Fracture mechanics

Fracture mechanics and complexity sciences

The course intends to provide the fundamental concepts of Nonlinear Fracture Mechanics as well as of Fractal Fracture Mechanics. Although this two advanced topics are both connected with Linear Elastic Fracture Mechanics, a specific and extended knowledge of the latter is not required to the attendants. On the other hand, the nonlinear and the fractal aspects are both very important for practical applications and may be treated in the framework of Complexity Sciences.

As a matter of fact, from simple nonlinear rules a catastrophic and/or chaotic mechanical behaviour may derive. Two significant examples are provided by the cohesive constitutive law and by the unilateral constraint condition between the crack faces. The former produces ductile versus brittle size-scale transitions, where the brittle crack propagation is described by cusp catastrophe or snap-back load versus deflection branches. The latter produces nonlinear or chaotic vibrations.

On the other hand, from apparently disordered or chaotic situations a relatively ordered and regular condition may emerge
Code:
ILTOF01-EN
Price:
Free of charge

Fundamentals in linear elastic fracture mechanics

The course intends to provide the fundamental concepts of Linear Elastic Fracture Mechanics. After introducing the pioneering energy approach by A.A.Griffith (1920), the stress intensification concept is widely discussed, presenting the two fundamental mathematical approaches to solve the singular stress field in the crack tip vicinity:

  • (i) the complex potential method by Westergaard (1939), and
  • (ii) the series expansion method by Williams (1952).

With the latter, it is possible to study also the stress intensification at the vertex of re-entrant corners. Then, the fundamental relationship between the energy and the stress- ntensity approaches is illustrated according to the original demonstration due to G.R.Irwin (1957). The stress-intensity fracture criterion is also generalized to Mixed Mode conditions. In addition, the size of the plastic zone at the crack tip is evaluated, according to the different approaches by Irwin and Dugdale (1960).

Finally, the brittleness number is defined as a function of yield strength, fracture toughness and structural size-scale
Code:
ILTOF02-EN
Price:
Free of charge

Concepts of fracture mechanics

This course has been prepared to meet the continuing demand for a course designed to present a clear, consistent, straight forward and unified interpretation of the basic concepts and underlying principles of Fracture Mechanics. The course begins with a brief account of some characteristic failures that could not be explained by the traditional failure criteria and of Griffith’s experiments which gave impetus to the development of a new philosophy in engineering design based on fracture mechanics. For the determination of the stress and deformation fields in cracked bodies the Westergaard method is introduced with particular emphasis on the local behaviour around the crack tip. The models of Irwin and Dugdale for the determination of the extent of plastic zone directly ahead of the crack are presented. The earliest attempt by Griffith to formulate a linear elastic theory of crack propagation will be discussed and analyzed. This is will lead us to the presentation of the theory of crack growth based on the global energy balance of the entire system and the Griffith criterion. The critical stress intensity factor criterion along with the experimental procedure for determining the plane strain critical intensity factor will be also presented and illustrated with examples. We will continue with the presentation of the J-integral in two dimensional problems and its physical intrpetation in terms of the rate of change of potential energy with respect to an incremental extension of crack. Experimental methods for the evaluation of the integral and the ASTM standard method for the determination of its critical value JIC will be described. Finally the usefulness and versatility of the strain energy density theory in solving a host of two and three dimensional problems of mixed mode crack growth in brittle and ductile fracture will be addressed. A selection of problems which cover the most important aspect of fracture mechanics is also included.
Code:
ILTOF08-EN
Price:
Free of charge

Advanced applications of nonlinear crack models

The course intends to provide an overview of advanced engineering applications of nonlinear crack models widely used in Fracture Mechanics, namely the cohesive crack model and the bridged crack model.

The first two lectures are dedicated to the cohesive crack model, which is today one of the most used numerical models for the analysis of nonlinear crack propagation problems. After a brief account of the main features and hypotheses of the cohesive crack model for Mode I and Mixed Mode crack propagation, the mathematical details regarding its implementation in the Finite Element Method are carefully discussed.

Several engineering applications will be presented...
Code:
ILTOF03-EN
Price:
Free of charge
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