Shock Wave Propagation in Composites and Electro-Thermomechanical Coupling of Ferroelectric Materials

Author: Agrawal, Vinamra

Year: 2016

Degree: Dissertation (Ph.D.)

Advisor: Bhattacharya, Kaushik

Committee Members: Ravichandran, Guruswami; Bhattacharya, Kaushik; Kochmann, Dennis M.; Lapusta, Nadia

Option: Mechanical Engineering

DOI: 10.7907/Z98G8HN8

Abstract

How is material behavior at the macro scale influenced by its properties and structure at the micro and meso-scales? How do heterogeneities influence the properties and the response of a material? How does nonlinear coupling of electro-thermo-mechanical properties influence the behavior of a ferroelectric material? How can design at the micro-scale be exploited to obtain selective response? These questions have been topics of significant interest in the materials and mechanics community. Recently, new materials like multifunctional composites and metamaterials have been developed, targeted at selective applications. These materials find applications in areas like energy harvesting, damage mitigation, biomedical devices, and various aerospace applications. The current thesis explores these questions with two major thrusts: (i) internal reflects of shocks in composite media and (ii) shocks in ferroelectric media.

Under the application of high-pressure, high strain rate loading, such as during high velocity impact, shock waves are generated in the material. They can cause the material to achieve very high stress states, and if transmitted without mitigation, can lead to failure of key components. An important question here is 'Can we design materials which can successfully mitigate damage due to shocks?' In a heterogeneous material, like a layered composite, the traveling waves undergo scattering due to internal reflections. In order to understand internal reflections, an idealized problem that focuses on nonlinear shocks and ignores less important elastic waves was formulated and studied in detail. The problem is studied by classifying all possible interactions in the material and then solving corresponding Riemann problems. Using dynamic programming tools, a new algorithm is designed that uses these solutions to generate a complete picture of the impact process. Different laminate designs are explored to study optimal design, by varying individual layer properties and their arrangement. Phenomena like spallation and delamination are also investigated.

Upon high strain rate loading, ferroelectric materials like lead zirconate titanate (PZT) undergo ferroelectric to anti-ferroelectric phase transition leading to large pulsed current output. These materials have thus found applications as pulsed power generators. The problem of shock induced depolarization and the associated electro-thermo-mechanical coupling of ferroelectric materials is studied in this thesis using theoretical and numerical methods. A large deformation dynamic analysis of such materials is conducted to study phase boundary propagation in the medium. The presence of high electrical fields can lead to formation of charges in the material, such as surface charge on the phase boundary. Using conservation laws and the second law of thermodynamics, a set of governing equations are formulated that dictate the phase boundary propagation in isothermal and adiabatic environments. Due to the possibility of surface charges on the phase boundary, the curvature of the phase boundary starts to play a role in the driving force acting on the phase boundary. The equations of motion and driving force see the contribution of nonlinear electro-thermomechanical coupling in the material. Using the equations derived, a canonical problem of impact on a ferroelectric material is studied. A new finite-volume, front-tracking method is developed to solve these equations. Finally, results from numerical simulations are compared to the experimental results.

Files