缝纫复合材料细观结构表征及面内力学性能的理论和模拟
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摘要
传统纤维增强复合材料层合板的不足之处在于相对较低的层间断裂强度和韧性以及较低的冲击损伤容限,在横向载荷尤其是低速冲击载荷作用下很容易发生分层破坏。缝纫作为一种能有效提高复合材料层间力学性能的低成本方法一直得到人们的广泛关注。厚度方向上的纤维直接增强可以充分提高层合板层间的断裂韧性、低速冲击损伤容限和冲击后压缩强度。也就是说,对于缝纫复合材料层合板,分层破坏已不再是破坏的主要形式。一个值得关注的问题是:缝纫过程中缝纫线的加入迫使原来均匀分布的面内纤维发生弯曲变形和聚集现象,造成面内结构的严重非均匀性,并使层合板面内产生局部损伤,在一定程度上影响层合板的面内力学性能。本文旨在对缝纫诱导的局部细观结构进行参数化、定量化的表征,深入地研究缝纫造成的结构和性能的严重非均匀性,探寻缝纫复合材料在拉伸载荷作用下的面内力学行为,发展一套预测缝纫复合材料面内力学性能的理论体系和模拟方法,揭示面内宏观力学性能与缝纫引起的纤维扰动之间的内在关系,力图将缝纫复合材料层合板在拉伸载荷作用下的面内刚度和强度与材料体系、体积分数、缝纫线直径以及缝纫密度等定量地联系起来。
基于对缝纫孔附近的局部细观结构的试验研究,本文将代表性单元体按材料性质的不同划分为四个不同的区域,即未变形区、纤维变形区、树脂富集区和厚度增强区。提取四个细观结构参数:包括变形区长度、变形区宽度、缝纫孔短轴和缝纫孔长轴,来表征缝纫诱导的局部细观结构。对细观结构的数字照片进行图像处理,进而对细观结构参数进行定量测量,测量结果表明细观结构参数的测量值服从正态分布。并且找到四个细观结构参数之间的定量关系,即:变形区长度约是缝纫孔短轴的12-20倍,变形区宽度和缝纫孔长轴约是缝纫孔短轴的3-4倍,缝纫孔短轴约是缝纫线直径的80%。在此基础上,发展了新型纤维弯曲模型,得到纤维偏转角和纤维体积含量的解析表达式,给出了缝纫引起的纤维偏转角和纤维体积含量在代表性单元体内的空间非均匀分布。
设计了六种复合材料单向板的拉伸试验件,包含不同的缝纫密度和缝纫线直径以及未缝纫的情况。对各试验件在单向准静态载荷下进行拉伸试验,记录其破坏模式和拉伸强度。研究结果表明:中低缝纫密度的复合材料单向板的主要破坏模式为纤维断裂,面内拉伸强度较高,约为未缝纫复合材料单向板拉伸强度的85-90%。拉伸强度随缝纫密度和缝纫线直径的增加而降低。当缝纫密度过高时,相邻缝纫孔之间相互干涉造成树脂富集区之间彼此联接贯通,复合材料的破坏模式为复合材料撕裂破坏,拉伸强度较低,约为未缝纫复合材料单向板拉伸强度的70%。
缝纫线的加入造成面内纤维的偏转变形,在单向拉伸载荷作用下,纤维不仅产生轴向位移,还产生横向位移。为此,采用欧拉-贝努利曲梁来描述单根纤维的力学行为,建立相互作用微曲梁模型。采用有限差分法对控制微分方程进行数值求解,得到与有限元模型相吻合的结果,表明该模型可以很好的预测缝纫诱导的局部应力集中。
由于纤维拉伸强度的分散性,采用双参数韦伯分布来描述纤维强度的统计分布。考虑纤维的随机断裂及基体剪切破坏两种破坏模式,建立了统一型微曲梁相互作用模型。发展了复合材料拉伸破坏过程的模拟方法,结合蒙特卡罗模拟技术,对缝纫复合材料单向板在单向拉伸载荷作用下的破坏过程进行数值模拟,得到与试验相吻合的结果,表明该理论模型和模拟方法的正确性。
研究了缝纫密度以及细观结构参数包括变形区长度、变形区宽度和缝纫孔短轴对复合材料单向板拉伸强度和弹性模量的影响。研究结果表明当纤维强度服从双参数韦伯分布时,缝纫复合材料单向板的拉伸强度也服从双参数的韦伯分布,且其形状参数与纤维强度韦伯分布的形状参数在数值上基本相当。拉伸强度随缝纫行距的增加而减小,随针距的增加而增大;拉伸强度随变形区宽度和缝纫孔短轴的增加而减小;变形区长度对拉伸强度的影响不是单调的,存在最优值。缝纫密度和细观结构参数对面内弹性模量的影响很小。
A serious problem with traditional fiber reinforced polymer(FRP) laminates is their relatively poor interlaminar fracture toughness and low impacted damage tolerance which makes them susceptible to delamination when subjected to interlaminar loading. Stitching as a cost-effective method has received recognition for the remarkable improvement in the through-the-thickness mechanical properties.The introduction of the through-the-thickness reinforcement can substantially improve the interlaminar properties of laminates,such as the interlaminar fracture toughness,low-velocity impact damage tolerance and compression-after-impact(CAI) strength.The significant improvement in the interlaminar fracture toughness implies that delamination might be no longer the main failure mode of stitched composite laminates.In contrast,for the stitched composite laminates,what calling attention of researchers is that the insertion of the stitch thread forces the fibers to distort and congregate,making the in-plane microstructure inhomogeneous and generating local damages,which will affect the in-plane mechanical properties of stitched composite laminates.In this study,we focus on the parameterized and quantificational characterization of the microstructure induced by stitching,the investigation of the inhomogeneous microstructure and material properties,development of a theoretical model to predict the in-plane mechanical properties of stitched composite laminates.And we try to uncover the inherent relationship of in-plane macro-mechanical properties and microstructure and obtain the quantified connection between the in-plane stiffness as well as strength of the stitched composite laminates under tensile loading and the material system,fiber content, stitching parameters such as diameter of stitch yarn and stitching density.
Based on the experimental research on the microstructure around a stitch,a representative elementary volume is divided into such domains as the undistorted region, the fiber distortion region,the resin-rich pocket and the through-thickness reinforcement section.Four microstructure parameters such as distortion length,distortion width, minor axis and major axis of stitch hole are introduced to describe the local structure induced by stitching.The microstructure parameters are measured quantificationally based on the analysis of digital images.The averaged values and the distributions of four structural parameters are obtained by statistical analysis of the dimensions.Image analysis revealed that the structural parameters are statistically distributed and fitted Gaussian density functions.The proportions between the minor axis and the other parameters are obtained.The dimension of distortion length is about 12 times(thin yarn) and 20 times(thick yarn) as that of the minor axis,the dimensions of distortion width and major axis are about 3-4 times as that of the minor axis,and the minor axis of stitch hole is about 80%of the diameter of stitch yarn.
A novel fiber distortion model(FDM) is developed based on the investigation of typical morphology to predict the in-plane fiber misalignment angle and inhomogeneous fiber content using the basic microstructure parameters.This will be the foundation for evaluating the inhomogeneous effective material properties of the stitched composite laminates.It is assumed that the path of a fiber in the distortion region can be represented by a cosine function.For simplicity,the fiber volume fraction is assumed to follow a liner variation along the y-axis.The analytical expressions of the fiber misalignment angle and fiber volume fraction are derived rigorously,and the spatial distributions of fiber misalignment angle and fiber content within the unit cell of the ply are obtained using fiber distortion model.
Six kinds of tensile samples of stitched unidirectional composite laminates including difference stitch densities and difference diameters of the stitch thread as well as unstitched laminate are designed in this study.The failure modes and tensile strength are recorded during the experimental process.The results show that at the low stitch density, the failure mode is fiber breakage,and the tensile strength of the stitched composite laminate is reduced by about 10-15%compared with that of unstitched laminate.The tensile strength of stitched composite laminates decreases with the stitch density and diameter of stitch thread.When the stitch density is very high,the failure mode is splitting of the composite instead of fiber breakage,so the tensile strength is very low, about 70%of that of the strength of unstitched one.
Because of the distortion and inhomogeneous distribution of the in-plane fibers induced by stitching,the deformation of a single fiber is not only in the longitudinal direction but also in the transverse direction even under unidirectional tensile loading. We establish a multiple curved micro-beam model and derive governing differential equations of the model,which take into account the interaction of adjacent fibers.The stress concentration around the stitch hole can be well predicted using this model compared with the results calculated by finite element method.
A two-parameter Weibull distribution is adopted to describe the statistics of fiber strength.Considering fiber random breakage and matrix shear failure,a unified multiply micro-beam model is developed to simulate the failure process of stitched unidirectional composite laminate under tensile loading,coupling with Monte-Carlo simulation technique.
The in-plane tensile strength of stitched unidirectional composite laminates is predicted using the unified multiply micro-beam model coupling with Monte-Carlo simulation technique.The results simulated by this model agree well with that of the experiment,which indicates that the theoretical model,the simulation method and the program are reliable.Then,the effects of stitch density and microstructure parameters including distortion length,distortion width and minor axis on the tensile strength and elastic modulus of stitched composite laminate are studied in this paper.The results show that the tensile strength increases with the decrease of stitch spacing and with the increase of stitch step;decreases with the distortion width and minor axis of stitch hole; the effect of distortion length on tensile strength is not monotonic.The effects of stitch density and microstructure parameters on the in-plane elastic modulus are very little. The tensile strength of the composite is dispersive because of the statistical distribution of fiber strength.It is found that the tensile strength of stitched unidirectional composite laminates can be described statistically by the two-parameter Weibull distribution when the strength of fiber obeys two-parameter Weibull distribution,and the shape parameter in the strength distribution of the composite is almost the same with that of the fiber.
基于对缝纫孔附近的局部细观结构的试验研究,本文将代表性单元体按材料性质的不同划分为四个不同的区域,即未变形区、纤维变形区、树脂富集区和厚度增强区。提取四个细观结构参数:包括变形区长度、变形区宽度、缝纫孔短轴和缝纫孔长轴,来表征缝纫诱导的局部细观结构。对细观结构的数字照片进行图像处理,进而对细观结构参数进行定量测量,测量结果表明细观结构参数的测量值服从正态分布。并且找到四个细观结构参数之间的定量关系,即:变形区长度约是缝纫孔短轴的12-20倍,变形区宽度和缝纫孔长轴约是缝纫孔短轴的3-4倍,缝纫孔短轴约是缝纫线直径的80%。在此基础上,发展了新型纤维弯曲模型,得到纤维偏转角和纤维体积含量的解析表达式,给出了缝纫引起的纤维偏转角和纤维体积含量在代表性单元体内的空间非均匀分布。
设计了六种复合材料单向板的拉伸试验件,包含不同的缝纫密度和缝纫线直径以及未缝纫的情况。对各试验件在单向准静态载荷下进行拉伸试验,记录其破坏模式和拉伸强度。研究结果表明:中低缝纫密度的复合材料单向板的主要破坏模式为纤维断裂,面内拉伸强度较高,约为未缝纫复合材料单向板拉伸强度的85-90%。拉伸强度随缝纫密度和缝纫线直径的增加而降低。当缝纫密度过高时,相邻缝纫孔之间相互干涉造成树脂富集区之间彼此联接贯通,复合材料的破坏模式为复合材料撕裂破坏,拉伸强度较低,约为未缝纫复合材料单向板拉伸强度的70%。
缝纫线的加入造成面内纤维的偏转变形,在单向拉伸载荷作用下,纤维不仅产生轴向位移,还产生横向位移。为此,采用欧拉-贝努利曲梁来描述单根纤维的力学行为,建立相互作用微曲梁模型。采用有限差分法对控制微分方程进行数值求解,得到与有限元模型相吻合的结果,表明该模型可以很好的预测缝纫诱导的局部应力集中。
由于纤维拉伸强度的分散性,采用双参数韦伯分布来描述纤维强度的统计分布。考虑纤维的随机断裂及基体剪切破坏两种破坏模式,建立了统一型微曲梁相互作用模型。发展了复合材料拉伸破坏过程的模拟方法,结合蒙特卡罗模拟技术,对缝纫复合材料单向板在单向拉伸载荷作用下的破坏过程进行数值模拟,得到与试验相吻合的结果,表明该理论模型和模拟方法的正确性。
研究了缝纫密度以及细观结构参数包括变形区长度、变形区宽度和缝纫孔短轴对复合材料单向板拉伸强度和弹性模量的影响。研究结果表明当纤维强度服从双参数韦伯分布时,缝纫复合材料单向板的拉伸强度也服从双参数的韦伯分布,且其形状参数与纤维强度韦伯分布的形状参数在数值上基本相当。拉伸强度随缝纫行距的增加而减小,随针距的增加而增大;拉伸强度随变形区宽度和缝纫孔短轴的增加而减小;变形区长度对拉伸强度的影响不是单调的,存在最优值。缝纫密度和细观结构参数对面内弹性模量的影响很小。
A serious problem with traditional fiber reinforced polymer(FRP) laminates is their relatively poor interlaminar fracture toughness and low impacted damage tolerance which makes them susceptible to delamination when subjected to interlaminar loading. Stitching as a cost-effective method has received recognition for the remarkable improvement in the through-the-thickness mechanical properties.The introduction of the through-the-thickness reinforcement can substantially improve the interlaminar properties of laminates,such as the interlaminar fracture toughness,low-velocity impact damage tolerance and compression-after-impact(CAI) strength.The significant improvement in the interlaminar fracture toughness implies that delamination might be no longer the main failure mode of stitched composite laminates.In contrast,for the stitched composite laminates,what calling attention of researchers is that the insertion of the stitch thread forces the fibers to distort and congregate,making the in-plane microstructure inhomogeneous and generating local damages,which will affect the in-plane mechanical properties of stitched composite laminates.In this study,we focus on the parameterized and quantificational characterization of the microstructure induced by stitching,the investigation of the inhomogeneous microstructure and material properties,development of a theoretical model to predict the in-plane mechanical properties of stitched composite laminates.And we try to uncover the inherent relationship of in-plane macro-mechanical properties and microstructure and obtain the quantified connection between the in-plane stiffness as well as strength of the stitched composite laminates under tensile loading and the material system,fiber content, stitching parameters such as diameter of stitch yarn and stitching density.
Based on the experimental research on the microstructure around a stitch,a representative elementary volume is divided into such domains as the undistorted region, the fiber distortion region,the resin-rich pocket and the through-thickness reinforcement section.Four microstructure parameters such as distortion length,distortion width, minor axis and major axis of stitch hole are introduced to describe the local structure induced by stitching.The microstructure parameters are measured quantificationally based on the analysis of digital images.The averaged values and the distributions of four structural parameters are obtained by statistical analysis of the dimensions.Image analysis revealed that the structural parameters are statistically distributed and fitted Gaussian density functions.The proportions between the minor axis and the other parameters are obtained.The dimension of distortion length is about 12 times(thin yarn) and 20 times(thick yarn) as that of the minor axis,the dimensions of distortion width and major axis are about 3-4 times as that of the minor axis,and the minor axis of stitch hole is about 80%of the diameter of stitch yarn.
A novel fiber distortion model(FDM) is developed based on the investigation of typical morphology to predict the in-plane fiber misalignment angle and inhomogeneous fiber content using the basic microstructure parameters.This will be the foundation for evaluating the inhomogeneous effective material properties of the stitched composite laminates.It is assumed that the path of a fiber in the distortion region can be represented by a cosine function.For simplicity,the fiber volume fraction is assumed to follow a liner variation along the y-axis.The analytical expressions of the fiber misalignment angle and fiber volume fraction are derived rigorously,and the spatial distributions of fiber misalignment angle and fiber content within the unit cell of the ply are obtained using fiber distortion model.
Six kinds of tensile samples of stitched unidirectional composite laminates including difference stitch densities and difference diameters of the stitch thread as well as unstitched laminate are designed in this study.The failure modes and tensile strength are recorded during the experimental process.The results show that at the low stitch density, the failure mode is fiber breakage,and the tensile strength of the stitched composite laminate is reduced by about 10-15%compared with that of unstitched laminate.The tensile strength of stitched composite laminates decreases with the stitch density and diameter of stitch thread.When the stitch density is very high,the failure mode is splitting of the composite instead of fiber breakage,so the tensile strength is very low, about 70%of that of the strength of unstitched one.
Because of the distortion and inhomogeneous distribution of the in-plane fibers induced by stitching,the deformation of a single fiber is not only in the longitudinal direction but also in the transverse direction even under unidirectional tensile loading. We establish a multiple curved micro-beam model and derive governing differential equations of the model,which take into account the interaction of adjacent fibers.The stress concentration around the stitch hole can be well predicted using this model compared with the results calculated by finite element method.
A two-parameter Weibull distribution is adopted to describe the statistics of fiber strength.Considering fiber random breakage and matrix shear failure,a unified multiply micro-beam model is developed to simulate the failure process of stitched unidirectional composite laminate under tensile loading,coupling with Monte-Carlo simulation technique.
The in-plane tensile strength of stitched unidirectional composite laminates is predicted using the unified multiply micro-beam model coupling with Monte-Carlo simulation technique.The results simulated by this model agree well with that of the experiment,which indicates that the theoretical model,the simulation method and the program are reliable.Then,the effects of stitch density and microstructure parameters including distortion length,distortion width and minor axis on the tensile strength and elastic modulus of stitched composite laminate are studied in this paper.The results show that the tensile strength increases with the decrease of stitch spacing and with the increase of stitch step;decreases with the distortion width and minor axis of stitch hole; the effect of distortion length on tensile strength is not monotonic.The effects of stitch density and microstructure parameters on the in-plane elastic modulus are very little. The tensile strength of the composite is dispersive because of the statistical distribution of fiber strength.It is found that the tensile strength of stitched unidirectional composite laminates can be described statistically by the two-parameter Weibull distribution when the strength of fiber obeys two-parameter Weibull distribution,and the shape parameter in the strength distribution of the composite is almost the same with that of the fiber.
引文
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