Statistical prediction of fatigue failure of fibre reinforced composite materials

A statistical approach is proposed to evaluate the residual strength and life of unidirectional and angle-ply composite laminates subjected to in-plane tensile cyclic stresses. The method is based on the extension of previous static failure criteria describing independently the fibre failure and matrix failure modes, combined with the statistical nature of fatigue failure of fibre-reinforced composites. The static and fatigue strengths of composite laminates at any off-axis angle are evaluated using the fatigue failure functions for the three principal failure modes, which are determined from the fatigue behaviour of unidirectional composites subjected to longitudinal and transverse tension as well as in-plane shear stresses. The evaluations of the fatigue strength of unidirectional E-glass/epoxy laminates under off-axis fatigue loading and angle-ply S-glass/epoxy laminates under in-plane fatigue loading show good agreement between theoretical predictions and experimental results.     

Fatigue life prediction of composite materials using polynomial classifiers and recurrent neural networks

Due to their massively parallel structure and ability to learn by example, artificial neural networks can deal with nonlinear problems for which an accurate analytical solution is difficult to obtain. These networks have been used in modeling the mechanical behavior of fiber-reinforced composite materials. Although promising results were obtained using such networks, more investigation on the appropriate choice of their structure and their performance in the presence of limited and noisy data is needed. On the other hand, polynomials networks have been known to have excellent properties as classifiers and are universal approximators to the optimal Bayes classifier. Not being dependant on various user defined parameters, having less computational requirements makes their use over other methods, such as neural networks, an advantage.

In this work, the fatigue behavior of unidirectional glass fiber/epoxy composite laminae under tension–tension and tension–compression loading is predicted using feedforward and recurrent neural networks. These predictions are compared to those obtained using polynomial classifiers. Experimental data obtained for fiber orientation angles of 0°, 19°, 45°, 71° and 90° under stress ratios of 0.5, 0 and –1 is used.

It is shown that, even when a small number of experimental data points is used to train both polynomial classifiers and neural networks, the predictions obtained are comparable to other current fatigue life-prediction methods. Also, polynomial classifiers are shown to provide accurate modeling between the input parameters (maximum stress, R-ratio, fiber orientation angle) and the number of cycles to failure when compared to neural networks.     

A Stiffness Degradation Based Fatigue Damage Model for FRP Composites of (0/<Emphasis Type="BoldItalic">θ</Emphasis>) Laminate Systems

The present study develops a stiffness reduction—based model to characterize fatigue damage in unidirectional 0˚ and θ° plies and (0/θ) laminates of fiber-reinforced polymer (FRP) composites. The proposed damage model was constructed based on (i) cracking mechanism and damage progress in matrix (Region I), matrix-fiber interface (Region II) and fiber (Region III) and (ii) corresponding stiffness reduction of unidirectional composite laminates as the number of cycles progresses. The proposed model enabled damage assessment of FRP (0/θ) composite laminates by integrating the fatigue damage values of 0˚ and θ° plies. A weighting factor η was introduced to partition the efficiency of load carrying plies of 0° and θ° in the (0/θ) composite lamina. The fatigue damage curves of unidirectional FRP composite samples with off-axis angles of 0˚, 30˚, 45˚, and 90˚ and composite laminate systems of (0˚/30˚), (0˚/45˚) and (0˚/90˚) predicted based on the proposed damage model were found in good agreement with experimental data reported at various cyclic stress levels and stress ratios in the literature.     

Damage Assessment of CFRP [90/±45/0] Composite Laminates over Fatigue Cycles

The present paper develops a stiffness-based model to characterize the progressive fatigue damage in quasi-isotropic carbon fiber reinforced polymer (CFRP) [90/±45/0] composite laminates with various stacking sequences. The damage model is constructed based on (i) cracking mechanism and damage progress in matrix (Region I), matrix-fiber interface (Region II) and fiber (Region III) and (ii) corresponding stiffness reduction of unidirectional plies of 90°, 0° and angle-ply laminates of ±45° as the number of cycles progresses. The proposed model accumulates damages of constituent plies constructing [90/±45/0] laminates by means of weighting factor η ₉₀, η ₀ and η ₄₅. These weighting factors were defined based on the damage progress over fatigue cycles within the plies 90°, 0° and ±45° of the composite laminates. Damage model has been verified using CFRP [90/±45/0] laminates samples made of graphite/epoxy 3501-6/AS4. Experimental fatigue damage data of [90/±45/0] composite laminates have fell between the predicted damage curves of 0°, 90° plies and ±45°, 0/±45° laminates over life cycles at various stress levels. Predicted damage results for CFRP [90/±45/0] laminates showed good agreement with experimental data. Effect of stacking sequence on the model of stiffness reduction has been assessed and it showed that proposed fatigue damage model successfully recognizes the changes in mechanism of fatigue damage development in quasi-isotropic composite laminates.     

基于纤维束/环氧树脂复合材料试验的单向层合板横向拉伸强度预测方法

实验研究表明,纤维束/环氧树脂复合材料试件的横向拉伸强度与工程上常用的单向层合板横向拉伸强度在趋势上具有很好的相关性,但是数值上存在一定差距。本文使用两种碳纤维和两种环氧树脂制备了三种纤维束/环氧树脂复合材料和单向层合板,并分别测量了纤维束/环氧树脂复合材料和单向层合板的横向拉伸强度,以及环氧基体的拉伸强度。在实验基础上,应用Griffith断裂强度理论建立了纤维束/环氧树脂复合材料和单向层合板的横向拉伸强度的关系模型,通过两种复合材料实验的结果拟合了该模型中的参数。利用第三种复合材料实验进行校验,发现该模型预测的单向层合板横向拉伸强度与实测强度之间达到很好的一致性,相对偏差为9%。采用本文提出的方法,可以用较为简单的纤维束/环氧树脂复合材料和环氧基体拉伸试验预测单向层合板的横向拉伸强度。     

E-GFRP单向板疲劳性能及失效机制的实验研究

对铺设角分别为0°、30°、45°、90°的玻璃纤维增强不饱和聚酯树脂单向板进行拉-拉疲劳试验, 得到不同铺设角玻璃纤维增强不饱和聚酯树脂(GFRP)单向板疲劳数据, 通过分析不同铺设角单向板中值S-N曲线及正则应力-寿命曲线特点, 得到了单向板疲劳性能随铺设角变化的关系。并且基于对不同铺设角单向板疲劳断口的宏观及微观形貌的分析, 研究了铺设角对单向板的疲劳损伤机制、失效模式的影响。分析表明, 对应于不同的铺设角, 单向板存在不同的失效机制, 从而导致不同形式的损伤模式。     

Fatigue life prediction of nanoparticle/fibrous polymeric composites based on the micromechanical and normalized stiffness degradation approaches

In this paper, a new model based on the micromechanical and normalized stiffness degradation approaches is established. It has been assumed that during the fatigue condition, only material properties of composites (fiber and matrix) were degraded and nanofillers remain intact under different states of stress. A normalized stiffness degradation model was proposed for laminated fibrous composites reinforced with nanoparticles to derive a novel model to predict the stiffness reduction. The developed model is capable of predicting the fatigue life of nanoparticle-filled fibrous composites based on the experimental data of fibrous composites without nanofillers. The new fatigue model is verified by applying it to different experimental data provided by different researchers. The obtained results by the new fatigue model are in very good agreement with the experimental data of nano-silica glass/epoxy composites under constant cyclic stress amplitude fatigue and also for silica/epoxy nanocomposites in various states of stress with negligible error.     

Fatigue life prediction of composite laminates by FEA simulation method

This paper is to simulate the fatigue damage evolution in composite laminates and predict fatigue life of the laminates with different lay-up sequences on the basis of the fatigue characteristics of longitudinal, transverse and in-plane shear directions by finite element analysis (FEA) method. In FEA model, considering the scatter of the material’s properties, each element was assigned with different material’s properties. The stress analysis was carried out in MSC Patran/Nastran, and a modified Hashin’s failure criterion was applied to predict the failure of the elements. A new stiffness degradation model was proposed and applied in the simulation and then a strength degradation model was deduced, which is coupled with the presented stiffness degradation model. The reduced or discounted elastic constants were determined based on the failure mechanism of the laminates and the restrictive conditions of orthotropic property. The fatigue behavior and fatigue life of six kinds of E-glass/epoxy composite laminates with different lay-up sequences were experimentally studied, and the S–N curves and stiffness degradation models in longitudinal, transverse and in-plane shear direction were obtained. These fatigue data were adopted in the simulation to simulate fatigue behavior and estimate life of the laminates. The simulation results, including the fatigue life predicted and the residual stiffness, were coincident with the experimental results well except for the quasi-isotropic laminate for the lack of consideration of the out-of-plane fatigue character in the simulation.     

A progressive damage simulation algorithm for GFRP composites under cyclic loading. Part II: FE implementation and model validation

The FE implementation of FADAS, a material constitutive model capable of simulating the mechanical behaviour of GFRP composites under variable amplitude multiaxial cyclic loading, was presented. The discretization of the problem domain by means of FE is necessary for predicting the damage progression in real structures, as failure initiates at the vicinity of a stress concentrator, causing stress redistribution and the gradual spread of damage until the global failure of the structure. The implementation of the stiffness and strength degradation models in the principal material directions of the unidirectional ply was thoroughly discussed. Details were also presented on the FE models developed, the computational effort needed and the definition of final failure considered. Numerical predictions were corroborated satisfactorily by experimental data from constant amplitude uniaxial fatigue of multidirectional glass/epoxy laminates under various stress ratios. The validation of predictions included fatigue strength, stiffness degradation and residual static strength after cyclic loading.     

Experimental and analytical study on fiber-kinking failure mode of laminated composites

Compressive behavior of composite materials has received significant attention in recent years. In the present work, a recently developed strain based fiber kinking model and stress based ones for unidirectional laminated composites are compared with experimental results. These models are implemented into a finite element code and the obtained results for glass/epoxy (Type C) ASNA 4197 unidirectional composites are presented and discussed in detail. Experimental investigations on compressive strength and kink band formation were also performed for several specimens with various dimensions and off-axis angles made of the same glass/epoxy prepreg composite material. A special compressive fixture was also fabricated in order to ensure that the specimens are in full contact with the loading machine elements and also to eliminate the potential bending moments.Comparison between the experimental and analytical results indicated that the proposed fiber kinking model and the developed code can be used to predict the compressive strength of laminated composites due to fiber kinking mode.     

Simulation of fatigue performance of cross-ply composite laminates

The fatigue life of cross-ply composite laminates was evaluated using a statistical model. A modified shear-lag analysis was applied to describe the cycle-number-dependent stiffness reduction and consequent stress redistribution processes in the laminates resulted from both progressive transverse matrix cracking in transverse plies and local delamination at tips of transverse cracks. From the strength degradation behaviour and the static strength distribution of 0° plies as well as the fatigue behaviour of 90° plies, the fatigue life of cross-ply laminates with various types of lay-up can be simulated from the model. Predictions of fatigue performance are compared with experimental data for [0/90₂] _s , [02/90₂] _s and [0₂/90₄] _s graphite/epoxy cross-ply laminates: good agreements are obtained.     

An investigation of the damage mechanisms and fatigue life diagrams of flax fiber-reinforced polymer laminates

In this paper we investigated the fatigue damage of a unidirectional flax-reinforced epoxy composite using infrared (IR) thermography. Two configurations of flax/epoxy composites layup were studied namely, [0]₁₆ unidirectional ply orientation and [±45]₁₆. The high cycle fatigue strength was determined using a thermographic criterion developed in a previous study. The fatigue limit obtained by the thermographic criterion was confirmed by the results obtained through conventional experimental methods (i.e., Stress level versus Number of cycles to failure). Furthermore, a model for predicting the fatigue life using the IR thermography was evaluated. The model was found to have a good predictive value for the fatigue life. In order to investigate the mechanism of damage initiation in flax/epoxy composites and the damage evolution, during each fatigue test we monitored the crack propagation for a stress level and at different damage stages, a direct correlation between the percentage of cracks and the mean strain was observed.     

Effect of fiber orientation on fracture toughness of laminated composite plates [0°/θ°]s

Fracture toughness of single edge notched fiber reinforced composite plates is investigated experimentally. Load–displacement curves for unidirectional carbon fiber/epoxy resin reinforced composite plates are obtained experimentally under tensile load. Fracture toughness is obtained by determining failure loads. For numerical study, ANSYS is used. Material properties of laminates are calculated with classical laminated plate theory and applied to the finite element model by using plane element. Stiffness matrix of laminates is determined and shell element is chosen for numerical solution. Critical stress intensity factors are calculated with Displacement Correlation Method under experimental failure load conditions.     

The mechanical characteristics of smart composite structures with embedded optical fiber sensors

In this study, the mechanical characteristics of composite laminates with embedded optical fiber sensors were evaluated to investigate the effect of embedded optical fiber on the mechanical properties of composite laminates under the static tensile and the low cycle fatigue load. Testing specimens were fabricated with glass fiber/epoxy composites with embedded optical fiber sensors to observe initiation and growth of damage in the specimens and laser signal behavior transmitted through the optical fiber visually and directly. By using this transparency of glass fiber/epoxy composites, the damage of sensors and associated laser signal behavior was observed. Under the static load, the embedded optical fibers do not have significant effect on the stiffness and the strength, while the embedded optical fibers show significant effect on the fatigue life of composite specimens. Especially, the embedded optical fiber sensors show the very low resistance to the fatigue load.     

层板复合材料的疲劳剩余寿命预报模型

应用可靠性分析的方法 ,导出了层板复合材料在疲劳载荷作用下的疲劳剩余寿命的预报模型。该模型已用典型层板复合材料在恒幅疲劳载荷作用下的实验数据进行了验证。实验结果表明 ,理论预测结果与实验值的接近程度是合理的     

Interfacial fatigue crack propagation in microscopic model composite using bifiber shear specimens

Interfacial fatigue crack growth behavior in GF/epoxy model composites was investigated using bifiber shear (BFS) specimens in a scanning electron microscope. The specimen is composed of two E-glass filaments with diameters of 23 and 40 μm, and bisphenol A type epoxy is impregnated between the filaments. The crack growth behavior under different stress ratios was investigated to clarify the fatigue crack growth mechanism. The change in the crack growth rate, da/dN, was not monotonic with crack length, suggesting a variation in the resistance to fatigue crack growth along a single filament. The resistance to fatigue crack growth of the interface is much smaller than that of composite laminates. The fatigue crack growth mechanism of the glass fiber/epoxy interface under different stress ratios is controlled by the maximum energy release rate, G_max, which is completely different from that of composite laminates.     

A progressive damage simulation algorithm for GFRP composites under cyclic loading. Part I: Material constitutive model

A life prediction algorithm and its implementation for a thick-shell finite element formulation for GFRP composites under constant or variable amplitude loading is introduced in this work. It is a distributed damage model in the sense that constitutive material response is defined in terms of meso-mechanics for the unidirectional ply. The algorithm modules for non-linear material behaviour, pseudo-static loading-unloading-reloading response, Constant Life Diagrams and strength and stiffness degradation due to cyclic loading were implemented on a robust and comprehensive experimental database for a unidirectional glass/epoxy ply. The model, based on property definition in the principal coordinate system of the constitutive ply, can be used, besides life prediction, to assess strength and stiffness of any multidirectional laminate after arbitrary, constant or variable amplitude multi-axial cyclic loading. Numerical predictions were corroborated satisfactorily by test data from constant amplitude fatigue of glass/epoxy laminates of various stacking sequences.     

考虑三维应力的复合材料层压板疲劳寿命分析

由于层间应力的存在,受面内载荷作用的复合材料层压板实际处于多轴应力状态。构建了由刚性元、弹簧元和二维板元构成的准三维有限元模型,结合单向板在典型应力状态下的疲劳试验结果和疲劳损伤模型,发展了一种考虑三维应力的、预测任意铺层多向层压板疲劳寿命的分析方法,包括应力分析、静力和疲劳累积损伤失效分析及材料性能退化3个主要部分,能够模拟面内和层间损伤产生、发展直至层压板整体破坏的完整过程,并得到疲劳寿命。对2种T300/QY8911多向铺层板进行了实际计算,寿命预测结果与试验结果吻合较好。      

碳纤维增强树脂基复合材料组分疲劳强度表征

对微观力学失效（Micro-mechanics of failure,MMF）理论的应用做了扩展,将其用于分析连续纤维增强树脂基（FRP）复合材料的三维复杂结构的疲劳强度。基于MMF理论,建立了连续FRP复合材料层合板疲劳强度表征方法。分别对碳纤维/树脂（UTS50/E51）复合材料单向层合板进行静载和疲劳试验,得到层合板的基本力学性能和宏观强度指标;对UTS50/E51层合板组分疲劳强度进行了表征,得到了纤维和树脂的拉伸、压缩MMF疲劳特征参量S-lgN曲线,为MMF方法应用于连续纤维增强复合材料层合板结构的疲劳强度分析提供了判断依据。使用建立的方法对UTS50/E51多向层合板的拉伸疲劳强度进行了分析,并将预测结果与试验结果进行对比。