Fastener pull-through in a carbon fibre epoxy composite joint

This paper considers the capability of finite element (FE) modelling to accurately predict fastener pull-through failure of composite laminates. Such failures are dominated by inter-ply delamination and through-thickness shear failure of the laminate and the common modelling approach is to use computationally expensive, detailed three-dimensional models that include delamination for every ply interface, fastener contact and prestress. This paper considers a simplified FE modelling strategy achieved through judicious use of symmetry boundary conditions, hybrid shell/solid modelling and reduced numbers of interfaces for delamination. The LS-DYNA FE software was used for this study using the available composite material and cohesive failure models. The conclusion drawn from this work is that the use of simplified FE models does have merit in modelling fastener pull-through provided the material is quasi-isotropic and the boundary conditions are uniform around a circular perimeter. Additional work is however required to determine suitable cohesive properties and progressive shear failure parameters.     

Mixed-Mode Delamination – Experimental and Numerical Studies

Abstract: A fracture energy approach for modelling mixed-mode delamination of composite materials and other bonded structures is introduced. The model is incorporated within an explicit finite element (FE) code and ties layered shell elements together via a stiffness condition, a failure criterion and post-failure damage law. The procedure for predictive modelling of delamination using the approach is described and the set of required input parameters is presented. A benchmark test comparing experimental results for a continuous filament random E-glass/polyester composite and explicit FE simulations for standard fracture toughness tests for a range of mode mixities is included.     

Spatial Evolution of the Thickness Variations over a CFRP Laminated Structure

Ply thickness is one of the main drivers of the structural performance of a composite part. For stress analysis calculations (e.g., finite element analysis), composite plies are commonly considered to have a constant thickness compared to the reality (coefficients of variation up to 9% of the mean ply thickness). Unless this variability is taken into account reliable property predictions cannot be made. A modelling approach of such variations is proposed using parameters obtained from a 16-ply quasi-isotropic CFRP plate cured in an autoclave. A discrete Fourier transform algorithm is used to analyse the frequency response of the observed ply and plate thickness profiles. The model inputs, obtained by a mathematical representation of the ply thickness profiles, permit the generation of a representative stratification considering the spatial continuity of the thickness variations that are in good agreement with the real ply profiles spread over the composite part. A residual deformation FE model of the composite plate is used to illustrate the feasibility of the approach.     

Numerical prediction of damage in composite structures from soft body impacts

The paper summarises recent progress on materials modelling and numerical simulation of soft body impact damage in fibre reinforced composite aircraft structures. The work is based on the application of finite element (FE) analysis codes to simulate damage in composite shell structures under impact loads. Composites ply damage models and interply delamination models have been developed and implemented in commercial explicit FE codes. Models are discussed for predicting impact loads on aircraft structures arising from deformable soft bodies such as gelatine (synthetic bird) and ice (hailstone). The composites failure models and code developments are briefly summarised and applied in the paper to numerical simulation of synthetic bird impact on idealised composite aircraft structures.     

Non‐linear seismic behaviour of concrete gravity dams using coupled finite element–boundary element technique

In this paper, the seismic response of concrete gravity dams is presented using the concept of Continuum Damage Mechanics (CDM) and adopting the hybrid Finite Element–Boundary Element technique (FE–BE). The finite element method is used for discretization of the near field and the boundary element method is employed to model the semi‐infinite far field. Because of the non‐linear nature of the discretizied equations of motion modified Newton–Raphson approach has been used at each time step to linearize them. Damage evolution based on tensile principal strain using mesh‐dependent hardening modulus technique is adopted to ensure the mesh objectivity and to calculate the accumulated damage. The methodology employed is shown to be computationally efficient and consistent in its treatment of both damage growth and damage propagation in gravity dams. Other important features considered in the analysis are: (1) realistic damage modelling for concrete that allows isotropic as well as anisotropic damage state and exhibits stiffness recovery upon load reversals. (2) softening initiation and strain softening criteria for concrete, and (3) proper modelling of semi‐infinite foundation using FE–BE method that allows to consider dam–foundation interaction analysis. As an application of the proposed formulation a gravity dam has been analysed and the results are compared with different foundation stiffnesses. The results of the analysis indicate the importance of including rock foundation in the seismic analysis of dams. Copyright © 1999 John Wiley & Sons, Ltd.     

Motorcyclist helmet composite outer shell characterisation and modelling

In this study a new finite element model of composite outer shell of motorcyclist helmet is proposed, by modelling each layer of the composite material that builds the laminated structure of the outer shell of the helmet. Elastic and rupture properties of the laminate are taken into account for developing the finite element (FE) model and are extracted experimentally. A coupled experimental–numerical method combined with experimental modal analysis on beam samples is used to obtain the elastic characteristics of each layer of the outer shell. The rupture properties for each layer are extracted by experimental impact tests. The FE model of the outer shell is then validated with experimental data for elastic and rupture behaviour.     

Analytical modelling of laminated composites

A significant number of research papers has been published on the analytical modelling of composite laminates over the past 20 years. The drive for more accurate analysis has led us to techniques which have become computationally more and more burdensome, while the engineering world continues to use simple, first-older shear deformable plate theory as its primary tool. This paper presents a unique approach to the analysis of thick laminated composites by presenting two simple finite element methods. The first uses the Predictor Corrector technique to extend the simple Mindlin type element to achieve greater accuracy, and the second develops a new Least Squares element which can approximate a C¹ continuous element. The Least Squares element has the capability to incorporate a simplified higher order basis into a piecewise continuous displacement field creating an accurate, yet computationally simple, element. These two methods have the potential to upgrade analysis methods significantly with little additional computational cost. It is hoped that this work can instigate further research into efficient modelling of composite laminates.     

Non-local regularization for FE simulation of damage in ductile materials

The paper presents an application of the non-local regularization to the finite element modelling of ductile damage and tearing. In order to model the damage growth in ductile materials of structural components, integral limiters have been introduced. These integral limiters, which are spatial averaging operators, can prevent the problem of mesh-sensitivity of the finite element computations. Hence, it was important to establish the characteristic length l_c for spatial averaging operators of the non-local regularization. More formally, the in-plane distance l_c and the out-of-plane FE dimension have been specified, characterizing the volume over which averaging of stress and strain was carried out to ensure that the continuum theory can represent the physical process of damage.

In order to check the reliability and transferability of the method, FE simulations of various testing examples have been carried out, namely ductile fracture in notched tensile specimens, ductile crack growth in C(T) specimens and application to the pipe-bending test.     

Sensitivity analysis of potential tests for determining the interlaminar shear modulus of fibre reinforced composites

A sensitivity analysis using finite element (FE) simulations was conducted as part of an overall attempt to develop a new and robust parameter identification method for determining the interlaminar shear moduli G₁₃ and G₂₃ of laminated composite materials. It is proposed that the new method will use an integrated experimental and numerical technique. Six different shear and bending tests were investigated numerically using three-dimensional FE models to determine their suitability for this integrated technique. The sensitivity of the potential tests to changes in the different material properties, especially the interlaminar shear moduli, G₁₃ and G₂₃, and the elastic modulus in the through-thickness direction, E₃, was determined. It was discovered that several configurations within three of the six potential tests considered are suitable for the new proposed parameter identification method. This is based on the criteria that they are more sensitive to the interlaminar shear moduli than to other material constants. When manufacturing factors were considered, the two most suitable tests were identified for use in the new proposed method.     

A combined experimental and numerical approach to study ballistic impact response of S2-glass fiber/toughened epoxy composite beams

A combined experimental and 3D dynamic nonlinear finite element (FE) approach was adopted to study damage in composite beams subject to ballistic impact using a high-speed gas gun. The time-histories of dynamic strains induced during impact were recorded using strain gages mounted on the front of the composite beam specimen. During ballistic impact tests, the impact velocity was also measured. The commercially available 3D dynamic nonlinear FE code, LS-DYNA, modified with a proposed user-defined nonlinear-orthotropic damage model, was then used to simulate the experimental results. In addition, LS-DYNA with the Chang–Chang linear-orthotropic damage model was also used for comparison. Good agreement between experimental and FE results was found from the comparisons of dynamic strain and damage patterns. Once the proposed nonlinear-orthotropic damage model was verified by experimental results, further FE simulations were conducted to predict the ballistic limit velocity (V₅₀) using either the number of damaged layer approach or a numerically established relation between the projectile impact velocity versus residual velocity or energy similar to the classical Lambert–Jonas equation for metals.     

Micromechanical modelling for onset of distortional matrix damage of fiber reinforced composite materials

A new multi-scale modelling approach is applied to specimen testing to define the critical strain invariants for the damage onset theory proposed by Gosse, Christensen and Hart-Smith. The onset theory is a micromechanics theory that uses critical strain invariants to predict the onset of damage within fiber polymer composites. To obtain the critical strain invariants for the matrix, finite element analyses are required of unidirectional off-axis specimens that have been tested to failure. The strains remain linear to failure and critical strain invariants can be determined from a linear finite element analysis but the use of continuum models to obtain the critical values requires strain enhancement factors. In this paper a new micromechanics-based modelling approach is proposed. A finite element analysis of the composite specimen is implemented with a square fiber array embedded within the polymeric matrix. Failure initiation sights are identified to obtain the critical values directly without the need for the strain enhancement factors. Numerical examples of the modelling process are provided including a 10° off-axis coupon with rectangular tabs. The results are compared to different modelling approaches. The tests and modelling are repeated for a 20° off-axis coupon but with oblique as well as rectangular tabs.     

Mechanical analysis of bi-component-fibre nonwovens: Finite-element strategy

In thermally bonded bi-component fibre nonwovens, a significant contribution is made by bond points in defining their mechanical behaviour formed as a result of their manufacture. Bond points are composite regions with a sheath material reinforced by a network of fibres’ cores. These composite regions are connected by bi-component fibres — a discontinuous domain of the material. Microstructural and mechanical characterization of this material was carried out with experimental and numerical modelling techniques. Two numerical modelling strategies were implemented: (i) traditional finite element (FE) and (ii) a new parametric discrete phase FE model to elucidate the mechanical behaviour and underlying mechanisms involved in deformation of these materials. In FE models the studied nonwoven material was treated as an assembly of two regions having distinct microstructure and mechanical properties: fibre matrix and bond points. The former is composed of randomly oriented core/sheath fibres acting as load-transfer link between composite bond points. Randomness of material’s microstructure was introduced in terms of orientation distribution function (ODF). The ODF was obtained by analysing the data acquired with scanning electron microscopy (SEM) and X-ray micro computed tomography (CT). Bond points were treated as a deformable two-phase composite. An in-house algorithm was used to calculate anisotropic material properties of composite bond points based on properties of constituent fibres and manufacturing parameters such as the planar density, core/sheath ratio and fibre diameter. Individual fibres connecting the composite bond points were modelled in the discrete phase model directly according to their orientation distribution. The developed models were validated by comparing numerical results with experimental tensile test data, demonstrating that the proposed approach is highly suitable for prediction of complex deformation mechanisms, mechanical performance and structure-properties relationships of composites.     

Finite element modeling of impact, damage evolution and penetration of thick-section composites

Impact, damage evolution and penetration of thick-section composites are investigated using explicit finite element (FE) analysis. A full 3D FE model of impact on thick-section composites is developed. The analysis includes initiation and progressive damage of the composite during impact and penetration over a wide range of impact velocities, i.e., from 50 m/s to 1000 m/s. Low velocity impact damage is modeled using a set of computational parameters determined through parametric simulation of quasi-static punch shear experiments. At intermediate and high impact velocities, complete penetration of the composite plate is predicted with higher residual velocities than experiments. This observation revealed that the penetration-erosion phenomenology is a function of post-damage material softening parameters, strain rate dependent parameters and erosion strain parameters. With the correct choice of these parameters, the finite element model accurately correlates with ballistic impact experiments. The validated FE model is then used to generate the time history of projectile velocity, displacement and penetration resistance force. Based on the experimental and computational results, the impact and penetration process is divided into two phases, i.e., short time Phase I - shock compression, and long time Phase II - penetration. Detailed damage and penetration mechanisms during these phases are presented.     

Simulating Initial and Progressive Failure of Open-Hole Composite Laminates under Tension

A finite element (FE) model is developed for the progressive failure analysis of fiber reinforced polymer laminates. The failure criterion for fiber and matrix failure is implemented in the FE code Abaqus using user-defined material subroutine UMAT. The gradual degradation of the material properties is controlled by the individual fracture energies of fiber and matrix. The failure and damage in composite laminates containing a central hole subjected to uniaxial tension are simulated. The numerical results show that the damage model can be used to accurately predicte the progressive failure behaviour both qualitatively and quantitatively.     

Finite element modelling of low velocity impact of composite sandwich panels

This paper outlines a finite element procedure for predicting the behaviour under low velocity impact of sandwich panels consisting of brittle composite skins supported by a ductile core. The modelling of the impact requires a dynamic analysis that can also handle non-linearities caused by large deflections, plastic deformation of the core and in-plane degradation of the composite skins. Metal honeycomb, frequently used as a core material, is anisotropic and requires a non-standard approach in the elasto-plastic part of the analysis. A suitable yield criteria based on experimental observations is proposed. Comparisons of experimental and finite element responses are shown for sandwich panels with carbon fibre skins and aluminium honeycomb cores.     

Methods for modelling the ultimate strength of orthotropic plate with a central hole under uniaxial tension

The stress state in plates with circular holes made of orthotropic homogeneous material has no singularities and it can be exactly determined. The numerical stress distribution calculation by the finite element method will be compared with those obtained by the analytical equations developed by several authors. The goal of this work is to validate the finite element method, in conjunction with in-plane and out of plane failure criteria, in order to calculate not only the stress distribution for orthotropic plates with circular holes but also to determine their ultimate strength.The tool used has been a user subroutine (UMAT) specially developed for this work that implements the features of the commercial FE program (ABAQUS). The code performs an implicit analysis of the stress-state with progressive damage modelling.Finally, both of them, numerical and analytical method, will be checked with experimental tests by means of strain gauges.     

Prediction of Impact-Induced Fibre Damage in Circular Composite Plates

A simple analytical impact damage model for preliminary design analysis is developed on the basis of experimental findings observed from quasi-static lateral load and low velocity impact tests. The analytical model uses a non-linear approximation method (Rayleigh–Ritz) and the large deflection plate theory to predict the number of failed plies and damage area in a quasi-isotropic composite circular plate (axisymmetric problem) due to a point load at its centre. It is assumed that the deformation due to a static transverse load is similar to that occurred in a low velocity impact. It is found that the model, despite its simplicity, is in good agreement with finite element (FE) predictions and experimental data for the deflection of the composite plate and gives a good estimate of the number of failed plies due to fibre breakage. The predicted damage zone could be used with a fracture model developed by the second investigator to estimate the compression after impact strength of such laminates. This approach could save significant running time when compared to FE numerical solutions. Corresponding author.     

Finite element analysis of impact damage response of composite motorcycle safety helmets

The energy absorption during impact provided by a motorcycle safety helmet is always of critical importance in order to protect the rider against head injury during an accident. In the present study, a parametric analysis has been performed in order to investigate the effect of the composite shell stiffness and the damage development during impact, on the dynamic response of a composite motorcycle safety helmet. This kind of parametric analysis may be used as a tool during helmet design for minimising testing needs.The LS-DYNA3D explicit hydrodynamic finite element code was used to analyse a detailed model of the helmet-headform system (composite shell/foam liner/metallic headform) and to simulate its dynamic response during impact. A significant part of the work was focused on the modelling of the mechanical behaviour of the composite materials, including damage and delamination development. The dynamic response of the different helmet-headform systems was judged in terms of the maximum acceleration monitored at the centre of gravity of the headform and the maximum value of head injury criterion.It was shown that composite shell systems exhibiting lower shear performance provide additional energy absorbing mechanisms and result to better crashworthiness helmet behaviour.     

Damage detection of surface cracks in composite laminates using modal analysis and strain energy method

This paper presents an approach to detect surface cracks in various composite laminates. Carbon/epoxy composite AS4/PEEK was used to fabricate laminated plates, [0]₁₆, [90]₁₆, [(0/90)₄]_S and [±45/0/90]_2S. Surface crack damage was created on one side of the plate using a laser cutting machine. Modal analysis was performed to obtain the mode shapes from both experimental and finite element analysis results. The mode shapes were then used to calculate strain energy using the differential quadrature method (DQM). Consequently, the strain energies of laminated plates before and after damaged were used to define a damage index which successfully identified the surface crack location.     

Finite element micromechanical modelling of unidirectional fibre-reinforced metal-matrix composites

Typical finite element formulations and models for unidirectional composite materials are reviewed. The application of micromechanical finite element analysis to the modelling of unidirectional fibre-reinforced metal-matrix composites is demonstrated by presenting some studies from recent publications. It is shown that while analytical models offer a simple tool for obtaining the overall response of composites, finite element analysis provides more accurate and detailed characterisation of composite properties for complicated geometries and constituent property variations. Various effects that influence the stress/strain response and fibre/matrix deformation of composites are studied through modelling. These effects include the fibre coating and reaction layer, fibre shape and distribution, metallurgical and environmental factors, stress distributions and damage. It is demonstrated that the properties and constituent phase interaction of metal-matrix composites are best modelled by finite element analysis. It is emphasized that in order to obtain good predictions, the models must be coupled with first-hand characterisations of the constituent phases and their interactions, including the thermal history of the specimens.