复合材料层合板单钉双剪连接挤压强度的一种工程估算方法

将上限理论应用到复合材料层合板单钉双剪连接挤压强度分析中, 把连接结构的位移场划分为动态区域(层合板)和静态区域(紧固件), 并认为失效发生在位移可动场和不动场之间的钉孔边受挤压部分。由于受挤压孔孔边各层应力状态不一样, 受挤压孔边各层的失效区域和失效模式也各不相同。从宏观上研究复合材料层合板单钉连接孔边的失效区域和失效模式, 结合上限理论提出了一种估算复合材料单钉连接挤压强度的工程算法。通过与试验结果对比, 发现该方法能较好地预测出复合材料单钉双剪连接挤压强度。     

Strength prediction in CFRP woven laminate bolted double-lap joints under quasi-static loading using XFEM

The current paper is concerned with modelling damage and fracture in woven fabric composite double-lap bolted joints that fail by net-tension. A 3-D finite element model is used, which incorporates bolt clamp-up, to model a range of CFRP bolted joints, which were also tested experimentally. The effects of laminate lay-up, joint geometry, hole size and bolt clamp-up torque were considered. An Extended Finite Element (XFEM) approach is used to simulate damage growth, with traction–separation parameters that are based on previously reported, independent experimental measurements for the strength and toughness of the woven fabric materials under investigation. Good agreement between the predicted and measured bearing stress at failure was obtained.     

Predicting the effects of geometry on the behaviour of fibre metal laminate joints

The effects of geometry on the bearing response of fibre metal laminate (FML) joints are numerically investigated. Specimens designed to fail in bearing, net-tension and shear-out are analysed using a continuum damage mechanics approach. Plasticity in the aluminium layers, fibre and matrix damage in the composite plies and, importantly, delamination between the plies of the laminate are accounted for. The effects of mesh sensitivity, associated with strain-softening material models, are mitigated using a nonlocal averaging scheme. Results are compared to experimental bearing stress–strain and bearing stiffness–strain responses, and surface strain measurements. Variations in the development of damage for the different joints are investigated, and the effect of damage on the joint responses is discussed. Very good agreement was achieved for the specimens of interest, without varying the model parameters for the different joint configurations, which highlighted the suitability of the model for FML structural analysis. The combined numerical and experimental information provide an in-depth understanding of the failure sequences of FML joints.     

激光选区熔化成形铝合金板与CFRP复合材料层合板螺栓连接结构失效分析方法评估

对激光选区熔化成形(SLM)铝合金板与碳纤维增强树脂基(CFRP)复合材料层合板两列四排沉头螺栓单剪连接件在拉伸载荷作用下进行了数值分析和试验研究。基于渐进损伤法的三维有限元模型准确地预测了连接件材料损伤萌生和演变,对比试验和三维有限元所得钉载比例、极限载荷及失效模式,可以发现,通过拟合SLM铝合金板断裂应变和应力三轴度曲线,编写UMAT子程序引入韧性准则和Hashin失效准则的三维有限元模型预测的连接件失效载荷与试验值误差仅为1.9%,且失效模式均为净截面拉断,两者吻合,此方法可以满足工程精度要求。利用经过验证的数值模型,分别预测了SLM铝合金板和CFRP层合板损伤演变过程,并分析了SLM铝合金板刚度对连接结构失效模式的影响,当SLM铝合金板厚度增大到4mm时,连接结构失效模式由SLM铝合金板净截面拉断转移到CFRP层合板上。     

Fastener pull-through in a carbon fibre epoxy composite joint

This paper considers the capability of finite element (FE) modelling to accurately predict fastener pull-through failure of composite laminates. Such failures are dominated by inter-ply delamination and through-thickness shear failure of the laminate and the common modelling approach is to use computationally expensive, detailed three-dimensional models that include delamination for every ply interface, fastener contact and prestress. This paper considers a simplified FE modelling strategy achieved through judicious use of symmetry boundary conditions, hybrid shell/solid modelling and reduced numbers of interfaces for delamination. The LS-DYNA FE software was used for this study using the available composite material and cohesive failure models. The conclusion drawn from this work is that the use of simplified FE models does have merit in modelling fastener pull-through provided the material is quasi-isotropic and the boundary conditions are uniform around a circular perimeter. Additional work is however required to determine suitable cohesive properties and progressive shear failure parameters.     

Towards a Predictive Design Methodology Based on the Physical Modelling of the Fracture of Fiber Composites

A predictive design methodology based on modelling the fracture stress (notched tensile strength) and post-fatigue residual strength of laminated fiber composites is presented. The approach is based explicitly on the development of models of the physical processes by which damage accumulates at a notch-tip and the application of these models to cross-ply laminates for a variety of material systems, including thermosetting and thermoplastic matrices containing carbon, glass and Kevlar fiber reinforcements. The effects of temperature and humidity on composite fracture can also be examined in the context of this modelling strategy.A pre-requisite of the model is that it has to be calibrated for each material system by performing tensile tests on notched and unnotched cross-ply laminate. From this initial calibration, which takes relatively little time, it is possible to apply the model to a prediction of the dependence of fracture stress on notch size; to an understanding of the effects of laminate stacking sequence (within the same cross-ply family) on fracture stress; and to provide insight into the effects of thermal or load cycling history on fatigue damage-growth and residual or fatigue strength.The advantages and deficiencies of this modelling strategy are assessed, as well as the applicability of such a physical modelling approach to the predictive design and failure of composite materials in general.     

Experimental and numerical investigation of the crushing response of an open section composite energy absorbing element

The quasi-static crushing response of carbon epoxy composite hat-shaped crush elements is described herein. A steeple-type triggering mechanism was used to ensure the specimens exhibited a continuous stable crushing mode of failure. The explicit finite element software PAM-CRASH was used to predict the crushing failure of these energy absorbing elements. A four-layer, stacked-shell model of the composite hat-shaped element, after calibration against experimental test data, was found to be capable of closely approximating the failure modes and provide agreement with the load vs. displacement behaviour observed during the experiments. The predicted steady state load and specific energy absorption were respectively within 1.5 and 0.2% of the experimental average. With further validation, the developed stacked-shell methodology could help provide a predictive tool to characterise the energy absorption of open section crush elements and significantly reduce the cost associated with an extensive experimental material characterisation test program.     

A criterion for modelling initiation and propagation of matrix cracking and delamination in cross-ply laminates

A variational approach is used to model the behaviour of composite cross-ply laminates damaged by transverse, longitudinal cracking and delamination. An energetic criterion is proposed. It is based on the strain energy release rate associated with each of the three damage modes. The first part of this paper is concerned with the modelling of the transverse and longitudinal cracking. In the second part, a model for studying delamination damage is presented. The numerical results show that these models provide a consistent level of accuracy for a variety of thin laminate material systems and configurations, with various combinations of delaminations and matrix cracks. In this paper several numerical simulations meant to describe initiation for each damage mode are proposed. The estimation of damage modes contributions is achieved for two thin laminates in order to predict the evolution of damage mode transition.     

碳纤维/环氧树脂复合材料缠绕接头拉伸失效机制

通过试验及数值模拟对碳纤维/环氧树脂复合材料缠绕接头轴向拉伸失效机制进行研究。基于ABAQUS有限元软件,通过连续介质损伤模型及内聚区模型,分别对碳纤维/环氧树脂复合材料缠绕接头各部件及界面进行模拟,编写用户自定义材料子程序(UMAT),建立复合材料的渐进损伤模型,最终得到碳纤维/环氧树脂复合材料缠绕接头的应力分布和载荷-位移曲线,并与试验结果对比确定结构的失效机制。结果表明:有限元分析所得碳纤维/环氧树脂复合材料缠绕接头损伤部位及失效模式与试验吻合,失效载荷与试验值相差较小,证明仿真分析方法的有效性。通过对比失效模式发现,拉伸载荷作用下,链环是主承力部件,其弧形端部是应力集中处,纤维断裂即从此处开始发生并向外扩展,导致链环断裂及整体结构破坏。      

复合材料连续损伤力学模型在螺栓接头渐进失效预测中的应用

提出考虑层合板面内(纤维和基体失效)和层间失效的复合材料连续损伤力学模型,对螺栓接头的渐进失效行为进行预测。基于Tsai-Wu强度准则,发展可以判定复合材料面内和层间失效的强度准则。采用幂指数衰减材料退化模型模拟复合材料的损伤扩展过程。建立连续损伤力学模型用以研究0°铺层比例和螺栓直径对复合材料螺栓接头挤压性能的影响,预测结果与实验结果吻合。结果表明:0°铺层比例过高,接头发生剪切破坏,降低连接结构承载能力;增大螺栓直径,层合板损伤受到抑制,可提高复合材料螺栓接头的挤压强度。      

复合材料层合板缺口强度的CDM三维数值模型

针对复合材料层合结构缺口强度问题,基于连续损伤力学（CDM）提出了一种三维损伤数值模型。模型区分了层内损伤（纤维失效、纤维间失效）和层间分层损伤的不同失效模式。采用三维Puck准则与Aymerich准则对上述2类损伤进行判定,材料失效后基于CDM中线性软化模型对材料损伤进行演化。模型考虑了复合材料层合板子层的就位效应和剪切非线性行为。对Carlsson的AS4/3501-6缺口拉伸强度试验进行数值模拟。结果表明:分析结果与试验结果吻合良好,证明了该模型能够准确地预测含缺口复合材料层合板面内拉伸强度。      

Modelling off-axis ply matrix cracking in continuous fibre-reinforced polymer matrix composite laminates

The fracture process of composite laminates subjected to static or fatigue tensile loading involves sequential accumulation of intra- and interlaminar damage, in the form of transverse cracking, splitting and delamination, prior to catastrophic failure. Matrix cracking parallel to the fibres in the off-axis plies is the first damage mode observed. Since a damaged lamina within the laminate retains certain amount of its load-carrying capacity, it is important to predict accurately the stiffness properties of the laminate as a function of damage as well as progression of damage with the strain state. In this paper, theoretical modelling of matrix cracking in the off-axis plies of unbalanced symmetric composite laminates subjected to in-plane tensile loading is presented and discussed. A 2-D shear-lag analysis is used to determine ply stresses in a representative segment and the equivalent laminate concept is applied to derive expressions for Mode I, Mode II and the total strain energy release rate associated with off-axis ply cracking. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

Improving bearing performance of composite bolted joints using z-pins

The effect of z-pins on the bearing properties and damage tolerance of composite bolted joints is experimentally studied in this paper. The region around bolt-holes in carbon/epoxy laminates was reinforced in the through-thickness direction with different volume contents and sizes of fibrous z-pins. Bearing test results show that the z-pins improved the bearing stiffness (by 7.5–9.6%), ultimate load (7.7–12.8%), failure strength (7.4–9.8%), and elastic strain energy absorption to bearing failure (8.5–16.3%) of the composite joints. The bearing properties increased at a quasi-linear rate with the z-pin content, but were not dependent on pin diameter. Stiffness is improved by z-pins increasing the through-thickness tensile modulus around the bolt-hole of the joint. Post-mortem microstructural examination of the failed joint specimens revealed that z-pins improve the bearing strength by reducing cracking near the bolt-hole via an interlaminar bridging toughening mechanism that involves debonding and frictional sliding of pins within the damaged region. The elastic strain energy to failure is increased by the through-thickness stiffening and toughening provided by the z-pins. This study proves that the reinforcement of bolt-holes with z-pins increases the bearing properties without the weight penalty incurred with the traditional strengthening method of thickening the laminate around holes.     

An automated finite element analysis of the initiation and growth of damage in carbonfibre composite materials

The analysis and prediction of the development of damage in composite materials up to the point of final failure is important in the assessment of whether composite structures and components are fit for their purpose. Progressive damage modelling, using finite element analysis, has demonstrable potential as a tool for this.

If this approach is to be of real value, it needs to be automated so that the application of specialist knowledge is minimized. The ABAQUS finite element (FE) code has been used to develop fully-automated, threedimensional modelling of damage development in carbon fibre composites under tensile loading.

This paper describes the approach used in the development of these models. It covers work on the development of suitable FE meshes, the identification of suitable criteria to control the onset and effects of local damage, and the extension of the methodology to real component geometries.     

结合改进单胞模型的单钉双剪层合板螺栓连接结构挤压性能的多尺度表征分析

为提高螺栓连接层合板结构的可靠性和承载能力,基于ABAQUS软件及用户子程序(USDFLD),结合改进的单胞模型,建立了考虑组分材料失效的多尺度数值模型。利用该模型表征分析了单钉双剪层合板螺栓连接结构的力学性能,研究了铺层形式及几何尺寸对连接结构性能的影响。该模型的预报结果与试验结果吻合较好。结果表明:准各向同性层合板螺栓连接结构的挤压强度高于正交各向异性层合板连接结构的挤压强度,前者的失效模式为挤压失效,后者为剪出失效,该模式导致结构承载能力降低,设计中应避免。层合板边径比大于3时,不同宽径比连接结构的挤压强度趋近稳定值;但相同边径比的连接结构,其挤压强度随宽径比的增大而增大,连接结构设计时应给予考虑。      

FATIGUE DAMAGE AND SHAKEDOWN IN METAL MATRIX COMPOSITE LAMINATES

SUMMARY

Fatigue failure of metal matrix composite laminates is often preceded by a substantial loss of stiffness associated with cyclic plastic straining and subsequent low-cycle fatigue crack growth in the matrix. Experimental observations suggest that two principal crack patterns are involved; these are related here to the deformation modes predicted by the bimodal plasticity theory of fibrous composites. The relation is utilized in modelling the damage process such that matrix crack growth is regarded as a shakedown mechanism leading to a saturation damage state. For a given program of variable cyclic loading, evaluation of the saturation state is formulated as a non-linear optimization problem, where the total damage in a laminate is minimized subject to non-linear constraints derived from the ply yield criterion, hardening rule, and physically motivated bounds on the damage parameters. Effective elastic stiffness reduction and local stress redistribution predicted by the optimization procedure are compared with experimental measurements on several B/AI laminates. Stress transfer to and overloading of the fibres in certain plies appears to cause final fatigue failure of the laminate.     

基于连续损伤力学的复合材料单剪螺栓连接强度估算策略

针对中国缺少T800级复合材料螺栓连接设计参数的问题,发展一种综合连续损伤力学（CDM）和工程算法的单剪连接强度估算策略,以替代试验,降低研究周期和成本。在该强度估算策略中,首先建立试件的CDM有限元模型,通过数值模拟得到单剪螺栓连接的设计参数,包括单剪挤压强度修正系数、无缺口层合板拉伸强度和应力集中减缓因子等。随后根据上述参数,建立工程算法,估算复合材料单剪螺栓连接的最终挤压强度。结果表明:通过该策略得到的T800级复合材料螺栓连接设计参数和强度估算结果与试验结果有较好的一致性,说明该强度估算策略的可行性。      

Micromechanical modelling for onset of distortional matrix damage of fiber reinforced composite materials

A new multi-scale modelling approach is applied to specimen testing to define the critical strain invariants for the damage onset theory proposed by Gosse, Christensen and Hart-Smith. The onset theory is a micromechanics theory that uses critical strain invariants to predict the onset of damage within fiber polymer composites. To obtain the critical strain invariants for the matrix, finite element analyses are required of unidirectional off-axis specimens that have been tested to failure. The strains remain linear to failure and critical strain invariants can be determined from a linear finite element analysis but the use of continuum models to obtain the critical values requires strain enhancement factors. In this paper a new micromechanics-based modelling approach is proposed. A finite element analysis of the composite specimen is implemented with a square fiber array embedded within the polymeric matrix. Failure initiation sights are identified to obtain the critical values directly without the need for the strain enhancement factors. Numerical examples of the modelling process are provided including a 10° off-axis coupon with rectangular tabs. The results are compared to different modelling approaches. The tests and modelling are repeated for a 20° off-axis coupon but with oblique as well as rectangular tabs.     

Characterization of damage onset in glass-ceramic matrix composite angle-ply laminates

The tensile mechanical properties of a series of model [0/θ/0] glass-ceramic matrix composite angle-ply laminates have been measured at room temperature in an attempt to characterize the onset of damage in this class of material as a function of fibre orientation. The material selected for this study was a silicon carbide fibre-reinforced calcium aluminosilicate composite. The experimentally determined values of composite elastic modulus, strength and first ply failure stress have been compared with those predicted from classical laminate theory. Work carried out to date has shown that at high angles of θ, the damage onset of [0/θ/0] laminates is accurately predicted by the Tsai-Hill first ply failure stress whilst at low angles of θ the onset of damage is in reasonable agreement with that predicted by the Aveston-Cooper-Kelly model for multiple fracture (with the Tsai-Hill failure criterion predicting the ultimate strength of the composite). However, these models give no account of the mechanisms by which failure occurs and assume well-defined and single-valued failure strengths. In reality, glass-ceramic matrices have a distribution of strengths as a result of the inherent flaws within them and an attempt to quantify this has been made by mechanical and structural evaluation of the monolithic matrix material.