Damage assessment in layered composites using spectral analysis and Lamb wave

Piezo-ceramic transducers of the surface mounted type are commonly used for structural health monitoring (SHM) techniques. But, there is a disadvantage to use piezo-ceramic transducers of the surface mounted type in Lamb wave application. Due to the symmetric and antisymmetric Lamb wave modes generated by the surface mounted piezo-ceramic transducers simultaneously, the received signals are very complex and it is difficult to extract damage information from the signals.

In this paper, the practical method for SHM was proposed using piezo-ceramic transducers of the surface mounted type and Lamb wave. In order to overcome the difficulties in the signal processing of the simultaneous modes, the symmetric and antisymmetric modes were separated by using the two sensors bonded on the opposite surfaces at the same point. Also, spectral analyses of the separated symmetric and antisymmetric Lamb waves showed that each mode propagated with different frequency characteristics in the exciting frequency range.

By making use of these findings, the changes of power spectrum density in characteristic frequency band of symmetric and antisymmetric modes are proportional to the delamination size in quasi-isotropic Gr/Ep laminates. Therefore, this paper presents the damage assessment technique to extract damage information from the complicated PZT signals that could not be interpreted in time domain.     

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。     

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.     

Numerical and experimental studies on propagation of A0 mode in a composite plate containing semi-infinite delamination: Observation of turning modes

Propagation of the anti-symmetric fundamental Lamb mode (A₀) in a composite laminate containing a semi-infinite delamination was studied through numerical simulations and experimental studies. Here, the wave was generated on a sub-laminate above the delaminated region, and the reflection and transmission of the Lamb modes at the edge of the discontinuity were quantitatively studied. The wave group (named as ‘turning mode’), which was made to propagate from one side of the delamination to the other side (through delaminations) was captured and its transmission factor was estimated. Reflection and transmission factors of wave groups were estimated for three different laminates – quasi-isotropic, unidirectional and cross-ply, containing delamination at various interfaces across thickness. Propagation of ‘turning modes’ were also captured experimentally, employing air-coupled transducers, in quasi-isotropic laminates containing delaminations at different interfaces. Attenuation compensation was incorporated in the experimental signals to improve the comparison of transmission and reflection factors between numerical simulations and experiments.     

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.     

Lamb wave excitation by Hertzian contacts with applications in NDE

Excitation of Lamb waves in solid plates by point-like Hertzian contacts for material characterization and nondestructive testing is investigated. A 2 dimensional model using normal mode theory is used to predict the relative excitation efficiency of the lowest order Lamb waves in anisotropic solid plates. Hertzian contact transducers with PZT-5H piezoelectric material and quartz buffer rods are realized to operate in the 200 to 500 kHz range for experimental verification. Single mode operation with the lowest order antisymmetric Lamb wave (A ₀) mode is achieved in various plates at in agreement with theoretical predictions. The technique is applied for material characterization on single crystal silicon samples and defect detection in composite plates. The phase velocity anisotropy of the A₀ mode is measured with signal-to-noise levels exceeding 65 dB. In (111) cut silicon plates the absolute phase velocity is measured with ±0.05% accuracy. The phase velocity anisotropy and effects of delamination in layered composite plates are calculated using the surface impedance approach. The experiments on graphite/epoxy composite plates agree with these calculations and show the potential of the method for defect detection with high resolution     

基于概率损伤算法的复合材料板空气耦合Lamb波扫描成像

采用非接触空耦传感器在准各向同性复合材料板中激励出单一的Lamb波模态,用于分层缺陷的扫描检测。扫描时,激励和接收传感器置于复合材料板同侧并相对倾斜布置,传感器沿2个正交方向同步线性扫描,得到不同位置的检测信号。对不同扫描路径下的检测信号进行连续小波变换,提取激励频率下的小波系数包络信号,对分层缺陷进行成像。在此基础上,利用概率损伤算法定义损伤指数,结合不同方向的损伤指数实现分层缺陷成像。采用全加法和全乘法对2个正交扫描方向得到的成像结果进行数据融合,实现了分层缺陷的定位和重构。并在成像算法中引入阈值,进一步提高了分层缺陷的定位精度以及重构质量。     

板状结构中基于Lamb波单模态的缺陷成像试验研究

Lamb波技术非常适于板类结构的各种缺陷检测。为了得到模态较为单一的Lamb波,使得接收信号更具有解释性,缺陷更容易识别,该文中在板上下表面的相同位置分别布置压电传感器阵列,采用同一位置上下表面的双压电片同相或反相激励,激励出单一S₀或A₀模态。运用这种单模态的Lamb波激励方式对板中缺陷进行检测,结合椭圆成像算法与数据融合方法对压电传感器阵列接收到的多组信号进行缺陷成像。该方法有效的实现了板中缺陷的二维成像定位,检测出人工缺陷,并提高了缺陷的可识别能力和定位精度。     

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.     

Effects of local stiffness changes and delamination on Lamb wave transmission using surface-mounted piezoelectric transducers

The paper presents a set of numerical results on the use of surface mounted piezoelectric transducers to analyse the effects of impact damage and delamination of plate-like structures on the Lamb wave mode. The effects of the size, properties and orientation of the damage upon a propagating Lamb wave is qualitatively determined. In this paper, impact damage was simulated by a local change in the stiffness of the material in the structure and a delamination. The effects on the transmission of the incident Lamb wave when it propagates through a region of change in density are analysed. This paper will also demonstrate how the properties of a propagating Lamb wave can be affected by the existence of a delamination in a plate.     

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.     

Annealing effects on the thermoelectric power of thin copper and silver films

The effect of annealing on the thermoelectric power of thin copper and silver films has been investigated. Using Matthiessen's rule, the thermoelectric power is separated into three components: S₀ due to bulk lattice scattering, S_s due to surface scattering and S_i due to scattering by imperfections. The values of S₀ and S_s are independent of the film thickness, whereas S_i varies with film thickness. However, S_i approaches a constant value for both copper and silver when the film thickness is larger than 1000 Å. The values of S_s obtained for copper and silver films are 1.33 μV/°K and 3.23 μV/°K respectively. For thicker films (t>1000 Å), the values of S_i for copper and silver films are 3.89 μV/°K and 9.63 μV/°K respectively.     

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.     

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.     

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。     

Effect of the shear and coupling elements of the Aij and Dij matrices on the impact behavior of glass, aramid and hybrid fabric composites

The impact behavior of glass, aramid and glass–aramid hybrid fabric epoxy matrix composites was evaluated. Delamination was identified as the main macroscopic failure mode of the composites. A simple relationship based on the macromechanical behavior of laminated composites was established, relating coupling—A₂₆, D₂₆—and shear—A₁₆, D₁₆—elements of the extensional and bending stiffness matrices to the total energy absorbed at impact. The results obtained show that the A₆₆/D₆₆ ratio is a relevant parameter of concern, correlated with the behavior of the composites under impact. Additionally, the coupling matrix B_ij was shown to restrain the macroscopic delamination of the composites.     

Effect of strain rate on interlaminar shear properties of carbon/epoxy composites

In this paper, the effect of strain rate on interlaminar shear properties of laminates is studied. The material tested was a T300/5208 carbon/epoxy composite, and the range of strain rates explored was about 10⁻³ − 10³ s⁻¹. The specimens used were designed and optimized by finite element analysis, and the calculations are presented here. One of the specimens permitted the determination of the interlaminar shear modulus, G₁₃, and the other permitted the determination of the interlaminar shear strength, S₁₃. No influence of testing speed on interlaminar properties was observed at low, intermediate and high strain rates. Fracture surfaces were studied by scanning electron microscopy: a slight difference was observed between specimens tested at low and high strain rates.     

兰姆波在裂纹处的模态转换及散射特性研究

该文采用散射矩阵表征兰姆波在缺陷处的模态转换和散射特性, 研究了S₀模态兰姆波与亚波长级槽形裂纹的交互作用. 由板中导波模态位移场的特性, 提出了只存在零阶模态时的模态分离方法. 求解了S₀模态在不同尺寸裂纹处的多模态散射矩阵. 结果表明, S₀模态入射到裂纹时, 散射波动场周向分布不均, 与入射角度相关;散射特征的强弱由裂纹长度决定, 长度越短, 散射特征越明显;各散射模态的能量分配由裂纹的深度决定, 随着裂纹深度增加, 散射的S₀和SH₀模态能量增加, 而A₀模态先增加后急剧减小.     

An investigation of non-linear elastic behavior of CFRP laminates and strain measurement using Lamb waves

This paper investigates the non-linear elastic behavior of unidirectional and cross-ply CFRP laminates and proposes a new method to measure tensile strain using Lamb waves. Young’s modulus was measured as a function of strain in situ using Lamb wave velocity during a tensile test. The stiffening effect of the carbon fibers on [0]₈ specimens and the softening effect of the epoxy matrix on [90]₈ specimens were accurately evaluated. Young’s modulus of the 0° ply was obtained as a quadratic function of strain. Using the function and the rule of mixture, the dependence of Young’s modulus on strain was accurately predicted for cross-ply laminates. Based on the results, the tensile strain was quantitatively correlated with the corresponding arrival time of the Lamb waves. The strains obtained from the proposed method agreed well with those from the strain gauge. Finally, the effect of transverse cracks on the in situ Young’s modulus of the cross-ply laminate under a tensile load was investigated. This method clearly detected even a small decrease in the Young’s modulus due to the transverse cracks in stiffening cross-ply laminate.     

Fracture angle and strain-energy-density-factor of a crack at hole at an arbitrary angle

For both the maximum stress criterion and strain-energy-density-factor (S) theory, fracture angle (the initial angle of crack growth) − θ_o is predicted by using opening and sliding mate stress intensity factors, k₁ and k₂. These theoretical predictions are consistent with experimental fracture angles.

For the S theory, the crack spreads in the negative θ_o-direction in a plane for which S is a minimum, S_min. This quantity was obtained analytically. The experimental data of the critical S (S_cr) on plexiglass fracture specimens remains essentially constant.