A phase-field fracture model for 3D film-substrate systems

Thin films bonded to substrates are widely used in various engineering applications, including microelectromechanical systems (MEMS), integrated circuits (ICs) packaging, flexible electronics and thermal barriers. Understanding the fracture behavior of film-substrate systems is critical, as complex fracture patterns often emerge due to the differing material properties between the film and substrate. This work is the first to present a unified phase-field fracture formulation that captures damage in both the film and substrate by integrating surface mechanics (Gurtin-Murdoch theory) and bulk mechanics within a thermodynamically consistent framework. Unlike previous studies that neglect substrate damage or rely on computationally intensive 3D film modeling, our approach enables efficient simulation with distinct damage evolution across material interfaces. This study proposes a novel phase-field fracture model to capture the damage evolution in film-substrate composites, where the film is treated as a two-dimensional membrane bonded to a threedimensional substrate. Leveraging the surface mechanics in Gurtin-Murdoch theory, the model treats the film as a zero-thickness membrane with surface parameters distinct from the substrate. This approach significantly reduces computational costs compared to traditional methods that require fine 3D meshing for thin films. The finite element implementation employs a thermodynamically-consistent framework and a staggered solution scheme to solve the nonlinear governing equations, allowing for efficient simulation of coupling phase-field damage and large deformation. Two numerical examples are provided to validate the model and explore fracture behavior: (i) a 3D edge-cracked plate subjected to uniaxial tension, and (ii) an indentation test of a tough film-coated substrate. Results demonstrate distinct damage progression in the film and substrate, highlighting the role of the film in predicting the fracture. This study not only contributes to the theoretical understanding of film-substrate fracture but also paves the computational approach for future work on complex multi-layered systems and multi-physics fracture modeling.