Course ILTOF02 - Fundamentals in linear elastic fracture mechanics
Course ILTOF02 - Fundamentals in linear elastic fracture mechanics
Lecturer: Prof. Dr. Alberto CARPINTERI
Fundamental reference for the course: A. Carpinteri, Structural mechanics: a unified approach, Chapman & Hall, London, 1997
Topic 1: Griffith’s Theory (1 h)
The pioneering energy approach by A.A.Griffith is illustrated, leading to the well-known formula where the critical stress of crack extension is expressed as a function of the material properties (elastic modulus, specific surface energy) and of the crack length.
Lecture 1:
Topic 2: Westergaard’s method of complex potentials (3 h)
The mathematical method of the complex potentials is completely treated, leading to the fundamental concept of stress-intensity factor. All the three fracture Modes (opening, sliding, tearing) are represented, with their characteristic displacement fields.
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Topic 3: Williams’method of series expansion (2 h)
The mathematical method of the series expansion is completely treated, leading to the description of the singular stress field at the vertex of a re-entrant corner. When the corner angle is tending to zero, a semiinfinite crack is obtained with its characteristic order ½ stress singularity.
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Topic 4: Irwin’s fundamental relationship (1 h)
The fundamental relationship of Linear Elastic Fracture Mechanics (LEFM) is demonstrated, connecting stress-intensity factor and strain energy release rate. In the particular case of critical condition, the relationship between fracture toughness and fracture energy is obtained.
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Topic 5: Mixed Mode fracture criteria (1 h)
The problem of defining the critical condition, when both Mode I (opening) and Mode II (sliding) are active, is considered. In particular, the Maximum Circumferential Stress Criterion is discussed in the details.
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Topic 6: Crack tip plastic zone (1 h)
The crack tip plastic zone is evaluated following two different paths: (i) the cutoff of the stress-singularity with stress redistribution (Irwin); (ii) the cohesive closing stress distribution imposing zero intensification (Dugdale).
Lecture 9: please register to the website to access this lecture.
Topic 7: Brittleness number and size-scale transition (1 h)
Considering independent structural failures due to brittle crack propagation or to plastic collapse at the ligament, a nondimensional number can be defined
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