CZM-based Finite-Volume Homogenization and Optimization of Periodic Composites

A novel finite-volume based homogenization theory for damage evolution in periodic materials is proposed, verified and utilized to uncover previously undocumented phenomena at micro- and meso-levels. Displacement discontinuity functions are introduced into the formulation which facilitate separation of the system of equations that controls the response of a periodic composite undergoing damage evolution into primary and auxiliary systems, with the primary system solved just once. The formulation eliminates the necessity to re-assemble the global system of equations during damage evolution, determined by iteratively solving the auxiliary system of equations which governs damage progression. This formulation facilitates the implementation of any traction-displacement separation law to model damage, including traction-free boundary conditions to simulate crack growth and concomitant energy release rates, and a cohesive zone model (CZM) incorporated into the framework.
The proposed CZM-based finite-volume direct averaging micromechanics (FVDAM) theory is verified upon comparison with exact elasticity solutions in the elastic stage of damage evolution, and experimental data and finite-element simulations at both the micro-level and macro-level in the nonlinear stage. The comparison with finite-element simulations of interfacial debonding in a SiC/Titanium composite reveals the beauty of the newly developed approach wherein once the stress normal to a failing interface become compressive, the corresponding governing equations are simply eliminated in the auxiliary system of equations to avoid interfacial interpenetration. This contrasts with the finite-element damage simulation approaches based on carefully chosen interfacial stiffness to resist the interpenetration. Following the extensive verification of CZM-based FVDAM, the newly developed approach is incorporated into a global optimization method, Particle Swarm Optimization (PSO) algorithm, and the marriage produces a powerful design tool for identifying optimal material architectures as well as parameters that are not easily measured experimentally, such as the CZM parameters or the elastic moduli of graphite fibers.
With the newly developed computation tool in modeling damage evolution in composite materials, three practical and important engineering problems are investigated and important fundamental findings are uncovered and documented. The first one is the study of interfacial debonding in SiC/Ti unidirectional composites under transverse loading. The simulation produces good correlation with test data and correctly captures the evolution of fiber/matrix interfacial debonding and subsequent arrest due to the development of compressive stress normal to the interface. The importance of residual stresses is revealed, demonstrating that correct simulation of fiber/matrix debonding is not possible without these stresses.
The second application involves the simulation of evolving damage on the fly in polymeric matrix cross-ply laminates, caused by progressive cracking of the inner 90 degree plies leading to subsequent delamination of adjacent plies. The effect of evolving damage on the homogenized axial stress-strain and transverse Poisson's responses, as well as crack density, are compared with available experimental results, taking account of residual stresses, interfacial resin-rich region and variable strength of the 90 degree plies. The comparison demonstrates the theory's ability to capture the dramatic effect of transverse cracking on the homogenized transverse Poisson's ratio that increases with increasing 90 degree ply thickness, and the damage mode bifurcation from transverse cracking to interfacial delamination, both for the first time. Moreover, the finite-volume simulations indicate that many features observed in the transverse and through-thickness Poisson's response of graphite/epoxy cross-ply laminates may be related to the underpinning damage modes more readily than in the axial response.
The last application involves simulation of damage in graphite/polyimide unidirectional off-axis specimens based on the hypothesis of shear-dominated fiber/matrix interfacial degradation as the primary cause of the observed nonlinearity. For the first time, this study reveals that the off-axis dependent nonlinearity in this material system comprised of elastic fibers and brittle, linearly elastic matrix may be accurately captured using a damage evolution model rather than plasticity, viscoelasticity or viscoplasticity approaches typically employed for the matrix phase.
The results presented in this dissertation demonstrate that the CZM-based FVDAM and the FVDAM-driven PSO algorithm are efficient and robust tools to model damage evolution in heterogeneous materials characterized by complex microstructures, optimize material performance through microstructural identification and calibrate micro-level material properties.