复合材料宏观强度准则预测能力分析

对复合材料宏观强度准则进行了总结和评述,对最具有代表性的5种强度准则的预测能力进行了综合评估。首先,由各强度准则得到了不同平面应力状态下AS4/3501-6材料的理论失效包线,以此阐明了各强度准则的物理本质。然后,考虑到强度的分散性,采用Monte-Carlo方法并基于各强度准则建立了4种材料的概率失效包线和强度分散带。最后,结合多组试验数据,客观评估了各强度准则的预测能力。评估结果表明:各强度准则的预测结果都不可能完好地吻合所有的试验结果;相比于Max-Stress准则、Hashin准则和Tsai-Wu准则,Puck准则和LaRC03准则的预测能力相对较好,且对复合材料的损伤机理有更为合理的解释。     

Enhancing compressive strength of unidirectional polymeric composites using nanoclay

Morphology of nanoclay dispersed in resin and suspended in acetone was studied using scanning electron microscopy (SEM) and transmission electron microscopy (TEM). SEM and TEM images show intercalation of resin in the gallery spaces of nanoclay and regions of exfoliated clay with random orientation. A vacuum assisted wet lay-up (VAWL) process was used for the inclusion of nanoclay in conventional fiber reinforced composites. The VAWL specimen displayed improvement in off-axis compressive strength for nanoclay enhanced fiber composites. Addition of nanoclay produced a substantial increase in longitudinal compressive strengths (extracted from off-axis tests) of glass fiber reinforced composites. An elastic–plastic model was used to predict the compressive strength of fiber reinforced composites based on the matrix properties. The model predictions matched well with the experimental results.     

Notched strength prediction of centre-hole carbon/carbon composites

The present work investigates the behaviour of 2D carbon/carbon (C/C) composites containing centre holes and proposes methodologies for the prediction of the residual strength of such C/C laminates. Two different concepts were adopted in order to understand the fracture behaviour of C/C composites in the presence of holes and to evaluate their strength. The first approach is based on the hypothesis of the existence of a damage zone around the hole, which originates during tensile loading. The second uses monitoring of the acoustic emission (AE) activity of the centre-hole specimen, loaded up to a stress level well below its failure strength, as an indication of damage formation, and combines it with a defined calibration curve. Both models predict very accurately the strength of notched laminates for a number of specimens tested.     

Active learning polynomial chaos expansion for reliability analysis by maximizing expected indicator function prediction error

Assessing the failure probability of complex aeronautical structure is a difficult task in presence of uncertainties. In this paper, active learning polynomial chaos expansion (PCE) is developed for reliability analysis. The proposed method firstly assigns a Gaussian Process (GP) prior to the model response, and the covariance function of this GP is defined by the inner product of PCE basis function. Then, we show that a PCE model can be derived by the posterior mean of the GP, and the posterior variance is obtained to measure the local prediction error as Kriging model. Also, the expectation of the prediction variance is derived to measure the overall accuracy of the obtained PCE model. Then, a learning function, named expected indicator function prediction error (EIFPE), is proposed to update the design of experiment of PCE model for reliability analysis. This learning function is developed under the framework of the variance-bias decomposition. It selects new points sequentially by maximizing the EIFPE that considers both the variance and bias information, and it provides a dynamic balance between global exploration and local exploitation. Finally, several test functions and engineering applications are investigated, and the results are compared with the widely used Kriging model combined with U and expected feasibility function learning function. Results show that the proposed method is efficient and accurate for complex engineering applications.     

A variable kinematic doubly-curved MITC9 shell element for the analysis of laminated composites

The present article considers the linear static analysis of composite shell structures with double-curvature geometry by means of a shell finite element with variable through-the-thickness kinematic. The refined models used are grouped in the Unified Formulation by Carrera (CUF) and they permit the distribution of displacements and stresses along the thickness of the multilayered shell to be accurately described. The shell element has nine nodes and the mixed interpolation of tensorial components (MITC) method is used to contrast the membrane and shear locking phenomenon. The governing equations are derived from the principle of virtual displacement (PVD) and the finite element method (FEM) is employed to solve them. Cross-ply spherical shells with simply-supported edges and subjected to bi-sinusoidal pressure are analyzed. Various laminations, thickness ratios, and curvature ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in the literature and the analytical solutions obtained using the CUF and the Navier’s method. From the analysis, one can conclude that the shell element based on the CUF is very efficient and its use is mandatory with respect to the classical models in the study of composite structures. Finally, shells with different lamination, boundary conditions, and loads are also analyzed using high-order layer-wise theories in order to provide FEM benchmark solutions.     

A statistical theory of the tensile strength of short-fiber-reinforced composites

This paper is concerned with the prediction of the tensile strength of short-fiber-reinforced composites by following the statistical theory of the strength of fiber bundles. Unidirectional, misaligned, and random-fiber directions are all treated. Depending on the fiber length, two failure modes can be distinguished. When the fiber length is smaller than 2L_c, where L_c is the critical transfer length, the composite should fail by direct fiber pull-out. By contrast, it the fiber length is longer than 2L_c, most fibers break first and are then pulled out. At small fiber lengths, the prediction of the present theory is one-half the value predicted by the conventional model. However, the prediction of the present theory is in close agreement with that of the conventional approach if the fiber length is long.     

基于单胞解析模型的单向复合材料强度预报方法

基于单胞解析模型,建立一种从复合材料细观组分到宏观单向板的强度预报方法。根据连续介质力学和均匀化方法构建细-宏观关联矩阵,通过该关联矩阵将细观组分材料的弹性和损伤性能传递到宏观单向板中。考虑复合材料细观损伤状态,当纤维和基体满足各自强度准则时失效,并通过失效因子折算成刚度的衰减。在此基础上,结合有限元分析,实现复合材料单向板纵横向拉伸模拟,从而预报单向板的拉伸强度。结果表明:该方法预报的模量和强度与实验值基本一致,验证了该方法的有效性与高效性。     

三维编织复合材料渐进损伤模拟及强度预测

采用考虑纤维束相互挤压的纤维束截面八边形单胞模型, 引入周期性边界条件, 对三维编织复合材料的渐进损伤过程进行数值模拟, 并预测了材料的拉伸强度。通过在应变能密度函数中引入损伤状态变量, 建立了含损伤材料的刚度矩阵, 运用基于不同失效模式下损伤状态变量的刚度渐进折减法表征材料积分点损伤, 通过数值结果与试验结果的对比, 分析了Hashin和Tsai-Wu两种准则作为判定纤维束起始损伤的适用性。分析表明: 基于引入不同失效模式的Tsai-Wu准则的数值模拟和试验结果吻合良好; Hashin准则不适合作为编织纤维束的损伤判据; 不同编织角材料的失效机制不同。      

应用桥联模型预测复合材料吸湿老化剩余强度

采用试验与理论相结合的方法, 研究了玻璃纤维/环氧树脂复合材料的吸湿老化剩余强度, 测试了基体的吸湿性能, 对老化前后基体、 纤维及其复合材料的拉伸性能进行了试验研究。根据纤维和基体性能测试数据, 应用桥联模型计算了复合材料的吸湿老化剩余强度, 计算结果与试验结果一致。结果显示: 在小吸湿率条件下, 利用桥联模型能够准确预测复合材料的破坏演化规律及其最大剩余强度。当主承力层破坏由纤维控制时, 由湿老化引起的纤维强度的下降直接导致复合材料最大拉伸强度的下降; 当破坏由基体控制时, 影响复合材料吸湿剩余强度的主要因素是基体硬化及强度的下降。较小吸湿率对纤维与基体的界面粘结强度影响有限, 界面破坏不是层合板破坏的主要因素。      

基于细观结构的2.5维机织复合材料强度预测模型

采用经纱矩形截面及纬纱六边形截面假设,将经纱的屈曲轨迹简化为折线形式,建立了2.5维机织复合材料单胞几何模型。以单胞为研究对象,引入改进的三维Hashin失效准则和Mises准则作为组分材料的失效判据,采用不同的刚度退化方式来表征不同的失效模式,建立了基于逐渐损伤理论的强度预测模型。利用有限元分析（FEA）技术,开发了相应的参数化2.5维机织复合材料逐渐损伤分析程序,预测了浅交弯联结构不同机织参数2.5维机织复合材料的拉伸强度,并模拟了经向拉伸和纬向拉伸的损伤扩展过程。与静拉伸试验结果相比,拉伸强度的预测误差在10%以内;模拟的失效模式与试验结果吻合较好。     

三维六向编织复合材料渐进损伤模拟及强度预测

基于三维六向编织复合材料的细观结构,假设第六向纱线的截面形状为菱形,建立了三维六向编织复合材料的渐进损伤有限元模型。采用Linde等提出的失效准则,引入周期性位移边界条件,对三维六向编织复合材料的纵向拉伸应力-应变行为进行了渐进损伤数值模拟,讨论了单胞模型在纵向拉伸载荷作用下的细观损伤起始、扩展和最终失效的演化过程,并预测了材料的拉伸强度。在此基础上,进一步研究了编织角、纤维体积分数和编织纱水平取向角等参数对材料纵向拉伸力学性能的影响规律。研究结果表明,三维六向编织复合材料的轴向纱线拉伸断裂是导致其破坏的最主要因素。所得数值结果与现有试验值吻合较好,验证了该模型的有效性,为更深入研究此类材料的力学性能奠定了基础。     

平纹编织SiC/SiC复合材料多尺度建模及强度预测

连续SiC纤维增强SiC基体复合材料（SiC/SiC）具有优异的高温力学性能、辐照稳定性及较低的氚渗透率,在核工程结构领域具有良好的应用前景,掌握其承载状态下的损伤演化和强度性能,对SiC/SiC复合材料的应用具有重要指导意义。本文基于平纹编织SiC/SiC复合材料的制备过程和组分材料分布的多尺度特性,考虑复合材料微观结构的局部近似周期性,建立了纤维丝尺度和纤维束尺度单胞模型。使用有限元分析软件对纤维丝尺度模型的弹性性能和强度性能进行预测,将这些性能参数代入纤维束尺度模型,引入Tsai-Wu失效准则,根据材料的不同失效模式并对失效单元进行方向性刚度折减,模拟了平纹编织SiC/SiC复合材料在单轴拉伸载荷下的渐进损伤过程。数值模拟曲线与试验曲线吻合较好,实现了对平纹编织SiC/SiC复合材料强度的有效预测。      

Incorporation of statistical length scale into Weibull strength theory for composites

In this paper an extension of Weibull theory by the introduction of a statistical length scale is presented. The classical Weibull strength theory is self-similar; a feature that can be illustrated by the fact that the strength dependence on structural size is a power law (a straight line on a double logarithmic graph). Therefore, the theory predicts unlimited strength for extremely small structures. In the paper, it is shown that such a behavior is a direct implication of the assumption that structural elements have independent random strengths. By the introduction of statistical dependence in the form of spatial autocorrelation, the size dependent strength becomes bounded at the small size extreme. The local random strength is phenomenologically modeled as a random field with a certain autocorrelation function. In such a model, the autocorrelation length plays the role of a statistical length scale. The focus is on small failure probabilities and the related probabilistic distributions of the strength of composites. The theoretical part is followed by applications in fiber bundle models, chains of fiber bundle models and the stochastic finite element method in the context of quasibrittle failure.     

基于纤维束增强树脂基复合材料测试的单向层合板层间剪切性能的预估方法

纤维束增强树脂基复合材料（FBC）及其单向层合板在标准Iosipescu剪切实验中表现出非常相似的破坏特征,然而测量得到的剪切强度却有明显差异。本文使用两种碳纤维和两种环氧树脂制备了3种FBC和单向层合板,对FBC剪切强度和单向层合板层间剪切强度进行了测量与分析。应用界面单元方法分析了纤维束与基体之间的界面应力场,发现FBC剪切试件中纤维束/基体界面附近的应力状态为拉剪耦合,而单向层合板中界面处于纯剪切应力状态,这一差异导致FBC剪切实验测量的强度低于单向层合板的剪切强度。本文基于Yamada-Sun强度理论建立了FBC剪切强度与单向层合板剪切强度之间的关系模型,应用该模型预测的单向层合板剪切强度与实测强度之间达到良好的一致性,相对偏差为10%左右。根据本文提出的方法,通过制样较简单的FBC试验能够预测和评估相应单向层合板的层间剪切性能。     

连续纤维增强树脂复合材料纵向压缩强度预测模型的发展及其影响因素

基于高强、高韧、高模和压拉平衡为特征的第三代先进复合材料的需求,综述了连续纤维增强树脂复合材料纵向压缩强度预测模型的发展历程。基于纤维微屈曲、纤维扭结带、联合预测模型及渐进损伤失效模型,分别讨论了连续纤维增强树脂复合材料压缩失效机制,并在联合预测模型基础上,探究了碳纤维（直径、模量、体积分数、初始偏角）、树脂基体（弹性模量、剪切模量）及纤维/树脂界面三要素对连续纤维增强树脂复合材料纵向压缩强度和压缩失效形式的影响。      

Interfacial debonding in laminated titanium matrix composites

The results of an experimental program in which multiaxial loads were applied to [0₄] and [±45]_s silicon carbide/titanium (SiC/Ti) tubes are reviewed showing that stress coupling, matrix viscoplasticity (including room temperature creep) and fiber/matrix interfacial damage all contribute to nonlinear response and permanent strains in titanium matrix composites (TMC). A micromechanical model that explicitly considers the aforementioned phenomena is presented herein. The model assumes a periodic microstructure and uses finite elements to analyze a representative volume element. The composite is assumed to be in a state of generalized plane strain making it possible to discretize only a generic transverse plane while still being able to apply three-dimensional loading through appropriate boundary conditions. The response of laminated composites is predicted by incorporating the micromechanical results into nonlinear lamination theory. Predictions are presented to show the influence of the model parameters on the effective composite response of unidirectional [0₄] and angle-ply [±45]_s TMC laminates.     

Residual compressive strength of laminated plates with delamination

A study of residual compressive strength in delaminated laminates is presented. A methodology is proposed for simulating the whole compressive failure responses, such as initial buckling, postbuckling, contact of delamination front region, delamination propagation, fiber breakage, and matrix cracking etc. An finite element analysis (FEA) of the residual compressive strength is conducted on the basis of the Von Karman's nonlinearity assumption and the first-order shear deformation plate theory, combined with a stiffness degradation scheme. The numerical analysis models and methods are briefly introduced in this paper and some numerical examples are presented to illustrate it. From numerical results and discussion, it is clear that the compressive failure response involves complex multi-failure modes during compressive process. The method and numerical conclusions provide in this paper should of great value to engineers dealing with composite structures.     

Analysis of mechanical properties and SEM for laminated SiC/W composites

In this letter, it is reported that a laminated SiC/W composite has been developed using the hot pressing method. It is found that a chemical reaction between W and SiC occurs during the preparation process. Making use of SEM, the components within the sandwiched-in metal and the fracturing crack for the laminated SiC/W composite are determined. Testing mechanical properties of the laminated SiC/W composite indicates that fracture toughness increases while bending strength reduces, with an increase of the thickness of the sandwiched-in metal ranging from 10–50-μm thickness.     

单向碳/碳复合材料拉-拉疲劳寿命及剩余强度预测模型

基于预测单向复合材料纵向拉伸强度的随机核模型,引入纤维单丝剩余强度二参数Weibull模型及纤维单丝与基体界面剩余强度模型,研究建立了单向复合材料纵向拉-拉疲劳寿命及剩余强度的预测模型。对经过一定次数拉-拉疲劳载荷循环后的纤维束抽取其纤维单丝进行剩余强度拉伸试验,建立了纤维单丝剩余强度的二参数Weibull模型,测试单向碳/碳（C/C）复合材料的纤维与基体界面强度。通过单向C/C复合材料算例分析表明,92.5%、90.6%和87.5%应力水平下对数预测寿命与对数试验寿命比值分别为0.79、1.00和1.11,表明所建立的寿命预测模型用于预测单向C/C复合材料疲劳寿命是可行的;纵向拉伸剩余强度预测值与试验值误差在10%以内,吻合较好,表明所提出的剩余强度预测模型具有较高的精度。     

Probabilistic failure prediction for FRP composites

Results are presented from a theoretical study on failure-locus prediction for unidirectional FRP laminae under complex in-plane loading, taking into account statistical aspects of the basic strengths of the material. The purpose of the analysis is to establish simple rules and methodologies for failure prediction under specific reliability requirements. Therefore, the problem one is faced with is the definition of the cumulative distribution function (CDF) of the failure condition if the respective CDFs of the basic material strengths are known by experiment. To this end, two analytical approaches, namely a functional expansion technique and the introduction of Pearson’s semi-empirical distribution function, were developed and implemented in software. Both methods were shown to predict satisfactory results compared with Monte Carlo simulated ones and experimental data, wherever available. Finally, a semi-deterministic approach was examined according to which the failure criterion is used in the usual deterministic way but with basic strength values of a certain reliability level. Results from this simple and fast method were found in good agreement with those derived by expensive pure statistical methods or numerically simulated ones and experimental data.