Issue34

T.-T.-G. Vo et alii, Frattura ed Integrità Strutturale, 34 (2015) 237-245; DOI: 10.3221/IGF-ESIS.34.25 239 (a) (b) (c) Figure 1 : A representation of a crack with additional degrees of freedom for enriched elements (circle symbols represent the elements enriched by the Heaviside function and square symbols represent the elements enriched by the singular functions) (a) , global Cartesian coordinate system (r,z), local Cartesian coordinate system (n,t), local polar coordinate system (  ,  ) and representation of the level sets (b) and flowchart for Code_Aster model with X-FEM crack propagation (c) . [4] Criteria of propagation – The maximum hoop stress criterion Erdogan and Sih [5] proposed the maximum hoop stress criterion. The maximum hoop stress criterion assumes that the crack will propagate where the hoop stress   is maximised. Near the crack front, a good approximation of the hoop stress field is given by Eq. (4). 2 1 1 1 3 cos cos sin 2 2 2 2 I II K K r                           (4) The angle of propagation is deduced by differentiating the Eq. (4) and is given in Eq. (5).   2 1 1 2 tan 8 4 I I II II II K K sign K K K                              (5) where K I , K II are the values of the stress intensity factors. For non-planar crack propagation, at each point along the crack front, a plane perpendicular to the crack front at this point will be considered. The directions of the non-planar crack paths are also computed using Eqs. (4) and (5). C RACK PROPAGATION IN AGEING GRAPHITE BRICKS Algorithms of crack propagation in ageing graphite bricks using X-FEM he analysis is done in two steps (see Fig. 2). The first one is the ageing analysis. In order to perform this calculation, the complex ABAQUS User MATerial (UMAT) routine, developed by Amec Foster Wheeler since the 1990s, was used (Code_Aster being able to directly read UMAT routines). From this calculation, it is possible to extract the different material properties at any instant t crack which also vary in space. For this study, the assumption is made that the crack will propagate instantly, therefore the properties of graphite are not evolving during crack propagation and the behaviour can be considered elastic. The important values from the UMAT calculation are the Young’s modulus and T