Learning objectives
<br />To present basic concepts of mechanics of materials and mechanics of fracture and fatigue in order to assess safety of civil, mechanical, aeronautical, nuclear, and so on structures.
Prerequisites
<br />Propedeuticities (suggested)<br />Analisi A-B, Analisi C, Geometria, Meccanica Razionale, Scienza delle Costruzioni A-B.
Course unit content
<br />Constitutive laws of materials<br />Generalised Hooke's law for isotropic, orthotropic and transversally isotropic materials. <br />Material's non-linear behaviour: plasticity (yielding function, isotropic and kinematic hardening, associative and non-associative flow rule). Yielding criteria for structural materials. Practical examples.<br /><br />Basic concepts of fracture mechanics.<br />Analytical results of the theory of elasticity for problems involving stress concentration.<br />Infinite plate with a circular hole. Complex analytic functions. Kolosoff (1909)-Muskhelishvili (1933) method. Infinite plate with an elliptical hole. <br />Mode of fracture. The problem of cracked bodies.<br />Linear elastic fracture mechanics. Westergaard's solution. Stress intensity factor (SIF) concept. Energetic aspects and fracture energy (Griffith's approach). Relation between fracture energy and critical value of the stress intensity factor. Elasto-plastic fracture mechanics. Dugdale's approach. Crack opening displavement (CTOD), J-integral.<br /><br />Methods for SIF evaluation<br />Analitical methods, superposition principle in fracture mechanics<br />Finite element method applied to fracture mechanics problems; quarter point elements. Use of the stress and displacement field (Ingraffea and Manu (1980)). Use of the J-integral (E.D.I., Equivalent Domain Integral) and its numerical evaluation; virtual crack extension method (V.C.E).<br />Use of the weight function method.<br /><br />Crack growth directions in mixed mode: criterion of the maximum circumferential stress, criterion of the minimum strain energy density.<br /><br />Fatigue<br />Mechanism of crack propagation. Crack propagation due to cyclic loading (fatigue phenomena): Constant amplitude cyclic loads : experimental approach (Whöler's curves) and analytical approach (Paris-Erdogan law). Variable amplitude cyclic loads: experimental approach and analytical approach (cycle counting). Closing remarks of fatigue crack propagation.
Bibliography
<br />Literature/Course material<br /><br /><br />Carpinteri, "Meccanica dei Materiali e della Frattura", Ed. Pitagora, Bologna.<br /><br /><br />Carpinteri, "Handbook of Fatigue Crack Propagation in Metallic Structures", Ed. Elsevier Science Publishers B.V., Amsterdam (Olanda).<br /><br /><br />Carpinteri: "Scienza delle Costruzioni", Vol. 1 e 2, Ed. Pitagora, Bologna.<br /><br /><br />Broek, D. (1982). Elementary engineering fracture mechanics, Martinus Nijhoff Publishers.<br /><br /><br />Broek, D. (1986). The practical use of fracture mechanics, Martinus Nijhoff Publishers.<br /><br /><br /> <br />Specialised books and Literature<br /><br />Murakami Y. et al., (Editors), Stress intensity factor handbook, Vol. I, II, Pergamon Press, Oxford, U.K., 1987; Vol. III; The Society of Material Science, Japan, Pergamon Press, Oxford, U.K., 1992.<br /><br /><br />Muskhelishvili N. I., Some basic problems of the matematical theory of elasticity, I ed. in Russo 1933, II ed. in inglese, Noordhoff-Groningen, 1953.<br /><br /><br />Barsom J. M., Rolfe S. T., Fracture and fatigue control in structures, Prentice-Hall, Inc., New Jersey (U.S.A.), 1987.<br /><br /><br />Kolosoff G.V., On an application of complex function theory to a plane problem of the matematicall theory of elasticity, Yuriev, 1909.<br /><br /><br />Muskhelishvili N. I., Some basic problems of the matematical theory of elasticity, I ed. in Russo 1933, II ed. in inglese, Noordhoff-Groningen, 1953.<br /><br /><br />Timoshenko S.P., History of strength of materials, McGraw-Hill, New York, 1953.<br />
Teaching methods
<br />Form of teaching<br />Theory supported by exercises.<br />Assessment method<br />Oral examination
