First-ply Failure Load Research Articles

First-Ply Failure Analysis of Helicoidal/Bouligand Bio-Inspired Laminated Composite Plates

Among the first, the present paper focuses on studying the first-ply failure load for bio-inspired helicoidal laminated composite plates. Five different layup schemes, namely, helicoidal recursive, helicoidal semicircular, helicoidal exponential, Fibonacci helicoidal, and linear helicoidal, were studied. The performance of the five helicoidal layups was compared with the commonly used cross-ply and quasi-isotropic lamination schemes. Maximum stress, maximum strain, Tsai–Hill, Tsai-Wu, and Hoffman failure theories were employed in the framework of the recently proposed finite-element-based higher-order zigzag theory to determine the first-ply failure load. It was observed that the maximum strain theory predicted the lowest value of the first-ply failure load, whereas Tsai–Wu predicted the highest one. For some cases, Tsai–Hill and Tsai–Wu theories were not able to predict the first-ply failure load. For plates having free edges, the bio-inspired plates exhibited the first-ply failure load compared to the conventional layup sequences.

Postbuckling Strengths of Composite Laminates with a Central Circular/Elliptical Cutout Under In-Plane Combined Loads

This paper deals with the effect of cutouts (i.e., circular and elliptical) aspect ratio on the buckling and postbuckling strengths, and failure characteristics of a simply-supported quasi-isotropic composite laminate subjected to in-plane shear and uni-axial compression combined with in-plane shear loads. The present study is carried out using self developed finite element program. The finite element formulation is based on the first order shear deformation theory and von Karmans assumptions to incorporate geometric nonlinearity. The resulting nonlinear algebraic equations are solved by Newton-Raphson method. The postbuckling strength of the laminate is defined in terms of the first-ply failure load of the lamina predicted by tensor polynomial form of the 3-D Tsai-Hill criterion. It is observed that for maximum buckling and first-ply failure strengths of the laminate with a cutout, it is preferred to have elliptical shape of the cutout as compared to the circular shape of the same area. It is also found that irrespective of load conditions and cutout shapes and sizes, shear load direction has significant effects on buckling and postbuckling stiffness of the laminate; although buckling stiffness is greater under negative shear, but the laminate shows stiffer postbuckling response under positive shear load.

First-Ply Failure Analysis of Bioinspired Double and Cross-Helicoidal Laminated Sandwich Plates

Inspired from the helicoidal schemes available from biological creatures, the present paper aims to predict the first-ply load for laminated composite and sandwich plates inspired from biological creatures. The laminated composite and sandwich plates are assumed to be made up of double- and cross-helicoidal lamination schemes. The first-ply failure load is determined using the recently proposed higher-order zigzag theory. Five different failure criteria (namely, maximum stress, maximum strain, Tsai–Hill, Tsai–Wu, and Hoffman’s theory) are used to predict the first-ply failure load. The performance of the helicoidal plate is compared with the cross-ply and quasi-isotropic lamination schemes. The influences of the end conditions, the ratio of the thickness of the core to the face layers, and the thickness-to-side ratio on the first-ply failure load are carried out. It has been observed that for helicoidal plates, a higher value of the first-ply failure load is observed as compared to quasi-isotropic and cross-ply laminates, especially for plates having free edges. The maximum strain theory should not be used for predicting the failure load for helicoidal laminated plates because it undermines the strength of the plate.

Implementation of point interpolation meshless method for failure analysis of laminated composite beams

The present study develops computationally efficient meshless model for the first-ply failure analysis and predicts the weakest ply, based on various failure criteria via one-dimensional, higher-order beam theory. The effective property of lamina is obtained with the help of micromechanics based Eshelby’s-Mori-Tanaka model. The governing equation is obtained with the help of point interpolation method based on polynomial basis function. The effects of different essential and natural boundary conditions, aspect ratio, lamination angle and volume fraction on the first-ply failure load of composite beam is studied.

Analytical solution for first ply failure analysis of laminated plates using Reddy–Legendre higher-order theory

The existing finite element formulation generally leads to overestimation on the first ply failure (FPF) load. Reasons of this phenomenon have been less cleared in detail. Therefore, it requires to propose an analytical solution to provide an accurate prediction of the FPF with the high efficiency-cost ratio. To this end, the following work has been carried out: (1) Legendre polynomials as local terms are first introduced into Reddy-type higher-order theory, which provide a novel alternative form of global-local displacement field. (2) Compared with the classical first-order and higher-order shear deformation theories, the proposed model can predict transverse shear stresses directly by constitutive equations which is close to the results obtained by the three-dimensional finite element method (3D-FEM). Therefore, the accuracy and efficiency of the FPF analysis can be improved, attributing to the accurate prediction of the quasi-three-dimensional stress field. (3) The static response and the FPF of laminated composite plates are analyzed, which have been compared with the results of selected models in the published literature and 3D-FEM. Influences of different failure theories, transverse loads, stacking sequence on prediction of the FPF loads are also explored. (4) By visualizing full-field displacement, stress and damage variables rather than those obtained from key points, it is easier to find the failure tendency and the failure modes. As a result, it is necessary to propose an analytical solution for predicting the FPF of composite laminated plates, which can provide a reference for other investigators.

Numerical and experimental investigation of first ply failure response of multi-walled carbon nanotubes/epoxy/glass fiber hybrid laminated tapered curved composite panels

In this study, first ply failure (FPF) analysis of multi-walled carbon nanotubes (MWCNTs)/epoxy/glass fiber laminated curved composite panels with various taper configuration under transverse uniform pressure load distributed over the panel surface has been performed. In this regard, various failure criterion were considered, including Hoffman, Tsai–Wu, Tsai–Hill, and maximum stress, to investigate the numerical FPF load using finite element (FE) formulation with displacement fields derived from high order shear deformation theory (HSDT) with displacement field having seven degrees of freedom. The effectiveness of the proposed formulation was validated by comparing the numerically predicted FPF load with experimentally obtained FPF load using a universal testing machine from displacement/strain measurement. Finally, the effects of aspect ratio, different weight fraction of MWCNTs, taper configuration, curved geometry, and aspect ratio on the FPF load of the laminated tapered composite panels are studied. The numerical and experimental studies of the first ply failure behavior have demonstrated that the use of MWCNTs ensures a significant improvement in the FPF load of the analyzed laminated tapered curved composite panels. The taper configuration 3 (TC-3) with hyperbolic curved geometry exhibited the highest resistance to failure than taper configuration 1 (TC-1) and taper configuration 2 (TC-2). Moreover, the aforementioned parameters significantly influence the FPF load of laminated curved panels with various taper configurations. Furthermore, this study can be effectively used as a benchmark problem for researchers and as a tool to design practical laminated tapered curved composite panels with sufficient accuracy.

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.

Finite element prediction of first-ply failure loads of composite thin skewed hypar shells using nonlinear strains

The application of skewed hypar shell as civil engineering roofing unit is an established fact. Such use has gained a greater momentum when this shell is fabricated with advanced materials like the laminated composites. Research attempts in studying the first ply failure behaviour of laminated composite structural units are common now among engineers and the novelty of this paper lies in continuation of such efforts being applied to composite skew hypar shell. For accurate modelling of the failure behaviour of this thin shell, nonlinear strains are considered together with eight noded isoparametric serendipity finite element. Different well-established failure criteria including the failure criterion of Puck are used to extract the first ply failure pressure values, failure locations and failure modes as well. The finite element code developed is used for numerical experimentation with parametric variations and the results are post processed and interpreted to extract meaningful engineering conclusions.

Progressive failure analysis of laminated composite plates

Failure of laminated composite plates has been a crucial issue that numerous researches have been conducted on the matter. Several modes of failure of laminated composites include fibre failure in tension, matrix failure in tension, fibre failure in compression, matrix failure in compression and delamination. This paper analyses failures of the composites to determine the first ply failure load (FPL) and last ply failure load (LPL) using the progressive failure approach that combines the effect of several modes of failure. Finite element method (FEM) was used via the commercial software of ANSYS APDL where the laminated composite plates were first modelled. Validation of the analysis was firstly conducted through a simple stress and deflection analysis. Progressive analysis was then conducted as the composite is loaded with an incremental combined tensile and transverse loading. The Tsai-Wu failure and the maximum stress criteria have been used to detect the FPL. With the failure occurred in an element, the degradation of that element mechanical properties was applied. As the load was further increased, more elements will fail and be degraded until the LPL was reached. A parametric study was conducted on the effect of varying angles of orientation of the composite. The results showed that the FPL and the LPL of the composites due to the Tsai-Wu criterion and the maximum stress criterion were in good agreement. The progressive failure behaviour of laminated composite plates subjected to uniaxial load and combined uniaxial load and transverse load was successfully established.

Non-linear stability and failure of laminated composite stiffened cylindrical panels subjected to in-plane impulse loading

In this article, the non-linear dynamic buckling behavior and failure of laminated composite stiffened cylindrical (LCSC) panel is performed in the finite element framework when subjected to sinusoidal and rectangular in-plane pulse loading. Balanced symmetric cross-ply laminates and balanced symmetric angle ply laminates are considered in this study. The first ply failure load (FPFL) of the panel is evaluated and checked whether it occurs before the non-linear dynamic buckling phenomenon considering four different failure theories. Convergence and validation studies are carried out using the present mathematical formulation and compared with the results from the existing literatures. The effect of loading duration, loading function, aspect ratio of stiffener and the ply orientation of the skin and stiffener on the non-linear dynamic buckling of LCSC panel is studied in detail and the results are reported. It is observed that the non-linear dynamic buckling load (DBL) of balanced and symmetric angle ply (45°/−45°/−45°/45°) stiffened panel is lower than those of unstiffened composite cylindrical panel upto aspect ratio of the stiffener (ds/bs) equal to 8 when subjected to rectangular pulse load. In case of balanced and symmetric cross ply (0°/90°/90°/0°) stiffened panel the DBL of stiffened panel is lower than those of unstiffened panel when the aspect ratio of the stiffener is less than 4 with rectangular pulse load. Further, the free vibration, static buckling and static post-buckling analyses of the panels are carried out as and when required.

The Influence of Axial Compression on the Free Vibration Frequencies of Cross-ply Laminated and Moderately Thick Cylinders

In this study, the free vibration behavior of axially compressed cross-ply laminated composite cylinders is investigated using a semi-analytical shell finite element based on a consistent first order shear deformable shell theory, which includes the influences of rotatory inertia and thickness coordinate/radius ratio. First, a verification study is conducted to validate the axisymmetric shell finite element used in this study and, for the non-compressed cases, the free vibration frequencies obtained using the finite element developed are found out to be in excellent agreement with the published results found in the literature. The same element is also validated for first-ply failure analysis and good agreement is observed with the first-ply failure loads obtained using a shear deformable and curved shell element. Then, numerical results for free vibration analyses are presented for axially compressed composite cylinders having different boundary conditions and for which the level of axial compression is kept below the corresponding linear buckling and first ply failure loads. It is observed that, the fundamental free vibration frequencies decrease sharply for axial load levels higher than about 60~80% of the buckling loads of the cylindrical structures considered. It is also determined that the first-ply failure load is lower than the buckling load for some of the thicker cylinders.

Ply-by-ply failure analysis of laminates using finite element method

Ply-by-ply failure analysis of anti-symmetric and symmetric laminated composite plates under uniformly distributed transverse load is carried out in this study. The successive failure analysis includes the determination of ply-by-ply failure load along with the failure mode using different stress-based failure theories. Ply-discount material degradation model is adopted to modify the properties of the failed lamina. The laminate has been modeled using eight noded isoparametric plate bending element having seven degrees of freedom at each node. A computer code is written using FORTRAN based on finite element formulation. The first-ply failure load has been compared with the reported results and a good conformity is found. Further comparison of different failure theories is made based on their ability to predict the failed ply, failure load along with the failure mode. The results are computed for both angle-ply and cross-ply laminates with simply supported and clamped edges. The importance of stacking sequence in terms of strength of the laminate is highlighted in the study.

An Experimental and Numerical Study of Repairs on Composite Substrates with Composite and Aluminum Doublers Using Riveted, Bonded, and Hybrid Joints.

In this work, experimental and numerical analyses of repairs on carbon fiber reinforced epoxy (CFRE) substrates, with CFRE and aluminum alloy doublers typical of aircraft structures, are presented. The substrates have a bridge gap of 12.7 mm (simulated crack), repaired with twin doublers joined with riveted, adhesive bonded, and hybrid joints. The performance of the repairs using different doubler materials and joining techniques are compared under static loading. The experimental results show that riveted joints have the lowest strength, while adhesive bonded joints have the highest strength, irrespective of the doubler material. Finite element analysis (FEA) of the studied joints is also performed using commercial FEA tool Abaqus. In the FEA model, point-based fasteners are used for the rivets, and a cohesive zone contact model is used to simulate the adhesive bond. The FEA results indicate that the riveted joints have higher tensile stresses on the metal doublers compared to the composite doublers. As per the failure modes, interestingly, for hybrid joints using composite doublers, the doublers fail due to net-section failure, while, for hybrid joints using metal doublers, it is the composite substrate that fails due to net-section failure. This suggests vulnerability of the composite structures to mechanical fastener holes. Lastly, the Autodesk Helius composite tool is used for prediction of first-ply failure and ply load distribution, and for progressive failure analysis of the composite substrate.

Finite Element-Based Stochastic Nonlinear Progressive Failure Response of Piezo-Laminated Composite Plate with Elliptical Cutouts

This paper presents the second-order statistics of hygro-thermo-electrically-induced progressive failure in terms of first-ply failure load (FPFL) and last-ply failure load (LPFL) analysis for laminated composite material plate (LCMP) under out of plane mechanical loading with random system properties. Basic governing equation of nonlinear progressive failure analysis is based on shear deformation theory (higher order) with von-Karman nonlinear kinematics using Newton’s Raphson approach through Tsai–Wu failure criteria. The random input variables are assumed as uncorrelated type and are evaluated using second-order perturbation method (SOPT). Laminated composite plate with elliptical cutouts are subjected to uniformly distributed, point and hydrostatic load. The effect of boundary conditions, temperature variation, moisture content and voltage variations by utilizing piezoelectric layer position and various cutout shapes on the mean and corresponding covariance (COV) of FPFL and LPFL load are evaluated. Convergence of numerical analysis is performed, and results are validated with those available in literatures to check the efficiency of present methodology. It is observed that the presence of elliptical hole always causes an increase in the failure load of plates subjected to bending, even further increase for LPFL due to the reduction of stresses.

Stability and failure analyses of delaminated composite plates subjected to localized heating

A layerwise B-spline finite element formulation is used to study the stability and first-ply failure of composite plates with embedded delaminations and subjected to localized thermal heating over the plate surface with uniform temperature rise through its thickness. The step functions are used to represent jump discontinuities in displacement fields at the zone of delamination between layers of composite plates. As the applied thermal loading is nonuniform, in the first step the prebuckling stress distribution within the plate is evaluated by solving the thermoelasticity problem. Subsequently, thermal buckling temperature is computed using the plate prebuckling stress distribution. Postbuckling response of the plate is obtained considering the von Kármán type geometric nonlinearity. In the delaminated region, virtual springs are added to prevent interpenetration of lower and upper sublaminates. The localized thermal load at which the first-ply failure of the lamina occurs has been detected by Tsai-Wu quadratic interaction criterion. The effects of the area of heating region, delamination size and its position in the thickness direction and plate boundary condition on the composite plate critical buckling temperature and on first-ply failure load are reported. The present model can capture global, local and combined global–local buckling mode shapes.

The role of n-3 polyunsaturated fatty acids in the formation of the psychophysiological status of ski racers

A layerwise B-spline finite element formulation is used to study the stability and first-ply failure of composite plates with embedded delaminations and subjected to localized thermal heating over the plate surface with uniform temperature rise through its thickness. The step functions are used to represent jump discontinuities in displacement fields at the zone of delamination between layers of composite plates. As the applied thermal loading is nonuniform, in the first step the prebuckling stress distribution within the plate is evaluated by solving the thermoelasticity problem. Subsequently, thermal buckling temperature is computed using the plate prebuckling stress distribution. Postbuckling response of the plate is obtained considering the von Kármán type geometric nonlinearity. In the delaminated region, virtual springs are added to prevent interpenetration of lower and upper sublaminates. The localized thermal load at which the first-ply failure of the lamina occurs has been detected by Tsai-Wu quadratic interaction criterion. The effects of the area of heating region, delamination size and its position in the thickness direction and plate boundary condition on the composite plate critical buckling temperature and on first-ply failure load are reported. The present model can capture global, local and combined global–local buckling mode shapes.

Computational structural analysis of composites with spectral-based stochastic multi-scale method

Composite materials and structures may be characterized at different length scales, ranging from the micro-scale at the fiber–matrix level, meso-scale at the lamina–laminate level, to structural macro-scale. However, uncertainties in material properties and geometric parameters due to manufacturing, defects and assembly processes may occur at various length scales. This paper presents a computational framework for stochastic analysis of composites with consideration of stochastic parameters at micro- and meso-scales. The novelty of the proposed framework is the integration of the spectral stochastic finite element method and asymptotic homogenization method within a finite element technique, which was implemented through $$\hbox {ABAQUS}^{\circledR }$$ . This spectral stochastic homogenization method efficiently predicts the propagation of uncertainties from the constituent to ply levels. The derived probability distributions of effective properties were verified by Monte Carlo simulation. Another novelty is the study of the influence of stochastic parameters at both micro-scale and meso-scale on the failure prediction of composite structures, without assumptions of probabilistic characteristic of ply properties commonly used in a single-scale stochastic analysis. The up-scaled uncertainties combined with other randomness at meso-scale (strength properties and ply orientations) are provided as the input of meso-scale stochastic strength analysis of a quasi-isotropic laminate based on classical lamination theory (CLT) and ply discount. The probability distribution of first-ply failure and ultimate failure loads are obtained and their sensitivity factors with respect to input variations are presented.

Optimal design of variable stiffness laminated composite truncated cones under lateral external pressure

The purpose of this paper is to present optimal designs for variable stiffness laminated composite truncated cones under lateral external pressure. The objective is to maximize the failure load which is defined as the minimum of the buckling load and the first-ply failure (FPF) load. The numerical results are obtained using a semi-analytical degenerated shell element based on a refined first-order shear deformable shell theory and the influences of the pressure stiffness (PS) and the thickness/radius ratio are taken into account. A 2D degenerated shell element is also used for verification purposes. Results are presented for the related verification problems solved and the semi-analytical shell element is validated. Optimal designs, where FPF and buckling are imposed as design constraints, are presented for laminated composite thin and relatively thick cones having variable thickness and ply-angle. A simple graphical optimization technique and a modified Micro-Genetic Algorithm are employed. It is shown that, FPF constraint may be active for thicker cones having lower cone angles, PS slightly decreases the buckling pressures, and the stacking sequence has considerable influence on the failure load. The numerical results presented show that restraining the large end against rotation significantly increases the failure load.

First-ply Failure Analysis of Delaminated Rotating Composite Conical Shells: A Finite Element Approach

The present analysis evaluates the first-ply failure load of delaminated composite conical shells. Single and multiple delamination is considered across the thickness of the conical shell. The dynamic equilibrium equation considers only moderate rotational speeds for which Coriolis effect is neglected. Convergence studies are performed in respect of mesh sizes, and comparisons of the present solutions and those reported in open literature are provided to verify the accuracy of the present finite element formulation. Computer codes are developed to obtain the numerical results for the failure loads of delaminated composite conical shells. The first-ply failure load considering different failure criteria namely Maximum stress (independent), Tsai-Hill, Tsai-Wu-Hahn and Tsai-Hill-Hoffman are evaluated. The variation of the failure loads with the position of delamination across the thickness as well as along longitudinal direction are illustrated and presented.

Optimal design of filament wound truncated cones under axial compression

In this study, filament wound truncated cones under axial compression are with the objectives of minimizing the total weight and maximizing the failure load, which is defined as the minimum of the buckling and the first-ply failure (FPF) loads. The numerical results are obtained using an axisymmetric degenerated shell element based on a refined first-order shear deformable shell theory and a 2D degenerated shell element is used for verification purposes. It is shown that, FPF is more critical than buckling for thicker cones with lower cone angles.Optimal designs, where FPF and buckling are imposed as design constraints, are presented for filament wound cones using Micro-Genetic Algorithms. The results show that, using more layers having different winding angles has negligible influence on the failure load and the optimal design is not FPF critical for moderate levels of axial compression. The influence of the rotational boundary conditions on the optimal failure load is also demonstrated.