Bridging effects on Mixed Mode delamination: experiments and numerical simulation

Composite materials and, in particular, Carbon Fibre Reinforced Polymers (CFRP) have been well studied and developed in the past years due to their advanced mechanical characteristics. These materials are used in several different application fields, such as aerospace, automotive, energy production, bio-prosthesis and sport equipment. The combination of carbon fibers with epoxy resin allows obtaining materials characterized by high specific stiffness, low weight, and extremely high ultimate strength. Although the mechanical properties of the single carbon fiber are impressive, damage initiation often occurs at lower stresses. These materials are produced by stacking a sequence of several layers, which makes them prone to delamination. This process may lead to the creation of bridging fibers across the crack surfaces, which increases the total fracture toughness. Several efforts have been devoted in the past years to study the delamination process of composite materials under pure Mode I and pure Mode II. However, studies of delamination and bridging in Mixed Mode have not received adequate attention in the literature. The first goal of this project is to study the delamination process for unidirectional CFRP under Mixed Mode conditions. Experiments are performed over a wide range of different mode mixities, by using a Mixed Mode Bending (MMB) setting and monitoring the applied displacement, reaction force, crack propagation and internal strains. Axial strain values are measured in specific specimens by embedding optical fibers with Bragg grating sensors (FBGs) between the carbon layers. Delamination tests are performed at pure Mode I, Mixed Mode at 20%, 30%, 40%, 60% and pure Mode II, in order to obtain a complete set of experimental data. The results allowed characterizing both the energy release rate at crack initiation Gc and the corresponding bridging energy contribution Gb, as a function of the applied mode mixity. The second goal of this work is to create a numerical FE Model, based on cohesive elements, able to reproduce the correct delamination behavior and bridging contribution for each tested mode mixity, by using a unique cohesive law. Unfortunately, the cohesive law formulations for Mixed Mode delamination known so far show several limitations since they are not able to properly predict the delamination behavior in a MMB test when large scale bridging occurs. For this reason, an innovative mode-dependent cohesive formulation is implemented: it extends the constitutive laws of the previous models to incorporate the proper bridging contribution, by using an external customized routine. The bridging tractions are defined by three parameters: the corresponding energy contribution Gb, the maximum stress Imax and the crack opening displacement at failure IŽf . These bridging parameters are described by three different functions, dependent on the local mode mixity, by means of the coefficients IŸi =[IŸGb , IŸImax , IŸIŽf ]. The coefficients IŸi are obtained by using an inverse method, where the strains measured by the FBGs and the ones computed by the Finite Element Model (FEM) are involved in an optimization process. In contrast to the standard Mixed Model models, this algorithm provides a unique mode-dependent cohesive law able to properly simulate all the different delamination tests, from pure Mode I up to pure Mode II, predicting the load, the crack propagation, the energy release rate (ERR) and the strains evolution.