PSI - Issue 39

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Jesús Toribio et al. / Procedia Structural Integrity 39 (2022) 730–734 Author name / Procedia Structural Integrity 00 (2021) 000–000

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Fig. 2. Types of loading: (a) remote stress; (b) nut loading.

The SIF is a function of the crack depth, the crack aspect ratio and the position at the crack front, as follows: K I = K I ( a / d , a / b , s / s 0 ) (1) The results are expressed in terms of dimensionless SIF Y : Y = K I / σ (π a ) 1/2 (2) where σ = 4F/ π d 2 for remote tension and σ = 4F TOT , z / π d 2 for nut loading, F being the remote load externally applied, F TOT , z the total load in the axis direction applied by the nut and d the diameter of the net section of the bolt. 3. Numerical computation of the stress intensity factor (SIF) The numerical computations were carried out by using the finite element method (FEM) with an elastic code and isoparametric quadratic elements: 20-node brick elements and 15-node prismatic elements to reproduce the bolt geometry. To model the r- 1/2 singularity at the crack tip, singular quarter-point elements were used by shifting the mid side nodes of a conventional element to the quarter-point position. To obtain the SIF, the stiffness derivative method was used upon a virtual crack extension of the main nodes over the crack front (Astiz and Elices, 1980). 4. Stress intensity factor (SIF) solutions Fig. 3 plots the SIF vs . crack depth and Fig. 4 the SIF variation along the crack line.

Fig. 3. SIF versus crack depth for SC-cracks (left) and for C-cracks (right). The values for remote tension (*) are also represented.