Ply Failure Criterion Research Articles

Numerical and Experimental Analysis of the Mode I Interlaminar Fracture Toughness in Multidirectional 3D-Printed Thermoplastic Composites Reinforced with Continuous Carbon Fiber.

It is well known that the use of continuous reinforcing fibers can largely improve the typical low in-plane mechanical properties of 3D-printed parts. However, there is very limited research on the characterization of the interlaminar fracture toughness of 3D-printed composites. In this study, we investigated the feasibility of determining the mode I interlaminar fracture toughness of 3D-printed cFRP composites with multidirectional interfaces. First, elastic calculations and different FE simulations of Double Cantilever Beam (DCB) specimens (using cohesive elements for the delamination, in addition to an intralaminar ply failure criterion) were carried out to choose the best interface orientations and laminate configurations. The objective was to ensure a smooth and stable propagation of the interlaminar crack, while preventing asymmetrical delamination growth and plane migration, also known as crack jumping. Then, the best three specimen configurations were manufactured and tested experimentally to validate the simulation methodology. The experimental results confirmed that, with the appropriate stacking sequence for the specimen arms, it is possible to characterize the interlaminar fracture toughness in multidirectional 3D-printed composites under mode I. The experimental results also show that both initiation and propagation values of the mode I fracture toughness depend on the interface angles, although a clear tendency could not be established.

Non-probabilistic interval model-based system reliability assessment for composite laminates

Composite materials have been widely applied to engineering fields by virtue of its superior mechanical properties. Therefore, the problem of composite laminates safety assessment has also been discussed. This paper develops the non-probabilistic interval model-based system reliability evaluation strategy based on the last ply failure criterion (LPF), which improves the rough reliability solution based on first ply failure criterion (FPF) for composite laminates, and overcomes the shortage of traditional LPF method based on the probabilistic reliability theory. Obviously, the probability density function (PDF) is difficult to be calculated due to the experimental cost and time. In the proposed method, considering the fiber failure and matrix failure (limit state functions) for composite laminates, the failure possibility of every single ply is evaluated by the non-probabilistic interval model method. Subsequently, the progressive damage method is combined with the branch-bound method (B&B) to search the significant failure paths of composite laminates, and then the whole system analysis process is completed based on LPF criterion. Finally, the system reliability model of composite laminates can be constructed by introducing non-probabilistic interval model. Furthermore, the correlation description for the non-probabilistic interval model among is applied to the failure modes, and the Cornell first-order bound theory is applied to achieve the system reliability of composite laminates. After the detailed analysis steps, the numerical example of laminated plate is presented to demonstrate the validity and reasonability of the developed methodology.

Nonlinear deformation and failure analysis of laminated composites

An approach to the characterization of different types of nonlinearity in the behavior of composite materials is proposed. One of them is concerned usually observed in experimental studies the dependence of deformation properties of composite materials on the type of external forces. Another type of nonlinearity lies in the fact that the shear stress-strain curves are nonlinear, though they are linear ones when the load is applied along the reinforcement. To describe these effects, the additional matrix is introduced into the proposed constitutive relations. There are different mechanisms of deformation of these materials, which are dependent on the type of reinforcement, matrix properties, loading conditions, directions of loads with respect to reinforcement and some others. These mechanisms and their interactions determine the stress-strain behavior of materials that influence the damage evolution and fracture properties of composite materials. To describe the damage accumulation process, the system of general failure model assumptions is formulated that include the choice of first ply failure criterion, constitutive relations for damaged materials with the use of corresponding damage parameters, the dependence of first ply failure criterion and elastic properties on the damage rate parameters and others. Some particular models are considered taking into account different types of nonlinearities, Lomakin et al. (1981, 2007, 2014, 2015 and 2017). This approach is verified using complex loading experiments. The theoretical dependencies obtained on the base of proposed models are compared with the results of experimental studies and good correspondence of them is shown. The proposed approach to the formulations of constitutive models from simple to more complex ones allows to describe adequately the behavior of composite materials under different loading conditions with the necessary precision.

Modelling Damage of Composite Laminates with Different Stacking Sequences

This paper considers damage development mechanisms in composite laminates subjected to tensile loading. The continuum damage mechanics is the most widely used approach to capture the non linear behaviour of laminates due to cracking. In this study, a continuum damage model based on ply failure criteria, which is initially proposed by Ladevèze has been extended to cover all plies failures mechanisms using an accurate numerical model to predict the equivalent damage accumulation. However, this model requires a reliable representation of the elementary damage mechanisms which can be produced in the composite laminate. To validate this model, a numerical application has been carried on the cross-ply laminates of type [0n/90m]s..A shear lag model was adapted to calculate the average stress of the 0° and 90° plies. The solution presented is obtained by using finite element analysis which implements progressive failure analysis. The effect of the stacking sequences has been done by varying the thickness of the 90° plies.

Time-varying reliability analysis using a response surface method for a laminated plate under a dynamic load

Composite materials are finding increased usage in a variety of applications such as civil, aerospace and marine structures. A key feature of such structures is the dynamic nature of loadings and the uncertainties. Accurate prediction of the failure of composite structures has become more challenging to designers in the presence of inherent scatter in the material properties and the dynamic load such as that due to an earthquake, which varies with time. The present work aims at time-varying reliability analysis of a laminated composite plate. The method combines transient vibration analysis, first ply failure analysis and reliability analysis by the response surface method to predict the reliability of the laminated plate. Transient analysis is investigated by using the eight-node isoparametric quadratic elements of the first-order shear deformable theory. The Newmark time integration algorithm is employed for solving the time-dependent equations. The first ply failure criterion was used as the criterion for probabilistic failure analysis. Parametric studies are made by varying the ply orientation and the boundary conditions.

Cross-Ply Laminates under Static Three-Point Bending: A Numerical Development Model

This paper considers damage development mechanisms in cross-ply laminates using an accurate numerical model. Under static three points bending, two modes of damage progression in cross-ply laminates are predominated: transverse cracking and delamination. However, this second mode of damage is not accounted in our numerical model. After a general review of experimental approaches of observed behavior of laminates, the focus is laid on predicting laminate behavior based on continuum damage mechanics. In this study, a continuum damage model based on ply failure criteria is presented, which is initially proposed by Ladevèze. To reveal the effect of different stacking sequence of the laminate; such as thickness and the interior or exterior disposition of the 0° and 90° oriented layers in the laminate, an equivalent damage accumulation which cover all ply failure mechanisms has been predicted. However, the solution algorithm using finite element analysis which implements progressive failure analysis is summarized. The results of the numerical computation have been justified by the previous published experimental observations of the authors.

Numerical investigation to prevent crack jumping in Double Cantilever Beam tests of multidirectional composite laminates

During the experimental characterization of the mode I interlaminar fracture toughness of multidirectional composite laminates, the crack tends to migrate from the propagation plane (crack jumping) or to grow asymmetrically, invalidating the tests. The aim of this study is to check the feasibility of defining the stacking sequence of Double Cantilever Beam (DCB) specimens so that these undesired effects do not occur, leading to meaningful onset and propagation data from the tests. Accordingly, a finite element model using cohesive elements for interlaminar delamination and an intralaminar ply failure criterion are exploited here to thoroughly investigate the effect of specimen stiffness and thermal residual stresses on crack jumping and asymmetric crack growth occurring in multidirectional DCB specimens. The results show that the higher the arm bending stiffness, the lower the tendency to crack jumping and the better the crack front symmetry. This analysis raises the prospect of defining a test campaign leading to meaningful fracture toughness results (onset and propagation data) in multidirectional laminates.

Optimization of laminated composites considering different failure criteria

The purpose of the present work is to analyse how different the optimal structures are when different first ply failure criterion are considered in the optimization of laminated composites. Two problems are solved: the minimum weight and the minimum material cost of laminated plates subjected to in-plane loads. The failure criterion is taken into account by means of constraints introduced in the optimization problem. Three different failure criteria are tested independently: maximum stress, Tsai–Wu and the Puck failure criterion (PFC). Emphasis is given to the PFC as it appears to agree better with practical observations. The design variables are the ply orientations, the number of layers and the layer material, and the optimization problem is solved by a genetic algorithm (GA). The results show that optimal structures highly differ when different failure criterion are considered and that none of the failure criteria is always the most or the least conservative when different load conditions are applied.

Numerical simulation of delamination in laminated composite components – A combination of a strength criterion and fracture mechanics

An approach for the numerical treatment of delamination in laminated composite components is presented. A first ply failure criterion is employed to predict delamination initiation, while delamination propagation is analyzed using linear elastic fracture mechanics. The combination of initiation and propagation criteria yields a conservative estimation of the load earring capacity of a structure. Furthermore, the growth stability, the sensitivity of the results with respect to a change in the interface properties, and the non-linear structural response caused by the delamination growth process are determined. Two structures are investigated, which show the capability of the proposed approach, a curved laminate and a double lap shear test specimen.

Numerical Estimates of the Compressive Strength of Impact-damaged Sandwich Composites

Improved numerical models have been developed for predicting the compressive strength of impact-damaged sandwich composites comprised of woven-fabric graphite-epoxy facesheets and Nomex honeycomb cores. The proposed methodology contains three key elements: (1) the use of nondestructive inspection estimates of damage, (2) the incorporation of nonlinear through-the-thickness core-crush constitutive response to account for core failure, and importantly (3) the simulation of progressive loss of facesheet structural integrity based upon userspecified ply failure criteria. The finite element predictions of residual strength for panels impacted with relatively blunt objects correlate well with the experimental observations; this is in contrast to a number of estimates from literature that tend to overestimate the strength. The proposed approach may potentially facilitate sandwich design by providing insight into the relationships between material configuration and damage that lead to improved damage tolerance characteristics.

An approach for failure analysis of composite bridge deck systems with openings

Design details pertaining to the connection between some recently developed fiber reinforced polymer (FRP) composite deck systems and the supporting girders require openings through cells of the deck. This significantly changes the stress distribution in these components. As a result, the conventional assumptions that deck designs are controlled by their stiffness, and not strength, needs a closer examination. This paper proposes an analytical method to investigate the stress states and failure mechanisms using a type of "global-local" modeling perspective, incorporating classical lamination theory and first ply failure criterion with use of appropriate stress concentration factors around the cutouts. The use of a "smeared-stress" approach is presented as a potential means of simplifying certain FRP specific complexities, while still enabling prediction of overall failure.

Assessment of a Steel-Free Fiber Reinforced Polymer-Composite Modular Bridge System

The paper describes the development and characterization of a modular bridge system incorporating fiber reinforced polymer (FRP) composite girders connected by stiffened FRP deck panels which serve as both formwork and flexural reinforcement for a steel free concrete deck cast on top. The response of individual components and a two girder deck assemblage are characterized through full scale tests and it is shown that capacity is substantially greater than the design demand levels. Analytical predictions, based on laminated beam theory using progressive ply failure criteria, moment-curvature analysis and finite element models, are seen to compare well with experimental results.

소형 항공기 복합재 주익 구조의 기본 설계

In this study preliminary structural design has been performed to develop an all composite wing box for experimental aircraft(classified in FAR Part 21). Considerations on composite materials and their manufacturing process were taken into account throughout the design phase. Aerodynamic loads were estimated by using Shrenk method(NACA TM No 948) and FAR Part 23 Appendix A. The structural layout has been determined to carry effectively the critical loads and to maximize the benefit of composite structure. Maximum strain failure allowable and first ply failure criteria were applied for the sizing of major structural members. Finally, the designed composite wing box structure is presented in the form of drawings, which include material specifications, stacking sequences and joint design.

Application of Lamination Parameter to Reliability-Based Optimization of Symmetric Laminated Composite Plate.

In this paper, the two types of the reliability-based design of a laminated composite plate subject to in-plane loads are formulated in terms of lamination parameters to improve the calculation efficiency. One is the reliability-maximized design of the constant-thickness plate. The other is the thickness-minimized design under the reliability constraint. The first ply failure (FPF) criterion is adopted as the plate failure, so that the laminated plate system is modeled as a series system consisting of each ply failure. The ply reliability is evaluated by the first order reliability method (FORM), where the material properties and applied loads are treated as random variables. Then, the system reliability is approximated by Ditlevsens bounds. Through numerical calculations, it is demonstrated that the reliability is distributed smoothly in the lamination parameter space and that a quick convergence is achieved in the reliability-based optimization.

Relialility Analysis of Laminated Composite Plate with Initial Imperfection.

This paper describes the reliability analysis of a simply-supported laminated composite plate with an initial imperfection under a bi-axial compression load. For a plate loaded in compression, a small initial imperfection can cause large bending stress that decreases a plate failure load. The first ply failure criterion is adopted as that of the plate failure. On the reliability analysis, the laminated composite plate is modeled as a series system consisting of the composed plies, which means that failure in any one ply reduces to failure of the plate. The initial imperfection, material properties and applied loads are considered as random variables. The mode reliability is evaluated by the first order reliability method (FORM). The system reliability is approximated by Ditlevsen's upper bound. Through numerical calculations, the effect of variations of the random variables is evaluated on the reliability. The change of the reliability in terms of ply orientation angles is also investigated. The reliability-based optimum design is demonstrated to be different from the design of deterministic strength maximization. The results show the importance of considering variations of the random variables for the safety of a laminated composite plate.

A Finite Element Model for Predicting Time-Dependent Deformations and Damage Accumulation in Laminated Composite Bolted Joints

To assess and predict the long-term durability of advanced composite joints, a general, nonlinear finite element program was developed and implemented to model the localized time-dependent deformations and damage accumulation in the vicinity of a fastener hole in a polymer matrix composite (PMC) laminate. This code incorporates an elastic-viscoplastic constitutive model for unidirectional, orthotropic laminae, coupled with classical lamination theory, to determine the time-dependent stresses and deformations in the laminate. The accumulation of damage in the composite, and the subsequent deterioration of mechanical properties, is predicted by a set of ply failure criteria and an associated property degradation model. The results from this analysis were compared to experimental data and were found to provide reasonable correlation with time-dependent bolt-hole elongation measurements obtained from a graphite fiber reinforced PMC.

Analysis of filament-wound cylindrical shells under combined centrifugal, pressure and axial loading

An analytical procedure is developed to assess the stresses and deformations of filament-wound structures under loading conditions particular to centrifuge rotors and to assess the effects of wind angle variation through the centrifuge wall. This procedure is based on classical laminated plate theory and models both plane stress and plane strain states of a cylindrical shell comprising a number of cylindrical sublayers, each of which is cylindrically orthotropic. Available loading conditions are: radial body force due to rotation about the cylinder axis, internal and external pressures and axial force. The analysis is applied to three examples: a pressure vessel, a centrifuge rotor and a flywheel. It is shown that the benefit of wind angle variation is more significant for applications in which there is no axial loading to the cylindrical shell. It is also shown that, where axial loading is present, the benefits of wind angle variation are more significant under the last ply failure criterion than under the first ply failure criterion.

Heuristic design of composite laminates for strength, stiffness and multiple load cases

AbstractThe problem of designing a composite laminated plate subject to multiple loading cases is addressed using the methodology of heuristic redesign. Lower bounds on extensional stiffnesses together with a maximum strain first ply failure criterion constitute the design constraints. The general theory of heuristic redesign and its application to this particular problem are described. Results for different combinations of loading cases and redesign strategies are presented.

Residual Tensile Strength Prediction on a Ply-by-Ply Basis for Laminates Containing Impact Damage

Impact loading on composite laminates can cause surface or internal damage in the form of fiber breakage, delamination and matrix cracking. Such damage can reduce laminate tensile strength. In the work presented here, impact damage was modelled as part through-the-thickness damage and laminate residual strength was evaluated by ex amining the behavior of each individual ply of the laminate. A residual strength prediction procedure, proposed previously for laminates containing cut internal fibers, was used here for laminates containing impact damage. The prediction of laminate residual strength was performed based on 3-D finite element results in conjunction with a principal load carry ing ply failure criterion. The predicted residual strength agreed with the experimental data within the bounds of 0.85 to 1.08 times the experimental data, indicating the applicability of the procedure and the damage modelling technique.

Optimization of Antisymmetric Angle-Ply Strip for Maximum Strength Including Hygrothermal Effects

The transverse failure load on an antisymmetrically laminated angle-ply strip is maximized with respect to fiber volume ratio. The failure load is determined using the Tsai-Hill failure theory based on initial ply failure criterion. Hygrothermal conditions and the presence of voids in the resin are taken into account in computing the material and strength properties from micromechanical relations. Numerical results are given for graphite, boron and E-glass fibers and the effects of hot-wet conditions and voids are investigated on the efficiency and the fiber content of the optimal designs. Sensitivity of the designs to changes in the design variable is graphically studied.