Composite panels containing multiple through-the-width delaminations and subjected to compression. Part II: Experiments & verification

The objective of this investigation was to perform compression tests on laminated composites for verifying the analytical model and the finite element analysis previously developed by the authors for analyzing compression response of composite panels containing multiple delaminations. T300/976 graphite/epoxy composite was selected for the study. Specimens with various ply orientations were fabricated from both flat and cylindrical composite panels containing one to two pre-implanted through-the-width delaminations. Specimens were tested by uniaxial compression, and strain gauges were utilized to record the strain history as a function of the applied load from initial loading to final failure. Numerical simulations were performed according to the test conditions. Comparisons were then made between the predictions and the measured test data. Overall, the predictions agreed with the data very well. Parametric studies were also performed using the finite element analysis to demonstrate the effect of the size, location and number of the delaminations on the compression response of laminated composites.     

Characterization of high-velocity impact damage in CFRP laminates: Part I – Experiment

This study investigated mechanisms of the extension of high-velocity impact damage in CFRP laminates. To this end, damage states due to near-perforation impact were studied in detail. This study consists of two parts. Part I presents the experiment results of high-velocity impact tests for CFRPs with specified stacking sequences. A crater and splits were observed on the impacted surface, while multiple splits with fiber breaks extended on the back surface. The cross-section beneath the impact point included catastrophic ply failure with extensive fiber breaks. Impacted specimens also exhibited a particular delamination pattern consisting of pairs of symmetric fan-shaped delaminations emanating from to the impact point and elongated delamination along the cracks in the bottom ply. These damage patterns were common to all of the stacking sequences. Part II of this study presents a numerical analysis of high-velocity impact based on smoothed-particle hydrodynamics and discusses damage extension mechanisms.     

Damage and its growth in laminated composite circular/rectangular plates undergoing large deformations

A nonlinear finite element static analysis is used to predict the damage in rectangular/circular plates due to large deformation simulating low-velocity impact. The impact due to the ball impactor is modelled by an equivalent static load and load distribution is taken according to Hertzian law. Tsai-Wu criterion is used to predict the failure of each ply at Gauss points. The failure mode (fibre breakage or matrix cracking) is identified using maximum stress criterion. The material properties at each failed Gauss point is degraded appropriately and the stress analysis is carried out again. This iterative process is repeated until no further damage condition occurs. Numerical examples for both circular and rectangular composite plates are presented.     

Delaminations at the free edge of a composite laminate

The concept of a fracture process zone where damage takes place is used to analyse the delaminations at the free edges of angle ply laminates under uniaxial tension. The use of a fracture process zone removes the singularity in the interlaminar stresses and enables the initiation and growth of delaminations to be modelled for a perfect laminate without any assumed prior defects. Two different models for the stress displacement relationship in the fracture process zone are examined: a constant stress up to critical displacement and a linear relationship. Finite element analysis shows that there is little difference in the predictions obtained from the two models. An approximate analysis is presented for the constant stress stress-displacement model which is shown to agree with a finite element solution and experimental data. Hence it is argued that the approximate method using a constant stress model for the fracture process zone is sufficient for accurate prediction of delaminations.     

Progressive failure and ultimate collapse of laminated composite plates in bending

A method is presented to study the non-linear behaviour, first ply failure and ultimate collapse of laminated composite plates with clamped edges, subjected to transverse pressure. Several failure criteria, including Hashin's and Tsai-Wu's, are used to predict the failure mechanisms. The effect of aspect ratio on the strength and stiffness of laminated composite plates is studied. Non-linear strain-displacement relations that contain large strain and large rotation are used in the analysis. The general purpose finite element program ABAQUS is used for the analysis. The stiffness reduction is carried out at the Gauss points of the finite element mesh depending on the mode of failure. The predictions of the model correlate well with experimental data for different aspect ratios.     

Numerical and experimental investigation of free vibration of multilayer delaminated composite beams and plates

The use of vibration-monitoring techniques as non-destructive methods for detection of delaminations in layered composite beam and plate structures is a current field of interest for many researchers. However, an extensive search of published literature shows that information on numerical and especially experimental investigations into the dynamic behaviour of delaminated layered composite beams and plates is limited. For this reason the present authors have developed theoretical models and carried out an extensive experimental investigation to establish changes in the first three bending natural frequencies due to delaminations. The subsequent results of these numerical calculations are consistent with the results of the corresponding experimental investigations. As the result of this work models of a finite delaminated beam element and delaminated plate element have been developed. The method of modelling delaminations presented in this work enables its easy modification according to specific cases of damage (i.e. multiple delaminations). Received 12 December 99     

含多分层损伤平面编织层合板的振动特性

基于层合板Mindlin一阶剪切变形理论,研究了多处分层损伤对复合材料层合板固有特性的影响规律。根据一般分层模型,并采用线性接触模型模拟分层区域上、下子板的相互作用,建立含多个椭圆内埋型分层损伤平面编织层合板自由振动分析有限元模型。通过典型算例分析,讨论了椭圆分层区域长轴与试件纵向夹角对平面编织层合板固有频率的影响。结果表明,对于内埋型分层损伤,表面分层与中间分层对固有频率的影响区别很小;分层区域的长轴与试件纵向夹角越大,损伤对固有频率的影响越大。     

Delamination buckling: A finite element study with realistic delamination shapes,multiple delaminations and fibre fracture cracks

This paper presents a finite element model of a carbon fibre composite laminate with multiple delaminations of realistic shape and including fibre fracture cracks loaded under compression. The modelling technique is initially applied on circular and elliptical delaminations of single ply sublaminates, which are compared with existing analytical solutions. The techniques are then applied to models with multiple delaminations of realistic shape and their behaviour in buckling and post-buckling is captured. An inverse method is used to determine the stiffness reduction caused by the damage, and shows significant stiffness reduction caused by peanut shaped delaminations. When fibre fracture cracks are added, their contribution to further stiffness reduction is minimal but they have some significant effects on the buckling shapes.     

Damage resistance of single lap adhesive composite joints by transverse ice impact

This paper focuses specifically on the high velocity transverse impact of composite joints by hailstones. Impact tests with ice spheres onto composite lap joint specimens were conducted to determine the failure threshold energy describing damage initiation, and to investigate the modes of damage. The damage areas imaged by ultrasonic scanning were quantitatively measured and the specimens were also sectioned and observed with optical microscopy to determine the exact location of damage. The damage area versus impact kinetic energy was found to increase dramatically for impacts beyond the failure threshold. Delamination of the composite originated at the bond overlap termination facing away from the impact side. The damage usually occurred at specific ply locations and a transition of the delamination to other ply locations was also observed. Numerical simulation of the impact was conducted and the results show that the plies where delaminations were observed to occur have the highest peel and shear stresses.     

Stress around square and rectangular cutouts in symmetric laminates

The solution presented in this paper is useful for finding the stress distribution around holes in symmetric laminates as well as in isotropic plates and also to determine the failure strength of the laminate on first ply failure basis by Tsai-Hill, Hashin-Rotem and Tsai-Wu criteria. This is a one stop solution for all kinds of in-plane loading on symmetric laminates as well as isotropic plates with any shape of cutout. Using Savin’s basic solution for anisotropic plates, the stress functions are derived for generalized mapping function for the hole and arbitrarily oriented in-plane loading. Square and rectangular holes in symmetric laminates of Graphite/epoxy and Glass/epoxy are studied. It is noted that the maximum stress and its location is mainly influenced by the type of loading. Larger stresses are noted for shear loading. The stress results are also obtained by ANSYS for comparison.     

Structural design of single lap joints with delaminated FRP composite adherends

This paper deals with the structural design of single lap joints (SLJs) with delaminated adherends using fracture mechanics principles. The interlaminar stresses and Strain Energy Release Rate (SERR) are considered as damage characterizing parameters used for designing the SLJ when delamination damages are pre-embedded in both the adherends at similar positions. Three dimensional geometrically non-linear finite element analyses (FEAs) of SLJ with delaminated adherends have been performed to determine the interlaminar and SERR values along the delamination fronts by simulating the simultaneous interaction delamination damages when pre-embedded at similar positions in both the adherends. SERR values are evaluated using Modified Crack Closure Technique (MCCI) which is based on energy principle. The delaminations are assumed to be of linear front, and have been considered to be embedded in both the laminated FRP composite adherends beneath the surface ply of the adhesively bonded SLJ. The delamination damages are presumed either to pre-exist or get evolved at the interlaminar locations. Such delaminations have been modelled using the sublaminate technique. The critical issues of modelling pre-embedded delamination damages are discussed in detail. The numerical results presented in this paper are based on the validated FE model compared with the available literature. Based on the present analyses, the structural design recommendations have been made for the SLJ when pre-embedded delamination damages are present in both the adherends. It is observed from the stress based design that the delamination damage when present in the bottom adherend is more detrimental for failure of SLJ compared to that for the case when it is present in the top adherend. Also, SERR based design reveals that the opening mode predominantly governs the propagation of delamination damage for all positions of the pre-embedded delaminations in both the adherends of the SLJ.     

Acoustic Emission as a Tool for Damage Identification and Characterization in Glass Reinforced Cross Ply Laminates

Loading of cross-ply laminates leads to the activation of distinct damage mechanisms, such as matrix cracking, delaminations between successive plies and fibre rupture at the final stage of loading. This study deals with the investigation of the failure of cross ply composites by acoustic emission (AE). Broadband AE sensors monitor the elastic waves originating from different sources of failure in coupons of this material during a tensile loading-unloading test. The cumulative number of AE activity, and other qualitative indices based on the waveforms shape, were well correlated to the sustained load and mechanical degradation as expressed by the gradual decrease of elastic modulus. AE parameters indicate the succession of failure mechanisms within the composite as the load increases. The proposed methodology based on Acoustic Emission for the identification of the damage stage of glass reinforced cross ply laminates is an initial step which may provide insight for the study of more complex laminations.     

Buckling analysis for delaminated composites using plate bending elements based on higher‐order zig‐zag theory

A finite element based on the efficient higher‐order zig‐zag theory with multiple delaminations is developed. The bending part of the formulation is constructed from the concept of DKQ element. Unlike conventional elements, a developed element has its reference in the bottom surface which simplifies zig‐zag terms on formulation. Exact patch solutions are developed on elements which have the bottom reference system. The present element passes proper bending patch tests in the arbitrary mesh configurations in isotropic materials. Zig‐zag formulation is adopted to model laminated plates with multiple delaminations. To assess the accuracy and efficiency of the present element based on higher‐order zig‐zag theory with multiple delaminations, the linear buckling problem of laminated plates with multiple delaminations has been analysed. The results have been compared with three‐dimensional elasticity solutions. The present element works as an efficient tool for analysing the behaviour of the laminated composites with multiple delaminations. Copyright © 2002 John Wiley & Sons, Ltd.     

Damage and residual strength of laminated carbon–epoxy composite circular plates loaded at the centre

The research dealt with the characterization of damage in quasi-isotropic carbon fibre reinforced epoxy resin laminate loaded at the centre. Load was applied by means of a servo hydraulic machine and it was supposed to simulate a low velocity impact. The acoustic emission (AE) technique was used to detect damage progression. Tensile resistance after indentation was investigated and correlated with acoustic emissions parameters. This was been done for different lamination sequences on specimens cut from the damaged plates.A numerical model to predict both the first ply failure (FPF) and the ultimate ply failure (UPF) of the laminate was developed by means of the ANSYS^® software.     

Matrix crack-induced delamination in composite laminates under transverse loading

Fibre-reinforced multidirectional composite laminates are observed in experiments under transverse static or low-velocity impact loading to suffer considerable delamination damage. The intensity of this damage depends on the difference in the ply angles above and below the interface. In this paper a fracture mechanics model is presented for investigating the role of matrix cracks in triggering delaminations and the influence of ply angles in adjacent plies on delamination cracking. The fracture mechanics analysis shows that for a graphite fibre-reinforced composite laminate containing a transverse intraply crack, the crack-induced largest interfacial principal tensile stress is a maximum when the difference between the ply angles across the interface is 90 °, and it attains a minimum when the difference is 40 °. When the crack tips touch the interfaces, the minimum mode II stress singularity, which is weaker than the usual square-root type, appears when the difference between the ply angles is about 45 ° for one glass fibre-reinforced laminate and three graphite fibre-reinforced laminates. These results are in agreement with the experimental observation that the largest delaminations appear at the interface across which the difference between the ply angles is the largest i.e. 90 °.     

Analytical approaches to compression after impact (CAI) behavior of carbon fiber-reinforced composite materials

Analytical efforts to understand problems involving compression after impact (CAI) are reviewed. A theoretical solution of beam plate modeling is introduced to understand the buckling of multiple delaminated plates. Numerical efforts on CAI-related matters for rectangular plates are then briefly described to show the difficulties in evaluating the effects of the various factors on the compressive properties of impact-damaged laminates. Also, the reason for the simplification of the double-spiral damage to multiple circular delaminations is briefly explained from a mechanical viewpoint. Analytical schemes to evaluate the compressive strength of the impact-damaged laminates are introduced based on fracture mechanics. The accuracy and meaning of the solutions are discussed by comparing the present solutions with finite element analysis results.     

基于低能量冲击损伤阻抗的复合材料薄壁结构铺层顺序设计

建立了有效的复合材料层合板结构冲击损伤分析方法,层合板面内损伤采用改进的Chang/Chang 失效准则做判据,得到面内各类损伤形式。层间损伤采用与Mixed-Mode粘接元等效的TIEBREAK接触模拟。利用此分析方法,从复合材料薄壁结构设计需要出发,研究了在低能量冲击下,铺层的层间角度、铺层方向、铺层重叠对层合板结构冲击损伤阻抗的影响规律,并对它们的综合影响进行了总体分析,得到了能提高层合板结构损伤阻抗的铺层顺序设计指导。最后用该设计指导对某种铺层结构进行了重新设计和有限元模拟,验证了该设计指导的可行性和有效性。     

An experimental investigation on the low velocity impact response of composite plates repaired by VARIM and hand lay-up processes

This paper presents results of an experimental investigation on the impact response of repaired and unrepaired glass/epoxy composite plates. Repaired samples were prepared by two different manufacturing methods; vacuum assisted resin infusion process and hand lay-up technique. In order to compare impact response of the repaired and unrepaired samples a number of single impact tests were performed under various impact energies. Damage process of the samples is analyzed from cross-examining load–deflection curves and damaged specimens. From the visual inspection, for the impacted side of the samples, it is noted that the main damage modes for repaired samples are matrix and fiber cracks around point of impact and delaminations while severe matrix cracks expanded through fiber directions are the dominant damage mode for unrepaired samples. At the back surfaces, delaminations and fiber–matrix debonding oriented in the fiber directions are observed for unrepaired samples. However, for repaired samples the fiber fractures through repair line as well as the delaminations become dominant modes. For a reasoning justification in discussing impact test results, interlaminar fracture toughness (Mode I and Mode II) and flexural tests for repaired and non-repaired samples were also conducted.     

碳纤维复合材料层合板低速冲击损伤应力分析

目的 为掌握碳纤维复合材料板在低速冲击载荷作用下的损伤规律,延缓失效破坏,对其冲击损伤的应力状态进行研究。方法 基于ABAQUS平台,建立碳纤维复合材料层合板低速冲击有限元模型,采用Hashin失效准则和VUMAT用户子程序,对碳纤维复合材料层合板的冲击过程进行数值模拟,同时考虑层合板层内与层间失效,以此来研究低速冲击条件下复合材料的损伤机理,分析冲击损伤过程中的应力变化趋势,讨论应力的分布状态。重点研究铺层角度及铺层距离冲头远近对应力的影响。结果 不同角度铺层的应力传播轨迹均沿着纤维方向和垂直于纤维方向同时扩展,应力均先增加至极限值而后迅速下降;铺层角度越大,板料的承载能力越弱,0°铺层的极限应力为1 432 MPa,而90°铺层的极限应力降至1 206 MPa;离冲头越远的铺层应力越小,达到峰值的时间更早且率先下降,说明远离冲头的铺层更早发生失效。结论 揭示了碳纤维层合板在低速冲击载荷作用下的应力状态及其对损伤的影响规律,能够为复合材料层合板零件设计提供参考。