三维机织复合材料的压缩性能和冲击后压缩性能研究
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摘要
由于三维机织复合材料(3D woven composites或者简称为3DWC)整体性能好，且有高的厚向力学性能、较强的抗损伤、抗分层能力和较好的耐冲击性能，所以，三维机织复合材料在航空、航海、土木、医学、装甲、智能结构等领域得到了越来越广泛的应用，特别是在承受多向载荷和抗冲击结构中的应用有着良好的前景。这主要归功于三维机织复合材料：（1）预制件的制造机械化程度高，所以能快速大量生产，从而可降低制造成本、缩短生产周期；（2）纤维束、纱线等可在多方向交织，使其满足不同的力学性能需求；（3）采用熟知的液态成型技术固化成型制成三维机织复合材料，例如：树脂传递模塑（RTM）、真空辅助树脂传递模塑（VARTM）和树脂膜熔渗（RFI），将三维机织预制件与树脂基体固化成型。
三维机织复合材料又可分为如下几类：三维多轴机织复合材料，斜交三维机织复合材料和正交三维机织复合材料。本文研究涉及正交三维机织复合材料。正交三维机织复合材料（3DWOC）由正交三维机织预制件制成。此类预制件为多层预制件，由机织机将三组纤维束排列、交织而成。第一组纤维束，在机器方向（机织方向）上延伸，称作经纱；第二组纤维束在横向延伸，称为填充物或纬纱；第三组纤维束把在厚度方向上以十字铺层（0/90）形式交替堆放的经纱和纬纱捆绑加固，称为Z向纤维。Z向纤维也被称作经向捆绑纱，因为要达到捆绑的目的，需要一组与经纱方向相同的独立的纤维束。
三维机织预制件可以以单一形式生产，即只使用一种增强材料，也可以采用混合形式，即使用玻璃纤维、芳纶纤维、碳纤维、超高分子量聚乙烯（UHMWPE）纤维、陶瓷纤维等多种增强材料。混合形式可以存在于层间（层与层）、层内（纤维束与纤维束）、密切混合或是选择性布局。
虽然三维机织复合材料的整体力学性能要比层合板优越，但由于其压缩性能相对较差，所以在压缩强度方面仍然有一定的限制。查阅关于三维机织复合材料的相关文献，如其机织方法、对于力学性能表征、冲击行为表征、耐损伤性能表征的建模策略等，鲜见有关于其压缩性能及耐损伤性能表征的研究报道。其主要原因是压缩性能受多种因素影响而变得十分复杂，甚至用实验也不容易测正确。
由于冲击后的压缩(Compression After Impact或简称为CAI)性能是用来衡量材料耐损伤性能好坏的一种指标，因此，对于一种称为混杂正交三维机织复合材料(3D wovenorthogonal-interlock hybrid composite或简称为3DWOHC)的新材料来说，研究其压缩性能和冲击后压缩性能不但具有重要的理论意义而且也有实际工程应用价值。研究中涉及的3DWOHC的经向为T300碳纤维束和E玻璃纤维束，纬向和Z向均为E玻璃纤维束。拟从试验、理论分析和数值模拟三方面开展研究，通过对试验件进行力学测试，获得其压缩性能和冲击后压缩性能；通过研究建立理论分析模型和有限元预测模型，然后通过分析计算预测其性能。
在压缩性能实验中，对六根混杂正交三维机织复合材料（3DWOHC）的试件进行了准静态压缩试验，确定了其杨氏模量、压缩强度和失效机制。进行压缩实验的试件的长度方向均沿经向，并且保证试件在压缩过程中始终处于压缩实验夹具中。使用单轴应变计来记录试件的宏观应变数据，试验机记录施加的载荷数据。由名义应力和名义应变曲线可获得杨氏模量，其最大名义应力定义为试件的压缩强度。由于试验数据有一定的分散性，使用线性回归法处理所有试样的试验数据，从而得到经向的平均杨氏模量和平均抗压强度。
为了对失效的试件进行微观图像分析从而确定其失效机制，将失效的试样进行打磨，然后通过数码显微镜进行观察。由图像分析可知，所有的试样都是由于传载纤维束的扭折而导致失效。因为Z向纤维同样承受经向载荷，所以Z向纤维束也能观察到扭折的现象。值得一提的是，在力学测试时可观察到，基体首先开裂，然后才会观察到试件破坏性的失效。
冲击后压缩实验的目的是确定低速冲击下受损的混杂正交三维机织复合材料（3DWOHC）的剩余压缩强度。该实验分为两个阶段进行：在第一阶段，六块试验件在无仪表的落锤冲击试验台上受到低速冲击。在落锤冲击实验中，为了确定各级初始冲击能量对混杂正交三维机织复合材料冲击损伤程度的影响，采用不同的初始冲击能量对每个试件进行冲击。在冲击测试中使用了分别为5.0J、10.0J、13.3J、15.0J、16.7J和20.0J的能量作为初始冲击能。
借助数码显微镜可确定每个试件的冲击损伤区域。结果表明，冲击损伤面积随着初始冲击能量的增加而增大，并且冲击损伤区域的形状为带圆角的长方形，长边沿经线方向，说明损伤主要沿经线方向扩展，因为在纬线方向上由于Z向纤维的捆绑作用抑制了损伤的扩展。为了进一步观察冲击损伤试件的层间分离，对试件进行了C扫描，由于Z向纤维的捆绑机制，冲击损伤试件内没有发现有层间分离现象。
在冲击后压缩性能实验的第二阶段，为了确定三维机织复合材料的剩余压缩强度，采用自行设计的试验夹具对受冲击后损伤的复合材料试验件施加准静态压缩载荷。由于条件限制，使用的混杂正交三维机织复合材料（3DWOHC）试件的厚度仅为2.4mm，小于用于冲击后压缩试验试件的标准厚度（4-6mm，目标厚度为5mm），所以当对未损伤的试件进行试验时，试件发生了屈曲而失效。因此，基于对混杂正交三维机织复合材料板屈曲分析，改进了自行设计的冲击后压缩试验实验夹具。最终，采用改进后的自行设计的试验夹具成功地对含冲击损伤的试件施加准静态压缩载荷直到破坏，获得了其剩余压缩强度。
通过对实验数据的分析，可发现当冲击能量在10.0J以下时，冲击对混杂正交三维机织复合材料的剩余强度没有影响；当冲击能量在10.0J到20.0J之间时，尽管冲击损伤面积随冲击能量的提高而增大，但是冲击损伤试件的剩余强度相同。这要归功于Z向纤维抑制了损伤在纬线方向上扩展，由于冲击损伤主要沿经线方向扩展，所以余下的未受损的承载截面积基本保持不变。
共研究了五种预测模型：（1）几何模型，（2）刚度模型，（3）压缩强度模型，（4）冲击损伤模型，（5）冲击后压缩强度模型。由于混杂正交三维机织复合材料（3DWOHC）具有周期性结构，所以几何模型、刚度模型以及压缩强度模型的建立都基于代表性体单元（RVE）。
先建立了一种新颖的几何模型，称为通用几何模型(Generic Geometric model或简称为GG模型)。建立该模型的目的是：（1）为了方便的描述混杂正交三维预制件的内部几何形状；（2）为了确定不同的机织参数对于混杂正交三维预制件的几何参数的影响；（3）为了确定材料杂交对于混杂正交三维预制件的几何参数的影响。对于不同的三维机织预制件和三维机织复合材料的几何表征，GG模型适用于多种横截面形状的纤维束、多种杂交增强系统以及不同的模型（理想模型或者实际模型）。
在通用几何模型中，提出了一种称为“通用形状函数”（Generic Shape Function或简称为GS函数）的新颖形函数，以参数形式描述多种多样的纤维束的横截面几何特性。这种方法的好处在于它能够转化成许多离散的形状函数，诸如六角形、菱形、椭圆形、圆形、矩形、椭圆环形、圆环形、椭圆弧双曲形以及圆弧双曲型。此外，所提出的通用形函数还能被应用于任何一种二维或三维机织复合材料的几何公式中。
建立几何模型时，由于采用了混杂增强方法和通用形函数，使得通用几何模型可以灵活地用于采用不同材料、数量以及纵横纤维束都不相同材料的几何描述。基于干性预制件的几何实体建立了模型，并且着重关注了纤维的截面形状以及Z向纤维的精确路径。这么做主要是为了准确估计预制件的参数，诸如：三个相互正交方向上纤维的体积和体积百分比、面密度、预成型体的厚度。此外，通用几何模型还能适用于混杂斜交三维机织复合材料（3DWAHC）。
为确定混杂正交三维机织复合材料（3DWOHC）的工程弹性常数，基于体积平均和各向同性应变边界条件，提出了一种新的刚度分析模型，称为通用刚度模型(Generic StiffnessModel或简称为GS模型)。这种通用刚度模型使用了增强纤维和基体的工程弹性常数，并且可获得混杂正交三维机织复合材料的工程弹性常数。该模型中计及了杂交增强效应和z-向纤维的起伏效应，利用该模型可方便地确定三维机织复合材料的工程弹性常数。该模型也适用于混杂斜交三维机织复合材料（3DWAHC）和混杂复合材料层合板的工程弹性常数的确定。
为了研究混杂正交三维机织复合材料（3DWOHC）中各种组分材料的承载机理并确定其力学性能，在前面提出的分析模型的基础上，建立了相应的有限元模型。在对复合材料试件进行抛光和电子显微镜分析，获得了纤维束和整个试件的几何细节后，通过Pro/E建立了三维实体模型，并将实体模型导入有限元软件ABAQUS建立了有限元模型。有限元模型采用了三维线性四面体单元C3D4。同时，为了体现混杂正交三维机织复合材料所具有的周期性特性，有限元分析时施加了基于纵向和横向上的平移对称特性的周期性边界条件。为了计算工程弹性常数，在有限元模型上施加一个单位宏观应力（1MPa），计算该宏观应力下的宏观应变，最终由所加载的宏观应力和计算所得的宏观应变获得工程弹性常数。通过分析计算，由通用刚度模型和有限元模型获得了材料的工程弹性常数，预测结果与实验结果比较吻合验证了这两个模型的正确性。此外还对材料的混杂效应进行了研究，确定了在纵向增加T300碳纤维对于混杂正交三维机织复合材料（3DWOHC）的工程弹性常数的影响，发现随着纵向T300碳纤维数量的增加，纵向的杨氏模量也随之增加。
基于验证过的有限元模型，进一步研究了混杂正交三维机织复合材料（3DWOHC）的压缩性能。在混杂正交三维机织复合材料（3DWOHC）中，纵向承载纤维是纵向T300碳纤维和纵向E玻璃纤维。以前的数据表明：当复合材料受到压缩载荷时，一般由于传载纤维束的扭折而导致材料失效，而这种扭折失效的主要原因是传载纤维束存在的初始几何缺陷所造成的。基于在纯基体内的纵向纤维束的第一阶屈曲模态，提出了一个可描述传载纤维束的初始几何缺陷的数学模型。纯基体可视为弹性支撑，而纵向纤维束则视为受弹性支撑约束的圆柱杆。对于纯基体内的纵向纤维束采用有限元法进行了屈曲分析，发现该纵向纤维束的第一阶屈曲模态含有两个半波。因此，在所提出的几何缺陷模型中也假设含有两个半波。在分析过程中，通过ABAQUS中的用户定义子程序“ORIENT”来引入几何缺陷，其中“ORIENT”为ABAQUS的可选选项。
对于纤维束结构损伤的初始形成及后续演化，采用了基于三维应力的失效准则-Hashin准则；各向同性基体材料采用了J2流动理论并结合von-Mises失效准则进行建模。基于三维应力准则来降低已失效材料的工程弹性常数，通过用户定义子程序“UMAT”引入该失效准则和刚度折减模型。对于有限元模型，在纵向，一端施加约束，另一端施加位移载荷。每一计算步后都需求出约束端节点的累积支反力。将最大累积节点支反力除以截面积，就可确定出混杂正交三维机织复合材料（3DWOHC）的压缩强度。采用这样的模拟策略，利用ABAQUS预测了材料的压缩强度特性，并通过与实验结果的比较，验证了该模型和模拟策略的正确性。同时，通过材料的混杂研究，确定了在增加纵向碳纤维对于混杂正交三维机织复合材料（3DWOHC）压缩强度的影响。研究结果表明，由于T300碳纤维的压缩强度与玻璃纤维几乎相同，所以复合材料的整体压缩强度并未提高。
为了确定混杂正交三维机织复合材料（3DWOHC）低速冲击后所引起的损伤并了解损伤的产生机理，通过ABAQUS/Explicit建立了一种基于有限元的冲击损伤模型。该有限元模型由混杂正交三维机织复合材料（3DWOHC）板（和试验件相同）和一个圆冲头组成。为了节省计算资源，利用关于平行于纵向和横向中面的几何、材料和载荷对称性，仅取正交三维机织复合材料板的四分之一进行建模；圆冲头采用三维实体建模，用刚体模拟； Z向纤维束被模拟成矩形截面，并具有理想的纤维方向。整个混杂正交三维机织复合材料（3DWOHC）有限元模型采用C3D8R三维线性六面体单元进行建模。
横向各向同性纤维束定义为无损的线弹塑性材料，基体材料采用J2流动理论进行建模。对于横向各向同性纤维束，采用了基于三维应力的Hashin失效准则；而对于各向同性基体材料，采用了von-Mises失效准则。纤维束的力学特性由Chamis微观力学理论计算得到。采用基于三维应力的失效准则来降低已失效材料的工程弹性常数。通过用户定义子程序“VUMAT”引入上述失效准则和刚度折减模型。对于冲击的数值模拟，采用了与试验一致的不同初始冲击能量。
为了确定受冲击损伤后的混杂正交三维机织复合材料（3DWOHC）的剩余压缩强度，建立了冲击后压缩模型。在建立混杂正交三维机织复合材料（3DWOHC）平板模型时采用了无损材料和含损伤的材料（有损材料），并使用C3D20三维六面四边形体单元进行建模。无损材料由传载的E-玻璃纤维复合材料和T300碳纤维/玻璃纤维混杂复合材料构成，其力学特性可由前面建立的方法确定。在纵向，采用基于Hashin准则的纤维失效模型来判断单元是否失效。对无损材料的工程弹性常数进行折减，就可得到有损材料的工程弹性常数，并且该折减系数与无损材料失效时的折减系数相同。
对于无损材料，通过编写用户定义子程序“UMAT”就可引入失效准则和折减模型。有限元模型一端完全约束，另一端施加位移载荷。每一计算步后都要求出约束端节点的累积的支反力，将最大累积节点支反力除以截面积，就可确定有效剩余压缩强度，并可确定有效剩余强度和强度折减系数。通过将预测参数与实验结果进行比较对比，发现预测结果与试验数据相吻合，验证了所建立的模型的正确性。
论文最后是全文的总结和展望，总结了全文的研究工作，指出了有创新意义的研究成果，并给出了需要进一步研究的一些内容。下面简要地给出主要研究工作和有创新性的研究成果：
1.建立了可用于如渗透模型、微观力学模型之类的预测模型的新几何模型。提出了一种新颖形函数-GS函数，该函数可以参数形式描述多种多样的纤维束的横截面几何特性，能够用于任何机织复合材料的几何建模。同时，还建立了一种新颖的适用性广泛的通用几何模型(GG模型)，除能够用于本文研究所涉及的三维机织预制件/复合材料的几何表征外，也适用于其他三维编制件的几何表征。
2.提出了一种新的刚度分析模型(GS模型),该模型中计及了杂交增强效应和z-向纤维的起伏效应，利用GS模型可方便地确定三维机织复合材料的工程弹性常数。
3.通过电镜分析获得复合材料纤维束和整个试件的几何细节，然后建立实际材料/试件的几何模型和代表体的有限元模型，有限元分析时施加周期性边界条件以体现混杂正交三维机织复合材料的周期性特性。通过分析计算，确定了各组份的承载机理及其力学性能，并由建立的GS模型获得了材料的工程弹性常数。预测结果与实验结果吻合验证了所建立的模型的正确性。
4.基于验证过的有限元模型，研究了混杂正交三维机织复合材料的压缩性能。根据试验和电镜分析先确定了一般的压缩失效机理：即当复合材料受到压时，传载纤维束的初始几何缺陷使其发生扭折，从而导致材料失效。由此提出了一个可用于描述传载纤维束初始几何缺陷数学模型，并通过用户定义子程序“ORIENT”引入；对于纤维束结构损伤的初始形成及后续演化，通过用户定义子程序“UMAT”引入基于三维应力的失效准则；各向同性基体材料采用了J2流动理论并结合von-Mises失效准则进行建模。采用这样的模拟策略，最终利用ABAQUS成功预测了材料的压缩强度特性，计算结果与实验结果吻合验证了模拟策略的正确性。同时，还研究了混杂效应对材料的压缩性能的影响，给出了有参考意义的结论。
5.开展了冲击后压缩性能试验和数值模拟研究。复合材料试验件先受落锤冲击，然后采用自行设计的试验夹具成功地对受冲击后有损伤的复合材料试验件施加压缩载荷直致破坏。同时采用有限元法数值模拟了受冲击后的复合材料试验件的压缩性能，冲击后压缩试件采用了无损的单体材料、无损的混杂材料和有损材料并用三维六面四边形体单元进行建模，模拟时采用位移加载方式。通过数值模拟获得了受冲击后复合材料试验件的有效的弹性模量、剩余强度和强度折减系数，预测结果与试验数据相吻合说明了建模的正确性。
Three dimensional (3D) woven composites possess higher through-the-thickness mechanicalproperties, damage resistance, delamination resistance and impact resistance in comparison withtraditional laminated composites. Apart from the good mechanical properties,3D woven compositesare generally weak in compression and consequently put a limit on their strength. From the literaturereview, it was found that this area is less understood field in composites, especially for woven fabriccomposites.3D woven composites, due to good impact resistance properties, are gaining popularityin armor industry but there is very limited literature available on the characterization of their damagetolerance performance. Since the compression after impact (CAI) is the measure of damage tolerance,therefore, it is important to determine the compression and compression after impact performance of3D woven composites.
The objective of this research was to investigate the compression and compression after impactperformance of a new material named “3D woven orthogonal-interlock hybrid composite(3DWOHC)”. This objective was achieved by conducting experimental study and through analyticaland FE based predictive modeling. The predictive parameters were compared with the experimentaldata. The scope of the thesis includes literature review, geometric modeling, stiffness analysis,compression performance analysis, low velocity impact analysis and compression after impactanalysis, summary and recommendations. Some innovative research results are pointed out. And afew topics for further study are recommended.
A novel geometrical model called “Generic Geometric model (GG-model) has been proposed todescribe internal geometry of the composite. The GG-model is capable to deal with a variety of towcross-sectional shapes through a novel “Generic Shape Function”, hybrid reinforcement system andvarious methods to represent geometry of3D woven interlock preforms/composites. The geometryestablished by GG-model was used to develop of a novel analytical stiffness model called “GenericStiffness model (GS-model). Based on volume averaging method and iso-strain boundary conditions,the model can determine the engineering elastic constants of3D woven interlock composites.
A finite element (FE) based model is also developed at repeating unit cell level to understand theload carrying mechanism of various constituents of3DWOHC and to determine the mechanicalproperties of3DWOHC. Through digital image analysis, it was observed that constituent tows of3DWOHC are not perfectly straight. Therefore, a mathematical model has been proposed to modelthe initial geometrical imperfections of the tows. The geometrical imperfection was implemented through a user defined subroutine “ORIENT”. Another subroutine UMAT was used to implement thematerial properties and failure criteria of constituents of3DWOHC. The analysis was executed andpredicted compression strength was compared well to the experimental data. Sensitivity studies werealso been conducted to investigate the influence of void fraction, geometrical imperfection of tows,and material hybridization on the compression strength of3DWOHC.
FE based method has been used to simulate the damage resistance of3DWOHC subjected to lowvelocity impact. The FE model of3DWOHC plate was developed at microstructure level in order tocapture the damage at microstructure level. The impact simulation was conducted for5J,10J,13.33J,15J,16.67J and20J initial impact energies. The results of impact induced damage area werecompared well to the experimental data. To simulate the compression after impact performance, FEbased plate-model composed of virgin monolithic material, virgin hybrid material and damagedmaterial was developed. The damaged material was provided with the discounted properties. Themodel was subjected to displacement controlled compressive loading. The compressive residualstrength was determined and compared with the experimental data.
The predicted compression strength has been found in good agreement with the experimental data;the relative difference is within1%for4.25%geometric imperfection and5.8%voids in the purematrix. Both, voids and geometric imperfection of tows have been found to reduce the compressionstrength non-linearly. Addition of carbon fibers has been found to enhance stiffness only. Hence,high stiffness and high strength fibers are required to enhance both stiffness and strength of3DWOHC.
The impact simulation and experimental data shows that impact induced damage area increasesnon-linearly with the initial impact energy. The compression after impact simulation andexperimental data shows that compressive residual strength reduces after10J impact energy. Hence10J impact energy can be regarded as minimum threshold energy to affect the compressive residualstrength of3DWOHC.
三维机织复合材料又可分为如下几类：三维多轴机织复合材料，斜交三维机织复合材料和正交三维机织复合材料。本文研究涉及正交三维机织复合材料。正交三维机织复合材料（3DWOC）由正交三维机织预制件制成。此类预制件为多层预制件，由机织机将三组纤维束排列、交织而成。第一组纤维束，在机器方向（机织方向）上延伸，称作经纱；第二组纤维束在横向延伸，称为填充物或纬纱；第三组纤维束把在厚度方向上以十字铺层（0/90）形式交替堆放的经纱和纬纱捆绑加固，称为Z向纤维。Z向纤维也被称作经向捆绑纱，因为要达到捆绑的目的，需要一组与经纱方向相同的独立的纤维束。
三维机织预制件可以以单一形式生产，即只使用一种增强材料，也可以采用混合形式，即使用玻璃纤维、芳纶纤维、碳纤维、超高分子量聚乙烯（UHMWPE）纤维、陶瓷纤维等多种增强材料。混合形式可以存在于层间（层与层）、层内（纤维束与纤维束）、密切混合或是选择性布局。
虽然三维机织复合材料的整体力学性能要比层合板优越，但由于其压缩性能相对较差，所以在压缩强度方面仍然有一定的限制。查阅关于三维机织复合材料的相关文献，如其机织方法、对于力学性能表征、冲击行为表征、耐损伤性能表征的建模策略等，鲜见有关于其压缩性能及耐损伤性能表征的研究报道。其主要原因是压缩性能受多种因素影响而变得十分复杂，甚至用实验也不容易测正确。
由于冲击后的压缩(Compression After Impact或简称为CAI)性能是用来衡量材料耐损伤性能好坏的一种指标，因此，对于一种称为混杂正交三维机织复合材料(3D wovenorthogonal-interlock hybrid composite或简称为3DWOHC)的新材料来说，研究其压缩性能和冲击后压缩性能不但具有重要的理论意义而且也有实际工程应用价值。研究中涉及的3DWOHC的经向为T300碳纤维束和E玻璃纤维束，纬向和Z向均为E玻璃纤维束。拟从试验、理论分析和数值模拟三方面开展研究，通过对试验件进行力学测试，获得其压缩性能和冲击后压缩性能；通过研究建立理论分析模型和有限元预测模型，然后通过分析计算预测其性能。
在压缩性能实验中，对六根混杂正交三维机织复合材料（3DWOHC）的试件进行了准静态压缩试验，确定了其杨氏模量、压缩强度和失效机制。进行压缩实验的试件的长度方向均沿经向，并且保证试件在压缩过程中始终处于压缩实验夹具中。使用单轴应变计来记录试件的宏观应变数据，试验机记录施加的载荷数据。由名义应力和名义应变曲线可获得杨氏模量，其最大名义应力定义为试件的压缩强度。由于试验数据有一定的分散性，使用线性回归法处理所有试样的试验数据，从而得到经向的平均杨氏模量和平均抗压强度。
为了对失效的试件进行微观图像分析从而确定其失效机制，将失效的试样进行打磨，然后通过数码显微镜进行观察。由图像分析可知，所有的试样都是由于传载纤维束的扭折而导致失效。因为Z向纤维同样承受经向载荷，所以Z向纤维束也能观察到扭折的现象。值得一提的是，在力学测试时可观察到，基体首先开裂，然后才会观察到试件破坏性的失效。
冲击后压缩实验的目的是确定低速冲击下受损的混杂正交三维机织复合材料（3DWOHC）的剩余压缩强度。该实验分为两个阶段进行：在第一阶段，六块试验件在无仪表的落锤冲击试验台上受到低速冲击。在落锤冲击实验中，为了确定各级初始冲击能量对混杂正交三维机织复合材料冲击损伤程度的影响，采用不同的初始冲击能量对每个试件进行冲击。在冲击测试中使用了分别为5.0J、10.0J、13.3J、15.0J、16.7J和20.0J的能量作为初始冲击能。
借助数码显微镜可确定每个试件的冲击损伤区域。结果表明，冲击损伤面积随着初始冲击能量的增加而增大，并且冲击损伤区域的形状为带圆角的长方形，长边沿经线方向，说明损伤主要沿经线方向扩展，因为在纬线方向上由于Z向纤维的捆绑作用抑制了损伤的扩展。为了进一步观察冲击损伤试件的层间分离，对试件进行了C扫描，由于Z向纤维的捆绑机制，冲击损伤试件内没有发现有层间分离现象。
在冲击后压缩性能实验的第二阶段，为了确定三维机织复合材料的剩余压缩强度，采用自行设计的试验夹具对受冲击后损伤的复合材料试验件施加准静态压缩载荷。由于条件限制，使用的混杂正交三维机织复合材料（3DWOHC）试件的厚度仅为2.4mm，小于用于冲击后压缩试验试件的标准厚度（4-6mm，目标厚度为5mm），所以当对未损伤的试件进行试验时，试件发生了屈曲而失效。因此，基于对混杂正交三维机织复合材料板屈曲分析，改进了自行设计的冲击后压缩试验实验夹具。最终，采用改进后的自行设计的试验夹具成功地对含冲击损伤的试件施加准静态压缩载荷直到破坏，获得了其剩余压缩强度。
通过对实验数据的分析，可发现当冲击能量在10.0J以下时，冲击对混杂正交三维机织复合材料的剩余强度没有影响；当冲击能量在10.0J到20.0J之间时，尽管冲击损伤面积随冲击能量的提高而增大，但是冲击损伤试件的剩余强度相同。这要归功于Z向纤维抑制了损伤在纬线方向上扩展，由于冲击损伤主要沿经线方向扩展，所以余下的未受损的承载截面积基本保持不变。
共研究了五种预测模型：（1）几何模型，（2）刚度模型，（3）压缩强度模型，（4）冲击损伤模型，（5）冲击后压缩强度模型。由于混杂正交三维机织复合材料（3DWOHC）具有周期性结构，所以几何模型、刚度模型以及压缩强度模型的建立都基于代表性体单元（RVE）。
先建立了一种新颖的几何模型，称为通用几何模型(Generic Geometric model或简称为GG模型)。建立该模型的目的是：（1）为了方便的描述混杂正交三维预制件的内部几何形状；（2）为了确定不同的机织参数对于混杂正交三维预制件的几何参数的影响；（3）为了确定材料杂交对于混杂正交三维预制件的几何参数的影响。对于不同的三维机织预制件和三维机织复合材料的几何表征，GG模型适用于多种横截面形状的纤维束、多种杂交增强系统以及不同的模型（理想模型或者实际模型）。
在通用几何模型中，提出了一种称为“通用形状函数”（Generic Shape Function或简称为GS函数）的新颖形函数，以参数形式描述多种多样的纤维束的横截面几何特性。这种方法的好处在于它能够转化成许多离散的形状函数，诸如六角形、菱形、椭圆形、圆形、矩形、椭圆环形、圆环形、椭圆弧双曲形以及圆弧双曲型。此外，所提出的通用形函数还能被应用于任何一种二维或三维机织复合材料的几何公式中。
建立几何模型时，由于采用了混杂增强方法和通用形函数，使得通用几何模型可以灵活地用于采用不同材料、数量以及纵横纤维束都不相同材料的几何描述。基于干性预制件的几何实体建立了模型，并且着重关注了纤维的截面形状以及Z向纤维的精确路径。这么做主要是为了准确估计预制件的参数，诸如：三个相互正交方向上纤维的体积和体积百分比、面密度、预成型体的厚度。此外，通用几何模型还能适用于混杂斜交三维机织复合材料（3DWAHC）。
为确定混杂正交三维机织复合材料（3DWOHC）的工程弹性常数，基于体积平均和各向同性应变边界条件，提出了一种新的刚度分析模型，称为通用刚度模型(Generic StiffnessModel或简称为GS模型)。这种通用刚度模型使用了增强纤维和基体的工程弹性常数，并且可获得混杂正交三维机织复合材料的工程弹性常数。该模型中计及了杂交增强效应和z-向纤维的起伏效应，利用该模型可方便地确定三维机织复合材料的工程弹性常数。该模型也适用于混杂斜交三维机织复合材料（3DWAHC）和混杂复合材料层合板的工程弹性常数的确定。
为了研究混杂正交三维机织复合材料（3DWOHC）中各种组分材料的承载机理并确定其力学性能，在前面提出的分析模型的基础上，建立了相应的有限元模型。在对复合材料试件进行抛光和电子显微镜分析，获得了纤维束和整个试件的几何细节后，通过Pro/E建立了三维实体模型，并将实体模型导入有限元软件ABAQUS建立了有限元模型。有限元模型采用了三维线性四面体单元C3D4。同时，为了体现混杂正交三维机织复合材料所具有的周期性特性，有限元分析时施加了基于纵向和横向上的平移对称特性的周期性边界条件。为了计算工程弹性常数，在有限元模型上施加一个单位宏观应力（1MPa），计算该宏观应力下的宏观应变，最终由所加载的宏观应力和计算所得的宏观应变获得工程弹性常数。通过分析计算，由通用刚度模型和有限元模型获得了材料的工程弹性常数，预测结果与实验结果比较吻合验证了这两个模型的正确性。此外还对材料的混杂效应进行了研究，确定了在纵向增加T300碳纤维对于混杂正交三维机织复合材料（3DWOHC）的工程弹性常数的影响，发现随着纵向T300碳纤维数量的增加，纵向的杨氏模量也随之增加。
基于验证过的有限元模型，进一步研究了混杂正交三维机织复合材料（3DWOHC）的压缩性能。在混杂正交三维机织复合材料（3DWOHC）中，纵向承载纤维是纵向T300碳纤维和纵向E玻璃纤维。以前的数据表明：当复合材料受到压缩载荷时，一般由于传载纤维束的扭折而导致材料失效，而这种扭折失效的主要原因是传载纤维束存在的初始几何缺陷所造成的。基于在纯基体内的纵向纤维束的第一阶屈曲模态，提出了一个可描述传载纤维束的初始几何缺陷的数学模型。纯基体可视为弹性支撑，而纵向纤维束则视为受弹性支撑约束的圆柱杆。对于纯基体内的纵向纤维束采用有限元法进行了屈曲分析，发现该纵向纤维束的第一阶屈曲模态含有两个半波。因此，在所提出的几何缺陷模型中也假设含有两个半波。在分析过程中，通过ABAQUS中的用户定义子程序“ORIENT”来引入几何缺陷，其中“ORIENT”为ABAQUS的可选选项。
对于纤维束结构损伤的初始形成及后续演化，采用了基于三维应力的失效准则-Hashin准则；各向同性基体材料采用了J2流动理论并结合von-Mises失效准则进行建模。基于三维应力准则来降低已失效材料的工程弹性常数，通过用户定义子程序“UMAT”引入该失效准则和刚度折减模型。对于有限元模型，在纵向，一端施加约束，另一端施加位移载荷。每一计算步后都需求出约束端节点的累积支反力。将最大累积节点支反力除以截面积，就可确定出混杂正交三维机织复合材料（3DWOHC）的压缩强度。采用这样的模拟策略，利用ABAQUS预测了材料的压缩强度特性，并通过与实验结果的比较，验证了该模型和模拟策略的正确性。同时，通过材料的混杂研究，确定了在增加纵向碳纤维对于混杂正交三维机织复合材料（3DWOHC）压缩强度的影响。研究结果表明，由于T300碳纤维的压缩强度与玻璃纤维几乎相同，所以复合材料的整体压缩强度并未提高。
为了确定混杂正交三维机织复合材料（3DWOHC）低速冲击后所引起的损伤并了解损伤的产生机理，通过ABAQUS/Explicit建立了一种基于有限元的冲击损伤模型。该有限元模型由混杂正交三维机织复合材料（3DWOHC）板（和试验件相同）和一个圆冲头组成。为了节省计算资源，利用关于平行于纵向和横向中面的几何、材料和载荷对称性，仅取正交三维机织复合材料板的四分之一进行建模；圆冲头采用三维实体建模，用刚体模拟； Z向纤维束被模拟成矩形截面，并具有理想的纤维方向。整个混杂正交三维机织复合材料（3DWOHC）有限元模型采用C3D8R三维线性六面体单元进行建模。
横向各向同性纤维束定义为无损的线弹塑性材料，基体材料采用J2流动理论进行建模。对于横向各向同性纤维束，采用了基于三维应力的Hashin失效准则；而对于各向同性基体材料，采用了von-Mises失效准则。纤维束的力学特性由Chamis微观力学理论计算得到。采用基于三维应力的失效准则来降低已失效材料的工程弹性常数。通过用户定义子程序“VUMAT”引入上述失效准则和刚度折减模型。对于冲击的数值模拟，采用了与试验一致的不同初始冲击能量。
为了确定受冲击损伤后的混杂正交三维机织复合材料（3DWOHC）的剩余压缩强度，建立了冲击后压缩模型。在建立混杂正交三维机织复合材料（3DWOHC）平板模型时采用了无损材料和含损伤的材料（有损材料），并使用C3D20三维六面四边形体单元进行建模。无损材料由传载的E-玻璃纤维复合材料和T300碳纤维/玻璃纤维混杂复合材料构成，其力学特性可由前面建立的方法确定。在纵向，采用基于Hashin准则的纤维失效模型来判断单元是否失效。对无损材料的工程弹性常数进行折减，就可得到有损材料的工程弹性常数，并且该折减系数与无损材料失效时的折减系数相同。
对于无损材料，通过编写用户定义子程序“UMAT”就可引入失效准则和折减模型。有限元模型一端完全约束，另一端施加位移载荷。每一计算步后都要求出约束端节点的累积的支反力，将最大累积节点支反力除以截面积，就可确定有效剩余压缩强度，并可确定有效剩余强度和强度折减系数。通过将预测参数与实验结果进行比较对比，发现预测结果与试验数据相吻合，验证了所建立的模型的正确性。
论文最后是全文的总结和展望，总结了全文的研究工作，指出了有创新意义的研究成果，并给出了需要进一步研究的一些内容。下面简要地给出主要研究工作和有创新性的研究成果：
1.建立了可用于如渗透模型、微观力学模型之类的预测模型的新几何模型。提出了一种新颖形函数-GS函数，该函数可以参数形式描述多种多样的纤维束的横截面几何特性，能够用于任何机织复合材料的几何建模。同时，还建立了一种新颖的适用性广泛的通用几何模型(GG模型)，除能够用于本文研究所涉及的三维机织预制件/复合材料的几何表征外，也适用于其他三维编制件的几何表征。
2.提出了一种新的刚度分析模型(GS模型),该模型中计及了杂交增强效应和z-向纤维的起伏效应，利用GS模型可方便地确定三维机织复合材料的工程弹性常数。
3.通过电镜分析获得复合材料纤维束和整个试件的几何细节，然后建立实际材料/试件的几何模型和代表体的有限元模型，有限元分析时施加周期性边界条件以体现混杂正交三维机织复合材料的周期性特性。通过分析计算，确定了各组份的承载机理及其力学性能，并由建立的GS模型获得了材料的工程弹性常数。预测结果与实验结果吻合验证了所建立的模型的正确性。
4.基于验证过的有限元模型，研究了混杂正交三维机织复合材料的压缩性能。根据试验和电镜分析先确定了一般的压缩失效机理：即当复合材料受到压时，传载纤维束的初始几何缺陷使其发生扭折，从而导致材料失效。由此提出了一个可用于描述传载纤维束初始几何缺陷数学模型，并通过用户定义子程序“ORIENT”引入；对于纤维束结构损伤的初始形成及后续演化，通过用户定义子程序“UMAT”引入基于三维应力的失效准则；各向同性基体材料采用了J2流动理论并结合von-Mises失效准则进行建模。采用这样的模拟策略，最终利用ABAQUS成功预测了材料的压缩强度特性，计算结果与实验结果吻合验证了模拟策略的正确性。同时，还研究了混杂效应对材料的压缩性能的影响，给出了有参考意义的结论。
5.开展了冲击后压缩性能试验和数值模拟研究。复合材料试验件先受落锤冲击，然后采用自行设计的试验夹具成功地对受冲击后有损伤的复合材料试验件施加压缩载荷直致破坏。同时采用有限元法数值模拟了受冲击后的复合材料试验件的压缩性能，冲击后压缩试件采用了无损的单体材料、无损的混杂材料和有损材料并用三维六面四边形体单元进行建模，模拟时采用位移加载方式。通过数值模拟获得了受冲击后复合材料试验件的有效的弹性模量、剩余强度和强度折减系数，预测结果与试验数据相吻合说明了建模的正确性。
Three dimensional (3D) woven composites possess higher through-the-thickness mechanicalproperties, damage resistance, delamination resistance and impact resistance in comparison withtraditional laminated composites. Apart from the good mechanical properties,3D woven compositesare generally weak in compression and consequently put a limit on their strength. From the literaturereview, it was found that this area is less understood field in composites, especially for woven fabriccomposites.3D woven composites, due to good impact resistance properties, are gaining popularityin armor industry but there is very limited literature available on the characterization of their damagetolerance performance. Since the compression after impact (CAI) is the measure of damage tolerance,therefore, it is important to determine the compression and compression after impact performance of3D woven composites.
The objective of this research was to investigate the compression and compression after impactperformance of a new material named “3D woven orthogonal-interlock hybrid composite(3DWOHC)”. This objective was achieved by conducting experimental study and through analyticaland FE based predictive modeling. The predictive parameters were compared with the experimentaldata. The scope of the thesis includes literature review, geometric modeling, stiffness analysis,compression performance analysis, low velocity impact analysis and compression after impactanalysis, summary and recommendations. Some innovative research results are pointed out. And afew topics for further study are recommended.
A novel geometrical model called “Generic Geometric model (GG-model) has been proposed todescribe internal geometry of the composite. The GG-model is capable to deal with a variety of towcross-sectional shapes through a novel “Generic Shape Function”, hybrid reinforcement system andvarious methods to represent geometry of3D woven interlock preforms/composites. The geometryestablished by GG-model was used to develop of a novel analytical stiffness model called “GenericStiffness model (GS-model). Based on volume averaging method and iso-strain boundary conditions,the model can determine the engineering elastic constants of3D woven interlock composites.
A finite element (FE) based model is also developed at repeating unit cell level to understand theload carrying mechanism of various constituents of3DWOHC and to determine the mechanicalproperties of3DWOHC. Through digital image analysis, it was observed that constituent tows of3DWOHC are not perfectly straight. Therefore, a mathematical model has been proposed to modelthe initial geometrical imperfections of the tows. The geometrical imperfection was implemented through a user defined subroutine “ORIENT”. Another subroutine UMAT was used to implement thematerial properties and failure criteria of constituents of3DWOHC. The analysis was executed andpredicted compression strength was compared well to the experimental data. Sensitivity studies werealso been conducted to investigate the influence of void fraction, geometrical imperfection of tows,and material hybridization on the compression strength of3DWOHC.
FE based method has been used to simulate the damage resistance of3DWOHC subjected to lowvelocity impact. The FE model of3DWOHC plate was developed at microstructure level in order tocapture the damage at microstructure level. The impact simulation was conducted for5J,10J,13.33J,15J,16.67J and20J initial impact energies. The results of impact induced damage area werecompared well to the experimental data. To simulate the compression after impact performance, FEbased plate-model composed of virgin monolithic material, virgin hybrid material and damagedmaterial was developed. The damaged material was provided with the discounted properties. Themodel was subjected to displacement controlled compressive loading. The compressive residualstrength was determined and compared with the experimental data.
The predicted compression strength has been found in good agreement with the experimental data;the relative difference is within1%for4.25%geometric imperfection and5.8%voids in the purematrix. Both, voids and geometric imperfection of tows have been found to reduce the compressionstrength non-linearly. Addition of carbon fibers has been found to enhance stiffness only. Hence,high stiffness and high strength fibers are required to enhance both stiffness and strength of3DWOHC.
The impact simulation and experimental data shows that impact induced damage area increasesnon-linearly with the initial impact energy. The compression after impact simulation andexperimental data shows that compressive residual strength reduces after10J impact energy. Hence10J impact energy can be regarded as minimum threshold energy to affect the compressive residualstrength of3DWOHC.
引文
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