Doctoral Dissertations

Date of Award

12-2024

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mechanical Engineering

Major Professor

Reza Abedi

Committee Members

Stephanie TerMaath, Timothy Truster, Vasilios Alexiades

Abstract

Fracture is a prevalent phenomenon in engineering structures, critically influencing their lifespan. Fragmentation has gained significant attention within engineering and academic communities, given its diverse application applications, such as in military armor and projectile design, as well as for its complex mechanisms. This process often occurs when a high-velocity impactor collides with a target object, breaking it into numerous smaller pieces called fragments. The formation of these fragments is triggered by micro-scale flaws or defects and gradually evolves into macrocracks. As a result, this phenomenon encompasses multiple scales and rate effects, making it challenging to model computationally.

Numerical models of fracture can be categorized into smeared and discrete approaches. The smeared approach regularizes a sharp crack using a continuous damage variable, and is favored over the discrete approach due to its simplicity in tracking evolving cracks without requiring additional criteria for crack kinking and branching. As a smeared approach, the phase field method has demonstrated success in engineering applications. Nonetheless, its application to fragmentation has remained limited, mainly due to its difficulty in cleanly resolving fragment boundaries, relative to sharp crack models. Additionally, the nonconvex nature of coupled governing equations necessitates the use of optimization solvers or complex numerical schemes, giving rise to increased computational costs.

This work aims to address these challenges. A phase field approach is proposed, adhering to a thermodynamically-consistent framework, applicable to both brittle and ductile fracture. Particularly, the evolution equation is formulated using different types of partial differential equations (PDEs), enabling it to accommodate a wide range of strain rates while ensuring efficient, robust, and straightforward numerical solvers. An extensive mathematical analysis on low dimensions of the presented models is conducted to gain insight in rate-dependency of the phase field models on fragmentation response, in which analytical and numerical solutions are provided. As fragments are initiated from weak points within microstructures, material properties can be treated as random fields in the presented numerical models, reducing mesh dependency and accounting for realistic heterogeneity of materials in nature.

Download
Files over 3MB may be slow to open. For best results, right-click and select "save as..."

Share

COinS