Numerical Modeling of Combined Matrix Cracking and Delamination in Composite Laminates Using Cohesive Elements

Sub-laminate damage in the form of matrix cracking and delamination was simulated by using interface cohesive elements in the finite element (FE) software ABAQUS. Interface cohesive elements were inserted parallel to the fiber orientation in the transverse ply with equal spacing (matrix cracking) and between the interfaces (delamination). Matrix cracking initiation in the cohesive elements was based on stress traction separation laws and propagated under mixed-mode loading. We expanded the work of Shi et al. (Appl. Compos. Mater. 21, 57–70 2014) to include delamination and simulated additional [45/?45/0/90]_s and [0₂/90_n]_s {n?=?1,2,3} CFRP laminates and a [0/90₃]_s GFRP laminate. Delamination damage was quantified numerically in terms of damage dissipative energy. We observed that transverse matrix cracks can propagate to the ply interface and initiate delamination. We also observed for [0/90_n/0] laminates that as the number of 90° ply increases past n?=?2, the crack density decreases. The predicted crack density evolution compared well with experimental results and the equivalent constraint model (ECM) theory. Empirical relationships were established between crack density and applied stress by linear curve fitting. The reduction of laminate elastic modulus due to cracking was also computed numerically and it is in accordance with reported experimental measurements.     

Failure Analysis of Bolted Joints in Cross-ply Composite Laminates Using Cohesive Zone Elements

A strength prediction method is presented for double-lap single fastener bolted joints of cross-ply carbon fibre reinforced plastic (CFRP) composite laminates using cohesive zone elements (CZEs). Three-dimensional finite element models were developed and CZEs were inserted into subcritical damage planes identified from X-ray radiographs. The method makes a compromise between the experimental correlation factors (dependant on lay-up, stacking sequence and joint geometry) and three material properties (fracture energy, interlaminar strength and nonlinear shear stress-strain response). Strength of the joints was determined from the predicted load-displacement curves considering sub-laminate and plylevel scaling effects. The predictions are in a reasonable agreement with the experimental data.     

Modelling Strategies for Simulating Delamination and Matrix Cracking in Composite Laminates

The composite materials are nowadays widely used in aeronautical domain. These materials are subjected to different types of loading that can damage a part of the structure. This diminishes the resistance of the structure to failure. In this paper, matrix cracking and delamination propagation in composite laminates are simulated as a part of damage. Two different computational strategies are developed: (i) a cohesive model (CM) based on the classical continuum mechanics and (ii) a continuous damage material model (CDM) coupling failure modes and damage. Another mixed methodology (MM) is proposed using the continuous damage model for delamination initiation and the cohesive model for 3D crack propagation and mesh openings. A good agreement was obtained when compared simple characterization tests and corresponding simulations.     

Interface Cohesive Elements to Model Matrix Crack Evolution in Composite Laminates

In this paper, the transverse matrix (resin) cracking developed in multidirectional composite laminates loaded in tension was numerically investigated by a finite element (FE) model implemented in the commercially available software Abaqus/Explicit 6.10. A theoretical solution using the equivalent constraint model (ECM) of the damaged laminate developed by Soutis et al. was employed to describe matrix cracking evolution and compared to the proposed numerical approach. In the numerical model, interface cohesive elements were inserted between neighbouring finite elements that run parallel to fibre orientation in each lamina to simulate matrix cracking with the assumption of equally spaced cracks (based on experimental measurements and observations). The stress based traction-separation law was introduced to simulate initiation of matrix cracking and propagation under mixed-mode loading. The numerically predicted crack density was found to depend on the mesh size of the model and the material fracture parameters defined for the cohesive elements. Numerical predictions of matrix crack density as a function of applied stress are in a good agreement to experimentally measured and theoretically (ECM) obtained values, but some further refinement will be required in near future work.     

Calculations of Buckle-Driven Delamination Using Cohesive Elements

Plane strain, elastic calculations of buckle-driven thin film delamination from compliant substrates using finite element models are considered. The interfacial properties between the film and the substrate are modeled using cohesive elements with a tractionseparation law formulated in terms of a potential. The model yielded the geometry of the buckles given the properties of the film and the substrate, the interfacial toughness and the value of the compressive equi-biaxial stress. Results for the relation between the buckle width and the interfacial toughness were very close to similar results by Yu and Hutchinson (2002), thus giving confidence that the cohesive element approach presented can be used in applications where buckle-driven delamination of thin films is an issue.     

Delamination Depth in Composites Laminates With Interface Elements and Ultrasound Analysis

Abstract: This paper deals with the impact‐induced damage depth for laminated composite plates under low velocity impact. The numerical model developed here is an interface element compatible with the eight‐node isoparametric hexahedral element, present in Modulef software. This new element allows modelling the behaviour of the damage interface, considering a three‐dimensional stress state, the interpenetration constraint and the propagation of the delamination. The use of the interface element and of the damage model is proposed to predict damage for low impact velocities and to obtain accurately the shape, size and defect depth of delaminations in carbon‐epoxy [0,90,0,90]_2s and [0,90]₈ laminates. The laminate is also simulated using a damage model based on the indirect use of fracture mechanics implemented in Abaqus software. The defects in the impacted specimens were then inspected by ultrasonic C‐scan technique and by electronic speckle pattern interferometry as a comparative method. A good agreement between numerical results and experimental testing is demonstrated.     

A Cohesive Zone Approach for Fatigue-Driven Delamination Analysis in Composite Materials

A new model for prediction of fatigue-driven delamination in laminated composites is proposed using cohesive interface elements. The presented model provides a link between cohesive elements damage evolution rate and crack growth rate of Paris law. This is beneficial since no additional material parameters are required and the well-known Paris law constants are used. The link between the cohesive zone method and fracture mechanics is achieved without use of effective length which has led to more accurate results. The problem of unknown failure path in calculation of the energy release rate is solved by imposing a condition on the damage model which leads to completely vertical failure path. A global measure of energy release rate is used for the whole cohesive zone which is computationally more efficient compared to previous similar models. The performance of the proposed model is investigated by simulation of well-known delamination tests and comparison against experimental data of the literature.     

The Problem of the Cohesive Zone in Numerically Simulating Delamination/Debonding Failure Modes

This paper addresses the task of using a commercial non-linear Finite Element code as a design tool to simulate (and design) the behaviour and performance of laminated composite structures. It is shown that the need to model the stress field ahead of a crack tip, in a tiny ‘cohesive zone’, does not necessarily mean having to use tiny finite elements.     

Simulation of Lightning-Induced Delamination in Un-protected CFRP Laminates

Lightning is a major cause of damage in laminated composite aerospace structures during flight. The most significant failure mode induced by lightning is delamination, which might extend well beyond the visible damage zone, and requires sophisticated techniques and equipment to detect. Therefore, it is crucial to develop a numerical tool capable of predicting the damage zone induced from a lightning strike to minimize costly repair acreage and supplement extremely expensive lightning experiments. Herein, a detailed numerical study consisting of a multidirectional composite with user-defined, temperature-dependent, interlaminar elements subjected to a lightning strike is designed, and delamination/damage expansion is studied under specified conditions. It is observed both the size and shape of the delamination zone are strongly dependent on the assumed temperature-dependent fracture toughness; the primary parameter controlling lightning-induced delamination propagation. An accurate estimation of the fracture toughness profile is crucial in order to have a reliable prediction of the delamination zone and avoid sub-critical structural failures.     

Effect of Off – Axis Matrix Cracking on Stiffness of Symmetric Angle-Ply Composite Laminates

Matrix cracking models developed for cross-ply composite laminates cannot easily be applied to more complicated geometries. In this paper a detailed analysis of the effect of matrix cracking on the longitudinal Young’s Modulus of a [0/45]s plate under uniaxial tension is attempted. The theoretical approach, based on a semi-analytical generalized plane strain model, is compared to experimental data obtained by microscopic strain measurements on a fiber sensor using the technique of laser Raman Spectroscopy. The experimental results are in a good agreement with theoretical stiffness degradation predictions obtained using the semi-analytical model.     

含分层损伤缝合复合材料层板的剩余压缩强度

基于渐进损伤方法,研究了含单脱层缝合复合材料层板在压缩载荷下的剩余强度。通过商用软件ABAQUS建立了含单脱层缝合复合材料层板剩余压缩强度计算模型,考虑了子层屈曲和分层扩展对剩余强度的影响。通过UMAT子程序实现了层板失效、层间失效和缝线失效的模拟。通过嵌入式杆单元结构模拟了缝线桥联作用及失效。采用Hashin准则及刚度折减法对纤维拉压、基体拉压失效进行了模拟。通过渐进损伤分析,揭示了缝合情况下含单脱层复合材料层板的失效机理,讨论了缝合参数对剩余压缩强度的影响。所预测的破坏模式和剩余强度结果与实验能较好地吻合。分析表明缝合可以明显提高含分层损伤复合材料层板的子层屈曲载荷,抑制分层扩展,并提高层     

Behavior and Failure Modes of Sandwich T-Joint Using Cohesive Zone Material Model and Contact Elements

One of the significant concerns of sandwich panels is their joints. T-joint is one the most common joint in sandwich structures. This paper deals with the numerical study of triangle T-joint under static loading. The results of numerical solution obtained by ANSYS modeling are verified with the results of experimental tests obtained in the literature. In general, the results obtained for anticipated failure load by numerical solution with the results of experimental test is in good agreement. Contact elements and cohesive zone material model are used to model the adhesive layer, hence debonding and fracture of adhesive is observed by the numerical modeling. Also, by using a written macro code in the ANSYS software, the ability of damage is explained for the core of sandwich panels; thus both the modes in fracture of T-joints (core shear failure in base panel and debonding of adhesive) are modeled. Core materials consist of Divinycell H100, H160, H250, and HCP70 are used for modeling sandwich panels, so that the function of joint is studied under different conditions of the sandwich core material. Nine different geometrical models are created by changing the base angle of the core triangle. The absorbed energy associated with different segments of the T-joint are used to investigate the effect of joint geometry and core material on the load transfer and failure mode of the T-joint.     

Buckling and Delamination Growth Analysis of Composite Laminates Containing Embedded Delaminations

The objective of this work is to study the post buckling behavior of composite laminates, containing embedded delamination, under uniaxial compression loading. For this purpose, delamination initiation and propagation is modeled using the softening behavior of interface elements. The full layer-wise plate theory is also employed for approximating the displacement field of laminates and the interface elements are considered as a numerical layer between any two adjacent layers which delamination is expected to propagate. A finite element program was developed and the geometric non-linearity in the von karman sense is incorporated to the strain/displacement relations, to obtain the buckling behavior. It will be shown that, the buckling load, delamination growth process and buckling mode of the composite plates depends on the size of delamination and stacking sequence of the laminates.     

Lamb Wave Interaction with Delaminations in CFRP Laminates

In this paper, we investigate Lamb wave interaction with delamination in an infinite carbon fiber reinforced plastics (CFRP) laminate by a hybrid method. The infinite CFRP laminate is divided into an exterior zone and an interior zone. In the exterior zone, the wave fields are expressed by wave mode expansion. In the interior zone, the wave fields are modeled by the finite element method (FEM). Considering the continuity condition at the boundary between the exterior and interior zones, the global wave fields can be calculated. Lastly, numerical examples show how a delamination in the laminate influences the mode conversion of different incident wave modes.     

Three-Dimensional Analysis of the Effect of Material Randomness on the Damage Behaviour of CFRP Laminates with Stochastic Cohesive-Zone Elements

Laminated carbon fibre-reinforced polymer (CFRP) composites are already well established in structural applications where high specific strength and stiffness are required. Damage in these laminates is usually localised and may involve numerous mechanisms, such as matrix cracking, laminate delamination, fibre de-bonding or fibre breakage. Microstructures in CFRPs are non-uniform and irregular, resulting in an element of randomness in the localised damage. This may in turn affect the global properties and failure parameters of components made of CFRPs. This raises the question of whether the inherent stochasticity of localised damage is of significance in terms of the global properties and design methods for such materials. This paper presents a numerical modelling based analysis of the effect of material randomness on delamination damage in CFRP materials by the implementation of a stochastic cohesive-zone model (CZM) within the framework of the finite-element (FE) method. The initiation and propagation of delamination in a unidirectional CFRP double-cantilever beam (DCB) specimen loaded under mode-I was analyzed, accounting for the inherent microstructural stochasticity exhibited by such laminates via the stochastic CZM. Various statistical realizations for a half-scatter of 50 % of fracture energy were performed, with a probability distribution based on Weibull’s two-parameter probability density function. The damaged area and the crack lengths in laminates were analyzed, and the results showed higher values of those parameters for random realizations compared to the uniform case for the same levels of applied displacement. This indicates that deterministic analysis of composites using average properties may be non-conservative and a method based on probability may be more appropriate.     

On the Distribution of Delamination in Composite Structures and Compressive Strength Prediction for Laminates with Embedded Delaminations

In this study, large numbers of aircraft composite structures were inspected, and the distribution of delamination sizes and though thickness positions in the composite laminates are investigated. An experiment is conducted to probe into the influence of delamination sizes and through thickness positions on the compressive strengths of laminates with single embedded circular delamination, with the most dangerous delamination sizes and positions defined from the distribution. Furthermore, a shell model is established for compressive strength prediction, with delamination propagation assessed using a mixed mode criterion. The finite element (FE) prediction comes out to be in good agreement with the experimental measurements, for the predicted compressive strengths stand within 10% error of experimental results. It was observed that the compressive strength was highly influenced by the delamination size, while the through thickness position of delamination did not have significant effect on the compressive strength.     

Acoustic Emission Characterization of Failure Modes in GFRP Laminates Under Mode I Delamination

In order to design structural components using composite materials a deep understanding of the material behaviour and its failure mechanisms is necessary. To create a better understanding of the initiation, growth and interaction of the different types of damage, damage monitoring during mechanical loading is very important. To this direction, AE is a powerful non destructive technique for real time monitoring of damage development in materials and structures which has been used successfully for the identification of damage mechanisms in composite structures under quasi static and dynamic-cycle loading. In this present work, pure resin plate and GFRP composite laminates with stacking sequence of [0⁰]₆, are fabricated using Hand lay-up method. During the layup a Teflon tape of width 45 mm is kept in the mid plane of the laminate which serves as an initiator for delamination during loading. As per ASTM STD D5528 01 DCB (Double Cantilever Beam) specimens are cut out from the laminates and are subjected to tensile test in the transverse direction along with acoustic emission monitoring. While loading, Markings are made on the sides of the specimen to track the crack front using a magnifying lens. Parametric analysis is performed on the AE data obtained during crack propagation to discriminate the failure modes. Fast Fourier Transform (FFT) enabled the calculation of frequency content of each damage mechanism. Further STFFT analysis is performed on a portion of the waveforms representing the dominant frequency content pertaining to each damage mechanism.     

On a Formulation and Solutions for Doubly Periodic Cracking in hhh Laminates

Problem formulation and simple analytical procedure are presented for the determination of the distribution of averaged through the thickness displacements, strains and stresses in layers for the case of doubly periodic matrix cracking in [_1m,_2n ]_s composite laminates. The modeling accounts for the coupling between tensile and shear stresses in the layers.