showed that a greater differential angle resulted in a smaller stress concentration at the loading end of the anchor and the modifications led to a reduction in the stress concentration. In addition, the anchor with a curved profile was selected as the optimal design because it had the smallest stress concentration owing to the smooth transition of the differential angle distribution along the wedge profile.

Optimization of surface-profile of orthotropic cylindrical shell for maximizing its ultimate strength

An optimization strategy has been developed to determine the optimal surface-profile of a uniform thickness orthotropic shell for maximizing its ultimate load-carrying capacity. Ultimate load is obtained by considering both buckling and Tsai-Wu failure criteria. A parametric model of the laminated cylindrical shell is created in ANSYS to compute the ultimate load. Later, this finite element computation is coupled with MATLAB to obtain the optimal design parameters. It is shown that the optimal shapes, obtained for several loading conditions, can result in remarkable improvement in the ultimate strength in comparison to the base model of a circular cylindrical shell.

Insight into microstructure and flexural strength of ultra-high temperature ceramics enriched SICARBON™ composite

Research efforts on Ceramic Matrix Composites (CMCs) are aimed to increase the operating temperature in oxidizing environments by adding Ultra-High Temperature Ceramic (UHTC) phases to the matrix. The structural performances of UHTC-enriched CMCs are generally investigated through bending test because it requires simple fixture and specimen geometry with small quantity of plate material. However, there are hardly any scientific studies which bring out what bending test conditions are required to determine reliable flexural strength of these composites. In this study, the effect of span length and specimen orientation on the flexural strength of UHTC-enriched SICARBON™ material, produced by Airbus, was comprehensively evaluated and reported. Transition of the failure mode was obtained by tilting the specimens with horizontal build direction instead of lay-up configuration (vertical build direction). The tilted configuration allowed to get a valid flexural strength of 370 MPa even with small specimens of about 30 mm. To assess failure mode in different test configurations, virtual microstructure was generated on the base of cumulative distribution functions of observed microstructural features. Tsai-Wu failure criterion was extended in order to evaluate direction dependent failure indices for different lay-up configurations.

3D numerical modeling and experimental validation of machining Nomex® honeycomb materials

Machining of Nomex® honeycomb materials is the biggest challenge in industry because of the complex forms and geometry of the honeycomb structure. The latter is characterized by a low density with orthotropic mechanical behavior. The thin walls of the composite structure make the shaping of this material very difficult. Studying interactions between the cutting tool and material, cutting forces, and chip formation allow to understand the machining process of Nomex® honeycomb. This paper presents 3D numerical modeling of machining Nomex® honeycomb using different orthotropic approaches and failure criteria: (i) monolayer isotropic approach, (ii) monolayer orthotropic approach with Tsai-Wu failure criteria, and (iii) monolayer orthotropic approach with Hashin failure criteria. A comparison between experiments and numerical cutting forces was performed to validate the proposed model. The interaction between the tool and the honeycomb walls, which make it possible to observe the different stages of the chip formation process, was carefully modeled.Graphical abstract

Non-linear response and buckling of imperfect laminated composite plates under in-plane pulse forces

This study presents a semi-analytical solution of the non-linear dynamic response, shock spectrum, and dynamic buckling of an imperfect angle-ply laminated composite plate under various types of in-plane pulse forces. The laminated composite plate is modeled using a higher-order shear deformation theory and von-Kármán geometric nonlinearity. The non-linear governing partial differential equations (PDEs) of imperfect laminated composite plates are derived via Hamilton’s principle. Using Galerkin’s method, the non-linear PDEs are transformed into non-linear algebraic equations for the static stability problems and non-linear ordinary differential equations for the dynamic problem such as dynamic response, shock spectrum, and dynamic buckling. The buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the composite plate is evaluated using the post-buckling analysis based on the Tsai-Wu failure criterion. The dynamic response and shock spectrum of the composite plate are determined via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the Tsai-Wu failure criterion. Dynamic buckling is to be characterized by dynamic load factor (DLF), which is represented as the ratio of the dynamic failure load to the static failure load. Based on the pulse/shock duration time, the pulse forces are divided into three loading regimes known as impulsive, dynamic, and quasi-static. The study revealed that the DLF values are > 1, < 1, and [Formula: see text]1 respectively for the case of impulsive, dynamic, and quasi-static loading regimes of pulse force. The influences of various types of in-plane pulse forces, amplitude and time duration of pulse forces, and amplitude of initial geometric imperfections on the non-linear dynamic response, shock spectrum, and dynamic buckling behavior of the laminated composite plate are addressed in detail. The results will help in the appropriate design of the laminated composite plate against dynamic buckling.

Extreme response based reliability analysis of composite risers for applications in deepwater

As current oil reserves start to deplete, companies are looking to exploit deeper deposits. At these greater depths composite risers, with their high strength-to-weight ratio, reduce the effective tensions and bending moments compared to steel risers. However, there is still limited research into their behaviour, with one key missing element being a comparison with traditional riser designs which accounts for variances in material properties and wave loads. This paper therefore conducts a strength-based reliability analysis of composite catenary risers operating between 1,500 m and 4,000 m. A static global catenary model is combined with Classical Laminate Theory to determine the extreme response and its performance is verified against FEA. This response is evaluated with the Tsai-Wu failure criterion to determine first-ply failure. The effect of laminate moisture absorption on the long-term reliability of submerged composite-based risers is also investigated as it can cause a significant reduction in the strength of composite risers. The reliability analysis is conducted using the Monte Carlo Method, revealing that the composite risers perform well at 4000 m. The degradation in performance from moisture absorption becomes increasingly important at greater depths and needs further investigation for these applications.

Longitudinal compression failure of 3D printed continuous carbon fiber reinforced composites: An experimental and computational study

Fused filament fabrication (FFF) with continuous carbon fiber filaments has proven to be a promising manufacturing technique in engineering applications. To provide guidance in the design of 3D printed carbon fiber reinforced polymer (CFPR) components, the longitudinal compression failure of continuous CFPR composites using the FFF technique is investigated systematically. First, longitudinal compression tests are performed for 3D printed continuous CFRP composites with and without designed waved filaments. The degradation of the failure strength is remarkable when the waved filaments are introduced. Nevertheless, further degradation is limited when more waved filaments are adopted. Next, the fracture morphologies are analyzed, and in-plane and out-of-plane kink-bands are observed in the microscopic images. For the specimens with waved filaments, fracture occurs at the cross-section with the contact region of the waved and regular filaments, as well as the cross-section with the maximum misalignment angle. Correspondingly, a computational framework for 3D printed continuous CFPR composites is established to explore the longitudinal compression failure mechanisms. The meso-scale computational models are reconstructed according to the geometric features of the deposited continuous CFRP filaments and the actual void volume fraction. The elastic properties of the filament are calculated by a micro-scale representative volume element (RVE) model, which is based on the fiber random distribution algorithm. The plastic deformation and failure is described by a filament constitutive model which is established by the Liu-Huang-Stout yield criterion and a simplified Tsai-Wu failure criterion. The experimental validation demonstrates the feasibility of the computational models to predict the stress-strain curves of 3D printed materials, and also capture the realistic longitudinal compression failure behavior.

Adaptive sampling assisted surrogate modeling of initial failure envelopes of composite structures

Composite structures are increasingly analyzed in a multiscale way, where lower scale structures are homogenized and effective properties such as structural stiffness are passed to upper scales. However, strength properties are rarely treated this way to construct a complete failure envelope for the structural element. In this work, we propose to use the Gaussian process to approximate the overall shape of the initial failure envelope in the space of sectional forces and moments of composite beam cross-sections. Tsai-Wu failure criterion is used for the strength analysis at the material level and strength ratio is used as the output to be fitted. To better select training data without guessing and reduce the number of samples, adaptive sampling technique is used. Predicted variance scaled by predicted mean is used as the measure of the score to select the most promising point as the new sample for the next training iteration. Two sets of numerical examples are provided to demonstrate and test the proposed method.

Optimization of Running Blade Prosthetics Utilizing Crow Search Algorithm Assisted by Artificial Neural Networks

A crow search algorithm (CSA) was applied to perform the optimization of a running blade prosthetics (RBP) made of composite materials like carbon fibre layers and cores of acrylonitrile butadiene styrene (ABS). Optimization aims to increase the RBP displacement limited by the Tsai-Wu failure criterion. Both displacement and the Tsai-Wu criterion are predicted using artificial neural networks (ANN) trained with a database constructed from finite element method (FEM) simulations. Three different cases are optimized varying the carbon fibre layers orientations: –45°/45°, 0°/90°, and a case with the two-fibre layer orientations intercalated. Five geometric parameters and a number of carbon fibre layers are selected as design parameters. A sensitivity analysis is performed using the Garzon equation. The best balance between displacement and failure criterion was found with fibre layers oriented at 0°/90°. The optimal candidate with –45°/45° orientation presents higher displacement; however, the Tsai-Wu criterion was less than 0.5 and not suitable for RBP design. The case with intercalated fibres presented a minimal displacement being the stiffer RBP design. The damage concentrates mostly in the zone that contacts the ground. The sensitivity study found that the number of layers and width were the most important design parameters.