Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Organic fertilization of peach trees: implication on nitrogen availability, root growth and carbon distribution within plant

In the last years, sustainable horticulture has been increasing; however, to be successful this practice needs an efficient soil fertility management to maintain a high productivity and fruit quality standards. For this purpose composted organic materials from agri-food industry and municipal solid waste has been used as a source to replace chemical fertilizers and increase soil organic matter. To better understand the influence of compost application on soil fertility and plant growth, we carried out a study comparing organic and mineral nitrogen (N) fertilization in micro propagated plants, potted trees and commercial peach orchard with these aims: 1. evaluation of tree development, CO2 fixation and carbon partition to the different organs of two-years-old potted peach trees. 2. Determination of soil N concentration and nitrate-N effect on plant growth and root oxidative stress of micro propagated plant after increasing rates of N applications. 3. Assessment of soil chemical and biological fertility, tree growth and yield and fruit quality in a commercial orchard. The addition of compost at high rate was effective in increasing CO2 fixation, promoting root growth, shoot and fruit biomass. Furthermore, organic fertilizers influenced C partitioning, favoring C accumulation in roots, wood and fruits. The higher CO2 fixation was the result of a larger tree leaf area, rather than an increase in leaf photosynthetic efficiency, showing a stimulation of plant growth by application of compost. High concentrations of compost increased total soil N concentration, but were not effective in increasing nitrate-N soil concentration; in contrast mineral-N applications increased linearly soil nitrate-N, even at the lowest rate tested. Soil nitrate-N concentration influenced positively plant growth at low rate (60- 80 mg kg-1), whereas at high concentrations showed negative effects. In this trial, the decrease of root growth, as a response to excessive nitrate-N soil concentration, was not anticipated by root oxidative stress. Continuous annual applications of compost for 10 years enhanced soil organic matter content and total soil N concentration. Additionally, high rate of compost application (10 t ha-1 year-1) enhanced microbial biomass. On the other hand, different fertilizers management did not modify tree yield, but influenced fruit size and precocity index. The present data support the idea that organic fertilizers can be used successfully as a substitute of mineral fertilizers in fruit tree nutrient management, since they promote an increase of soil chemical and biological fertility, prevent excessive nitrate-N soil concentration, promote plant growth and potentially C sequestration into the soil.

Genetic basis of variation for root traits and response to heat stress in durum wheat

Durum wheat is the second most important wheat species worldwide and the most important crop in several Mediterranean countries including Italy. Durum wheat is primarily grown under rainfed conditions where episodes of drought and heat stress are major factors limiting grain yield. The research presented in this thesis aimed at the identification of traits and genes that underlie root system architecture (RSA) and tolerance to heat stress in durum wheat, in order to eventually contribute to the genetic improvement of this species. In the first two experiments we aimed at the identification of QTLs for root trait architecture at the seedling level by studying a bi-parental population of 176 recombinant inbred lines (from the cross Meridiano x Claudio) and a collection of 183 durum elite accessions. Forty-eight novel QTLs for RSA traits were identified in each of the two experiments, by means of linkage- and association mapping-based QTL analysis, respectively. Important QTLs controlling the angle of root growth in the seedling were identified. In a third experiment, we investigated the phenotypic variation of root anatomical traits by means of microscope-based analysis of root cross sections in 10 elite durum cultivars. The results showed the presence of sizeable genetic variation in aerenchyma-related traits, prompting for additional studies aimed at mapping the QTLs governing such variation and to test the role of aerenchyma in the adaptive response to abiotic stresses. In the fourth experiment, an association mapping experiment for cell membrane stability at the seedling stage (as a proxy trait for heat tolerance) was carried out by means of association mapping. A total of 34 QTLs (including five major ones), were detected. Our study provides information on QTLs for root architecture and heat tolerance which could potentially be considered in durum wheat breeding programs.