The behaviour of Kevlar fibre-epoxy laminates under static and fatigue loadings. Part I—experimental

Kevlar 49 fibre and unidirectional Kevlar fibre reinforced plastic (KFRP) laminates both show an increase in stiffness under monotonic tensile loading. This stiffening effect is time-dependent and is reversible once the load is removed. In contrast, the modulus of a cross-ply KFRP laminate is affected primarily by matrix cracking of the transverse (90°) ply, and is sensitive to strain-rate and temperature. In cyclic (tensile) loading, however, the modulus of the cross-ply laminate depends on a combination of the fibre stiffening effect and transverse matrix cracking.     

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。      

Microscopic fatigue damage progress in CFRP cross-ply laminates

Damage progress in toughened-type carbon fibre-reinforced plastic (CFRP) cross-ply laminates under tensile fatigue loading was measured using the replica technique. The laminate configuration was [0/90_m/0], where m = 4, 8 and 12. The damage parameters, transverse crack density and delamination ratio, were determined. A power-law model was proposed, relating the cyclic strain range and the number of cycles at transverse crack initiation. Based on experimental data, a simple shear-lag analysis combined with the modified Paris law was conducted to model the transverse crack multiplication. An extension of the shearlag analysis for laminates containing delaminations initiating from the tips of the transverse cracks was used to conduct a modified Paris law analysis for delamination growth.     

Health monitoring of cross-ply laminates: Modelling the correlation between damage evolution and electrical resistance change

In this work an analytical solution is developed to accurately predict the stiffness reduction in conductive cross-ply laminates, caused by matrix cracking in the transverse layers, as a function of the electrical resistance change of the laminate itself.To this end a closed form solution is initially developed with the aim to link the density of transverse cracks to the electric resistance of the cross-ply laminate. Such an expression is later used within a further model which allows the stiffness degradation associated to a given crack density to be estimated.The accuracy of the proposed model is verified by comparison with a bulk of FE analyses.     

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.     

Overall moduli and natural frequencies of composite laminates containing multiple interlaminar transverse cracks

In this paper, the overall tensile modulus of a composite laminate containing embedded multiple interlaminar transverse cracks is studied. The modulus is calculated based upon an energy method and the crack opening displacement which is obtained by solving a boundary-value problem. Numerical computation is applied to fibre-reinforced composite laminates following the theoretical analysis. The theoretical prediction is compared with the experimental data, and good agreement is found. The solution is then used to examine the natural frequencies of two representative cross-ply beams with multiple matrix cracks in some of the outer transverse layers. The difference between the natural frequencies of the intact and the damaged cross-ply beams is presented. It is found that for a graphite/epoxy composite, the multiple transverse cracks only have a minor influence on the frequency, whereas for a glass/epoxy composite, the multiple cracks may have a significant influence on the frequency when the cracks reach the saturation level in a relatively large area of a beam.     

Interaction between transverse cracks and delamination during damage progress in CFRP cross-ply laminates

In previous papers the microscopic failure process of (0/90_n/0) (n = 4,8,12) cross-ply laminates was investigated. Progressive damage parameters, such as the transverse crack density and the delamination ratio, were measured. A simple modified shear-lag analysis including the thermal residual strains was conducted to predict the transverse crack density and the delamination length. The analysis did not consider the interaction between the transverse cracks and the delamination. In the present paper, a prediction is presented for the transverse crack density including the effect of delamination growth. The prediction shows better agreement with the experimental results, especially for laminates with thicker 90 ° plies in which extensive delamination occurs.

Loading/unloading tests have also been performed to obtain the Young's modulus reduction and the permanent strain as functions of the damage state. The shear-lag predictions of the Young's modulus reduction and the permanent strain are compared with the experimental data. Better agreement is obtained when the interaction between transverse cracks and delamination is considered.     

The behaviour of Kevlar fibre-epoxy laminates under static and fatigue loading—Part 2: Modelling

A model has been developed for the modulus reduction of cross-ply Kevlar laminates under static loading as a function of applied strain. The effects of strain-rate and temperature have also been considered. The ‘stiffening’ of Kevlar fibres and Kevlar fibre-epoxy (KFRP) laminates under creep or fatigue conditions has been modelled using a kinetic approach. This has enabled stiffening effects to be subtracted out of the residual modulus-with-cycles behaviour of cross-ply KFRP laminates under fatigue loading, leaving a modulus-reduction-with-cycles curve which reflects the damage due to matrix cracking. The analyses compare well with experimental data reported in Part 1.     

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.     

Application of chirped fiber Bragg grating sensors for identification of crack locations in composites

Chirped fiber Bragg grating (FBG) sensors were applied for the identification of crack locations in carbon fiber reinforced plastic (CFRP) laminates since the reflection spectrum from a chirped FBG was expressed as a function of the position along the grating. For the crack identification in the 90° ply of a cross-ply laminate, a chirped FBG sensor, whose grating length and spectrum width were 50 mm and about 5 nm respectively, was embedded into the 0° ply of the CFRP cross-ply laminate, and the reflection spectra were measured after tensile loadings were applied to the laminate. As a result, the spectra had dips corresponding to locations of transverse cracks. This change in the form of the spectrum was also confirmed by a theoretical calculation. Hence, the crack locations could be identified from the form of the spectrum. Furthermore, it was demonstrated that a small-diameter chirped FBG sensor could also be applied for the identification of the crack locations.     

Prediction of initiation of transverse cracks in cross-ply CFRP laminates under fatigue loading by fatigue properties of unidirectional CFRP in 90° direction

A fatigue life to the initiation of transverse cracks in cross-ply carbon fiber-reinforced plastic (CFRP) laminates has been predicted using properties of the fatigue strength of unidirectional CFRP in the 90° direction. In the experiments, unidirectional [90]₁₂ laminates were used to obtain a plot of maximum stress versus number of cycles to breaking, and two types of cross-ply laminates of [0/90₄]_S and [0/90₆]_S were used to evaluate the initiation and multiplication of transverse cracks under fatigue loading. Transverse cracks were studied by optical microscopy and soft X-ray photography. Analytical and experimental results showed good agreement, and the fatigue life for transverse crack initiation in cross-ply laminates was predicted successfully from the fatigue strength properties of the unidirectional CFRP in the 90° direction. The prediction results showed a conservative fatigue life than the experimental results.     

True and apparent Young’s modulus in ferrous porous alloys

Residual porosity in ferrous powder metallurgical alloys induces the phenomenon of localized yielding, or first yielding, during tensile testing. This gives rise to the existence of a true (E₁) and apparent (E₂) Young’s modulus. The true Young’s modulus is similar to the dynamic modulus (E_d) determined by the acoustic resonance method, whereas the apparent Young’s modulus is lower than both E₁ and E_d. For alloys with hard microstructures the apparent Young’s modulus turned out to be about 6% lower than the true Young’s modulus and a negligible influence of matrix hardness and pore morphology was highlighted. However, for ferritic or ferritic–pearlitic materials this difference was higher, ranging between 14 and 31% and it decreases as pore roundness is increased. For austenitic AISI 316L alloys both E₁ and E₂ are lower than E_d because of the presence of oxides on the powder surface, which favour early decohesion at the necks during tensile testing.     

Residual Stiffness of Cracked Cross-Ply Composite Laminates Under Multi-Axial In-plane Loading

In this paper, the Equivalent Constraint Model (ECM) together with a 2-D shear lag stress analysis approach is applied to predict residual stiffness properties of polymer and ceramic matrix [0/90 _n /0] cross-ply laminates subjected to in-plane biaxial loading and damaged by transverse and longitudinal matrix cracks. It is found that the longitudinal Young’s modulus, shear modulus and major Poisson’s ratio undergo large degradation as the matrix crack density increases, with Poisson’s ratio appearing to be the most affected by transverse cracking. In cross-ply laminates with thick 90° layer strip-shaped delaminations begin to initiate and grow from the tips of matrix cracks at the 0°/90° interface. These delaminations contribute to further stiffness degradation of such laminates, and hence have to be taken into account in failure analysis models. The thickness of the 90° layer plays an important role; the thicker the 90° layer, the bigger stiffness reduction suggesting a size (volume) effect at ply level. In SiC/CAS cross-ply laminates reduction in the longitudinal modulus occurs mainly due to transverse cracks, while the shear modulus appears to be the most affected by the presence of longitudinal cracks. The shear modulus reduction ratio predicted previously by a semi-empirical formula is, in the most of cases, within 10% of the current ECM/2-D shear lag approach value. In some cases, though, the error of the semi-empirical finite element expression can be as big as 20% since it fails to capture damage mode interaction.     

Reinforcement of plasticized wheat gluten with natural fibers: From mechanical improvement to deplasticizing effect

Wheat gluten/glycerol-based materials were reinforced through natural fiber addition. Hemp and wood fiber addition increased both composite tensile strength and Young’s modulus, but decreased elongation at break. Resulting materials exhibited lower water sensitivity. Fiber addition does not modify the protein aggregation, but resulted in an increase of the composite matrix glass transition temperature (T_g). This increase was attributed to the plasticizer migration from the matrix to the fibers, which increased the matrix Young’s modulus. This migration called matrix deplasticization contributed to the improvement of the overall composite mechanical properties. The true reinforcing effect attributed to the fiber addition and the deplasticizing effect attributed to plasticizer migration were dissociated and quantified. At high fiber content, deplasticizing effect became significant and reduced material processability. This study suggested that the fiber lignin content is susceptible to influence both the water sensitivity and the matrix deplasticization.     

Positive size and scale effects of all-cellulose composite laminates

Negative size effects are commonly reported for advanced composite materials where the strength of the material decreases with increasing volume of the test specimen. In this work, the effect of increasing specimen volume on the mechanical properties of all-cellulose composites is examined by varying the laminate thickness. A positive size effect is observed in all-cellulose composite laminates as demonstrated by a 32.8% increase in tensile strength as the laminate thickness is increased by 7 times. The damage evolution in all-cellulose composite laminates was examined as a function of the tensile strain. Enhanced damage tolerance concomitant with increasing specimen volume is associated with damage accumulation due to transverse cracking and strain delocalisation. A transition from low-strain failure to tough and high-strain failure is observed as the laminate thickness is increased. Simultaneously, scale effects lead to an increase in the void content and cellulose crystallinity at the core, with increasing laminate thickness.     

Characterization and evolution of matrix and interface related damage in [0/90]S laminates under tension. Part I: Numerical predictions

This paper considers damage development mechanisms in cross-ply laminates using an accurate numerical method that assumes a Generalized Plane Strain (GPS) state. A 2D Boundary Element Method (BEM) model is generated to investigate the two types of damage progression in a [0/90]_S laminate: transverse cracks in the 90° lamina and delamination between both laminae. The model permits the contact between the surfaces of the cracks. The study is carried out in terms of the dependence of the Energy Release Rates (ERR) of the two types of crack on their respective lengths. A special emphasis is put on the mechanisms of the joining of the two aforementioned types of crack, including the study of the distribution of the stresses along the interface between the two plies when the transverse crack is approaching this interface.     

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.     

基于相移光纤光栅传感器的碳纤维增强树脂复合材料基体裂纹超声探伤

复合材料内部的微小裂纹常会引起后续严重的破坏,因此需要对其进行检测。然而超声探伤复合材料基体裂纹非常困难。本文搭建了一个具有高灵敏度、大带宽的相移光纤光栅超声传感系统,利用此系统探测了在正交铺层碳纤维增强树脂复合材料板中传播的Lamb波。对Lamb波进行数据处理发现,随着三点弯曲实验产生的基体裂纹个数增加,Lamb波的幅值和频谱峰值线性减少。通过和传统压电传感器比较表明,相移光纤光栅传感器测得的Lamb波信号随复合材料基体裂纹数的增加其幅值具有更高的下降速率,表明相移光纤光栅传感器更适合于复合材料基体裂纹的超声探伤。研究表明,新开发的传感系统能够探测到中心频率为300 kHz的微弱超声信号,并能够对碳纤维增强树脂复合材料板中微小基体裂纹个数进行精确评估。      

Influence of artificial pre-stressing during curing of CFRP laminates on interfibre transverse cracking

In this paper results are shown for a cross-ply laminate where the internal residual stresses in the 90° plies were influenced by mechanically pre-stressing the 0° plies during the curing process. After curing and cooling to room temperature the mechanical pre-stresses were released. The 90° plies were now under compressive stresses. This had the effect that under tensile loading the development of transverse cracks was delayed and shifted to higher strain and load values.     

How isotropic are quasi-isotropic laminates

The concept of quasi-isotropic laminates is very well documented in literature. Essentially, the laminate consists of laminae with fibers at equal angular spacing. The theoretical analysis of these laminates, based on the laminate theory, suggests that the elastic properties of the laminate will be isotropic. It is obvious that the theory makes some simplifying assumptions and hence the question remains that if this laminate is not really isotropic then how much anisotropic is it? Presented here is the experimental determination of the elastic modulus of a quasi-isotropic laminate [0/45/−45/90]_S by tensile mechanical testing and corroborated by a newly developed automated ultrasonic Lamb wave measurement. The Lamb wave velocity measurement in frequency domain is used to estimate the in-plane elastic constants: elastic modulus and the Poisson's ratio, non-destructively. The ultrasonic method provides a non-invasive and non-damaging method for the measurement.