Crack propagation modelling in layered structures by using moving mesh method

Abstract

The study presented in this PhD thesis is focused on development of advanced numerical models to describe crack propagation and interface decohesion phenomena in laminate and sandwich structures. The general idea is to simulate crack tip motion by using a moving mesh methodology to reproduce quasi-static and fast crack propagation phenomena in layered structures. Without going into too much details, the nodes are moved to predict changes of the geometry produced by the crack motion allowing to avoid several remeshing and saving computational time. The thesis presents a series of numerical investigations, which are performed in order to validate the introduced features in the numerical methodology along the development process. The starting point of the research was the investigation of the interface crack propagation phenomena in multilayered structures simulated by using shear deformable beam elements. The theoretical formulation was based on Arbitrary Lagrangian and Eulerian (ALE) methodology and cohesive interface elements, in which weak based moving connections are implemented by using a finite element formulation. In this framework, only the nodes of the computational mesh of the interface region are moved on the basis of the predicted fracture variables, reducing mesh distortions by using continuous rezoning procedures. The use of moving mesh methodology in the proposed model allow us to introduce nonlinear interface elements in a small region containing the process zone, reducing the numerical complexities and efforts, typically involved in standard cohesive approach. Furthermore, this numerical methodology was developed to investigate the strategy commonly adopted to improve the interlaminar strength of composite laminate. Basically, in order to simulate the z-pins reinforced area, a set of discrete nonlinear springs fixed to material domain was introduced. As is well known, a very important feature that should have a numerical model is the capability to simulate both crack onset condition and coalescence phenomena in structures with initial perfect interfaces. To this end, proper script files were carried out to manage the steps involved in the procedure, regarding the geometry variation due to the crack onset, the debonding length definition and the mesh enrichment in the process zone. The numerical strategy could be solved in both static and dynamic frameworks, taking into account time dependent effects produced by the inertial characteristics of the structure and the boundary motion involved by debonding phenomena. In both cases, the governing equations have been integrated by means of proper stop and restart conditions, to modify the computational mesh due to the onset of debonding phenomena. The ability of the proposed model has been verified by simulating several onset configurations, including the case, in which multiple debonding mechanisms with coalescence affect the interfaces. The research project has been focused on the study of the sandwich structure failure modes. From physical and mathematical viewpoints, two main issues are demanding a detailed understanding of the mechanical behaviour of sandwich panels: the propagation of internal macro-cracks in the core and the delamination at skin/core interfaces. To concern the delamination between skin and core, previous numerical strategy, already used in the framework of composite laminate, was generalized simply by modifying the relative displacement between skin (shear deformable beam) and core (2D plane stress formulation). In order to simulate the macro crack propagation in the core, the ALE approach has been generalized in two-dimensional framework. The approach has combined concepts arising from structural mechanics and moving mesh methodology, which was implemented in a unified framework to predict crack growth on the basis of Fracture Mechanics variables. In particular, moving computational nodes were modified starting from a fixed referential coordinate system on the basis of a crack growth criterion to predict directionality and displacement of the tip front. The use of rezoning mesh methods coupled with a proper advancing crack growth scheme has ensured the consistency of mesh motion with small distortions and an unaltered mesh typology. In addition, the moving grid was modified from the initial configuration in such a way that the recourse to remeshing procedures has been strongly reduced. Numerical formulation and its computational implementation have shown how the proposed approach can be easily embedded in classical finite element software. Numerical examples in presence of internal material discontinuities and comparisons with existing data obtained by advanced numerical approaches and experimental data have been proposed to check the validity of the formulation. Furthermore, the crack propagation in the core of sandwich structures has been analysed on the basis of fracture parameters experimentally determined on commercially available foams. The (summary) thesis comprises the following: Chapter 1 - Introduction (thesis topics, literature review, aims and scope); Chapter 2 and 3 - present theoretical formulation and numerical implementation followed by results of the numerical methodology to describe crack onset, propagation and coalescence respectively; Chapters 4 - reports the numerical investigation about sandwich structure failure modes and the generalization of the ALE approach to simulate crack propagation in 2D continuum (core); Chapters 5 -presents the conclusions and future works