Non-Local Continuum Models for Damage in Solids and Delamination of Composites

Abstract

The focus of the thesis is on developing new damage models for brittle materials and using these to study delamination of composite structures. Chapter 1 gives an introductory literature review in order to motivate the work undertaken in the chapters to follow. Chapter 2 deals with a new micropolar damage model for delamination in composites. By combining phase field theory and peridynamics, Chapter 3 develops a new formalism to study damage in brittle materials under dynamic loading. Chapter 4 exploits and extends this idea for modelling delamination of composites. An extended chapter-wise summary of the contributions in the thesis is provided below. In Chapter 2, a micropolar cohesive damage model for delamination of composites is proposed. The main idea is to embed micropolarity, which brings in an added layer of kinematics through the micro-rotation degrees of freedom within a continuum model to account for the micro-structural effects during delamination. The resulting cohesive model, described through a modified traction separation law, includes micro-rotational jumps in addition to displacement jumps across the interface. The incorporation of micro-rotation requires the model to be supplemented with physically relevant material length scale parameters, whose effects during delamination in modes I and II are brought forth using numerical simulations appropriately supported by experimental evidences. In Chapter 3, we attempt at reformulating the phase field theory within the framework of peridynamics (PD) to arrive at a non-local continuum damage model. This obtains a better criterion for bond breaking in PD, marking a departure from the inherently ad-hoc bond-stretch-based or bond-energy-based conditions and thus allowing the model to simulate fragmentation which a phase field model cannot by itself accomplish. Moreover, posed within the PD setup, the integral equation for the phase field eases the smoothness restrictions on the field variable. Taking advantages of both the worlds, the scheme thus offers a better computational approach to problems involving cracks or discontinuities. Starting with Hamilton’s principle, an equation of the Ginzburg-Landau type with dissipative correction is arrived at as a model for the phase field evolution. A constitutive correspondence route is followed to incorporate classical constitutive relations within our PD model. Numerical simulations of dynamic crack propagation (including branching) and the Kalthoff-Winkler experiment are also provided. To demonstrate the natural ability of the model to prevent interpenetration, a mode II delamination simulation is presented. A brief discussion on the convergence of PD equations to classical theory is provided in the Appendix B. In Chapter 4, we extend and exploit the phase field based PD damage model, developed in Chapter 3, for studying delamination of composites. Utilizing the phase field augmented PD framework, our idea is to model the interfacial cohesive damage through degradation functions and the fracture or fragmentation through the critical energy release rate. Our model eliminates the conventional traction-separation law (TSL) that is known to result in the popular cohesive zone model (CZM). In the process, the approach potentially addresses some limitations of the existing techniques, which make use of an empirical interaction among different modes of loading (e.g. mode I, mode II etc.). By regarding delamination under different loading conditions as problems that differ only in their boundary conditions, our approach provides for a more general scheme for tracking delamination. Our proposal thus accords no special treatment to the different modes and can handle general spatial locations of weaker interface layers. With no special crack tracking algorithms or additional ad-hoc criteria for crack propagation, considerable computational simplicity also accrues. The approach can tackle cases where cracks may propagate even in the bulk material body. The new bond breaking criterion that we employ replaces the ad-hocism inherent in bond-stretch-based or bond-energy-based conditions. Using numerical simulations on mode I (double cantilever beam test), mode II (end loaded split and end notched flexure tests) and mixed mode (fixed ratio mixed mode test) delamination cases, the model is validated against relevant experimental observations. Simulations on modified mixed mode bending test and multiple layer delamination test are also presented. The thesis is wound up in Chapter 5 with a summary of accomplished research and some suggestions for future research.