Continuum damage mechanics has been proven to be a valuable tool for the determination of material deterioration of composites. Within this framework, a continuum damage model for determination of effective response of fiber reinforced composites is presented. It is assumed that damage evolves on planes with normal orthogonal to the fiber direction and thus is capable of describing the matrix dominated failure of composites. The approach is based on a tensorial representation of damage and on a coordinate-free determination of thermodynamic and dissipative potentials. To simplify the expression of the thermodynamic potential, certain damage tensor components are used to describe the initial material anisotropy. Furthermore, dissipative potentials are formulated which are assumed to be isotropic functions of the thermodynamic forces associated with damage tensors. Parameters for the CDM model are determined using a microscale homogenization method, in which a representative cell of the periodic microstructure consists of fibers, matrix, and two crack fields which are parallel to the fiber direction and evolve independently. The assumption of two independent crack fields in an initially transversely isotropic media makes the material behaviour monoclinic. A representative cell is discretized by the finite element method and the CDM model is fitted by the least squares method to the results obtained. It is concluded from the obtained results that the proposed damage model is capable of describing elastic properties of the damage material. Finally, the CDM model is implemented into the general purpose finite element program ABAQUS in order to capture the effective response of composites. The proposed approach is illustrated by simulating damage growth at the meso-level by calculating the response of a unidirectional laminate loaded in tension. The obtained results show that the essential aspects of the mechanical behaviour of a continuous fiber composite loaded in tension can be captured by the present damage model.
Remarks concerning the analysis of thick sandwich shells are presented. The results obtained for a Mindlin type shell element and a technique which uses shell and solid elements are compared with the available analytical solution.
The bending of a thick composite plate is studied by using a 2-d plate element with a stiffness matrix derived by a 3-d solid model for a typical element. Constraint equations are used to ensure full displacement continuity between adjacent plate elements. After solving the global behaviour by 2-d elements the local behaviour is studied by using the 3-d model of the typical element. The approach is verified by comparing the full 3-d stress state obtained with an available analytical solution.
Accounting for environmental effects in fatigue has long been a necessity in Finland. This requirement was placed into the national regulatory guides in 2002 and the regulatory body, Radiation and Nuclear Safety Authority (STUK) required the license holders of operating reactors to respond by 2004. At that time, the international state-of-the-art was reviewed and found not mature. However, reasonable approaches for accounting environmental effects were developed and adopted by both utilities, Fortum and TVO. Adoption of the proposed new design curves was considered impractical and calculation of Fen factors was preferred. This placed the Finnish utilities among the first industries, who brought environment assisted fatigue (EAF) into practice. At the same time, fatigue design of the new EPR design (OL3) was also subject of the requirement. The experimental work and approaches developed by Areva have been widely discussed in previous PVP Conferences. A high number of PVP papers in these ‘ENVIRONMENTAL FATIGUE ISSUES’ sessions reveals that work remains to be done before the state-of-the-art in EAF is mature and an international consensus can be reached. Follow-up of evolving state-of-the-art is a part of the safety culture for Finnish utilities and regulator. Therefore, we encourage the researchers and engineers together to find solutions, which can be justified by sound arguments and brought into practice to reduce confusion and bias in fatigue management.
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