# Corsi gratuiti

## 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## 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## Design for Six Sigma: an introduction

Dr. Simon Barnard, Principal Consultant and Founder, SCB Associates Ltd.

Dr. David Moseley, Technical Director, EnginSoft UK Ltd.

This free introductory course covers the following topics:

- An introduction to Design for Six Sigma
- From problem solving to Design for Six Sigma
- Six Sigma roadmaps: the process improvement roadmap (DMAIC) and the design process roadmap (IDOV)
- Design for Six Sigma case study: Micro-actuator for Hard Disk Drive
- Identify Phase - Customer Requirements and Critical to Quality (CTQ)
- Design Phase
- Optimise Phase: Design for Six Sigma using modeFRONTIER Design Optimisation
- Validate Phase

The course is subdivided into 5 lectures with a total duration of about 1 hour. Each topic includes a questionnaire designed to test your comprehension.

To join this free course please do the following:

- register to improve.it website
- follow this link and log in

## Concepts of fracture mechanics

## Solidification of metals

The course gives an introduction to microstructure formation during solidification of metals. Nucleation and growth of crystals from the melt is treated and the morphology of different microstructural features such as cells and dendrites is described. Three phase reactions such as eutectic and peritectic solidification is treated. Redistribution of solute during solidification of alloys is described. Finally, some experimental techniques for studying solidification are described.

The total length of the multimedia lectures is 4 hours and 45 minutes## Statistical methods in fatigue testing

The course provides an introduction to statistical methods in the context of durability testing, in particular high-cycle fatigue.

The lifetime of a component under low stress is best described by a statistical distribution with a high variance (scatter). In the interest of safety, the lower quantiles of this distribution – e.g. the minimum lifetime that is reached by all but 1% of the parts – need to be estimated accurately. As fatigue tests are time consuming and expensive, we have to draw conclusions on rare events from a small number of observations...## Aluminium and magnesium foundry alloys

## 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...