Analysis Methods Of Microstress Concentrations Of Continuous Fiber Composites Under Transverse Loads

This dissertation systematically studied the analysis methods of microstress concentrations of continuous fiber composites under transverse loads based on the damage of the composites for hypersonic aircrafts.The fibers in Representative Volume Element(RVE)were divided into far-field fibers,near-field fibers and adjacent fibers according to the effect on the stress of the studied point.Equivalent Far Field Method(EFFM)and Equivalent Inhomogeneous Inclusion Method(EIIM)are proposed to study the effects of far-field and near-field fibers on stress concentration,respectively.Based on the real distribution characteristics of continuous fibers,Standard Adjacent Fibers Method(SAFM)was proposed to predict the stress concentrations of continuous fibers,which laid a foundation for the subsequent damage research.SAFM considers the effects of fiber volume fraction(FVF),nearest fiber distance and elastic constants of fiber and matrix.The surface microstructure of carbon/epoxy unidirectional composites,carbon/epoxy and glass/epoxy weaving composites were observed by microscope.The fiber distributions were measured and statistically analyzed by using Image J and Matlab software,respectively.The fiber distribution was characterised by using the nearest fiber distance,the nearest fiber direction and the Ripley＿f function.The fiber distributions in9 sampling areas with FVF located at [0.4,0.7] were measured.The real fiber distribution and the influence of FVF on fiber distribution were systematically studied.The real fiber distribution is not completely random,and the real nearest fiber distances are smaller than those of random fiber distributions.Nearest fiber approaching method(NFAM)is proposed to produce RVEs that satisfy the requirements of the nearest fiber distance distributions.On the basis of the completely random fiber distribution,each fiber is moved a random distance to its nearest fiber,so that the adjacent fibers are closer to each other and finally meet the requirement of the nearest fiber distance distribution.The corresponding nearest fiber close cell was generated according to the FVF.The results showed that the fiber distribution characteristics and mechanical properties of Nearest Fiber Approaching RVE were consistent with those of real RVEs.NFAM provides abundant RVE models for studying the mechanical properties of continuous fiber composites.EFFM is proposed and the effect of far field fibers on stress concentrations is studied.Firstly,the relationship between the far field load and the stress of ellipsoidal inhomogeneity is obtained by using the Equivalent Inclusion Method(EIM).The fibers and matrix in the far field were homogenized,and the homogeneous medium was replaced by the matrix.In order to keep the stress of the fiber and matrix unchanged in the near field,the original external load is replaced by the equivalent far-field load according to the relationship between the load and the stress in the inhomogeneity.Taking carbon/epoxy and glass/epoxy composites with different FVF as examples,the stress fields of two kinds of composites were predicted by using EFFM.The maximum errors of stress predictions were-5.57% and-4.529%,respectively.With the increase of FVF,the stress concentrations of regular RVE increased while that of random RVE decreased.On the basis of EIM,EIIM is proposed to solve the stress and strain fields of nearfield fibers in EFF-RVE analytically.The distribution of the fibers in the near-field is described by using the circular inhomogeneities in plane strain state.Firstly,the stress and strain fields of multiple inhomogeneities are decomposed into the superposition of multiple isolated equivalent inhomogeneous inclusions.Then,a single inhomogeneous inclusion under polynomial eigenstrain is equivalent to a homogeneous inclusion.The residual theorem is used to solve the stress and strain fields of circular homogeneous inclusion under polynomial eigenstrains,which is used to solve the stress and strain fields of multiple fibers.Finally,abundant numerical examples were presented to verify the reliability and accuracy of the method.The adjacent fibers method is proposed to predict the stress concentrations of two adjacent fibers in RVE.The effect of each near-field fiber on the stress concentrations of the center of EFF-RVE is solved by using EIIM,and the effect of all the near-field fibers is equivalent to the near-field equivalent load.And the superpositions of the far-field and the near-field equivalent load are taken as the external load of the two fibers.In order to eliminate the randomness between near-field fibers and adjacent fibers,SAFM was proposed and the maximum stress of the whole RVE was predicted.There is no need to generate real RVE structure,and the prediction can be made based on the fiber volume fraction,the minimum distance between fibers and the elastic constants of fibers and matrix.With the increase of FVF of RVE,the error of maximum stress predicted by SAFM decreased,from small to close to or even slightly exceed the simulation results.The research in this paper is not only applicable to continuous fiber composites,but also applicable to heterogeneous materials containing spherical and cylindrical inclusions,such as carbon nanotubes,nanoparticles,rocket propellant columns,etc.,and also applicable to study the thermal expansion stress of solids or the piezoelectric effect of piezoelectric materials.