Study On Basic Mechanical Parameters Of Dendritic Branched Reinforced Composites

The dendritic stiffener reinforced composite has many excellent mechanical properties due to the existence of the branched structure,such as high strength,etc.In this paper,the equivalent elastic constants of dendritic branched composites in two-dimensional and three-dimensional cases are predicted about theoretical analysis and numerical simulation.The main contents are as follows:(1)Firstly,representative unit cells(RUCE)are established for 2D dendritic stiffener reinforced composites(with either single long or multiple uniformly distributed branched stiffeners)by taking account of the arrangement of stiffener inside matrix and the geometric symmetries.Then,within the framework of linear elasticity theory,their longitudinal equivalent elastic modulus and transverse equivalent Poisson's ratio are derived by employing piecewise integration method.Factors,such as constituent material properties and different dimensions,are investigated focusing on the possible effects on the two composite's properties.It is found that the two elastic constants increase with the increase of the area fraction r of the reinforcing stiffener and the elastic modulus ratio E_s/E_m of the composite.The size of the trunk stiffener has a significant effect on the two elastic constants while maintaining the reinforcing stiffener area fraction.However,the size of the branch reinforcing stiffener,the branched angle,and the number of branched reinforcing stiffener have few effects on the elastic constants.Furthermore,when the number of branched reinforcing stiffener is 2,the equivalent elastic modulus reaches a minimum.The finite element method is used to calculate the two equivalent elastic constants of the composite,thus to compare the simulation results with the theoretical predictions.Meanwhile,all the results are then compared with the theoretical predictions based on Wang Yaoxian's method.It is found that the predicted values from current method are closer to the numerical simulation results.(2)In the three-dimensional case,similarly,we give the theoretical solution of the longitudinal equivalent elastic modulus of the dendritic single long branched stiffener reinforced composite and the dendritic multiple short branched stiffener reinforced composite,and the effects of different influencing factors(material factors and size factors)on the equivalent elastic modulus are discussed.The data analysis shows that the equivalent elastic modulus increases with the composite material modulus elastic modulus ratio E_f/E_m and the fiber volume fraction V_f,which is similar to two-dimensional situation.Secondly,when the volume fraction of the fiber is kept constant,the influence of the trunk fiber radius,the branched fiber radius and the bifurcation angle on the equivalent elastic modulus is not obvious,but for the three-dimensional dendritic multiple short-branched structural fiber composites.When the ratio of the branched fiber radius and the length of RUCE r/a is 0.04,the equivalent elastic modulus reaches the minimum,and when the number of branch reinforcing stiffener is 2,the equivalent elastic modulus also reaches the minimum.Finally,the numerical simulation results are compared with the theoretical predictions and Wang Yaoxian method values by finite element method.The results show that the theoretical prediction values are closer to the numerical simulation values,and the errors in the three-dimensional case are less than the error in the two-dimensional case.This method of predicting the equivalent elastic constant can predict the longitudinal equivalent elastic modulus and the transverse equivalent Poisson's ratio of the dendritic stiffener reinforced composite well,which provides a guiding role for the prediction of the equivalent elastic constant of this type of composite and the design of the material.