Chapter 8 **Fracture Toughness Determination with the Use of Miniaturized Specimens 143** Jan Dzugan, Pavel Konopik and Martin Rund


Preface

During recent years, the contact mechanics and fracture mechanics have found a considera‐ ble application in the solution of engineering problems to increase the life of the component. Contact mechanics studies the stress and strain states of bodies in contact; it is a contact that leads to friction interaction and wear. In recent years, computational contact mechanics has been a topic of intense research. The aim of this research is to devise robust solution schemes and new discretization techniques for the description of contact phenomena, which can then be applied to a much broader range of engineering analysis areas than is currently the case. The focus will be on a detailed treatment of the theoretical formulation of contact problems with regard to mechanics and mathematics. Fracture is understood to be the sepa‐ ration of a body of material into two or more pieces, whereby the load carrying is reduced to zero. The process of fracture can be considered to be made up of two components, crack initiation and crack propagation. Fracture mechanics has developed into a useful tool in the design of crack-tolerant structures and in fracture control; it also has a place in failure analy‐ sis. Fracture mechanics makes it possible to determine whether a crack of a given length in a material of known fracture toughness is dangerous because it will propagate to fracture at a given stress level. If the cause of crack extension may not be controlled, the only thing left to

The different contributions of this book will cover the various advanced topics of research. It provides some needed background with respect to contact mechanics, fracture mechanics, and the use of finite element methods in both. All the covered chapters of this book are of a theoreti‐ cal and applied nature, suitable for the researchers of engineering, physics, applied mathemat‐ ics and mechanics with an interest in computer simulation of contact and fracture problems. This book contains two sections as its name; Chapters 1–7 deal with contact mechanics, and Chapters 8–13 deal with fracture mechanics. Hermetic sealing studies are carried out in Chapter 1. Sealing capacity depends on the contact characteristics—the relative contact area and the gap density in the joint. In this chapter, the contact of a single asperity is considered taking into account the influence of the remaining contacting asperities. The response of a nanometer-scaled single asperity onto flat surfaces is experimentally accessible using atomic force microscopy, which is studied in Chapter 2. The author describes three experimental methods based on atomic force microscopy and corresponding methods for statistical data analysis. Chapter 3 presents an update of theories involving the differential hardness prob‐ lem, starting from the hypothesis made by Tabor for the contact between a sphere and a

designer is to calculate the critical length in advance.

