The aim of this course is to provide the specific tools for thermo-mechanical analysis and design assessment of nuclear reactor structural components. This goal is achieved by taking into account the irradiation effects occurring in the materials selected for fission reactors, and for controlled thermo-nuclear fusion applications as well. On this basis, and in the light of the key neutronics features and the figures of merit concerning both the reactor and the fuel cycle, the course allows acquiring the main criteria of the "design-by-analysis" methodology adopted in the nuclear field. In particular, it develops - both from the conceptual and the quantitative point of view - an "engineering approach" to design and verification, with reference to thermal-hydraulic and thermo-mechanical modelling of reactor components under irradiation, to their technological limits and mutual compatibility requirements, to the main manufacturing and operational issues, and to nuclear regulatory specifications as well. To this end, a significant project of "design-by-analysis" is assigned every year to the class, in the frame of Project Lab activities aimed at the preliminary mechanical sizing and verification of a typical structural component of a fission reactor.

The student knows and understands:

selection principles, technological limits, failure mechanisms, and mutual compatibility requirements of primary materials in a nuclear reactor; thermal-hydraulic and thermo-mechanical modelling tools for the analysis and design assessment of a structural component, according to ASME verification criteria.

The student is able:

to make a critical choice of primary materials and assessment of technological issues, design data and figures of merit for current/Gen IV fission reactors; to evaluate stress and strain fields in a structural component under static loading conditions, including neutron irradiation effects on material behaviour; to tackle issues concerning fuel rod performance under irradiation.

The Project Lab will allow students:

to apply their knowledge and understanding of the "design-by-analysis" approach to a structural component, for its preliminary mechanical sizing and verification of thermo-mechanical limits; to develop team-working attitude, autonomous capabilities in terms of engineering-related cognitive competencies (modelling skills), practical abilities (problem solving), learning and communication skills.

Structural analysis and material constitutive relations. Recalls of continuum mechanics with notes on Cosserat theory of elasticity. Engineering stress-strain curve, Charpy impact test, ideal material models. Generalized equations for Hooke's law, Lamé relations, elastic compliance matrix, thermo-elastic effect. General approach (both in terms of displacements and stresses) for solving a thermo-elastic problem. Axial-symmetric problems, Euler equation for the thermo-elastic behaviour. Thermal stresses under static and transient conditions. Plasticity and creep (Prandtl-Reuss flow laws, Soderberg equations).

Strength of materials and failure assessment criteria. Recalls of multi-axial strength theories and their application. Ductile and brittle failure mechanisms. "Design-by-analysis" of structural components, general considerations on safety. Primary, secondary and peak stresses and verification criteria. Technological and design issues for pressure retaining members. Design criteria for protection against brittle fracture. Notes on cyclic response of materials and limit analysis theorems. Ashby maps and creep master curves.

Overview of nuclear reactor technologies. Primary materials of a nuclear reactor: functional requirements, selection principles, technological limits, mutual compatibility criteria, and their implications at level of plant and fuel cycle. Critical review of technological issues, design data and figures of merit in the different types of current/Gen IV fission reactors. Overview of materials adopted as fuel and cladding, and for pressure vessels.

Thermo-mechanics for nuclear reactor components. Neutron irradiation effects in structural materials (general principles, atomic displacements, embrittlement, induced activity, swelling, growth, irradiation creep), failure mechanisms of the main structural components of a nuclear reactor. Notes on nuclear safety, quality, regulation (ASME III code) and design. Main phenomena occurring in the fuel (e.g., relocation, restructuring, plutonium redistribution, densification, swelling, thermal conductivity degradation, high burnup structure, fission gas release, melting, pellet-cladding interaction) during operating/accidental conditions.

Case studies. Thin and thick cylindrical and spherical shells subject to temperature gradient, internal, and external pressure. Preliminary thickness sizing for vessel and piping design. Shrink-fit stresses in built-up cylinders, fully plastic pressure, autofrettage. Discontinuity stresses at vessel junctures. Interaction domains of membrane and bending stresses. Buckling and resistance verification of cylindrical shells under external pressure. Thermal creep verification based on Larson-Miller approach, design limits for creep. Recalls of thermo-hydraulic analysis of fission reactor core power channels. Thermo-mechanical modelling and analysis of the fuel rod behaviour under irradiation. Fuel rod performance, design and verification.

Project Lab of "design-by-analysis". The project is integral part of the course, and concerns the preliminary mechanical sizing and verification of a significant structural component of a fission reactor (e.g., pressure vessel, thermal shielding, fuel rod), chosen each year among those adopted in current/Gen IV fission reactors.

To attend the course, a knowledge (at least at an elementary level) of solid mechanics, heat transfer, reactor physics, dynamics and control of nuclear plants is required.

More advanced knowledge (not strictly necessary) is suggested on some topics, e.g., those ones addressed by the following recommended courses: Physics of nuclear materials; Machine design; Mechanical behaviour and failure of metals; Computational mechanics and inelastic structural analysis; Heat and mass transfer; Advanced thermal hydraulics and safety of nuclear reactors.

The evaluation consists in an oral examination, aimed at verifying deep knowledge and understanding of the course topics, and estimation skills as well.

The ability of making autonomous judgements to handle (through appropriate modelling and solving) thermo-mechanical problems not strictly related to the "case studies" (selected and illustrated to the class in the exercise sessions during the course) is addressed as well. To this end, simple and short written tests to be set and solved pen-on-paper by the student are assigned at the time of the examination.

Every year, a specific item of nuclear design and technology is thoroughly studied, and a project of "design-by-analysis" concerning a nuclear structural component is assigned to the class (divided in groups of three-five students), in the frame of Project Lab activities performed during the semester, which include tutorship activities consisting of: i) support for the explanation of the selected project; ii) classroom assistance to elaborate the excel sheets and the solution report assigned to class groups as homework (students who cannot take the Project Lab during the semester can work at the project on their own).

The project objective is allowing students to apply the approaches and principles taught in classroom, and to develop autonomous learning skills as well. To this regard, the students should be able to: i) independently, identify missing pieces of information necessary to complete the project tasks; ii) independently, find this information in literature sources; iii) critically, assess and use contents of references to reach the project objectives; iv) formulate, set up, and implement in excel sheets the thermo-mechanical analyses required by the assigned project; v) summarize and properly discuss in a brief technical report the achieved results.

The project outcomes (i.e., the brief report with excel sheets, prepared by each group) are expected to be delivered at a deadline fixed at the end of the course. These deliverables are discussed during the examination, in order to ascertain that the student is able in autonomy to make, discuss and communicate in a professional manner (i.e., with correct use of language and clarity of exposure) the analyses of the proposed project.

In: C. Lombardi, Nuclear Plants, Chap. 4 (Part II)

Chap. 7 (Vol. I), Chap. 9 (Vol. II)

Chap. 6, 7, 8, 9, 10, 11

Chap. 1, 2, 5, 8

Chap. 1, 2, 3, 8, 13 (Vol. I), Chap. 6, 7, 8 (Vol. II)

Chap. 1, 2, 3, 4, 6

Chap. 11, 12

Chap. 10, 21

Chap. 1, 3, 4, 5, 6

Chap. 9, 13, 14

In: Materials Science and Technology - A Comprehensive Treatment, Vol. 10