Tsai-Wu Failure Criterion Research Articles

Buckling Optimization of Composite Cylinders for Underwater Vehicle Applications Under Tsai-Wu Failure Criterion Constraint

An optimization framework is developed to maximize design pressure of composite cylindrical shell subjected to hydrostatic pressure. Genetic algorithm (GA) integrated with numerical analysis is used in the framework to find optimal winding pattern of the composite cylinders. As a novelty, unlike other studies only considering buckling, in this study, material failure is taken as design constraint in the optimization problem. Sensitivity analyses are performed to study the effects of design variables on the buckling pressure, material failure pressure and design pressure. Comparative study is carried out to analyze the buoyancy factors of the cylindrical shell made of metal alloys and composites. Results reveal that as the shell thickness of the cylinder increases, the material failure pressure instead of the buckling pressure determines the design pressure. It can be concluded that reliable winding pattern designs can be achieved for composite cylinders under hydrostatic pressure when the Tsai-Wu failure criterion is considered.

Optimum first failure load design of one/two-core sandwich plates under blast loads, and their ultimate loads

We consider a sandwich plate with face sheets made of unidirectional fiber-reinforced composite with fibers being either glass, or carbon or aramid and the core made of balsa wood loaded by a blast pressure, and find optimal geometries and materials for maximizing the first failure load. While analyzing the problem, we assume that the areal density is fixed and use the Nest-Site Selection optimization algorithm, a third-order shear and normal deformable plate theory, a one-step stress recovery scheme, and the Tsai-Wu failure criterion. We also delineate the effect on the first failure load of inertia forces and uncertainties in values of various parameters. For a sandwich plate optimally designed for the first failure load, we find the ultimate load by progressively degrading elasticities of failed elements. We find that the optimal single-core sandwich designs are symmetric about the mid-surface with thick face sheets and the optimal two-core sandwich designs have a thin middle face sheet, and thick top and bottom face sheets. The first failure load of the optimal clamped single-core (two-core) design is approximately 20% (30%) more than that of the corresponding simply-supported plate. For simply-supported (clamped) sandwich structures, the failure initiates at the centroid (center of the clamped edge) of either the top or the bottom surfaces. It is also found that the first failure occurs in a face sheet (core) due to the in-plane transverse axial stress (transverse shear stress) exceeding its critical value. The collapse load of a clamped (simply-supported) sandwich structure is approximately 15%–30% (0%–17%) higher than the first failure load. The maximum deflection of the collapsed structure may be in a direction opposite to that of the applied load. A novelty of the work is in considering inertia effects in ascertaining the first and the ultimate failure loads and quantifying the benefits, if any, of two-core over one-core sandwich structures, and determining effects of uncertainties in values of parameters.

Optimization of the Layers of Composite Materials from Neural Networks with Tsai–Wu Failure Criterion

The use of composite materials has increased lately and the need to know the behavior of these materials is very important once these devices are subject to suffer from damage such as cracks and delamination. Normally, to analyze failure problems in composite materials, the following steps are necessary: (1) structure geometry design, (2) numerical and/or experimental analysis and (3) use of failure criteria (e.g., Tsai–Wu failure criterion). If the used composite material has a non-expected failure criterion, the procedure must be repeated. In order to eliminate the procedure above, this study proposes the use of an artificial neural networks (ANN) inversion which can be used to determine an adequate configuration for the layers of the composite material from the desired failure criteria value. Numerical simulations, based on the finite element method, were made in order to create a database for ANN training and validation. After the inversion of the ANN, satisfactory results were obtained and this procedure could be used to minimize the high number of numerical simulations normally used in the design of a composite device.

Finite Element Modelling and Multi-Objective Optimization of Composite Submarine Pressure Hull Subjected to Hydrostatic Pressure

Excellent mechanical behavior and low density of composite materials make them candidates to replace metals for many underwater applications. This paper presents a comprehensive study about the multi-objective optimization of composite pressure hull subjected to hydrostatic pressure to minimize the weight of the pressure hull and maximize the buckling load capacity according to the design requirements. Two models were constructed, one model constructed from Carbon/Epoxy composite (USN-150), the other model is metallic pressure hull constructed from HY100. The analysis and the optimization process were completely performed using ANSYS Parametric Design Language (APDL). Tsai-Wu failure criterion was incorporated in the optimization process. The results obtained emphasize that, the submarine constructed from Carbon/Epoxy composite (USN-150) is better than the submarine constructed from HY100. Finally, an optimized model with an optimum pattern of fiber orientations was presented. Hopefully, the results may provide a valuable insight for the future of designing composite underwater vehicles.

Efficiency and Stiffness of the Single Lap Bolt Joints in Glass Epoxy Composites

The present work deals with the investigations on the joint efficiency and the joint stiffness of the single lap bolt joint made of two dimensional woven glass fibre reinforced composite materials. The effect of joint geometry, bolt pretension and washer has been determined on the bolt joint performance. To estimate the effect of geometric parameters; the edge-to-hole diameter (e/d) and width-to-hole diameter (w/d) ratios are varied from 3 to 4 and 3 to 5, respectively. To study the worst loading conditions; the bolt pre-tension is set to zero, whereas 5 Nm torque is applied to investigate the joint in fully clamped conditions. Two different sizes of washer i.e., the outer diameter of 12 mm and 16 mm have been studied to estimate the effect of the washer on failure load, joint stiffness, and joint efficiency. Progressive damage analysis has been performed on the single lap bolt joint. Characteristic curve method along with Tsai-Wu failure criteria has been used for the prediction of the failure loads and failure modes. The joint stiffness and the failure load of the joint are increased with the increase of w/d ratios. However, the joint efficiency was negatively influenced by w/d ratio.

Direct observation of micro delamination in graphene oxide incorporated carbon fiber/epoxy composite via in-situ tensile test

The microdelamination analysis is a critical issue in current failure analysis of delamination phenomenon in carbon fiber (CF) reinforced epoxy composites. Both, the improvement of delamination resistance of the CF/epoxy composites using filler materials and the microdelamination studies of these hybrid composites through nondestructive technique are great concern to the material researchers. Herein, 0.2 wt% graphene oxide (GO) nanofiller was incorporated in CF/epoxy composite to resist the micro crack formation during delamination and in-situ tensile test was conducted to investigate the microdelamination behavior of the hybrid composite using a microtester in the specimen chamber of a field emission scanning electron microscope. It was observed that the GO modified epoxy matrix showed better matrix cracking resistance than the pure epoxy resin. The improvement in matrix cracking resistance of the GO (0.2 wt%)/CF/epoxy composite is due to the good adhesion between GO modified matrix and CF. Besides the experimental study, Finite Element Analysis of the hybrid composite was performed to predict the generated stress in each ply as it is not possible through experimental study. Tsai-Wu failure criteria was also applied to analyze the damage in each ply of the composite laminate.

Failure analysis of rotating hybrid laminated composite beams

Rotating hybrid composite beams are prone to failure in industrial applications. The structure under consideration is a rotating beam of hybrid composite construction. The beam is made of a laminated composite material, with the top and bottom layers prepared from a high stiffness carbon fibre composite and the middle layers of a low stiffness glass fibre composite. The cost of carbon fibre is about ten times more than the glass fibre with the hybrid arrangement of fibres leading to cost savings. Three different stacking sequences are taken into consideration which are [0/30/0]S, [0/45/0]S, and [0/0/0]S.Numerical analysis of rotating beams was investigated using Matlab programming. For assessing the theoretical failure limits of non-hybrid and hybrid rotating beams, Tsai-Wu failure criterion was implemented. Minimum thickness of the high stiffness and expensive material (carbon fibre) required to avoid failure at different angular speeds were identified for various problem parameters such as beam thickness, stacking sequence and fibre orientation angle.It was found that the stacking sequence [0/0/0]S provides the highest failure load and uses less carbon fibres by increasing the axial and bending stiffness the hybrid beam, thereby leading to a cost effective hybrid beam.

Progressive Failure Analysis of an Integral Composite Joint for Thrust Reverser Cascade

The research work in this paper is focused on studying the failure behavior of an integral π-shaped laminated composite structure subjected to a bending load. A progressive damage model based on the 3D Tsai-Wu failure criterion and a developed gradual degradation model was employed to simulate and assess the load-carrying capacity, the onset and propagation of damage, and the failure mechanisms. For this unique π-shaped composite structure, disbonding was found to be the dominant damage mode under bending load, and the approximate maximum load could be maintained for a brief time during the final failure due to the gradual loss nature of the load-carrying capacity. The extent of damage was found to be more serious on the side of Rib II compared to the other side.

Comparison of damage mechanisms in curved composite laminates under static and fatigue loading

In this paper, damage progression in curved CFRP composite laminates are experimentally investigated for static and fatigue loadings. Two different cross-ply laminate thicknesses are examined with grouped plies to elucidate the failure mechanisms. A test fixture is designed to apply moment/axial combined loading to curved specimens and DIC method is used to obtain the strain distribution in the curved region until failure. Our major finding is that under fatigue loading, the failure location and mechanism are different from that under static loading. Fatigue failure is observed to form where the radial stress is maximum whereas static failure is observed to form where the combined radial, tangential and shear stresses attain a maximum value, in the form of Tsai-Wu failure criterion. For fatigue failure, micro-cracks existing in the maximum radial stress location in the group of 90° layers grow under cyclic loading and coalesce into one major matrix crack which reaches the 0/90 interface gradually to continue as a delamination. On the other hand, static failure initiates inside the group of 90° layers with a dominant crack growing dynamically and jumps to the 0/90 interface near the arms with a 40–50° angle to continue as a delamination.

Experimental and numerical studies on the low-velocity impact response of orthogrid epoxy panels reinforced with short plant fibers

Experimental and numerical studies were conducted to analyze the low-velocity impact response of orthogrid stiffened panels reinforced with short alfa fibers. Tensile specimens and orthogrid panels were fabricated with two types of epoxy resins and different fractions of crushed and sieved alfa fibers (fiber volume fraction (Vf) from 10% to 50%). Impact tests were conducted on the orthogrid panels to investigate their low-velocity transverse impact behavior. The resistance to damage increased with an increase in fiber content and improvement in the mechanical properties of the composites (measured in static). Bending tests carried out on pre-impacted and non-impacted panels revealed a change in the linearity of the initial bending behavior, which could be justified by the small cracks generated by impact. A numerical model of impact on the orthogrid stiffened composite panels was developed using the nonlinear Hertz’s contact model. To simulate the failure mechanism and load-time history, a standard Tsai-Wu failure criterion was used on ANSYS explicit dynamic software. The simulations show a good correlation with the experimental data. The dominant stresses for damage evolution are found to be normal stresses. The presence of a stiffener reduces the stress, which confirms that stiffeners limit the propagation of damage.

Ultimate in-plane strengths of two-dimensional tri-axial braided composites: experiments and numerical simulations

The ultimate in-plane strengths of a carbon/glass fibre reinforced tri-axial braided composite are studied by experiments and numerical simulations. The ultimate tensile, compressible and shear strengths are tested. Employing Tsai-Wu failure criterion, a progressive failure analysis is performed in finite element analysis. Reasonable agreement between the experiments and numerical simulations indicates that present finite element model has a potential to predict the ultimate strengths of a two-dimensional tri-axial braided composite.

Analytical and Numerical Studies of a Thick Anisotropic Multilayered Fiber-Reinforced Composite Pressure Vessel

In this paper, we developed an exact analytical 3D elasticity solution to investigate mechanical behavior of a thick multilayered anisotropic fiber-reinforced pressure vessel subjected to multiple mechanical loadings. This closed-form solution was implemented in a computer program, and analytical results were compared to finite element analysis (FEA) calculations. In order to predict through-thickness stresses accurately, three-dimensional finite element meshes were used in the FEA since shell meshes can only be used to predict in-plane strength. Three-dimensional FEA results are in excellent agreement with the analytical results. Finally, using the proposed analytical approach, we evaluated structural damage and failure conditions of the composite pressure vessel using the Tsai–Wu failure criteria and predicted a maximum burst pressure.

Residual stress and failure analyses of polymer matrix composites considering thermal cycling and temperature effects based on classical laminate plate theory

The effects of temperature and thermal cycling on the residual stress and failure behavior of different polymer matrix composites have been investigated in this paper. A new algorithm within the framework of the classical laminate plate theory (CLPT) has been presented to calculate the residual stresses. The modified Tsai-Wu failure criterion has been employed to study the failure behavior of different stacking sequences. Numerical results show that the residual stress and failure index of the composites decrease with the increase of the temperature. It has also been established that thermal cycling condition leads to reduction of the residual stresses and increment of the failure index.

Integrated design framework of next-generation 85-m wind turbine blade: Modelling, aeroelasticity and optimization

The National Energy Administration of China has promoted the use of wind energy to replace the conventional fossil energy, which provides an inexhaustible and eco-friendly alternative to the increasing energy demand. 10-MW wind turbine is the next-generation turbine with 85-m blade length, which poses great challenges in the engineering design, manufacturing, transportation, installation and maintenance. The paper aims to establish a numerical framework that integrates 3D full-scale modelling, analysis and parametric optimization. Isogeometric Analysis (IGA) enables seamless integration between structural modelling and computational analysis by using NURBS as basis functions. Aerodynamic forces and rotor power of blade subject to wind will be obtained by FAST. The Kirchhoff-Love shell element will be employed for 3D blade modelling to reduce rotational degrees of freedom and alleviate shear locking. The integrated framework residing within Rhino-based Grasshopper will be performed to model and analyse the wind turbine. Parametric optimization using pattern search algorithm targets at a family of turbines that satisfies the Tsai-Wu failure criterion and deformation constraint. The framework is deployed on a 10-MW turbine blade based on the initial design upscaled from the NREL 5-MW baseline model. The optimal blade design with shear webs has gained 20.9% improvement in performance.

Investigation and modeling of tensile failure properties of wound ceramic matrix composites

The paper presents enhanced studies of investigation and modeling of failure properties for wound ceramic matrix composites with varied fiber orientations under tensile loading. Based on mechanical tests and microstructure analysis, the characteristics of a virtual equivalent unidirectional layer (UD-layer) were examined and treated as input for modified Tsai-Wu failure criterion. In order to predict the mechanical properties with more accuracy, particular features of the investigated material have to be taken into consideration: definition of two material modeling groups based on the analysis of microstructure; interaction between failure strength and strain through inelastic deformation; inclusion of inhomogeneities created due to the manufacturing process in the analytical model. Based on the good correlation between the experiments and the modeling results, it can be shown that modeling approaches, considering the above mentioned particular material features, allow a very accurate prediction of the mechanical properties under in-plane tensile loading of CMC laminates.

Failure Analysis of Graphite Epoxy Composite Plate Under Transverse Sinusoidal Load

Composite material become interest on various applications in wide industry globally. The selection of composite material due to its versatile properties for instance high specific strength. Besides, the properties of composite material also tailorable for various application including automotive, aerospace and marine industry. The objective of this study is to perform the failure analysis of composite material under transverse sinusoidal load. Both failure criteria, Maximum Stress and Tsai-Wu Failure Criteria that provided in ANSYS used to carry out the analysis. Various aspect ratios will be used which are 5, 10, 20, 50 and 100 to perform the analysis with different thickness of laminate. Next, the boundary condition of the plate was set to simply and clamp supported. The finite element analysis of graphite/epoxy laminate with layup of (0/90/90/0) performed to determine the failure loads (First Ply Failure, FPF and Last Ply Failure, LPF loads). The un-normalized load obtained from the analysis is converted to normalized load using equation given. Finally, normalized load is plotted against aspect ratio for both failure criteria and boundary conditions.

A novel univariate method for mixed reliability evaluation of composite laminate with random and interval parameters

Requiring probability density distribution functions of uncertain variables, it is difficult for conventional structural reliability analysis methods to calculate the reliability of composite laminates with both random and interval variables. To evaluate the safety of composite laminated structures under this circumstance, this paper is aimed at developing a precise and efficient univariate method for the reliability assessment of composite laminates taking use of Legendre orthogonal polynomials and Monte Carlo Simulation. In this paper, based on the Tsai-Wu failure criterion and first-ply failure assumption, the failure criterion of composite laminate is constructed firstly. Then the performance function of each lamina is approximately expressed as the sum of univariate contributions of all uncertain variables on the basis of the univariate method. Taking use of Legendre orthogonal polynomials, the univariate functions of random and interval variables are constructed by the least square fitting method and the univariate contribution bounds of interval variables are derived afterwards. Furthermore, the interval of failure probability can be calculated by substituting contribution bounds of interval variables and sample points of random variables into univariate function. At last, two examples and an engineering application are provided to demonstrate the efficiency and accuracy of the proposed method.

A progressive failure analysis of all-C/SiC composite multi-bolt joints

A progressive damage model (PDM) was proposed to analyse the failure of plain-weave carbon fibre-reinforced silicon carbide (C/SiC) composite joints with C/SiC bolts, which were manufactured by the chemical vapour infiltration (CVI) technique. A bilinear constitutive model was established to describe the pseudo-plasticity of the C/SiC composites. Several failure criteria, including the maximum stress failure criterion, Tsai-Wu failure criterion, and Hashin-type criterion, and several material degradation models were compared. Moreover, the deposition models accounting for the deposition effects of CVI in the all-C/SiC composite joints were discussed. A series of comparative failure analyses of a C/SiC open-hole composite laminate with available experimental data in the literature was conducted to determine the most suitable combination of the Hashin-type criterion and the combined material degradation model was filtered for C/SiC composite structures. Based on the PDM, the failure strength and failure pattern of an all-C/SiC composite single-lap, three-bolt joint were predicted. Static tension experiments testing the all-C/SiC composite single-lap, three-bolt joints fabricated by the CVI technique were also conducted. Good consistency between the numerical failure predictions and the experimental outcomes was obtained, indicating the effectiveness of the proposed PDM for failure analyses of all-C/SiC composite multi-bolt joints.

Progressive failure behavior of composite flywheels stacked from annular plain profiling woven fabric for energy storage

Annular disk flywheels made of plain profiling woven carbon-fiber-reinforced composites possess favorable biaxial strength along radial and circumferential directions to get higher rotation speed and higher energy density in flywheel energy storage system. Each preform disk layer of fabric stacked for the new composite flywheel in our case study was profiling woven with a continuous fill yarn and radial arranged warp yarns in plain woven style. The progressive failure numerical algorithm was applied to reveal the failure phenomenon in fan-shaped representative volume unit of the plain woven fabric composite flywheel under centrifugal load in high speed running. In the numerical simulation of progressive failure, the analytical iterations were compiled with ANSYS-APDL based on 3D Tsai-Wu failure criterion and Reddy’s sudden material property degradation model. The analysis results indicated that the orthogonal plain profiling fabrics enhanced flywheel’s damage tolerance while the radial fiber yarns delayed transvers cracks. Spin experiments of the test flywheels were carried out on the one-point supporting shaft system driven by high speed motor in a vacuum chamber. All eight flywheel samples reached the tangential speed beyond 850 m/s in spin test, exhibiting a good consistency in material performance. The maximum speed was 898 m/s and the corresponding energy storage density was 64.5 W h/kg in the damage limitation spin test of the plain woven composite flywheel. The spin test verified the validity of the biaxial reinforcement using plain fabric by profiling woven method for composite flywheels with thick radial size. Progressive failure analysis simulation was useful in predicting the burst speed of woven fabric composite flywheels.

Failure Behavior and Strength of Composite I-Section Beam with Double Cutouts and Stiffener Reinforcement

This work is carried out to study the influence of double cutouts and stiffener reinforcements on the performance of I-section Carbon Fibre/Epoxy composites beam, including buckling, post-buckling behavior and the ultimate failure. The cantilever I-section beam with two diamond-shaped cutouts in the web and three longitudinal L-shaped stiffeners bonded to one side is subjected to a shear load at free end. Both numerical modelling and Experiment of I-section CFRP beam are performed. In numerical analysis, Tsai-Wu failure criterion is utilized to detect the first-ply-failure load in nonlinear analysis by predicting the load-deflection response. Good agreements are obtained from comparison between the numerical simulations and test results. For the double-hole beam web, the two cutouts show close surface deformation amplitude, which indicates that the stiffeners make the force transformation more effective. Comparing to the numerical result of corresponding beam with single cutout and stiffener reinforcement, the longitudinal stiffeners can not only play a significant role in improving the structural stability (increase about 30%), but also take effects to improve the deformation compatibility of structure. Local buckling happened within the sub-webs partioned by the stiffener and the buckling load is different but close. With post-buckling regime, the two areas show similar deformation characteristic, while the sub-web close to fixed end bears more shear load than the sub-web close to loading end with the increase of normal deformation of structure. The catastrophic failure load is approximate 75.6% higher comparing to buckling load. Results illustrate that the tensile fracture of the fiber is the immediate cause of the ultimate failure of the structure.