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.     

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.     

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。     

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.     

Determination of fracture energy and tensile cohesive strength in Mode I delamination of angle-ply laminated composites

The energy release rate in delamination of angle-ply laminated double cantilever composite beam specimens was calculated using the compliance equation, and interlaminar cohesive strengths were obtained. Instead of the traditional approach of a beam on an elastic foundation, a second-order shear-thickness deformation beam theory (SSTDBT) was considered. The equilibrium equations were obtained using the principle of minimum total potential energy and the system of ordinary differential equations were solved analytically. The problem was solved for [0°]₆ , [±30°]₅, and [±45°]₅ laminates with mid-plane delaminations and the results were verified using experimental evidence available in the literature.     

Effects of temperature on impact damages in CFRP composite laminates

In this paper, the effect of temperature variations (low and high temperatures) was studied experimentally on impact damage to CFRP laminates. The composite laminates used in this experiment were CF/EPOXY orthotropic laminated plates with lay-up [0₆/90₆]_s and [0₄/90₄]_s, and CF/PEEK orthotropic laminated plates with a lay-up of [0₆/90₆]_s. A steel ball launched by the air gun was used to generate the CFRP laminate impact damage. For impact-damaged specimens, nondestructive evaluation (NDE), such as a scanning acoustic microscopy (SAM) was performed on the delamination-damaged samples to characterize damage growth at different temperatures.

Therefore, this study was undertaken to experimentally determine the interrelations between impact energy and impact damage (i.e. the delamination area and matrix) of CFRP laminates (CF/EPOXY and CF/PEEK) subjected to foreign object damages (FOD) at low and high temperatures.     

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。     

Interfacial debonding in laminated titanium matrix composites

The results of an experimental program in which multiaxial loads were applied to [0₄] and [±45]_s silicon carbide/titanium (SiC/Ti) tubes are reviewed showing that stress coupling, matrix viscoplasticity (including room temperature creep) and fiber/matrix interfacial damage all contribute to nonlinear response and permanent strains in titanium matrix composites (TMC). A micromechanical model that explicitly considers the aforementioned phenomena is presented herein. The model assumes a periodic microstructure and uses finite elements to analyze a representative volume element. The composite is assumed to be in a state of generalized plane strain making it possible to discretize only a generic transverse plane while still being able to apply three-dimensional loading through appropriate boundary conditions. The response of laminated composites is predicted by incorporating the micromechanical results into nonlinear lamination theory. Predictions are presented to show the influence of the model parameters on the effective composite response of unidirectional [0₄] and angle-ply [±45]_s TMC laminates.     

Role of matrix resin in delamination onset and growth in composite laminates

The effect of the matrix resin on the onset and growth of delamination in composite laminates has been investigated in this work. Two kinds of graphite/epoxy composite materials (T300/648-BF₃/MEA and T300/634-DDS) with quite different matrix properties have been used. The study was done on two different layups, [(±30)₃/90₂]_s and [(±45)₂/O₂/90₂]_s. Out-of-plane moiré interferometry and diiodomethane-enhanced X-radiography were used to detect delamination. A strength criterion for the onset of delaminatoin is proposed and an assessment made of the effect of matrix properties on delamination onset. A modified energy release rate model is presented for characterization of delamination growth emphasis being placed on assessing the behavior of delamination resistance curves and delamination growth rate. The results indicate that enhancement of matrix strength and ductility increases the critical loads for delamination onset and delamination resistance in the composite laminates under static loading, and significantly reduces the delamination growth rate under cyclic loading.     

Fracture behavior of cross-ply graphite/ epoxy laminates

Fracture behavior of cross-ply (0/90)_4s, (0/90)_10s, (0₂/90₂)_2s and (0₄/90₈/0₄)_T laminates of T300/934 graphite/epoxy material was studied using compact tension specimens of several widths and thicknesses, center notched tension and three point bend specimens. The process of damage initiation and propagation was studied and is discussed in detail. The critical stress intensity factor was evaluated and its variation with specimen size and type is shown. On the basis of these investigations, a suitable specimen for the evaluation of meaningful fracture toughness is suggested.     

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.     

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.     

Measurement of the static compressive strength of carbon-fibre/epoxy laminates

This paper describes an experimental study of the compressive failure of T800/924C carbon-fibre/efoxy composite laminates. Undirectional laminates loaded parallel to the fibres have compressive strengths that are 70% of the tensile strength and fail by fibre-microbuckling. During microbuckling the fibre debonds from the matrix, and the fibres break in bending. Multidirectional [(±45/0₂)₃]_sm laminates were also tested in compression, and the critical failure mechanism observed was microbuckling of the 0° plies. The failure strain was almost the same as for the undirectional laminate, The failure strain was almost the same as for the unidirectional laminate, which indicated that the ±45° plies have no significant influence on the failure strength of the 0° plies.     

A damping analysis of composite laminates using the closed form expression for the basic damping of Poisson's ratio

Various methods have been presented to obtain the effective damping of a symmetric laminated composite. In this paper, modified classical lamination theory based upon the elastic–viscoelastic correspondence principle was utilized by developing the basic damping of Poisson's ratio for accurately predicting the damping of laminated composite beams. The analysis involves an extension of the elastic–viscoelastic approach. Futhermore, Ni and Adams' theory was used for verifying the modified classical lamination theory. Six typical laminated composites with [±θ]_s,[0/θ]_s,[0/±θ/90]_s,[90/±θ/0]_s,[0/90/±θ]_s and [90/0/±θ]_s, stacking sequences were employed for this study. Numerical results have shown that damping values were in some difference among prediction methods over the particular range of fiber orientation.     

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.     

A fracture criterion for three-dimensional crack problems

A criterion for predicting the growth of three-dimensional cracks is developed on the basis of the strain energy density concept which has been used successfully for treating two-dimensional crack problems. Fracture is assumed to initiate from the nearest neighbor element located by a set of spherical coordinates (r, θ, φ) attached to the crack border. The new fracture surface is described by a locus of these elements whose locations correspond to the strain energy function, dW/dV, being a minimum. The function dW/dV is found to be singular of the type 1/r and is of quadratic form in the three stress intensity factors k₁, k₂ and k₃ expressed through the strain energy density factor S. It is postulated that unstable crack propagation initiates from a region where S reaches a critical value S_cr = r₀(dW/dV)_cr. The locations of failure lying on the fracture surface is determined by holding (dW/dV)_cr = S_min/r₀ constant. The quantity S_min stands for the value of S minimized with respect to θ and φ and r₀ is a radial distance measured from the crack border.

An example of failure prediction for an embedded elliptical crack subjected to both normal and shear loads is presented. According to the S-criterion, fracture initiation takes place at the ends of the minor axis. An unexpected result is that for a narrow elliptical crack and Poisson's ratio of 1/3 the lowest failure load occurs when the uniaxial tensile load makes an angle of approximately 60° with the crack surface and is in the plane of the major axis. This is in contrast to the expectation that the lowest critical load occurs when the uniaxial tension is perpendicular to the crack surface. In the limit as the elliptical crack becomes increasingly narrower, the result reduces to the two dimensional line crack case of Mode I and III loading. The S-criterion is also applied to the failure prediction of three dimensional cracks under compressive loads.     

The relation between compressive strength of carbon/epoxy fabrics and micro-tow geometry with various bias angles

In this paper compressive tests of carbon/epoxy (plain weave, 3k) fabric composites were performed to investigate the relation between compressive strength and various bias angles and shear angles. Compressive properties such as chord modulus and maximum strength of the fabric composite materials are essential to analyze the drape behaviour and estimate the quality of the final products. Various specimens with different bias and shear angles which were fabricated by using autoclave de-gassing moulding process were prepared to estimate the strength and chord modulus with respect to the bias and shear angle variations. The stacking sequences of the compressive test specimens are [0]_10T, [15]_10T, [30]_10T and [45]_10T for bias specimens and [±37]_10T, [±32]_10T, [±28]_10T, [±22]_10T for sheared specimens. Micro-tow structures were observed to correlate the fabric compressive strength with crimp angle. Anti-buckling rig was involved to prevent specimens from buckling during the compressive tests. The compressive test was performed with 1.3 mm/min strain rates. Compressive test results were compared with calculation results. Facture modes which were classified in two different modes were analyzed using microscopic observation.     

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.     

Physical aging behavior of high-performance composites

The effect of physical aging on the viscoelastic creep properties of a thermoplastic-toughened cyanate ester resin (Fiberite 954-2) and its IM8/954-2 composites, and a semi-crystalline thermoplastic (Fiberite ITX) and its IM8/ITX composites was investigated. The study was carried out by using dynamic mechanical analysis (DMA) and tensile creep tests. Tests were performed on plain resin, [90 °]_4s, and [± 45 °]_2s composite specimens. Creep tests were conducted up to an aging time of 54 h with the logarithmic aging shift rate, μ, and its dependence on sub-glass transition aging temperature, being determined. The results showed significant physical aging in both material systems. To study the effect of long-term aging on creep behavior, momentary creep tests were conducted on the [± 45 °]_2s composites of both material systems at temperatures between 140 and 200 °C. Master curve plots were drawn from these momentary creep tests using the time/temperature superposition principle (TTSP). Effective time theory (ETT) was then used to modify TTSP and incorporate physical aging effects.     

Pyrolytic Trifluoromethylation of [76]-, [78]-, [84]-, and Aza[60]Fullerenes with Silver Trifluoroacetate; Evidence for Coordination of Fullerenes to Silver

Pyrolytic trifluoromethylation of [76], [78], [84], and aza[60]fullerenes with silver trifluoroacetate at 300°C results in extensive polyaddition of up to 18, 18, 20 and 20 CF₃ groups, respectively. In contrast to trifluoromethylation of [60]- and [70]fullerenes that give a full range of derivatives ranging upwards from C_n(CF₃)₂, [76]-, [78]-, and [84]-fullerenes only give C_n(CF₃)_6-18 derivatives, largely in the 10-12 CF₃ range; reaction with [76]fullerene is accompanied by formation of C₆₀(CF₃)₆ attributed to cage fragmentation. For aza[60]fullerene the hexa-addition level dominates, in contrast to its other reactions which give predominantly penta-addition products. All the compounds showed peaks at 1256±2 and 1180-1190 cm^-1, due to the CF₃ group, and peaks in this region are shown also by the soluble extract obtained on trifluoromethylation of nanotubes. As in trifluoromethylation of [60]- and [70]-fullerenes, the products obtained initially are involatile, attributed to formation os silver complexes; these are decomposed on subsequent solution in toluene. Mixed isomeric trifluoromethylated C₆₀F₈ derivatives viz. C₆₀F₇CF₃, C₆₀F₆(FG₃)₂, C₆₀F₅(CF₃)₃ and C₆₀F₄(CF₃)₄, and C₆₀F₄CF₃CF₂CF₃ (a C₆₀F₆ derivative) have been isolated from fluorination of [60]fullerene with MnF₃/K₂NilF₆ at 510°C.