Size-dependent damage and fracture of two-layer systems

Two-dimensional three-point bending and four-point bending of two-layer finite element models for a ceramic layer on a metallic substrate are developed to study the damage and fracture characteristics of two-layer systems by introducing an interface cohesive zone model. The damage evolution and fracture modes of ceramic layers of different thicknesses, with loading on the metallic substrates, are compared under different loading conditions based on simulation results. Multiple surface cracks, vertical to the interface between the ceramic and metallic layers, appear in all ceramic layers under four-point bending loading and only in the thinner ceramic layers under three-point bending. For the thicker ceramic layer systems under three-point bending loading, the interface fracture between the ceramic and metallic layers is the main failure mode, agreeing with previous experimental observations. Damage and damage rate, defined by the simulated crack evolution, are found to obey a power law relation with loading and to be consistent with the theoretical predictions based on a mathematical damage model. The damage coefficient, a parameter reflecting the damage rate, is found to be size-dependent based on the simulation and experimental results, and its energy mechanism is discussed. The damage is slower for the thinner ceramic layers with a smaller damage coefficient than that for the thick ceramic layers under three-point and four-point bending loading, and the damage of the ceramic layer systems is faster under three-point bending than under four-point bending, resulted from different crack distributions, damage localization degrees, and energy dissipation. Moreover, the damage is slower for the nanostructured ceramic layers with the stronger interface strength or toughness between two layers