PSI - Issue 37

Jesús Toribio et al. / Procedia Structural Integrity 37 (2022) 1037–1042 Jesús Toribio / Procedia Structural Integrity 00 (2021) 000 – 000

1039

3

Fig. 1. Crack shape.

The main objective of the present work is the achievement of K -solutions for a cracked bolt in tension. The stress intensity factor is a function of the crack depth, the position on the crack border and the crack aspect ratio (Fig.1): K I = K I ( a / d , a / b , s / s 0 ) (1) An important point is to know the variation of K along the crack front. Depending on the crack aspect ratio of the ellipse, K will be maximum or minimum at the center of the crack border, which is the deepest point of the crack. The results are expressed in terms of dimensionless correction factor Y : Y = K I /  ( ) (2) where  is the axial stress on the net cross section of the bolt (uniform stress distribution):  = 4 F /  d (3) and F is the remote load externally applied and d the diameter of the net section of the bolt. 3. Numerical computation of the stress intensity factor (SIF) 3.1. Mesh generation A computer program was written to automatically generate finite element meshes in general 3D geometries such as the cracked bolt (Fig. 2). The theoretical background for the program is transfinite mapping Solids are divided into macroelements so as to exactly match given geometry along the sides of them. Macroelements are then divided to define the elements. A bandwidth minimization algorithm was implemented to optimize memory occupation. 3.2. Stress-strain calculations The numerical computations were performed by using the finite element method (FEM) with an elastic code and isoparametric quadratic elements: 20-node brick elements and 15-node prismatic elements. In order model the r- 1/2 singularity at the crack tip, singular quarter-point elements were used. In these elements the singularity is modelled by translating the mid-side nodes of a conventional element to the quarter-point position.