A Study On Uncertainty Of Mechanical Properties Of Composite Materials Based On Multiscale Theory

With the progress of the times and the increasing demand for materials,new material technology has been developed rapidly.Composite materials have excellent comprehensive mechanical properties,which are favored by the majority of scholars and engineers.However,there are a variety of uncertain factors in the process of structural design and manufacturing process of composite materials,which have a significant impact on the mechanical properties of composite materials.Therefore,the uncertainty analysis of the mechanical properties of composites is of great engineering significance.In this paper,the stochastic multi-scale theory based on the asymptotic homogenization method is used to study the uncertainty of the mechanical properties of fiberreinforced composites.Initially,the stochastic multi-scale theory of n-phase composites is derived based on the asymptotic homogenization method,and the code is written to realize the development of the stochastic multi-scale analysis program of two-phase and three-phase composites,and the visualization of the results is realized.Moreover,Monte Carlo Simulation is used to verify the effectiveness of stochastic multi-scale theory and the accuracy of programming.Moreover,ABAQUS was redeveloped to realize the stochastic parametric modeling of periodic RVE of discontinuous fiber reinforced composites based on BORSA method.By setting the parameters of fiber diameter,fiber length,fiber orientation angle and fiber centroid position as random variables,the random RVE model of discontinuous fiber reinforced composites can be obtained.The geometry of real fiber composites at microscale can be simulated by the generated random RVE model.Then,the impact of the elastic modulus uncertainty of component materials(glass fiber and polypropylene polymer)on the uncertainty of macroscale properties is analyzed by taking unidirectional discontinuous fiber reinforced composites and randomly distributed fiber reinforced composites as the research objects,respectively.The results show that: For unidirectional fiber reinforced composites,the uncertainty of the equivalent elastic modulus in the longitudinal direction of the fiber is mainly affected by the uncertainty of the elastic modulus of the fiber,and is less affected by the uncertainty of the elastic modulus of the matrix;the uncertainty of the equivalent elastic modulus in the transverse direction of the fiber and the equivalent shear modulus is mainly affected by the uncertainty of the elastic modulus of the matrix,but is not sensitive to the uncertainty of the elastic modulus of the fiber.For randomly distributed fiber reinforced composites,the uncertainty of equivalent elastic modulus and equivalent shear modulus is basically affected by the uncertainty of matrix elastic modulus,while the uncertainty of fiber elastic modulus has little effect,which is quite different from unidirectional fiber reinforced composites.It can be seen that completely different fiber orientations can change the influence mechanism of elastic modulus uncertainty of constituent materials on macroscopic properties uncertainty.The influence of the elastic modulus uncertainty of randomly distributed fiber reinforced composites on the uncertainty of microscopic stress is also studied.It is found that the glass fiber modulus uncertainty has an influence on the microscopic stress uncertainty throughout the whole RVE,and the degree of influence gradually decreases from the inside of the glass fiber to the interface and then to the matrix.The uncertainty of matrix modulus has a great influence on the uncertainty of microscopic stress of matrix,but has no influence on the uncertainty of microscopic stress inside the fiber.The uncertainty of microscopic stress on fiber surface(or interface)is affected by the uncertainty of fiber and matrix collectively.The uncertainty of the material modulus parameters has the greatest influence on the stress uncertainty at the interface.In addition,the probability distribution of homogenization modulus of unidirectional fiber-reinforced composites is estimated by Gaussian mixture distribution considering both material uncertainty and geometric uncertainty at microscale.It is found that the fiber volume fraction has a significant effect on the uncertainty of macroscopic properties.The standard deviation of equivalent elastic modulus and equivalent shear modulus increases with the increase of fiber volume fraction.The standard deviation of equivalent elastic modulus increases with the increase of fiber length,and the standard deviation of equivalent shear modulus is insensitive to the increase of fiber length.Finally,a microscopic failure criterion considering uncertainties is proposed based on the traditional microscopic failure criterion of fiber reinforced composites.It provides a guiding idea for the microscopic failure research or damage evolution analysis of fiber reinforced composites.In addition,the microscopic stress under different confidence levels is analyzed considering the uncertainty of material properties,and the results are compared with those of traditional analysis.