AN ENTROPIC THEORY OF DAMAGE WITH APPLICATIONS TO CORROSION-FATIGUE STRUCTURAL INTEGRITY ASSESSMENT

This dissertation demonstrates an explanation of damage and reliability of critical components and structures within the second law of thermodynamics. The approach relies on the fundamentals of irreversible thermodynamics, specifically the concept of entropy generation due to materials degradation as an index of damage. All failure mechanisms that cause degradation, damage accumulation and ultimate failure share a common feature, namely energy dissipation. Energy dissipation, as a fundamental measure for irreversibility in a thermodynamic treatment of non-equilibrium processes, leads to and can be expressed in terms of entropy generation. The dissertation proposes a theory of damage by relating entropy generation to energy dissipation via generalized thermodynamic forces and thermodynamic fluxes that formally describes the resulting damage. Following the proposed theory of entropic damage, an approach to reliability and integrity characterization based on thermodynamic entropy is discussed. It is shown that the variability in the amount of the thermodynamic-based damage and uncertainties about the parameters of a distribution model describing the variability, leads to a more consistent and broader definition of the well know time-to-failure distribution in reliability engineering. As such it has been shown that the reliability function can be derived from the thermodynamic laws rather than estimated from the observed failure histories. Furthermore, using the superior advantages of the use of entropy generation and accumulation as a damage index in comparison to common observable markers of damage such as crack size, a method is proposed to explain the prognostics and health management (PHM) in terms of the entropic damage. The proposed entropic-based damage theory to reliability and integrity is then demonstrated through experimental validation. Using this theorem, the corrosion-fatigue entropy generation function is derived, evaluated and employed for structural integrity, reliability assessment and remaining useful life (RUL) prediction of Aluminum 7075-T651 specimens tested.

REDUCING TEACHER ATTRITION: THE ROLES AND RESPONSIBILITIES OF BUILDING PRINCIPALS IN A LARGE URBAN DISTRICT TO SUPPORT TEACHER RETENTION

The high rate of teacher attrition in urban schools is well documented. While this does not seem like a problem in Carter County, this equates to hundreds of teachers that need to be replaced annually. Since school year (SY) 2007-08, Carter County has lost over 7,100 teachers, approximately half of (50.1%) of whom resigned, often going to neighboring, higher-paying jurisdictions as suggested by exit survey data (SY2016-2020 Strategic Plan). Included in this study is a range of practices principals use to retain teachers. While the role of the principal is recognized as a critical element in teacher retention, few studies explore the specific practices principals implement to retain teachers and how they use their time to accomplish this task. Through interviews, observations, document analysis and reflective notes, the study identifies the practices four elementary school principals of high and relatively low attrition schools use to support teacher retention. In doing so, the study uses a qualitative cross-case analysis approach. The researcher examined the following leadership practices of the principal and their impact on teacher retention: (a) providing leadership, (b) supporting new teachers, (c) training and mentoring teaching staff, (d) creating opportunities for collaboration, (d) creating a positive school climate, and (e) promoting teacher autonomy. The following research questions served as a foundational guide for the development and implementation of this study: 1. How do principals prioritize addressing teacher attrition or retention relative to all of their other responsibilities? How do they allocate their time to this challenge? 2. What do principals in schools with low attrition rates do to promote retention that principals in high attrition schools do not? What specific practices or interventions are principals in these two types of schools utilizing to retain teachers? Is there evidence to support their use of the practices? The findings that emerge from the data revealed the various practices principals use to influence and support teachers do not differ between the four schools.