Multiscale Modeling of Fiber Kinking in Fiber-Reinforced Polymers

This work presents a framework to simulate fiber kinking in unidirectional layers of fiber reinforced composite laminates in a multiscale scheme. This offers the opportunity to better capture the sequence of events of fiber kinking phenomenon and deeper study the effects of micromechanical failure mechanisms such as fiber micro-buckling and fracture on the global behavior of the macro-structure. The scales of interest consist of a micro-mechanical scale on the level of fiber, matrix and their interface, where these constituents are modeled explicitly using the Finite Element Method, and the macro-mechanical scale, where the micromechanical properties are homogenized and considered as a transversely isotropic material model for a lamina or each ply of a composite laminate. Since the scale difference between the micromechanical level and the level of a lamina is significant, a Multiscale Projection Method (MPM) is applied to project the micromechanical effects of the fiber kinking locally on certain parts of the macroscopic problem. The numerical simulation of fiber kinking deals with two types of nonlinearities, the geometric nonlinearity regarding the large deformations of fiber buckling and the material nonlinearity in terms of matrix plastic deformation and macroscopic delamination of composite layers. Therefore, a finite deformation formulation is considered throughout this study for micro-mechanical constituents as well as macro-mechanical components. The multiscale projection technique is adjusted to ensure its consistency with those nonlinear effects. A geometrically nonlinear cohesive element is also developed to take into account the delamination or debonding between fiber and matrix. In order to define the location where the fine scale domain should be projected in the multiscale framework, a physically based criterion for composite laminates is applied. This class of criteria could calculate the initial condition of fibers that could lead to failure of the laminate due to fiber kinking. Applying this failure criterion on a linear analysis of the laminate in the global scale, the regions where a kink band will initiate are detected and, based on this information, a fine scale domain is generated and projected on the determined area. After this point, a multiscale simulation is carried out until the formation of a kink band in that region which generally terminates the solution procedure when the fibers break at the edges of the kink band. Multiple multiscale simulations which are presented as the results of this process demonstrate the strengths and shortcomings of the applied method.