DOKUZ EYLÜL UNIVERSITY MECHANICAL ENGINEERING DEPARTMENT INTRODUCTION TO FRACTURE MECHANICS Prof. Dr. M. Evren Toygar DEÜ, Makina MÜhendisliği Bölümü

FRACTURE MECHANICS REFERENCES: 1. Anderson, “Fracture Mechanics Fundamentals and Applications.” 2. Richard W.Hertzberg, “Deformation and Fracture Mechanics Of Engineering Materials.” 3. Dowling, "Mechanical Behavior of Materials" 4. Broek, “Elementary Engineering Fracture Mechanics” 5. Ağah Uğuz, “Kırılma Mekaniğine Giriş “

FRACTURE When material damage like micro-cracks and voids grow in size and become localized, the averaging procedure can no longer be applied and discontinuities must be taken into account.This localization results in a macroscopic crack, which may grow very fast, resulting in global failure.

Fracture Mechanics Definition: It is the field of mechanics concerned with the study of propagation of cracks in materails. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material’s resistance to fracture.

Fracture Mechanics In modern materials science, fracture mechanics is an important tool in improving the mechanical performance of mechanical components. It applies the physics of stress and strain, in particular the theories of elasticity and plasticity, to the microscopic defects found in real materials in order to predict the macroscopic mechanical failure of bodies.

Fracture Mechanics In fracture mechanics attention is basically focused on a single crack. Theoretical concepts and experimental techniques have been and are being developed, which allow answers to questions like: Will a crack grow under the given load ? When a crack grows, what is its speed and direction ?

Fracture Mechanics Will crack growth stop ? What is the residual strength of a construction (part) as a function of the (initial) crack What is the length and the load ? What is the proper inspection frequency ? When must the part be repaired or replaced ?

Fracture mechanics Fracture mechanics is a failure theory that determines material failure by energy criteria, possibly in conjunction with strength (or yield) criteria considers failure to be propagating throughout the structure rather than simultaneous throughout the entire failure zone or surface.

Linear elastic fracture mechanics (LEFM) A large field of fracture mechanics uses concepts and theories in which linear elastic material behavior is an essential assumption. This is the case for Linear Elastic Fracture Mechanics (LEFM). is the basic theory of fracture, that deals with sharp cracks in elastic bodies. It is applicable to any materials as long as the material is elastic except in a vanishingly small region at the crack tip (assumption of small scale yielding), brittle or quasi brittle fracture, stable or unstable crack growth

Elastic-plastic fracture mechanics is the theory of ductile fracture, usually characterized by stable crack growth (ductile metals) the fracture process is accompanied by formation of large plastic zone at the crack tip

Negligence during design, constuction, or operation of structure. Why structures Fail Negligence during design, constuction, or operation of structure. Application of a new design or material, which produces an unexpected result. DEÜ, Makina MÜhendisliği Bölümü

Historical Perspective Experiments performed by Leonardo da Vinci several centuries earlier provided some clues as to the root cause of fracture. He measured the strength of iron wires and found that the strength varied inversly with wire length. A quantitative connection between fracture stress and flaw size came from the work of Griffth 1920. He applied a stress analysis of an elliptical hole to the unstable propagation of crack. Griffth invoked the first law of thermodynamics to formulate a fracture theory based on a simple energy balance.

Figure 1 Galileo’ s tension bar Figure 2 Da Vinci’s cable

Figure 3 schematic representation of ancient Rome bridge

During Design some important titles are: Deformation and Fracture Exceed the Elastic Deformation Buckling (Burkulma) Plastic Deformation Fracture (Kırılma) Fatique (Yorulma) Creep (Sünme ) Stress Corrosion Cracking (Gerilme Korozyon Çatlağı )