Students attending the course are expected to gain a full understanding of such aspects as the consequences of the presence of defects and geometric irregularities and of the ensuing stress concentrations.

Issues such as the scale or size effect and the effect of cyclic loading will also be clarified.

Attendees will also be interactively involved in the use of the finite element code Abaqus for the computation of fracture parameters such as the stress concentration factor, the stress intensity factor and the strain energy release rate in simple 2D structural configurations.

Students will have to show their knowledge and understanding of subjects treated in undergraduate courses, such as strength of materials and structural mechanics, and master courses of the first semesters, such as the finite element method and limit analysis methods.

At the end of the course they will be required to show their ability in applying their knowledge and understanding to the conceptual treatment of structural problems involving the possibility of defect propagation up to structural failure. In particular, they will have to show their knowledge and understanding of concepts like stress concentration, role of defects and the conditions for their propagation, brittle versus ductile failure, size effects, different approaches to fatigue failure and they will be required to apply their gained knowledge and understanding to the computation of fracture parameters such as the stress concentration factor, the stress intensity factor and the strain energy release rate and the J integral in simple 2D structural configurations.

Plane problems in linear elasticity. Formulation of Beltrami’s problem. Airy’s function. Formulation of Beltrami’s problem in cylindrical coordinates. Stress concentrations in linear elasticity. Lamé’s analytical solution for the thick pipe. Kirsch’s analytical solution of the plate with a circular hole. Williams’ formulas for the stress singularity near a reentrant corner. Stress intensity factor.

Basic notions of linear elastic fracture mechanics. Griffith’s approach: strain energy release rate. Irwin’s approach. Crack tip plastic zone width estimate: Irwin and Dugdale models. Range of applicability of linear elastic fracture mechanics. Case histories concerning failures due to brittle fracture and fatigue. Computation of fracture parameters using the finite element method. X-FEM approach to the simulation of crack propagation.

Ductile elastoplastic fracture mechanics. Crack tip opening displacement. Nonlinear strain energy release rate. J integral. J integral finite element computation.

Experimental fracture behavior of structural materials: metals, polymers, quasi-brittle materials (e.g. concrete).

Strain localization. Notion of characteristic length. Size effects.

Quasi-brittle fracture mechanics: cohesive models. Cohesive modeling of delamination.

High-cycle fatigue. Experimental evidences: Wohler’s diagrams. Total life and defect tolerant approaches to fatigue. Paris-Erdogan law. Safe Life and Fail Safe design philosophies.

Experimental measurement of fracture parameters.

Strength of materials, statics of deformable elastic continua, introduction to the finite element method.

The exam consists of a written test on the course subject matter. The written test will be followed by a short colloquioum where the student work will be revised and possibly integrated with oral questions.

The written questions in the test are aimed at verifying the student knowledge and understanding of the different conditions for structural failure, the role of defects, the effects of stress concentrations, the size effect and the effect of cyclic loading. The student will also have to prove to know and to have understood the methods for the computation of fracture mechanics parameters such as the stress intensity factor, the strain energy release rate and the J integral.