Probabilistic modeling of short fiber-reinforced composites taking into account finite deformations – Numerical modeling and experimental validation –

Abstract

Due to the capability of mold injecting manufacturing short fiber-reinforced composites are increasingly in use in the aeronautical and automotive industries. However, a crucial aspect is their spatially distributed material properties induced by the probabilistic characteristics of the microstructure. To predict the structural response of components made of short fiber-reinforced composites by numerical simulation correctly the probabilistic information must be included in the modeling approach. Furthermore, commonly used matrix material is characterized by a distinct plastic deformation even at low stress levels. Therefore, in this work, a modeling approach is proposed that utilizes second-order Gaussian random fields for the representation of the spatially distributed material properties on the component level in the elastic and plastic domain. The modeling approach comprises the cross-correlation analysis of the material parameters describing the elastic-ideal plastic material behavior and a subsequent representation of the parameters by second-order Gaussian random fields. The analysis reveals a complex cross-correlation structure of the parameters, which depends on the window size on the mesoscale and requires the use of suitable numerical methods like the multiple correlated Karhunen-Loève expansion to synthesize the representation of the material parameters. The numerical simulations of tensile test specimens in the elastic and plastic domain predict the structural response under uniaxial loading accurately. The localized plastic deformation of the specimen is observable and meets the experimental validation by tensile tests until failure. Furthermore, the experimental data is used to determine the correlation length. Besides this, the modeling approach is validated by nanoindentation tests on the mesoscale, which reveal the spatial distribution of the material properties. Furthermore, it is shown that the area characterized by nanoindentation tests is 25 times larger than the projected area of the used Berkovich tip. In conclusion, the proposed modeling approach utilizing random fields is capable of representing the localized deformation of short fiber-reinforced composites induced by the probabilistic characteristics of the microstructure. Furthermore, the correlation structure can be derived by numerical simulation on the mesoscale, which can be experimentally analyzed by nanoindentation tests. Finally, the correlation length is an independent material parameter, which can be derived from experimental data.