PSI - Issue 37

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

1041

5

4. Stress intensity factor (SIF) solutions Stress intensity factor (SIF) versus crack depth was plotted at the crack center and bolt surface for both slightly curved (SC) and circular (C) cracks (Fig. 5; left). The variation of K along the crack front is also presented for both aspect ratios (SC and C cracks) and for shallow and deep cracks (Fig. 5; right). The following comments may be made on the numerical results for tension (Fig. 5). • SIF values at the crack center are higher for SC cracks. • SIF values at the bolt surface are higher for C cracks. Therefore, for SC cracks the SIF is higher at the crack center and for C cracks is higher at the bolt surface, as shown in the plots of Fig. 5.

Fig. 5. SIF for remote tension loading: influence of the crack depth (left) and variation along the crack front (right).

The results of the present paper for a circular crack ( a /b=1) of variable depth subjected to tension agree fairly well with values of the SIF in threaded bars published previously by Reibaldi (1984) and Nord and Chung (1986), as shown in Table 1. However, the number of combinations between crack geometries and loading conditions analyzed in the present paper is much higher (more than twice), since those previous works offer results only at the crack center and surface, but not at intermediate points of the crack.

Table 1. Comparison of present results (Toribio) with those from Reibaldi (1984) and Nord & Chung (1986) for a circular crack ( a / b =1) of variable depth subjected to remote tension loading. ___________________________________________________________________________ 0.5 ___________________________________________________________________________ a / d 0.1 0.2 0.3 0.4

CRACK CENTER

Present Results (Toribio) Reibaldi (1984) Nord & Chung (1986)

0.75 0.82 0.55 1.22 1.24 0.84

0.80 0.80

0.88 0.82 0.79 1.22 1.11 1.05

1.05 0.85

1.27

-

-

-

1.40

CRACK SURFACE

Present Results (Toribio)

1.16 1.09

1.31 1.13

1.43

Reibaldi (1984)

-

Nord & Chung (1986) 1.44 ___________________________________________________________________________ - -

A second order polynomial interpolation was performed with the numerical results, to provide closed-form SIF solutions (analytical expressions) to be used in fatigue life prediction and fracture analyses. The resulting polynoms for both types of cracks under remote tension are the following: