Predicting the effects of geometry on the behaviour of fibre metal laminate joints

The effects of geometry on the bearing response of fibre metal laminate (FML) joints are numerically investigated. Specimens designed to fail in bearing, net-tension and shear-out are analysed using a continuum damage mechanics approach. Plasticity in the aluminium layers, fibre and matrix damage in the composite plies and, importantly, delamination between the plies of the laminate are accounted for. The effects of mesh sensitivity, associated with strain-softening material models, are mitigated using a nonlocal averaging scheme. Results are compared to experimental bearing stress–strain and bearing stiffness–strain responses, and surface strain measurements. Variations in the development of damage for the different joints are investigated, and the effect of damage on the joint responses is discussed. Very good agreement was achieved for the specimens of interest, without varying the model parameters for the different joint configurations, which highlighted the suitability of the model for FML structural analysis. The combined numerical and experimental information provide an in-depth understanding of the failure sequences of FML joints.     

Predicting low velocity impact damage and Compression-After-Impact (CAI) behaviour of composite laminates

Low-velocity impact damage can drastically reduce the residual strength of a composite structure even when the damage is barely visible. The ability to computationally predict the extent of damage and compression-after-impact (CAI) strength of a composite structure can potentially lead to the exploration of a larger design space without incurring significant time and cost penalties. A high-fidelity three-dimensional composite damage model, to predict both low-velocity impact damage and CAI strength of composite laminates, has been developed and implemented as a user material subroutine in the commercial finite element package, ABAQUS/Explicit. The intralaminar damage model component accounts for physically-based tensile and compressive failure mechanisms, of the fibres and matrix, when subjected to a three-dimensional stress state. Cohesive behaviour was employed to model the interlaminar failure between plies with a bi-linear traction–separation law for capturing damage onset and subsequent damage evolution. The virtual tests, set up in ABAQUS/Explicit, were executed in three steps, one to capture the impact damage, the second to stabilize the specimen by imposing new boundary conditions required for compression testing, and the third to predict the CAI strength. The observed intralaminar damage features, delamination damage area as well as residual strength are discussed. It is shown that the predicted results for impact damage and CAI strength correlated well with experimental testing without the need of model calibration which is often required with other damage models.     

Nonlinear response in glass fibre non-crimp fabric reinforced vinylester composites

This paper addresses the nonlinear stress-strain response in glass fibre non-crimp fabric reinforced vinylester composite laminates subjected to in-plane tensile loading. The nonlinearity is shown to be a combination of brittle and plastic failure. It is argued that the shift from plastic to brittle behaviour in the vinylester is caused by the state of stress triaxiality caused by the interaction between fibre and vinylester. A model combining damage and plasticity is calibrated and evaluated using data from extensive experimental testing. The onset of damage is predicted using the Puck failure criterion, and the evolution of damage is calibrated from the observed softening in plies loaded in transverse tension. Shear loading beyond linear elastic response is observed to result in irreversible strains. A yield criterion is implemented for shear deformation. A strain hardening law is fitted to the stress-strain response observed in shear loaded plies. Experimental results from a selection of laminates with different layups are used to verify the numerical models. A complete set of model parameters for predicting elastic behaviour, strength and post failure softening is presented for glass fibre non-crimped fabric reinforced vinylester. The predicted behaviour from using these model parameters are shown to be in good agreement with experimental results.     

Numerical analysis of damage progression and strength of countersunk composite joints

A numerical investigation is conducted into the damage progression and strength of bolted joints between fibre-reinforced composite laminates using countersunk fasteners. Experimental tests were previously conducted on a bearing test specimen and countersunk fastener single-lap joints. In this work, computational models are developed for Abaqus/Explicit, with continuum shells employed to model in-plane ply failure. The bolt-nut assembly is modelled with rigid elements, and the models account for bolt torque and frictional contact. The material properties required in the computational model are determined from standard tests, with the compression fracture toughness of composite plies calibrated against experimental data from the bearing test. The analysis approach captures the load-carrying capability of all configurations, and provides reasonable accuracy in predicting damage patterns. The effects of bolt torque, clearance and countersink height ratio are investigated, and the analysis results compare well with experimental findings. Furthermore, the analysis provides rich insight into the damage progression and joint behaviour at the ply level, with the in-plane and through-thickness damage patterns mapped for increasing applied load. Delamination is incorporated using a cohesive element layer at the start of the countersunk region, though has minimal influence on damage progression and load-carrying capability, which agrees with the experimental results.     

Current research into modelling of shock damage to large scale composite panels

This study aims to model the damage incurred to large woven roving E-glass/vinyl-ester composite panels subjected to shock loads, with particular emphasis on developing an effective, simple to use delamination model. An energy criterion for failure is applied at resin-rich layers, which are modelled in between every ply. The finite element program Abaqus/Explicit together with a user material subroutine (VUMAT) is used to simulate both large and small scale impact tests. The resin-rich layers are modelled as non-linear elastic and matrix and fibre damage is modelled at the woven plies using Hashin’s 2D stress-based failure criteria with a once-only degradation of the material properties.     

纤维金属层板低速冲击试验和数值仿真

为开展纤维金属层板（FML）低速冲击有限元数值仿真研究,改进了传统的连续损伤力学（CDM）模型,然后对FML落锤低速冲击试验进行数值仿真,并与实验结果进行对比验证。分别采用5.11 J 和10.33 J冲击能量对FML进行落锤低速冲击试验,得到冲击载荷、位移和能量时程曲线,分析FML的动态响应和失效模式。建立了考虑塑性应变、压缩刚度衰减特征和纤维拉伸断裂损伤的新CDM模型,描述S2-玻璃纤维/环氧树脂（S2-galss/epoxy）复合材料的损伤本构,并编写VUMAT子程序,通过ABAQUS/Explicit求解器对FML落锤冲击试验进行数值仿真。研究结果表明：低能量冲击条件下,FML背面主要为鼓包和裂纹等失效模式,位移峰值随冲击能量的提高而增加,冲击载荷峰值在穿透前也随冲击能量的提高而增加;采用改进的CDM模型描述FML中S2-galss/epoxy复合材料铺层后,有限元数值计算可以较好地预测FML低速冲击载荷下的动态响应;有限元数值仿真结果表明,FML中第2层复合材料铺层发生的纤维断裂损伤比第1层的更严重。     

Simulation of High Velocity Impact on Composite Structures - Model Implementation and Validation

High velocity impact on composite aircraft structures leads to the formation of flexural waves that can cause severe damage to the structure. Damage and failure can occur within the plies and/or in the resin rich interface layers between adjacent plies. In the present paper a modelling methodology is documented that captures intra- and inter-laminar damage and their interrelations by use of shell element layers representing sub-laminates that are connected with cohesive interface layers to simulate delamination. This approach allows the simulation of large structures while still capturing the governing damage mechanisms and their interactions. The paper describes numerical algorithms for the implementation of a Ladevèze continuum damage model for the ply and methods to derive input parameters for the cohesive zone model. By comparison with experimental results from gas gun impact tests the potential and limitations of the modelling approach are discussed.     

Hybrid titanium–CFRP laminates for high-performance bolted joints

This paper presents an experimental and numerical investigation of the mechanical response of bolted joints manufactured using new hybrid composite laminates based on the substitution of CFRP plies with titanium plies. The local hybridization of the material is proposed to increase the efficiency of the bolted joints in CFRP structures. Two modeling strategies, based on non-linear finite element methods, are proposed for the analysis of the bolt-bearing and transition regions of the hybrid laminates. The bolt-bearing region is simulated using a three-dimensional finite element model that predicts ply failure mechanisms, whereas the free-edge of the transition region is simulated using plane stress and cohesive elements. The numerical and experimental results indicate that the use of hybrid composites can drastically increase the strength of CFRP bolted joints and therefore increase the efficiency of this type of connection. In addition, the numerical models proposed are able to predict the failure mechanisms and the strength of hybrid composite laminates with a good accuracy.     

Characterization and evolution of matrix and interface related damage in [0/90]S laminates under tension. Part II: Experimental evidence

A detailed numerical model based on the Boundary Element Method (BEM) to deal with the first appearance and progression of damage in a [0/90]_S laminate has been developed in Part I of this paper. In this paper (Part II), first of all the effects of thermal stresses are studied in order to connect numerical predictions with experimental results. Then, the experiments carried out are described and several observations at a specific load close to the final failure are explained. These observations are correlated with the numerical predictions previously obtained. It is of particular interest to mention the arrest of the transverse cracks in the 90° lamina before reaching the interface with the 0° lamina. It is also predictable and observable that, before the transverse crack reaches the interface, localised damage appears contributing to the formation of a delamination between plies.     

Bird strike damage analysis in aircraft structures using Abaqus/Explicit and coupled Eulerian Lagrangian approach

The subject of this paper is numerical prediction of bird strike induced damage in real aeronautical structures using highly detailed finite element models and modern numerical approaches. Due to the complexity of today’s aeronautical structures, numerical damage prediction methods have to be able to take into account various failure and degradation models of different materials. A continuum damage mechanics approach has been employed to simulate failure initiation and damage evolution in unidirectional composite laminates. Hashin’s failure initiation criteria have been employed in order to be able to distinct between four ply failure modes. The problem of soft body impacts has been tackled by applying the Coupled Eulerian Lagrangian technique, thereby avoiding numerical difficulties associated with extensive mesh distortion. This improvement in impactor deformation modelling resulted in a more realistic behaviour of bird material during impact. Numerical geometrical and material nonlinear transient dynamic analyses have been performed using Abaqus/Explicit. The main focus of the work presented in this paper is the application of the damage prediction procedure in damage assessment of bird impact on a typical large airliner inboard flap structure. Due to the high cost of gas-gun testing of aircraft components, experimental testing on the real flap structure could not have been performed. In order to evaluate the accuracy of the presented method, the bird and composite damage model have been validated against experimental data available in the literature.     

Influence of internally dropped-off plies on the impact damage of asymmetrically tapered laminated CFRP

This paper presents an experimental study of low velocity impact response of carbon/epoxy asymmetrically tapered laminates. The tests are realised at energy between 10 and 30 J on two types of layup with multiple terminated plies. The type and localisation of damage are analysed using C-scan and micrographs. Then, the data is compared with the response of corresponding respective plain laminate. The effects of some tapering parameters (taper angle, drop-off disposition and configuration) on the impact damage mechanisms are also investigated. Very similar impact damage phenomena are found between tapered and plain laminates. The presence of material discontinuity due to the resin pocket affects less the damage mechanism than the structural difference between the thick and the thin sections.     

Stacking Sequence Effects on Fatigue Intra-laminar Damage Progression in Composite Joints

In this paper the effects of the stacking sequence on the fatigue intra-laminar damage accumulation in pinned composite joints is investigated. A fatigue damage propagation numerical model based on gradual material degradation rules and Hashin fatigue failure criteria is formulated, implemented in a finite element platform and then used to simulate the intra-laminar fatigue damage evolution in the analysed composite joints. The model has been preliminary validated against literature experimental data in terms of s-n curves providing confirmation of its effectiveness in predicting the joints fatigue life. Different stacking sequences: zero-dominated, quasi-isotropic, cross-ply with different 0 ° and 90 ° plies distributions, have been considered when investigating the influence of the stacking sequence on the fatigue behaviour of the joints. The simulation of the joints’ fatigue life provided detailed information on the intra-laminar damage mechanisms on-set and evolution related to fatigue gradual degradation of material stiffness and strength for different values of the applied maximum stresses.     

Analysis of impact-induced damage and delamination in the composite shell of a helmet

The impact energy absorption by helmets is of vital importance to the safety of motorcyclists during accidents. The paper is concerned with the study of damage and delamination, which are the principal modes of failure and energy absorption, in a composite shell and their influence on the impact performance of a helmet. Numerical simulations were conducted with different composite shells made of cross-ply laminate, woven fabric, and glass mat. The effectiveness of the numerical model is established using available experimental results from the literature. Hashin failure criteria and cohesive zone model (CZM) were used for predicting the in-plane damage and delamination in composite plies, respectively. An interface layer having a bilinear relationship between traction and relative displacement was placed between the plies of the composite shell to predict the delamination. The influence of damage and delamination in shells made of composite materials on impact-induced forces is evaluated and their performance is compared with helmet shells made of Acrylonitrile Butadiene Styrene (ABS).     

Progressive damage analysis of composite bolted joints with liquid shim layers using constant and continuous degradation models

The structural behaviour of a single-lap, single-bolt composite joint is investigated using a three-dimensional finite element model. In contrast to previous investigations the influence of a liquid shim layer, added between the two laminates, on strength and structural behaviour of the joints is investigated by virtual testing. The finite element model is validated with experimental data. The experiments point out that the structural behaviour of these joints is dominated by progressive damage. Therefore, as a first approach, progressive damage is considered using Hashin’s three-dimensional failure criterion and a constant degradation model. It is shown that this combination yields very conservative results. As a second approach the model is improved by a continuous degradation model. Considering continuous degradation, the numerical results show very good correlation with the experimental data.     

Modelling complex progressive failure in notched composite laminates with varying sizes and stacking sequences

The emergence of advanced computational methods and theoretical models for damage progression in composites has heralded the promise of virtual testing of composite structures with orthotropic lay-ups, complex geometries and multiple material systems. Recent studies have revealed that specimen size and material orthotropy has a major effect on the open hole tension (OHT) strength of composite laminates. The aim of this investigation is develop a progressive failure model for orthotropic composite laminates, employing stepwise discretization of the traction–separation relationship, to predict the effect of specimen size and laminate orthotropy on the OHT strength. The results show that a significant interaction exists between delamination and in-plane damage, so that models without considering delamination would over-predict strength. Furthermore, it is found that the increase in fracture toughness of blocked plies must be incorporated in the model to achieve good correlation with experimental results.     

Experimental and numerical studies of initial cracking in CFRP cross-ply laminates

This work is concerned with the conditions for formation of the first (initial) cracks in composite laminates with cutouts or ply drop-offs subjected to in-plane loading. We study here the crack formation on the free edge of CFRP cross-ply laminates experimentally and by numerical stress and failure analysis. The free-edge surface strains are measured by the digital image correlation (DIC) technique. The numerical analysis consists of a two-scale approach, where the macro-level analysis is performed with a three-dimensional finite-element method (3D FEM) and the micro-level analysis uses a periodic unit-cell (PUC) in the transverse plies. The constitutive assumption made for the macro-level analysis is an orthotropic linear thermo-elastic solid for the unidirectional plies with a thin isotropic viscoplastic layer between the longitudinal and transverse plies. In the PUC, the fibers are assumed linear elastic, while the matrix is modeled as an elastic–viscoplastic solid. Crack formation is assumed to occur in the matrix by the dilatation induced brittle failure mechanism for which the dilatation energy density criterion is used.     

Numerical simulation of impact tests on GFRP composite laminates

The design of advanced composite structures or components subjected to dynamic loadings requires a deep understanding of the damage and degradation mechanisms occurring within the composite material. The present paper deals with the numerical simulation of low-velocity impact tests on glass fabric/epoxy laminates through the LS-DYNA Finite Element (FE) code. Two laminates of different thickness were subjected to transverse impact at different energy levels and modeled by FE. Solid finite elements combined with orthotropic failure criteria were used to model the composite failure and stress based contact failure between plies were adopted to model the delamination mechanism. The final simulation results showed a good correlation with experimental data in terms of both force–displacement curves and material damage.     

三维六向编织复合材料渐进损伤模拟及强度预测

基于三维六向编织复合材料的细观结构,假设第六向纱线的截面形状为菱形,建立了三维六向编织复合材料的渐进损伤有限元模型。采用Linde等提出的失效准则,引入周期性位移边界条件,对三维六向编织复合材料的纵向拉伸应力-应变行为进行了渐进损伤数值模拟,讨论了单胞模型在纵向拉伸载荷作用下的细观损伤起始、扩展和最终失效的演化过程,并预测了材料的拉伸强度。在此基础上,进一步研究了编织角、纤维体积分数和编织纱水平取向角等参数对材料纵向拉伸力学性能的影响规律。研究结果表明,三维六向编织复合材料的轴向纱线拉伸断裂是导致其破坏的最主要因素。所得数值结果与现有试验值吻合较好,验证了该模型的有效性,为更深入研究此类材料的力学性能奠定了基础。     

Creep rupture and viscoelastoplasticity of polypropylene

Observations are reported on isotactic polypropylene in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. Constitutive equations are derived for the viscoelastic and viscoplastic responses of semicrystalline polymers at three-dimensional deformations with small strains. The stress-strain relations involve eight material constants that are found by fitting the experimental data. The model is applied to the numerical analysis of creep failure of polypropylene under various deformation modes (uniaxial tension, equi-biaxial tension, shear, multiple-step creep tests).     

Overlay patch repair of scratch damage in carbon fiber/epoxy laminated composites

In this paper we present a numerical and experimental study on the overlay repair of scratch damage in carbon-fiber/epoxy composite laminates. The scratch damage severs several load bearing plies and results in a lack of symmetry in an originally symmetric multidirectional laminate. The ply-by-ply p-version finite element model is used to investigate the effects of the repair patch variables on the overall efficiency of the repair procedure and the lamina level stress states. The results show that interlaminar crack propagation in the direction parallel to the surface can be retarded with careful selection of repair parameters.