Analyses of breaking mechanics by the finite element method. On the meaning of J integrals and analogues

Technical Report · Tue Jul 01 04:00:00 EDT 1975

OSTI ID:4099123

Roche, R

Calculations carried out at Saclay by the method of finite elements show that the value of the integral J$sub 1$ depends on the contour chosen, when this latter passes through a zone which has undergone plastic deformation. An outline of the Boussinesq stress tensor properties is followed by an examination of the elastic energy density distribution, centred on cases where this depends not only on the deformation but also explicitly on the point considered. It is then useful to introduce the energy-impulsion tensor of the field theory. Any zone where the elastic energy density depends explicitly on the point considered is taken as a defect. The total energy variation of the body-loading device system in the event of development of the defect can be calculated, and is expressed in certain cases by surface integrals J$sub 1$ (translation) L (rotation). In Fracture Mechanics the defect includes the crack and its accompanying plastic zone, which explains why integrals such as J$sub 1$ have a single value only on contours taking in the crack and the whole plastic zone and justifies the numerical results obtained by the Pastel programme. Finally some brief comments are devoted to the deformation energy density and to the use of J type integrals as a criterion of crack propagation. (FR)

• Research Organization: CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Service des Etudes Mecaniques et Thermiques
• NSA Number: NSA-33-014148
• OSTI ID: 4099123
• Report Number(s): CEA-N--1807
• Country of Publication: France
• Language: French

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