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.     

Fatigue damage mechanics of composite materials Part III: Prediction of post-fatigue strength

A damage-based model for post-fatigue notch strength is presented. The model is an extension of a method developed previously to predict the notch strength of laminated composites. A simple finite element representation of the notch tip damage zone is used to obtain the localized damage-modified stress distribution. A uniaxial tensile stress failure criterion is applied to the 0° plies from which the laminate strength is evaluated. In conjunction with the fatigue damage growth law described in Part II, residual strength is calculated as a function of the applied loading conditions, specimen geometry and lay-up for (90/0)_s, (90/0)_2s and (90₂/0₂)_s T300/914C carbon-fibre/epoxy laminates subjected to tension-tension fatigue cycling.     

复合材料开孔层板压缩渐进损伤试验

为研究碳纤维增强树脂基复合材料开孔层板在压缩加载过程中的损伤起始、演化方式和损伤特点,采用微距拍摄、逐级加载超声C扫描、X光扫描和扫描电子显微镜观测4种观测手段对国产CCF300/5228A[45/0/-45/90]4s、[452/02/-452/902]2s、[454/04/-454/904]s3种铺层方式的开孔层板进行了压缩试验研究。对压缩载荷作用下开孔层板的损伤起始和损伤演化进行了观察和对比。对试验中观测到的纤维微屈曲、纤维挤出、孔边开裂和分层扩展等现象之间的关系进行了分析和说明。试验结果表明:压缩载荷下45°和90°铺层相邻位置为层板易分层位置,含45°和90°铺层相邻位置的开孔层板渐进损伤过程较为明显:开孔层板在压缩载荷下较早出现损伤,损伤的起始和演化缓解了孔边应力集中,促使压缩应变能在孔边逐步释放,推迟开孔层板压缩破坏的发生,提高层板压缩承载能力。研究结果可为材料结构损伤容限设计提供依据。     

Thermal and mechanical fatigue analysis of CFRP laminates

[0°/90°]_s and [±45°]_s CFRP laminated plates were analysed using a finite element formulation for their fatigue behaviour. A fatigue criterion which is based on the laminate interlaminar stresses and the basic lamina fatigue parameters was used. Thermal effects were included in the formulation. In particular, initial thermal stresses resulting from the curing of the laminate were also included in the analysis. The results showed that both laminates had predicted S-N behaviour similar to that from experiments of past investigators. Also, the fatigue behaviour for the [±45°]_s laminate between room temperature and the curing temperature were found to be the same. However, in the case of the [0°/90°]_s laminate the fatigue strength at high temperatures was found to be lower than that at low temperatures.     

An investigation of graphite PEEK composite under compression with a centrally located circular discontinuity

The failure characteristic of graphite polyetheretherketone (Gr/PEEK) under compression with a centrally located circular discontinuity was investigated through experimentation and a nonlinear ply-by-ply finite element technique. The stacking sequence of the laminates investigated were: [0 °₁₆], [90 °₁₆], [±45 °]_4S [0 °/90 °]_4S, and [0 °/ ± 45 0°/90 °]_2S. In the experimentation, [90 °]₁₆, [0 °/90 °]_4S, and [0 °/ ±45 °/90 °]_2S laminates, as well as three of the [0 °]₁₆, failed due to a crack that was normal to the loading direction and initiated from the edge of the hole progressing to the outer edges of the specimen. The [±45 °]_4S specimens failed to support the load due to an internal crack that originated from the hole's edge and then traveled at an angle of about 42% to the direction of loading. The finite element method used to analytically model the failure of Gr/PEEK accurately modeled the response of the specimens tested experimentally.     

The effects of geometric parameters on the failure strength for pin-loaded multi-directional fiber-glass reinforced epoxy laminate

A numerical and experimental study was carried out to determine the failure of mechanically fastened fiber-reinforced laminated composite joints. E/glass–epoxy composites were manufactured to fabricate the specimens. Mechanical properties and strengths of the composite were obtained experimentally. Tests have been carried out on single pinned joints in [0/90/0]_s and [90/0/90]_s laminated composites. A parametric study considering geometries was performed to identify the failure characteristics of the pin-loaded laminated composite. Data obtained from pin-loaded laminate tests were compared with the ones calculated from a finite element model (PDNLPIN computer code). Damage accumulations in the laminates were evaluated by using Hashin's failure criteria combined with the proposed property degradation model. Based on the results, ply orientation and geometries of composites could be crucial for pinned laminated composite joints.     

典型螺栓连接CFRP薄壁C型柱轴压失效行为:试验及数值模拟

为了研究典型螺栓连接碳纤维增强树脂复合材料(CFRP)薄壁C型柱的轴压失效模式及吸能特性,进行了5组不同铺层方式C型柱的准静态轴压试验,即[0/90]_4s、[±45]_4s、[±45/90₂/0₄]_s、[±45/90/0₂/90/0₂]_s、[90/±45/0]_2s,获得其失效形貌及载荷-位移曲线。采用Lavadèze单层壳单元模型、Puck-Yamada失效准则、层间胶粘单元及螺栓模型,建立C型柱层合壳模型进行轴压仿真,并与试验失效形貌、载荷-位移曲线及吸能特性评估指标进行对比分析。结果表明:0°、±45°、90°纤维可以显著影响C型柱轴压失效模式及吸能特性。在轴压载荷下,±45°纤维铺设C型柱发生局部屈曲失效模式,吸能特性差。±45°纤维铺设在外部,0°和90°纤维交替铺设在内部的C型柱,其轴压失效过程平稳,吸能特性好。与C型柱轴压试验结果相比,层合壳模型获得的整体变形和局部失效形貌吻合较好,载荷-位移曲线变化趋势和吸能特性评价指标基本一致。研究结果对CFRP薄壁C型柱吸能设计具有一定的指导意义。      

聚酰亚胺树脂基MT300/KH420复合材料高温力学性能(Ⅱ)——弯曲性能

从宏、微观的角度研究了碳纤维增强聚酰亚胺树脂基MT300/KH420复合材料的高温力学性能,重点揭示了MT300/KH420复合材料[0°]14和[±45°/0°/90°/+45°/0°2]s层合板在常温~500℃的弯曲性能变化规律。研究表明:MT300/KH420复合材料高温力学性能优异,[0°]14层合板在420℃的弯曲强度保持在51%以上,弯曲模量在500℃以内变化很小。[0°]14层合板在常温下断口粗糙,且贯穿厚度,表现为脆性破坏;随温度升高,树脂流动性增强,呈现出黏弹效应,破坏逐渐集中在加载点处,在500℃,部分树脂热解,纤维束脱离基体并氧化。[±45°/0°/90°/+45°/0°2]s层合板高温弯曲性能较为稳定,主要破坏为上、下表面沿45°方向开裂,并伴有层间分离,在500℃出现严重分层破坏;相比于受基体控制的层合板弯曲性能,温度对受纤维控制的层合板弯曲性能影响较小。     

基于断裂韧性预报复合材料层合板的开孔拉伸强度

开孔层合板的强度预报往往取决于孔边的临界长度,它不仅与材料性能,而且与铺层、孔径都有关。本文基于线弹性断裂力学,提出了一种预报对称铺层层合板开孔拉伸强度的新方法,只需提供正交层合板的断裂韧性和无缺口层合板的拉伸强度,显著降低对实验数据的依赖性。首先,将临界长度表作为层合板断裂韧性和无缺口拉伸强度的函数,再通过正交层合板[90/0]_8s的紧凑拉伸试验和虚拟裂纹闭合技术,确定出0°层断裂韧性,进而计算得到任意对称铺层层合板的断裂韧性。本文测试了T300/7901层合板[0/±45/90]_2s和[0/±30/±60/90]_s的开孔拉伸强度,孔径分别为3 mm、6 mm和9 mm。理论预报结果与试验值吻合较好,最大误差为15.2%,满足工程应用需求。      

Nonlinear analysis of interlaminar stress in graphite/epoxy laminates with and without delamination cracks

A quasi three-dimensional yield function, which is quadratic in stresses except for σ₁₁, is proposed for graphite/epoxy composites. The elastic-plastic interlaminar stress response near a free edge in the [90/0]_s, [0/90]_s, and [45/−45]_s laminates with and without delamination cracks was investigated using the pseudo three-dimensional finite element technique. The plasticity model was evaluated by comparison with off-axis experimental data. Since shear response is the key element for nonlinear stress-strain behavior of graphite/epoxy composites, the plasticity theory predicts interlaminar stresses in the [45/−45]_s laminate significantly different from linear elasticity. Moreover, the existence of a delamination crack caused more plasticity effects on interlaminar stresses.     

A study on the low-velocity impact response of laminates for composite railway bodyshells

This paper presents a study on the low-velocity impact response of woven fabric laminates for the composite bodyshell of a tilting railway vehicle. In this study, low-velocity impact tests for the three laminates with size of 100 mm × 100 mm were conducted at three impact energy levels of 2.4 J, 2.7 J and 4.2 J. Based on these tests, the impact force, the absorbed energy and the damaged area were investigated according to different energy levels and stacking sequences. The damage area was evaluated by visual inspection and C-scan measurement. The test results showed that the absorbed energy of [fill]₈ laminate was highest whereas [fill₂/warp₂]_s laminate was lowest. The [fill]₈ laminate had the largest delamination area because of the highest impact energy absorption.     

基于应变能耗散的复合材料层合板面内缺口强度分析CDM模型

基于伴随能量释放的渐进损伤演化思想,建立了复合材料层合板面内失效分析的连续介质损伤力学（CDM）分析模型,该模型包含损伤表征、损伤起始判定和损伤演化法则3个方面。基于CDM模型,通过引入损伤状态变量表征损伤,建立了平面应力状态下的材料损伤本构模型。采用损伤参量 f_E改写Hashin准则,以判定损伤的起始。损伤演化由特征长度内的应变能释放密度控制,建立了损伤状态变量关于等效应变的渐进损伤演化法则。模型中还同时考虑了面内剪切非线性和网格敏感性,并进行了对比分析。对含缺口的[90/0/±45]_3s和[（±θ）₄]_s 2类典型复合材料层合板的面内拉伸失效进行了分析,结果表明,本文中的模型能有效预测复合材料层合板的面内拉伸强度。     

Stress and strength analysis of pin joints in laminated anisotropic plates

Mechanical joints in composites can be tailored to achieve improved performance and better life by appropriately selecting the laminate parameters. In order to gain the best advantage of this possibility of tailoring the laminate, it is necessary to understand the influence of laminate parameters on the behaviour of joints in composites. Most of the earlier studies in this direction were based on simplified assumptions regarding load transfer at the pin-plate interface and such studies were only carried out on orthotropic and quasi-isotropic laminates. In the present study, a more rigorous analysis is carried out to study pin joints in laminates with anisotropic properties. Two types of laminates with (0/ + ₄/90)_s and (0/ ± ₂/90)_s layups made out of graphite epoxy T300/5208 material system are considered. The analysis mainly concentrates on clearance fit in which the pin is of smaller diameter compared to the hole. The main aspect of the analysis of pin joints is the changing contact between the pin and the plate with increasing load levels. The analysis is carried out by an iterative finite element technique and a computationally efficient routine is developed for this purpose. Numerical studies indicate that the location and magnitude of the peak stresses along the hole boundary are functions of fibre angle and the overall anisotropic properties. It is also shown that the conventional assumption of cosine distribution for the contact pressure between pin and the plate in the analysis lead to underestimation of bearing failure load and overestimation of shear and tensile failure loads in typical (0/90₅)_s cross-ply laminates.     

Analysis of stiffness reduction of cracked cross-ply laminates

Stiffness reduction of cracked [0°_m/90°_n]_s laminates is analyzed by variational methods on the basis of the principle of minimum complementary energy. For this purpose admissible stress systems are constructed which satisfy equilibrium and all boundary and interface conditions. The optimal stress field is then determined by minimization of complementary energy. The analysis allows for crack interaction and random crack distribution. Results are given for Young's modulus, shear modulus and Poisson's ratio. Young's modulus results are in excellent agreement with experimental data for [[0°/90°₃]]_s glass/epoxy laminate.     

Matrix cracking behavior of K3B/IM7 composite laminates subject to static and fatigue loading

The matrix cracking behavior of a new high-performance thermoplastic composite material, K3B/IM7, was systematically investigated. Laminates in various grouped thickness and ply stacking sequences, [0₂/90₂/0₂], [0₂/90₄/0₂], and a quasi-isotropic laminate [+45/0/−45/90]_s were tested under static and tension–tension fatigue loading. Depending on the stacking sequence of the laminates and the type of loading, various matrix cracking behavior were found. Under static loading, the matrix cracks were mainly close to the specimen edges. A few cracks were found to penetrate the specimen width, even when the load was large enough to break the specimen. However, under fatigue cyclic load, the edge initiated cracks propagated fully across the specimen width. Combined with the fatigue Paris Rule and considering the ply thickness and stacking sequence, the energy release rate method was applied to predict the relations between the loading strain amplitude and fatigue cycles for matrix cracking failure.     

Microdebonding investigation of the effects of thermal residual stress on the bond strength of a graphite/polymide composite

The microdebonding test was used to investigate the effects of thermal residual stresses resulting from different lay-ups in fabrication on the fiber/matrix bond strength of a graphite-fiber-reinforced polyimide composite. This was accomplished by comparing the results of a cross-plied laminate with those of a unidirectional laminate. The results indicated that the measured interfacial bond strength of the unidirectional composites was greater than that of the cross-plied laminate. The thermal radial stress distribution around the fiber for the unidirectional and the [0₂, 90₂]_s laminates were estimated, to explain this reduction of the interfacial bond strength.     

A damage identification technique for CF/EP composite laminates using distributed piezoelectric transducers

In this study, a damage identification approach was developed for carbon fibre/epoxy composite laminates with localized internal delamination. Propagation of the Lamb wave in laminates and its interaction with the delamination were examined. The fundamental symmetric Lamb wave mode, S₀, and the lowest order shear wave mode, S₀^′, were chosen to predict damage location. A real-time active diagnosis system was therefore established. This technique uses distributed piezoelectric transducers to generate and monitor the ultrasonic Lamb wave with narrowband frequency. The two-way switches were employed to minimize the number of transducers. A signal-processing scheme based on the time–frequency spectrographic analysis was utilised to extract useful diagnostic information. Also, an optimal identification method was applied on damage searching procedure to reduce errors and obtain the diagnostic results promptly. Experiments were conducted on [0/−45/45/90]_s CF/EP laminates to verify this diagnosis system. The results obtained show that satisfactory detection accuracy could be achieved.     

Advanced calculation of the room-temperature shapes of thin unsymmetric composite laminates

It is well known that the room-temperature shapes of unsymmetric laminates do not always conform to the predictions of classical lamination theory. Instead of being saddle shaped, as classical lamination theory predicts, the room-temperature shapes of unsymmetrically laminated composites are often cylindrical in nature. In addition, a second cylindrical shape can sometimes be obtained from the first by a simple snap-through action. Hyer developed for the class of all square unsymmetric cross-ply laminates which can be fabricated from four layers i.e., [0₃/90], [0₂/90/0], [0/90/0/90], [0₂/90₂], an extended classical lamination theory to predict whether these laminates have a saddle shape or one or two cylindrical shapes. The Finite Element Analysis (FEA) has just recently been used for the calculation of the room-temperature shapes of unsymmetric laminates, because more sophisticated finite element codes are now available and the calculations can be made in an acceptable time. The hope is to get more accurate results for the shape and the stresses and forces that occur during the snap through action. These results are needed for the development of active deformable composite structures based on unsymmetric laminates and incorporated shape memory alloy wires [Schlecht M. & Schulte K., Development of active deformable structures due to thermal residual stresses and incorporating shape memory alloys. In Proc. ECCM Smart Composites Workshop, ECCM6, Bordeaux, 1993, pp. 20–115.] Results for different lay-ups are presented and compared.     

High strain rate compressional behavior of stitched and unstitched composite laminates with radial constraint

This paper is concerned with the high strain rate compressional behaviour of glass/epoxy (Hy-E 9134B, Fiberite, USA) composite laminates with or without stitching reinforcement by untwisted Kevlar-49 threads (1140 denier). The split Hopkinson pressure bar (SHPB) apparatus is used in performing the high strain rate tests. Test data are analyzed in a manner similar to that reported by Hauser Exp. Mech., 6 (1966) 395. Specimens are tested at strain rates up to 10⁴ s⁻¹. Unidirectional laminated parallelepiped samples are impacted along their fiber direction. Their high velocity compressive ductility is observed. Both [0°]₂₄ and [(0°/90°)₆]_S glass/epoxy circular specimens with disc diameters of 10 and 50·8 mm are transversely impacted by an input bar in order to study their high strain rate behavior. Moreover, two sets of stitched circular specimens with disc diameters of 10 and 50·8 mm are also examined. The effect of strain rate and radial constraint on the dynamic properties of stitched and unstitched GFRP laminated specimens and their associated damage patterns are described.     

Beam analysis of angle-ply laminate end-notched flexure specimens

Analysis and experiments on quasi-unidirectional and angle-ply laminate end-notched flexure specimens are presented. The analysis is based on laminated beam theory incorporating first-order shear deformation theory. Compliance and strain-energy release rate determined for relatively thin unidirectional and angle-ply laminate ENF specimens were in good agreement with a previous classical plate theory formulation. For thicker laminates, however, effects of shear deformation on the compliance of the ENF specimen become significant. An experimental study on glass/polyester quasi-unidirectional and angle-ply laminate ENF specimens was conducted. Specifically, [0]₆, [±30]₅ and [±45]₅ laminates with mid-plane delaminations were considered. Experimental compliance data agreed well with analytical predictions. The fracture toughness increased with increased angle θ at the ±θ interface. This is attributed to the fracture work associated with the debonding of transversely oriented fiber bundles in the quasi-unidirectional plies. The angle-ply laminates displayed more yarn debonding than the quasi-unidirectional laminate. For all laminates it was observed that the crack propagated in a non-uniform manner which is correlated with elastic coupling effects with cracked regions of the laminate beams.