Development of smart composite structures with small-diameter fiber Bragg grating sensors for damage detection: Quantitative evaluation of delamination length in CFRP laminates using Lamb wave sensing

The authors and Hitachi Cable, Ltd. have recently developed small-diameter optical fiber and its fiber Bragg grating (FBG) sensor for embedment inside a lamina of composite laminates without strength reduction. The outside diameters of the cladding and polyimide coating are 40 and 52 μm, respectively. First, a brief summary is presented for applications of small-diameter FBG sensors to damage monitoring in composite structures. Then, we propose a new damage detection system for quantitative evaluation of delamination length in CFRP laminates using Lamb wave sensing. In this system, a piezo-ceramic actuator generates Lamb waves in a CFRP laminate. After the waves propagate in the laminate, transmitted waves are received by an FBG sensor attached on or embedded in the laminate using a newly developed high-speed optical wavelength interrogation system. This system was applied to detect interlaminar delamination in CFRP cross-ply laminates. When the Lamb waves passed through the delamination, the amplitude decreased and a new wave mode appeared. These phenomena could be well simulated using a finite element analysis. From the changes in the amplitude ratio and the arrival time of the new mode depending on the delamination length, it was found that this system could evaluate the delamination length quantitatively. Furthermore, small-diameter FBG sensors were embedded in a double-lap type coupon specimen, and the debonding progress could be evaluated using the wavelet transform.     

Modeling of the dynamic delamination of L-shaped unidirectional laminated composites

One of the widely used geometrically complex parts in advanced commercial aircraft is the L-shaped composite. Due to the sharp curved geometry, interlaminar opening stresses are induced and delamination occurs under considerable mode-mixities in L-shaped beams. Dynamic phenomena during delamination initiation and propagation of L-shaped beams are investigated using dynamic (explicit) finite element analysis in conjunction with cohesive zone methods. The 2-D model consists of 24 plies of unidirectional CFRP laminate with an initial 1 mm crack at the center of the laminate at the bend. Loading is applied parallel to one of the arms quasi-statically. The loading type yields different traction fields and mode-mixities in the two sides of the crack in which delamination occurs under shear stress dominated loading on one crack tip and opening stress dominated loading on the other. The speed of the delamination under shear dominated loading at one side is 800 m/s and under normal stress dominated loading is 50 m/s. In addition radial compressive waves at the interface are observed. Finally, as the thickness is changed, a different failure mode is observed in which a secondary crack nucleates at the arm and propagates towards the center crack.     

Interaction of Matrix Cracking and Delamination in Cross-ply Laminates: Simulations with Stochastic Cohesive Zone Elements

Two main damage mechanisms of laminates—matrix cracking and inter-ply delaminationare closely linked together (Joshi and Sun 1). This paper is focussed on interaction between matrix cracking and delamination failure mechanisms in CFRP cross-ply laminates under quasi-static tensile loading. In the first part of the work, a transverse crack is introduced in 90o layers of the cross-ply laminate [01/904/01], and the stresses and strains that arise due to tensile loading are analyzed. In the second part, the cohesive zone modelling approach where the constitutive behaviour of the cohesive elements is governed by traction-displacement relationship is employed to deal with the problem of delamination initiation from the matrix crack introduced in the 90o layers of the laminate specimen. Additionally, the effect of microstructural randomness, exhibited by CFRP laminates on the damage behaviour of these laminates is also accounted for in simulations. This effect is studied in numerical finite-element simulations by introducing stochastic cohesive zone elements. The proposed damage modelling effectively simulated the interaction between the matrix crack and delamination and the variations in the stresses, damage and crack lengths of the laminate specimen due to the microstructural randomness.     

模拟P波向无穷远域传播的一致边界

将人工边界设置在半无穷层单元和内部有限元区域的交界面上,建立了半无穷层单元的刚度矩阵后,得到了边界节点的动力平衡方程。任意给定激励圆频率,将边界节点系统的动力平衡方程转化为特征值方程。求解特征值方程得出边界节点系统的特征值和特征模态,利用模态叠加原理得到体现左半无穷层单元和右半无穷层单元对内部有限元区域作用的边界矩阵,这就是该文的一致边界。将其与内部有限元区域的刚度矩阵进行组装来模拟无穷远域介质对波的传播作用。最后用数值算例来说明一致边界的精确性和可行性。     

Numerical Investigation of Delamination in Drilling of Carbon Fiber Reinforced Polymer Composites

Drilling of carbon fiber reinforced polymer (CFRP) is a challenging task in modern manufacturing sector and machining induced delamination is one of the major problems affecting assembly precision. In this work, a new three-dimensional (3D) finite element model is developed to study the chip formation and entrance delamination in drilling of CFRP composites on the microscopic level. Fiber phase, matrix phase and equivalent homogeneous phase in the multi-phase model have different constitutive behaviors, respectively. A comparative drilling test, in which the cement carbide drill and unidirectional CFRP laminate are employed, is conducted to validate the proposedmodel in terms of the delamination and the similar changing trend is obtained. Microscopic mechanism of entrance delamination together with the chip formation process at four special fiber cutting angles (0°, 45°, 90° and 135°) is investigated. Moreover, the peeling force is also predicted. The results show that the delamination occurrence and the chip formation are both strongly dependent on the fiber cutting angle. The length of entrance delamination rises with increasing fiber cutting angles. Negligible delamination at 0° is attributed to the compression by the minor flank face. For 45° and 90°, the delamination resulted from the mode III fracture. At 135°, serious delamination which is driven by the mode I and III fractures is more inclined to occur and the peeling force reaches its maximum. Such numerical models can help understand the mechanism of hole entrance delamination further and provide guidance for the damage-free drilling of CFRP.     

New analytical method for electric current and multiple delamination cracks for thin CFRP cross-ply laminates using equivalent electric conductance

Carbon fiber reinforced polymer (CFRP) composites have low inter-lamina strength. One of the monitoring technologies is a self-sensing method that uses the electrical resistance change of a CFRP structure for detecting damage. The electric current distribution is vital information for the self-sensing method when optimizing the arrangement of probes to measure electric potential changes. We have developed a new orthotropic electric potential function analysis approach using affine transformation for unidirectional CFRP. In this study, the orthotropic electric potential function analysis method is improved to calculate the electric current of a thin cross-ply CFRP. Two types of stacking sequences for the beam-type cross-ply laminates were calculated to confirm the effectiveness of the improved method. The electrical voltage changes caused by multiple delamination cracks of a cross-ply laminate are new outcomes of this study. The analytical results were compared with computed results using the finite difference method. Consequently, the new equivalent electric conductance method proved to be effective for calculations of the electric current density of a cross-ply CFRP laminate. Furthermore, the new method for calculating the electric potential difference changes caused by multiple delamination cracks using orthotropic distributed doublet analysis, with the equivalent electric conductance, has also proved to be effective.     

A combined finite element/strip element method for analyzing elastic wave scattering by cracks and inclusions in laminates

 A new numerical technique combining the finite element method and strip element method is presented to study the scattering of elastic waves by a crack and/or inclusion in an anisotropic laminate. Two-dimensional problems in the frequency domain are studied. The interior part of the plate containing cracks or inclusions is modeled by the conventional finite element method. The exterior parts of the plate are modeled by the strip element method that can deal problems of infinite domain in a rigorous and efficient manner. Numerical examples are presented to validate the proposed technique and demonstrate the efficiency of the proposed method. It is found that, by combining the finite element method and the strip element method, the shortcomings of both methods are avoided and their advantages are maintained. This technique is efficient for wave scattering in anisotropic laminates containing inclusions and/or cracks of arbitrary shape. Received 2 February 2001     

Quantification of flexural fatigue life and 3D damage in carbon fibre reinforced polymer laminates

Carbon fibre reinforced polymer (CFRP) laminated composites have become attractive in the application of wind turbine blade structures. The cyclic load in the blades necessitates the investigation on the flexural fatigue behaviour of CFRP laminates. In this study, the flexural fatigue life of the [+45/−45/0]_2s CFRP laminates was determined and then analysed statistically. X-ray microtomography was conducted to quantitatively characterise the 3D fatigue damage. It was found that the fatigue life data can be well represented by the two-parameter Weibull distribution; the life can be reliably predicted as a function of applied deflections by the combined Weibull and Sigmodal models. The delamination at the interfaces in the 1st ply group is the major failure mode for the flexural fatigue damage in the CFRP laminate. The calculated delamination area is larger at the interfaces adjacent to the 0 ply. The delamination propagation mechanism is primarily matrix/fibre debonding and secondarily matrix cracking.     

Intersonic delamination in curved thick composite laminates under quasi-static loading

Dynamic delamination in curved composite laminates is investigated experimentally and numerically. The laminate is 12-ply graphite/epoxy woven fabric L-shaped laminate subject to quasi-static loading perpendicular to one arm. Delamination initiation and propagation are observed using high speed camera and load–displacement data is recorded. The quasi-static shear loading initiates delamination at the curved region which propagates faster than the shear wave speed of the material, leading to intersonic delamination in the arms. In the numerical part, the experiments are simulated with finite element analysis and a bilinear cohesive zone model. Cohesive interface elements are used between all plies with the interface properties obtained from tests. The simulations predict a single delamination initiating at the corner under pure mode-I stress field propagating to the arms under pure mode-II stress field. The crack tip speeds transition from sub-Rayleigh to intersonic in conjunction with mode change. In addition to intersonic mode-II delamination, shear Mach waves emanating from the crack tips in the arms are observed. The simulations and experiments are found to be in good agreement at the macro-scale, in terms of load-displacement behavior and failure load, and at the meso-scale, in terms of delamination initiation location and crack propagation speeds. Finally, a mode dependent crack tip definition is proposed and observation of vibrations during delamination is presented. This paper presents the first conclusive evidence of intersonic delamination in composite laminates triggered under quasi-static loading.     

PNF增韧层对CFRP复合材料分层影响的数值分析

尼龙无纺布增韧层能在保证良好工艺性能的前提下,显著提高纤维复合材料(carbon fiber reinforced polymer,CFRP)的断裂韧度,但其机制还不明晰。引入一种反映尼龙无纺布增韧层(polyamide non-woven fabric,PNF)厚度和力学特性的内聚力模型,建立PNF/CFRP复合材料分层损伤产生与扩展的力学模型,通过双悬臂梁弯曲实验和验证,得到如下结论:增韧层的厚度对复合材料Ⅰ型分层的峰值载荷几乎没有影响,增韧层厚度为20μm时,复合材料分层扩展阻力最大;界面最大法向应力分布可有效反映裂纹扩展前沿形貌,分层扩展开始后,其前沿形貌保持一致;在相同的外力载荷下,随着PNF/CFRP复合材料铺层从[012/012]变化到[012/9012],其Ⅰ型分层的峰值载荷和扩展距离不断减小。     

Delamination monitoring of CFRP laminate using the two-stage electric potential change method with equivalent electric conductivity

Carbon fiber reinforced plastics laminate (CFRP) has a high specific strength and stiffness compared to conventional metals, although it is very sensitive to impact. A low impact leads to a delamination and results in the deterioration of the structural reliability. The present study employs a two-stage electric potential change method (EPCM) to identify delamination. In the methods, delamination is estimated using response surfaces, which require numerous experiments. An equivalent electric conductivity method is introduced to reduce this number. Delaminations are successfully estimated using response surfaces based on the results of the finite element method with equivalent electric conductivity.     

Effect of delamination failure in crashworthiness analysis of hybrid composite box structures

In the present paper the effects of delamination failure of hybrid composite box structures on their crashworthy behaviour will be studied and also their performance will be compared with non-hybrid ones. The combination of twill-weave and unidirectional CFRP composite materials are used to laminate the composite boxes. Delamination study in Mode-I and Mode-II with the same lay-ups was carried out to investigate the effect of delamination crack growth on energy absorption of hybrid composite box structures. The end-loaded split (ELS) and double-cantilever beam (DCB) standard test methods were chosen for delamination studies. In all hybrid composite boxes the lamina bending crushing mode was observed. Regarding the delamination study of hybrid DCB and ELS the variation of the specific energy absorption (SEA) versus summation of G_IC and G_IIC were plotted to combine the effect of Mode-I and Mode-II interlaminar fracture toughness on the SEA. From this relationship it was found the hybrid laminate designs which showed higher fracture toughness in Mode-I and Mode-II delamination tests, will absorb more energy as a hybrid composite box in crushing process. The crushing process of hybrid composite boxes was also simulated by finite element software LS-DYNA and the results were verified with the relevant experimental result.     

Analytical and numerical calculation of strain energy release rate during delamination growth in a carbon epoxy laminate

Delamination of an infinite laminate subjected to a tension stress is studied. The stress state is studied by a numerical finite element analysis and by an analytical model based on the Love-Kirchhoff plate theory. The global strain energy release rate and its mode I, II and III components are calculated during delamination extension. A correlation is made between these two formulations. The analytical model has the advantage of permitting the analysis of different stacking sequences composed of a large number of plies and determination of their capacity for delamination.     

Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis

We use the semiclassical limit of electromagnetic wave scattering theory to determine the properties of the exterior caustics of a diagonally incident plane wave scattered by an infinitely long homogeneous dielectric circular cylinder in both the near zone and the far zone. The transmission caustic has an exterior/interior cusp transition as the tilt angle of the incident beam is increased, and each of the rainbow caustics has a farzone rainbow/exterior cusp transition and an exterior/interior cusp transition as the incident beam tilt angle is increased. We experimentally observe and analyze both transitions of the first-order rainbow. We also compare the predictions of the semiclassical approximation with those of ray theory and exact electromagnetic wave scattering theory.     

Feasibility on fiber orientation detection of unidirectional CFRP composite laminates using one-sided pitch–catch ultrasonic technique

It is important to assess fiber orientation, material properties and part defect because strength and stiffness of composites depend on fiber orientation of CFRP (carbon fiber reinforced plastics). A one-sided pitch–catch setup was used in the detection and evaluation of ultrasonic wave behavior and fiber orientation in the unidirectional CFRP composite laminates. Two Rayleigh wave transducers were joined head-to-head and used in the pitch–catch mode on the surface of the composites. The pitch–catch signal was found to be more sensitive than normal incidence backwall echo of longitudinal wave to subtle flaw conditions in the composite. Especially, one-sided ultrasonic measurement was made with using a Rayleigh wave transducers and the Rayleigh ultrasonic waves were extensively characterized in the CFRP composite laminates. Also, a conventional scanner was used in an immersion tank for extracting fiber orientation information in the unidirectional laminate. Therefore, it is thought that the proposed method is useful to evaluate integrity of CFRP laminates.     

A study of early-time response in dynamically loaded visco-elastic composites

Spalling is an important failure mode which triggers delamination, thus affects through-thickness integrity of a laminate and hinders the later integral plate action.The aim of the present study is to model the propagation of one-dimensional waves caused by a short-duration dynamic load through a visco-elastic medium. Two types of viscous effects are considered and described by means of partial differential equations. Four pulse load shapes are considered and four cases analysed. A higher order Lagrangian finite element is used to model the wave propagation and the weak-form Galerkin method is adopted to solve the differential equations. Numerical solutions are compared to analytical ones (where they exist) and excellent temporal and spatial correlation is achieved.It is found that damping leads to a decrease in peak stresses and strains by up to 11% for 5% of critical damping, even during the direct loading phase. It is shown that the inclusion of strain-rate did not have an effect on strains but led to an increase in stresses by almost 100%. The inclusion of damping and strain-rate effects increased stress values by up to 70% compared to the non-viscous cases, rendering strain-rate effects more pronounced than damping effects.     

Experimental and numerical analysis on Mode-I delamination of CFRP laminates toughened by polyamide non-woven fabric layer

The objective of this research is to put forward a toughening method by using the polyamide non-woven fabric (PNF) and investigate the Mode-I fracture toughness and delamination characteristic of the toughened CFRP laminates by performing the double cantilever beam test. The effect of PNF interlayer, which is formulated by a bilinear cohesive zone model, on the Mode-I fracture of U3160-PNF/3266 laminated composites is numerically analyzed. And the intralaminar damages are considered by using strength criteria and stiffness degradation law. The influences of PNF/3266 interlayer strength, U3160/3266 laminate thickness and initial crack length on the mechanical response of laminates are studied systematically. The work by combining the experiment and simulation is helpful for the optimal design of laminated composites used in aerospace and civil engineering.     

Damage resistance and damage tolerance of hybrid carbon-glass laminates

The influence of impact energy and stacking sequence on the damage resistance and Compression After Impact (CAI) strength of Carbon and Glass Fibre Reinforced Plastic (CFRP and GFRP respectively) hybrid laminates is investigated. CAI tests demonstrate that, in comparison to fully CFRP laminates, hybrid laminates show increases in structural efficiency of up to 51% for laminates subject to a 12J impact and 41% for those subject to an 18J impact. Laminates displaying the highest stresses at failure are those that exploit stacking sequences and GFRP content to prevent delaminations from forming close to the outer surface of the laminate during impact. This favourable damage morphology inhibits both sublaminate-buckling-driven delamination propagation and anti-symmetric laminate buckling failures.     

Delaminations of barely visible impact damage in CFRP laminates

CFRP laminates were impacted by projectiles of low masses, accelerated in an air gun, to have barely visible impact damage (BVID) to simulate damage to aircraft by runway debris. The delamination damage on individual interfaces was revealed by the destructive method of thin strips. In sub-BVID and BVID specimens, the damage was confined mostly to the front 30% of the laminate thickness. Delamination areas in the BVID specimens were found to be considerable — the largest dimension exceeding 12 mm on several interfaces. Nucleation of delamination damage was observed in interfaces adjacent to the mid plane in BVID specimens. At higher impact energies, about 110 to 150% more, the delamination damage was observed on almost all the interfaces with no sign of spalling at the rear surfaces. In comparison with a lightweight projectile of aluminium (4·4 g), a higher density steel projectile (11·8 g) caused more delamination damage for the same impact energy and an identical geometry of projectiles.     

Study of delamination in drilling carbon fiber reinforced plastics (CFRP) using design experiments

In this paper is presented a new comprehensive approach to select cutting parameters for damage-free drilling in carbon fiber reinforced epoxy composite material. The approach is based on a combination of Taguchi’s techniques and on the analysis of variance (ANOVA). A plan of experiments, based on the techniques of Taguchi, was performed drilling with cutting parameters prefixed in an autoclave carbon fiber reinforced plastic (CFRP) laminate. The ANOVA is employed to investigate the cutting characteristics of CFRP’s using high speed steel (HSS) and Cemented Carbide (K10) drills. The objective was to establish a correlation between cutting velocity and feed rate with the delamination in a CFRP laminate. The correlation was obtained by multiple linear regression. Finally, confirmation tests were performed to make a comparison between the results foreseen from the mentioned correlation.