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.     

Probabilistic anisomorphic constant fatigue life diagram approach for prediction of P–S–N curves for woven carbon/epoxy laminates at any stress ratio

A general engineering methodology to construct a family of anisomorphic constant fatigue life (CFL) diagrams with probability of failure as the parameter that allows efficiently predicting P–S–N curves at any stress ratios is developed and validated for a plain weave fabric carbon/epoxy laminate. Constant amplitude fatigue tests are first performed to obtain statistical samples of fatigue life at different stress levels and stress ratios, respectively. Static tensile and compressive strength data are also collected. The Kolmogorov–Smirnov and Anderson–Darling goodness-of-fit tests suggest that both two-parameter lognormal and Weibull distributions are acceptable as the distributions for the static strength and fatigue life data, respectively, at the significance level of 5%. Then, we attempt to develop a methodology for efficient construction of the anisomorphic CFL diagrams for different constant values of probability of failure. It requires the P–S–N curves for any percentile points of the distribution for the critical stress ratio. To come up with this requirement, a probabilistic scaling law is formulated. It takes account of the probability-of-failure dependence of the critical stress ratio and the stress-ratio dependence of the P–S–N curve for the critical stress ratio. Finally, the anisomorphic CFL diagrams for different constant values of probability of failure are predicted using the proposed methodology, and they are shown to be in good agreement with the experimental results. It is also demonstrated that the P–S–N curves can efficiently and accurately be predicted for the woven CFRP laminate at any stress ratios using the proposed probabilistic anisomorphic CFL diagram approach.     

A general method for predicting temperature-dependent anisomorphic constant fatigue life diagram for a woven fabric carbon/epoxy laminate

The anisomorphic constant fatigue life (CFL) diagram approach to prediction of fatigue lives of composites, which was developed in an earlier study, is developed further into a more general methodology that can deal with the mean stress sensitivity in fatigue of composites at different temperatures. The temperature dependence of the anisomorphic CFL diagram for a given composite is characterized by the temperature dependence of the static strengths in tension and compression and of the reference S–N relationship for a critical stress ratio. The temperature dependence of the static strengths in tension and compression is first formulated to describe the temperature dependence of the critical stress ratio. To predict the reference S–N relationships at different temperatures, the change in the value of critical stress ratio with temperature as well as the effect of temperature on fatigue should be taken into account. To this end, a new and efficient engineering method is developed which is based on a grand master S–N curve built by means of a modified fatigue strength ratio and a life-temperature parameter of the Larson–Miller type. The generalized anisomorphic CFL diagram approach developed in this study succeeds in efficiently and adequately predicting the CFL diagrams for a woven fabric carbon/epoxy quasi-isotropic laminate at different temperatures and thus the mean stress dependence of the S–N relationships of the laminate at different temperatures.     

Anisomorphic constant fatigue life diagrams for a woven fabric carbon/epoxy laminate at different temperatures

The effect of temperature on the constant fatigue life (CFL) diagram for a woven fabric carbon/epoxy quasi-isotropic laminate has been examined. Constant amplitude fatigue tests are first performed at different stress ratios on coupon specimens at room temperature (RT), 100 and 150 °C, respectively. The experimental results show that the CFL diagram for the woven CFRP laminate, which is plotted in the plane of mean and alternating stresses, becomes asymmetric about the alternating stress axis, regardless of test temperature, and shrinks as temperature increases. The CFL envelopes for given constant values of life are nonlinear over the range of fatigue cycles, regardless of test temperature, and they take peaks approximately at a particular stress ratio “critical stress ratio” that is given by the ratio of compressive strength to tensile strength. Then, the experimental CFL diagram for each temperature is compared with prediction using the anisomorphic CFL diagram approach that allows constructing the asymmetric and nonlinear CFL diagram for a given composite on the basis of the static strengths in tension and compression and the reference S-N relationship for the critical stress ratio. It is demonstrated that the anisomorphic CFL diagram approach can successfully be employed for predicting the CFL diagram and thus for predicting the S-N relationships for the woven CFRP laminate at any stress ratios, regardless of test temperature.     

A unified fatigue life model based on energy method

A new unified fatigue life model based on the energy method is developed for unidirectional polymer composite laminates subjected to constant amplitude, tension–tension or compression–compression fatigue loading. This new fatigue model is based on static failure criterion presented by Sandhu and substantially is normalized to static strength in fiber, matrix and shear directions. The proposed model is capable of predicting fatigue life of unidirectional composite laminates over the range of positive stress ratios in various fiber orientation angles. By using this new model all data points obtained from various stress ratios and fiber orientation angles are collapsed into a single curve.

The new fatigue model is verified by applying it to different experimental data provided by other researchers. The obtained results by the new fatigue model are in good agreements with the experimental data of carbon/epoxy and E-glass/epoxy of unidirectional plies.     

A three-segment anisomorphic constant life diagram for the fatigue of symmetric angle-ply carbon/epoxy laminates at room temperature

The anisomorphic constant fatigue life (CFL) diagram approach that was developed in an earlier study is further tested for applicability to the matrix-dominated fatigue failure in symmetric angle-ply carbon/epoxy laminates. An extension of the CFL diagram approach is also attempted to improve the accuracy of fatigue life prediction. The original anisomorphic CFL diagram approach can be used for approximately predicting the CFL diagrams for the [±30]_3S and [±45]_3S laminates, while it fails to accurately predict the CFL diagram for the [±60]_3S laminate due to its significant local distortion. For accommodating the anisomorphic CFL diagram approach to the local distortion in CFL curves due to a significant change in mean stress sensitivity in fatigue, a transitional segment is inserted between the tension–tension and compression–compression dominated segments. It is demonstrated that the three-segment anisomorphic CFL diagram approach allows improved predictions of the CFL diagrams and S–N relationships for the angle-ply laminates.     

Nonlinear constant fatigue life diagrams for carbon/epoxy laminates at room temperature

Exploration of a full shape of constant fatigue life (CFL) diagram and development of an efficient CFL diagram-based fatigue life prediction method are attempted for multidirectional CFRP laminates. On three kinds of CFRP laminates of [45/90/−45/0]_2s, [0/60/−60]_2s and [0/90]_3s lay-ups, tension–tension, tension–compression and compression–compression fatigue tests are performed at room temperature for two different stress ratios each. Experimental results clearly show that a stress ratio has a significant influence on the fatigue behavior of those CFRP laminates, and the CFL diagrams delineated using alternating stress and mean stress become asymmetric about the alternating stress axis. The alternating stress component of fatigue load for a given constant value of fatigue life turns maximum in the case of fatigue loading at a critical stress ratio that is nearly equal to the ratio of compressive strength to the tensile one. The shape of CFL diagrams progressively changes from a straight line to a nonlinear curve as a given constant value of fatigue life increases. A new and efficient method for accurately predicting an asymmetric nonlinear CFL diagram is then developed which is based on the static strengths in tension and compression and the reference S–N relationship fitted to the fatigue data for the critical stress ratio. The theoretical CFL diagram constructed following the proposed procedure agrees well with the experimental CFL diagram, regardless of the type of CFRP laminate. It is also demonstrated that the S–N relationships predicted using the proposed CFL diagram-based fatigue life prediction method adequately coincide with the experimental results for fatigue loading with a variety of different stress ratios in the range of fatigue life up to 10⁶ cycles.     

A comparative study of failure criteria in probabilistic fields and stochastic failure envelopes of composite materials

One of the major objectives of this paper is to offer a practical tool for materials design of unidirectional composite laminates under in-plane multiaxial load. Design-oriented failure criteria of composite materials are applied to construct the evaluation model of probabilistic safety based on the extended structural reliability theory. Typical failure criteria such as maximum stress, maximum strain and quadratic polynomial failure criteria are compared from the viewpoint of reliability-oriented materials design of composite materials. The new design diagram which shows the feasible region on in-plane strain space and corresponds to safety index or failure probability is also proposed. These stochastic failure envelope diagrams which are drawn in in-plane strain space enable one to evaluate the stochastic behavior of a composite laminate with any lamination angle under multi-axial stress or strain condition. Numerical analysis for a graphite/epoxy laminate of T300/5208 is shown for the comparative verification of failure criteria under the various combinations of multi-axial load conditions and lamination angles. The stochastic failure envelopes of T300/5208 were also described in in-plane strain space.     

基于宏微观分析的碳纤维增强高分子复合材料强度性能表征

微观力学强度理论(MMF)是一种新型的基于物理失效模式的复合材料强度理论。通过对碳纤维/树脂(UTS50/E51)复合材料单向层合板进行纵向、横向静载拉伸、压缩和弯曲试验, 得到层合板的基本力学性能和宏观强度指标。建立了碳纤维增强树脂基复合材料微观力学模型, 获取树脂基体和纤维不同位置的机械载荷应力放大系数和热载荷应力放大系数。结合获取的应力放大系数及试验测得的单向层合板宏观强度, 计算出层合板组分的MMF强度特征值。绘制了基于MMF强度理论的层合板破坏包络线, 并与Tsai-Wu失效准则预测结果进行对比。实现了对UTS50/E51层合板MMF强度特征值的表征。     

Flexural properties of z-pinned laminates

This paper examines the effect of pinning on the flexural properties, fatigue life and failure mechanisms of carbon/epoxy laminates. Five-harness satin weave carbon/epoxy laminates were reinforced in the through-thickness direction with different volume fractions and sizes of fibrous composite pins. Microscopic examination of the laminates before flexural testing revealed that the pins caused considerable damage to the microstructure, including out-of-plane crimping, in-plane distortion and breakage of the fibres and the formation of resin-rich zones around each pin. The pins also caused swelling of the laminate that reduced the fibre volume content. Despite the damage, the pins did not affect the flexural modulus of the laminate. However, increasing the volume content or diameter of the pins caused a steady decline in the flexural strength and fatigue life, which appear to be governed by fiber rupture on the tensile side of the laminate. Property changes are discussed in terms of transitions in the dominant failure mechanisms due to the presence of pins.     

A New Static and Fatigue Compression Test Method for Composites

Abstract: A new test method to determine the compressive properties of composite materials under both static and fatigue loading was developed. The novel fixture is based on the concept of transmitting the load by a fixed ratio of end‐to‐shear loading. The end‐to‐shear load ratio is kept fixed during the test through a mechanical mechanism, which automatically maintains the gripping pressure. The combined loading method has proven very efficient in static loading and is used in the new fixture which is specially designed for fatigue testing. Optimum gripping (shear loading) and alignment of the test coupon are achieved throughout the fatigue life. The fatigue strength obtained is more reliable because bending of the specimen due to poor gripping and alignment is minimised. The application of the new fixture to static and fatigue compression is demonstrated by using unidirectional carbon/epoxy and glass/polyester composite systems. Repeatable results and acceptable failure modes are obtained under both static and fatigue loading.     

A strategy for improving mechanical properties of a fiber reinforced epoxy composite using functionalized carbon nanotubes

Carbon fiber reinforced epoxy composite laminates are studied for improvements in quasi static strength and stiffness and tension-tension fatigue cycling at stress-ratio (R-ratio) = +0.1 through strategically incorporating amine functionalized single wall carbon nanotubes (a-SWCNTs) at the fiber/fabric-matrix interfaces over the laminate cross-section. In a comparison to composite laminate material without carbon nanotube reinforcements there are modest improvements in the mechanical properties of strength and stiffness; but, a potentially significant increase is demonstrated for the long-term fatigue life of these functionalized nanotube reinforced composite materials. These results are compared with previous research on the cyclic life of this carbon fiber epoxy composite laminate system reinforced similarly with side wall fluorine functionalized industrial grade carbon nanotubes. Optical and scanning electron microscopy and Raman spectrometry are used to confirm the effectiveness of this strategy for the improvements in strength, stiffness and fatigue life of composite laminate materials using functionalized carbon nanotubes.     

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.     

Stiffness and fracture analysis of laminated composites with off-axis ply matrix cracking

Matrix cracks parallel to the fibres in the off-axis plies is the first intralaminar damage mode observed in laminated composites subjected to static or fatigue in-plane tensile loading. They reduce laminate stiffness and strength and trigger development of other damage modes, such as delaminations. This paper is concerned with theoretical modelling of unbalanced symmetric laminates with off-axis ply cracks. Closed-form analytical expressions are derived for Mode I, Mode II and the total strain energy release rates associated with off-axis ply cracking in [0/θ]_s laminates. Stiffness reduction due to matrix cracking is also predicted analytically using the Equivalent Constraint Model (ECM) of the damaged laminate. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy and carbon/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

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.     

Investigation of fatigue crack growth rate in CARALL,ARALL and GLARE

Fibre metal laminates (FMLs) are being used to manufacture many structural components in aerospace industry because of their very high strength to weight ratios, yet the exact model for estimating fatigue crack propagation in FMLs cannot be developed because of many variable parameters affecting it. In this research, tensile strength, fatigue life and fracture toughness values of 2/1 configuration carbon reinforced aluminium laminate (CARALL), aramid reinforced aluminium laminate and glass laminate aluminium reinforced epoxy specimens have been investigated. Mechanical, chemical and electrochemical surface treatments were applied to AA 1050 face sheets to improve the adhesive properties of the laminates. The specimens were prepared using vacuum assisted resin transfer moulding technique and were cut to desired shapes. Fatigue tests were conducted on centre notched specimens according to ASTM Standard E399. Real time material data and properties of adhesive were used in definition of numerical simulation model to obtain the values of stress intensity factor at different crack lengths. It was observed that CARALL shows very superior tensile and fatigue strength because of stress distribution during failure. Numerical simulation model developed in this research accurately predicts fracture toughness of aramid reinforced aluminium laminate, CARALL and glass laminate aluminium reinforced epoxy with less than 2% error. An empirical analytical model using experimental data obtained during research was developed which accurately predicts the trend of FMLs fatigue life.     

Random fatigue life prediction of carbon fibre-reinforced composite laminate based on hybrid time-frequency domain method

To evaluate fatigue life of composite laminate with hole under random loading, a random fatigue life prediction model is established by hybrid time-frequency domain method in this paper. Firstly, dynamic response of composite laminate is obtained from FE model in frequency domain. Secondly, root mean square of stress of six stress components of critical damage point in frequency domain are transferred to stresses in time domain. At last, 3D Tsai–Hill static failure criterion is adopted to convert the multiaxial stress into the uniaxial equivalent stress. Fatigue life is predicted by equivalent stress fatigue life code. The method is validated with the random vibration fatigue test of carbon fibre-reinforced composite laminate. Numerical results are compared with random fatigue experiments which show good agreement with numerical results.     

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。