# Crack Growth and Delamination Analysis in GFR Composite Materials
## 1 Introduction  
Composite materials are extensively studied numerically and experimentally due to their increasing application in industry. Their behavior can be examined meticulously by incorporating multiscale methods that help achieving an in-depth understanding of the damage mechanisms. The transferring of information between scales allows for extracting the response of every material combination that consists of the microstructure and proceeding with the macroscale analysis, taking into account each phase's behavior. Furthermore, mean field methods are computationally fast methods that allow for obtaining the full microstructural information for the entire simulation domain without the need to perform the modeling in such small scales. The combination of multiscale methods with fracture mechanics' formulations permits the prediction of any damage mechanism that may appear in laminated composites under realistic constraints providing information with industrial relevance and value. The mechanism of transverse cracking positions and delaminations in cross-ply composite materials is a well studied problem [1, 2, 3]. The scale at which the composite material is modeled has a significant role in terms of the accuracy and the type of the damage mechanism that can be simulated. The smaller and more detailed the scale is, the more accurate the model will be and the more damage mechanisms that may be predicted. The governing damage mechanisms in a cross-ply Glass Fiber Reinforced Plastic (GFRP) loaded in uniaxial tension is the transverse cracking and the delaminations that could occur between the different oriented layers near the crack tips. There are different approaches and theories that can be applied to simulate cracks and delaminations successfully. In this study, a mesoscale and a microscale model are developed. The mesoscale approach is used in a dynamic explicit analysis along with rate dependent materials to predict the saturation of the transverse cracking and delaminations by using cohesive zone modeling techniques. The microscale approach is used to model the initiation of cracks and their propagation in a 3D cross-ply Representative Volume Element (RVE) using an extended finite element method (XFEM) in a quasi static analysis framework. The stress fields at the concentration areas around the crack tips of both methods are compared using strain concentration tensors to link the two scales. In the existing literature, there are models that have been suggested concerning the simulation of interfacial properties. The most common and widely used approach is the XFEM [4]. This method allows the modeling of discontinuities existing in the finite elements. Thus, it provides a tool for the insertion of matrix cracks independently of the mesh orientation. Despite the fact that most of the simulations of cracking initiation and propagation are performed using XFEM, this method has a limitation mainly imposed by the chosen analysis which has to follow the Implicit integration framework and not the Explicit. In the present mesoscale model, Explicit analysis is adopted where complex dynamic problems with contacts and large deformations can be solved. Another important fact introduced in the present investigation is the use of a cohesive interface instead of cohesive elements [5] thus reducing the continuum shell elements of the model and avoiding the matching restrictions for the mesh of the adjacent layers. In addition, homogenization theory was used to predict elastic properties for the multiphase materials instead of properties from literature or material databases. Homogenization methods and multi-scale analysis can easily be extended to the nonlinear regime [6] for plasticity and damage to get a clear understanding about the inelastic response in the microstructure and observe which component of the composite has conceived damage.