Dissertation Title: Effective fracture toughness of heterogeneous materials
Date: 2025/05/22 - 2025/05/22
Dissertation Title: Effective fracture toughness of heterogeneous materials
Speaker: Sen Liu, Ph.D. candidate at UM-SJTU Joint Institute
Time: 3:00 PM - 5:00 PM, Thursday, May 22, 2025 (Beijing Time)
Location: Room 403, Longbin Building
Abstract
Advances in the aerospace and automotive industries necessitate the investigation of the macroscopic fracture behavior of heterogeneous materials. Such behavior stems from degradation mechanisms at the microscale, such as crack initiation and propagation. These mechanisms are inherently driven by deformation redistribution caused by the heterogeneity in the stiffness, strength, and toughness of the material's constituents. Direct simulation of the macroscopic behavior poses a huge computational burden due to the necessity of resolving microstructures. To alleviate such computational burden, a popular approach is to develop a homogenization framework, which requires a comprehensive understanding of a so-called effective fracture toughness. However, existing formulations for this property fail to adequately account for the following ingredients: tortuosity, irreversibility, non-interpenetration, stress criterion for crack nucleation and conservativity.
To address this challenge, two formulations for the effective fracture toughness are proposed to account for the aforementioned ingredients.
The first formulation is obtained through asymptotic homogenization. This formulation assumes that the phase field model accurately describes the microscopic fracture behavior, which considers the stress criterion for crack nucleation, irreversibility and non-interpenetration constraints. The outcome of asymptotic homogenization is an anisotropic effective fracture toughness. This formulation enables the reproduction of the fracture behavior of the original heterogeneous microscopic model and quantitative prediction of the toughening effect under specific conditions. Specifically, when the fracture toughnesses of all constituents are the same, the toughening effect depends on whether there is a contrast in the toughness moduli of the constituents. Here, the toughness modulus refers to the energy absorbed by each constituent per unit volume before fracture.
The second formulation is obtained from numerical experiments at the microscale. This formulation assumes that the microscopic behavior is accurately described by a phase field model accounting for the stress criterion for crack nucleation, irreversibility and non-interpenetration constraints. In this formulation, the tortuosity is the natural outcome of the numerical experiments and the conservativity is accounted for with a numerical scheme. The resulting effective fracture toughness explicitly depends on the macroscopic crack direction, readily anisotropic. Moreover, this formulation is able to predict multiple toughening effects: that due to tougher inclusions, that resulting from microscopic cracking tortuosity, and that arising from the contrast in the tensile strength when fracture toughness is uniform.
Finally, the similarities and differences between these two formulations are discussed, and they are compared with other existing formulations. Compared to other formulations, the proposed formulations output similar predictions of effective fracture toughness across varying volume fractions and toughnesses of inclusions.
Biography
Sen Liu is a Ph.D. candidate at the University of Michigan-Shanghai Jiao Tong University Joint Institute, supervised by Prof. Shen Yongxing since September 2020. Before that, he graduated from Northeastern University with a bachelor’s degree in engineering from 2016 to 2020. His research focuses on the effective fracture toughness of heterogeneous materials. His work includes: (1) developing an asymptotic homogenization framework for the phase field fracture of heterogeneous materials and (2) proposing a formulation for the effective fracture toughness accounting for the worst-case scenario by conducting numerical experiments at the microscale. In 2024, he was awarded the Best Presentation Award at the International Interdisciplinary Mechanics Ph.D. Student Academic Forum held by Peking University.