拉压加载下纤维增强铝合金层板疲劳裂纹扩展的压载荷效应与预测模型

基于增量塑性损伤理论与纤维增强金属层板疲劳裂纹扩展唯象方法, 推导出在拉-压循环加载下, 纤维增强金属层板疲劳裂纹扩展速率预测模型。并通过玻璃纤维增强铝合金层板在应力比R=-1,-2的疲劳裂纹扩展实验对预测模型进行验证。结果表明, 纤维增强铝合金层板疲劳裂纹扩展的压载荷效应分为两种情况: 在有效循环应力比R_C>0时, 表现为压载荷对铝合金层所承受残余拉应力的抵消作用; 当R_C<0时, 表现为压载荷抵消残余拉应力后, 对纤维增强铝合金层板金属层的塑性损伤, 对疲劳裂纹扩展存在促进作用。纤维铝合金层板疲劳裂纹扩展的压载荷效应不可忽略, 本文中得出的在拉-压循环加载下疲劳裂纹扩展速率预测模型与实验结果符合较好。     

Cumulative fatigue damage of stress below the fatigue limit in weldment steel under block loading

To investigate the cumulative fatigue damage below the fatigue limit of multipass weldment martensitic stainless steel, and to clarify the effect of cycle ratios and high‐stress level in the statement, fatigue tests were conducted under constant and combined high‐ and low‐stress amplitude relative to stress above and below the fatigue limit. The outcomes indicate that neither modified Miner's nor Haibach's approach provided accurate evaluation under repeated two‐step amplitude loading. Moreover, effect of cycle ratios has been determined. Additionally, the cumulative fatigue damage saturated model is established and validated. Cumulative fatigue damage contributed by low‐stress below the fatigue limit in high stress of 700 MPa is higher than that with 650 MPa at identical conditions (fatigue limit 575 MPa). Thus, high stress affects fatigue damage behaviour below the fatigue limit. A new predicted approach has been proposed based on Corten‐Dolan law, whose accuracy and applicability have been proven.     

三维正交机织复合材料低周弯曲疲劳力学性能有限元模拟

为了深入理解三维正交机织复合材料（3DOWC）疲劳性能,改进材料抗疲劳设计,结合三维正交机织复合材料试样经纱方向准静态三点弯曲及60%应力水平下的三点弯曲疲劳实验与ABAQUS有限元软件,构建了全尺寸三维实体模型,研究了三维正交机织复合材料在低周循环载荷下的弯曲疲劳性能,经分析得到循环加载下模型应力分布情况和疲劳损伤形态。结果表明：经纱为材料最重要的承载部件,中间加载区域为材料应力集中区,损伤主要位于应力集中区的Z纱通道处的经纱上,随着循环增加,逐渐在中心加载区域的上部和下部形成三角形损伤区域,该研究在复合材料设计与优化中具有指导意义。     

Fatigue strength and damage progression in a circular-hole-notched GRP composite under combined tension/torsion loading

Fatigue strength and failure processes in a hole-notched glass-fiber-reinforced plastic (GRP) material under combined tension/torsion cyclic loading have been investigated. Thin-walled tubular specimens were used in the experiment. The reinforcing fibers (plain-weave glass cloth) were aligned parallel to the longitudinal and circumferential axes of the specimen. The damage state at each biaxiality stress ratio (: the ratio of normal stress to shear stress) was observed macroscopically and microscopically.

The fatigue damage progression is dependent on the combined stress ratio. In the case of = 1/0, damage spreads radically from the hole, but covers an area of only π/4 on either side of the circumferential axis. Damaged areas are symmetrical and opposite each other. When = 0/1, damage progresses radially along both longitudinal and circumferential axes. These areas of damage progression are called ‘fatigue bands’. Macro- and microscopical observations reveal that the damage state under combined loading has mixed features from the damage states at = 1/0 and = 0/1.     

On the notch sensitivity of flax fibre metal laminates under static and fatigue loading

Damage progression and failure characteristics of open‐hole flax fibre aluminium laminate (flax‐FML) specimens subjected to quasi‐static tensile or tension‐tension fatigue loading were experimentally investigated. Notched and unnotched flax‐FML composites exhibited brittle fracture with little or no fibre pull‐out and minimal delamination at the aluminium/adhesive interface. The flax‐FMLs were tested to failure under tension‐tension fatigue loading conditions (R ratio of 0.1; frequency of 10 Hz; applied fatigue stresses ranging between 30% and 80% of the respective ultimate tensile strength values). The fatigue cycles to failure decreased with the increase in the applied fatigue stress and hole diameter. A phenomenological modelling technique was developed to evaluate the fatigue life of an open‐hole flax‐FML composite. Fatigue tests on specimens subjected to a maximum load equivalent to 35% of the respective tensile failure strength were interrupted at around 85% of the corresponding fatigue life. The accumulated fatigue damage in these specimens was characterised using X‐ray computed tomography. For benchmarking purposes, the fatigue performance and related damage progression in the flax‐FML composite were compared with those of the glass‐FMLs.     

Fatigue behaviour and life prediction of fibre reinforced metal laminates under constant and variable amplitude loading

ABSTRACT Fatigue crack growth of fibre reinforced metal laminates (FRMLs) under constant and variable amplitude loading was studied through analysis and experiments. The distribution of the bridging stress along the crackline in centre‐cracked tension (CCT) specimen of FRMLs was modelled numerically, and the main factors affecting the bridging stress were identified. A test method for determining the delamination growth rates in a modified double cracked lap shear (DCLS) specimen was presented. Two models, one being fatigue‐mechanism‐based and the other phenomenological, were developed for predicting the fatigue life under constant amplitude loading. The fatigue behaviour, including crack growth and delamination growth, of glass fibre reinforced aluminium laminates (GLARE) under constant amplitude loading following a single overload was investigated experimentally, and the mechanisms for the effect of a single overload on the crack growth rates and the delamination growth rates were identified. An equivalent closure model for predicting crack‐growth in FRMLs under variable amplitude loading and spectrum loading was presented. All the models presented in this paper were verified by applying to GLARE under constant amplitude loading and Mini‐transport aircraft wing structures (TWIST) load sequence. The predicted crack growth rates are in good agreement with test results.     

Impact and subsequent fatigue damage growth in carbon fibre laminates

The influence of the ply stacking sequence on the impact resistance and subsequent O-tension fatigue performance of carbon fibre laminates has been investigated. Drop-weight impact tests were conducted on a range of 16 ply carbon fibre laminates with either all non-woven plies or mixtures of woven and non-woven plies. Damaged coupons were tested in O-tension fatigue for up to 10⁶ cycles, scanned using an ultrasonic probe and then loaded in tension until failure.The impact resistance and subsequent fatigue performance have been found to be sensitive to the ply stacking sequence. The non-woven composites showed a marked sensitivity to impact loading, but increases in residual static strength were noted after cycling. The inclusion of a woven fabric served to improve the impact resistance of the laminates. Fatigue cycling resulted in considerably improved residual static strengths; by 10⁶ cycles any effect of the impact damage had been removed.     

Effect of carbon fibres on the static and fatigue mechanical properties of fibre metal laminates

It is crucial to understand the characteristic fatigue crack initiation and its growth mechanisms, as well as the relationship between the mechanical properties and the fatigue damage evolution in fibre metal laminates (FMLs). Two types of FML were studied in this work: a polyacrylonitrile‐based carbon fibre epoxy matrix composite sandwiched by Ti‐6Al‐4V (Ti‐alloy) sheets (IMS60‐Ti) and a pitch‐based carbon fibre epoxy matrix composite sandwiched by Ti‐alloy sheets (K13D‐Ti). The static and fatigue mechanical properties of IMS60‐Ti and K13D‐Ti were investigated. The increased failure strain of the FML was greater than that of carbon fibre‐reinforced polymer (CFRP) matrix composites. The fatigue life of IMS60‐Ti was much longer than that of K13D‐Ti. The fatigue damage process in IMS60‐Ti was related to the fatigue creep behaviour of the Ti‐alloy face sheet and mode II cracking at the CFRP/Ti‐alloy interface, and the damage in K13D‐Ti was related to the K13D CFRP laminate.     

History influence exponent in cumulative fatigue damage determined using two-step loading experiments

ABSTRACT The only material parameter, which appears in quadratic phenomenological hypothesis of cumulative fatigue damage, is the history influence exponent ϑ reflecting the material sensitivity to loading sequence and loading level interactions. Methods of its determination on the basis of two-step loading experiments are presented. One method is based on the least-squares method using linearizing transformation, other two ones are based on concept of individual fatigue life curves and statistical concept of inexact structural model. Parameter ϑ has been evaluated in 24 cases representing various materials and different test conditions. Possibility of existence of a common ϑ value holding for all materials is discussed. Such a value does not follow from analysed experimental data. However, ϑ = 0.5 is recommended for improving the reliability of engineering fatigue life estimates in case when required experimental material data are not available.     

Response of notched carbon/PEEK and carbon/epoxy laminates subjected to tension fatigue loading

In this study a comparison is made between the tensile static and fatigue behaviours of quasi-isotropic carbon/PEEK and carbon/epoxy notched laminates, selected as separate representatives of both tough and brittle matrix composites. Damage progression was monitored by various non-destructive (ultrasonic scanning and x-radiography) and destructive (deply and microscopic examinations) techniques, and by continuously measuring the change in stiffness, in order to identify the effect of damage on mechanical properties.
The experimental observations indicated that fatigue damage in carbon/epoxy laminates consists of a combination of matrix cracks, longitudinal splitting and delaminations which attenuate the stress concentration and suppress fibre fracture at the notch; as a consequence, fatigue failure can be reached only after very high numbers of cycles while tensile residual strengths continuously increase over the range of lives investigated (10³–10⁶ cycles). Due to the superior matrix toughness and the high fibre-matrix adhesion, the nature of fatigue damage in carbon/PEEK laminates strongly depends on the stress level. At high stresses the absence of early splitting and delaminations promotes the propagation of fibre fracture therefore resulting in poor fatigue performances and significant strength reductions; while at low stress levels damage modes are matrix controlled and this again translates into very long fatigue lives. These results indicate a strong influence of the major damage mechanisms typical of the two material systems on the behaviour of the laminates, with the nature, more than the amount, of damage appearing as the controlling parameter of the material response up to failure.     

Fatigue in fibre metal laminates: The interplay between fatigue in metals and fatigue in composites

With the introduction of fibre metal laminates (FMLs) as a (fatigue) damage tolerant material concept in aeronautics, an interesting field emerged where fatigue damage interaction plays a dominant role. The hybrid concept effectively demands evaluating fatigue damage growth based on fracture phenomena typical for both metals and fibre‐reinforced composites that continuously interact with each other. This paper explains current understanding of the fatigue fracture phenomena in FMLs, and it demonstrates how this interaction limits the criticality of both the metallic and composite fracture phenomena. In addition, it explains how the laminated hybrid configuration can be further exploited scientifically to unravel the physics of the individual fatigue fracture phenomena.     

Damage behaviour of laminated composites during fatigue loading

This study deals with the modelling of damage evolution in the carbon/epoxy laminated composites under static and fatigue loading. A cumulative damage model is developed on the basis of damage evolution due to static and fatigue during cyclic loading. A continuum damage mechanics (CDM)‐based damage model coupling with the micromechanics has been utilized to predict the fatigue behaviour of laminate composites. A multicriterion approach has been introduced to predict the damage behaviour in the longitudinal, transverse, and shear direction at the ply scale. Extensive experimental results on T300/EPL1012 carbon/epoxy laminates are prepared to characterize under static and fatigue loading and to evaluate the proposed model in different conditions. The obtained results show that at the beginning of the cyclic loading, the damage grows suddenly and increases until final failure, which justifies the proposed method is able to predict the evolution of the damage due to static and fatigue loading separately during cyclic loading. The obtained results show that considering damage due to static loading leads to more accurate results, particularly in low‐cycle fatigue.     

Cumulative fatigue damage dynamic interference statistical model

After studying in depth the statistical characteristics of cumulative fatigue damage D(t) and its critical value D_c, a new dynamic interference statistical model for fatigue reliability analysis is presented in this paper. Because the non-linearity of fatigue damage accumulation has been taken into account, this model is able to predict the fatigue reliability for random spectrum loading. To verify the predicted results, two fatigue experiments were conducted in which the numbers of specimens were more than 100, using fighter spectrum loading (FALSTAFF spectrum) and constant-amplitude loading respectively. It is shown that the new model is reliable, practicable and better than existing models.     

平面编织复合材料层合板低速冲击后的拉伸性能

对两种不同铺层形式的平面编织复合材料层合板低速冲击后拉伸性能进行了实验研究,在此基础上建立了有限元损伤扩展仿真模拟。在所建立的有限元模型中,将低速冲击损伤等效为形状规则的软化夹杂,并针对两种铺层形式采用不同的损伤判据和模量衰减准则。研究结果表明:该有限元模拟结果与实验结果符合,说明该模型能够准确地预测低速冲击后平面编织复合材料层合板的损伤扩展规律和剩余拉伸强度;不同铺层形式的平面编织复合材料层合板在低速冲击后拉伸的损伤扩展规律不同;它们的冲击后拉伸强度降均>50%,在复合材料结构设计中应该受到重视。      

A generalized damage model for woven ply laminates under static and fatigue loading conditions

A generalized non-linear cumulative damage model for woven ply laminates subjected to static and fatigue loading is developed in this paper. The damage, consisting of small cracks running parallel to the fibers, leads to a loss of stiffness in the warp, weft and shear directions. The model presented here describes the evolution of the damage up to failure of the first ply. By replacing the woven ply by two stacked unidirectional plies corresponding to the warp and weft thicknesses, this general model is extended to cover a broad range of plies, from quasi-unidirectional to balanced woven plies. A continuum damage approach (CDM) is then used to define the behaviour of the two virtual unidirectional plies under static and fatigue loading conditions. The model is applied here to an unbalanced woven ply with glass reinforcement and the results of the simulations are compared with experimental data.     

Fatigue damage of medium carbon steel under sequential application of axial and torsional loading

Fatigue tests were conducted on S45C steel under fully reversed strain control conditions with axial/torsional ( at ) and torsional/axial ( ta ) loading sequences. The linear damage value (n₁/N₁+n₂/N₂) was found to depend on the sequence of loading mode ( at or ta ), sequence of strain amplitude (low/high or high/low) and life fraction spent in the first loading. In general, at loading yields larger damage values than ta loading and the low–high sequence of equivalent strain leads to larger damage values than the high–low sequence. The material exhibits cyclic softening under axial cyclic strain. Cyclic hardening occurs in the torsion part of ta loading, which elevates the axial stress in the subsequent loading, causing more damage than in pure axial fatigue at the same strain amplitude. Fatigue life is predicted based on the linear damage rule, the double linear damage rule, the damage curve approach and the plastic work model of Morrow. Results show that overly conservative lives are obtained by these models for at loading while overestimation of life is more likely for ta loading. A modified damage curve method is proposed to account for the load sequence effect, for which predicted lives are found to lie in the factor‐2 scatter band from experimental lives.     

碳纤维机织物增强热塑性树脂复合材料热冲压叠层模型

针对碳纤维增强热塑性树脂复合材料(CFRTP)在热冲压成型过程中涉及到大变形、各向异性和多场耦合的现象,为了表征CFRTP在成型中的力学特征,基于有限元方法与连续介质力学理论提出了一种热塑性树脂基体与碳纤维机织物的叠层模型。与单独采用碳纤维机织物超弹性本构模型预测CFRTP成型性能的方法相比,提出的叠层模型能够表征成型温度、压边力和纤维取向对CFRTP成型缺陷的影响,并能优化热冲压成型工艺参数。这一叠层模型具有简单实用和材料参数容易确定的优点,为碳纤维机织物增强热塑性树脂复合材料成型的数值模拟和成型工艺优化奠定了理论基础。     

Quadratic damage rule in random loading case

The simple mathematical structure of the quadratic damage rule (QDR) enables mathematical expression of the failure condition in the case of random loading. Random loading after modified rainflow analysis is considered as a random marked point process. Moments of the damage distribution can be expressed by use of ensemble averages. A condition for validity of the first damage moment solution is formulated. The QDR damage first moment solution involves failure predictions for both stationary and non‐stationary loadings. In these cases, final fracture conditions suitable for practical use are derived. QDR predicts fatigue lives that are always shorter than the linear damage rule (LDR) in the case of stationary loading with short interval of statistical dependence of random variables. QDR appears to be a suitable additional engineering tool for random loading fatigue life predictions considering loading sequence and loading level interactions.     

Frequency effects on the fatigue behaviour on carbon fibre reinforced polymer laminates

Test frequency exerts a considerable influence on dynamic mechanical behaviour of carbon fibre reinforced materials. In this study the effect of test frequency on the fatigue behaviour of the T300/914C system, a carbon fibre/epoxy matrix composite, is examined. Tension-tension fatigue tests were carried out at various stress levels and at three test frequencies (5, 10 and 20 Hz) for three specimen orientations (unidirectional, (0)₈, crossply (0°/90°)_4s and angleply (±45°c)_4s). A number of dynamic mechanical properties were monitored throughout specimen lifetimes and subsequently analysed — stress/life behaviour, maximum strain, normalised fatigue modulus, dynamic loss modulus, damping factor and specimen temperature. Frequency effects are found to profoundly influence the fatigue behaviour of both crossply and angle ply specimens. Angleply specimen fatigue response exhibits a strong dependence on test frequency, a fact that is reflected in the dynamic mechanical property responses monitored. The data obtained for unidirectional specimens is inconclusive due to the large degree of fatigue scatter observed.     

Fatigue crack growth in fibre metal laminates under selective variable-amplitude loading

To extend the predictive capability of existing crack growth models for fibre metal laminates under constant amplitude fatigue loading to variable-amplitude loading, further research on variable-amplitude fatigue mechanisms in fibre metal laminates is necessary. In response to this need, an experimental study into the effects of multiple overloads, underloads and various block-loading sequences on crack growth in the fibre metal laminate Glare was investigated. Crack growth retardation effects were observed in the tests; however, the magnitude of these effects was lower than seen in monolithic aluminium because of fibre bridging. As a result, predictions of the observed behaviour were attempted using an existing constant-amplitude fatigue crack growth model for Glare in combination with a linear damage accumulation law.