PSI - Issue 47

Teresa Morgado et al. / Procedia Structural Integrity 47 (2023) 882–887 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

885

4

In this study, the stress intensity factor (SIF Ref ) was used as reference given by equations 1 and 2 (Morgado, 2015). And, it was used to compare with those obtained by simulation (SIF Num ) for the different crack locations and element types.

Fig. 3. (a) One Contour with 3 contours; (b) Two Contour with 4 contours; (b) Six Contours with 8 contours.

3/2 f BW W max P S a

     

(1)

SIF

=

Re

f

1 2

3 2

5 2

7 2

9 2

   

   

a      

a      

a       W

a       W

a       W

a       W

(2)

2,9

4,6

21,8

37,6

38,7

f

=

−

+

−

+

W W

To study the influence of the mesh refines, eight tests were performed with different degrees of refinement at the crack edge, in the 10 crack length model, considering the element type CPS4. After deciding on the type of mesh geometry to be used, another study was carried out to analyse if the model could be realised without using contact (table1, study 3); this is using a pressure force that would have the same effect as the load. This study helps to understand the ideal methodology to apply to fatigue study or move to three-dimensional geometry. The model without contacts was created using a pressure force acting on a 4 mm surface, establishing the equivalent of a force of 7500 N. The fixed supports were recreated using boundary conditions at the nodes of the elements, which are located 40 mm from the centre. In two-dimensional models, the XFEM method does not allow obtaining solutions of J-Integral and SIF. However, it does enable getting the propagation of an arbitrary crack. Therefore, to develop a model that can simulate crack propagation is necessary to model the desired crack to propagate besides the specimen model. In this sense was created a crack of 2 mm (Fig.4 a)). The mesh developed in this type of simulation differed from that performed in the conventional method since a crack domain with spider geometry is unnecessary. In this model, it is essential to have a good geometry around the crack so that it propagates smoothly. Therefore, a study with four different refinements was carried out to study the effect of mesh refinement on crack propagation (Fig. 4).

Fig. 4. XFEM applied to 2D study: (a) Crack with 2 mm (b) Crack propagation, Mesh 1; (c) Crack propagation, Mesh 4.

Simulations using damage initiation and evolution usually result in problems of convergence of results, sometimes resulting in a longer computational time. The ABAQUS program allows a viscous regularisation tool for a more stable