PSI - Issue 37

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

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1. Introduction Threaded connections, usually in the form of bolted joints, are very common in metallic structures, e.g. in aircraft and aerospace industries. However, their fatigue and fracture behaviour is not yet fully understood. In recent years, damage tolerance analyses have been widely used in design to estimate the safe life and judge the failure behaviour of these structural elements subjected to different kind of loads. In the estimation of the safe service life of metallic components, a relevant topic is the knowledge of the stress intensity factor (SIF or K ) for the considered geometry. With regard to bolted joints, some difficulties arise because of the complex geometry of bolts. The primary difficulty in obtaining a viable K -solution for a round bar is the three dimensional (3D) nature of a surface crack, causing the SIF change along the crack front. A second important difficulty is to model the thread, whose helical shape involves not only geometric difficulties but also problems in applying the load on the bolt. Moreover, the uncertainties as to the real loads acting on the bolt make the problem even more difficult to solve. Published stress intensity factor (SIF) solutions referring to cracked bolts are quite scarce in the scientific literature. Reibaldi (1984) and Nord and Chung (1986) deal with certain configurations of the cracked threaded bar, and present stress intensity results, expressed as correction factors. Technical papers by Springfield and Jung (1988) and James and Mills (1988) present interesting reviews of K -solutions in scientific literature applicable to crack in bolts. The surprising conclusion is that, although a great number of K -solutions have been developed for cracks in unnotched round bars, few solutions have dealt with cracks in the vicinity of threads. Studies of fatigue crack growth in bolts are also scarce, although some published papers can be found (Mackay and Alperin, 1985). Most of the K -results applicable to cracked bolts have been calculated with smoothed geometries (i.e. cracked cylindrical bars), which demonstrates the scarcity of applicable stress intensity factor solutions for such complex geometries as bolts. The present paper offers a wide range of K -solutions for cracked bolts subjected to remote tension loading. Results for various crack shapes and crack depths are presented in different points along the crack front. Analytical expressions - second order interpolated - are provided, which are very useful for fatigue life prediction. 2. Problem statement: geometry and loading conditions The geometry analyzed consists of an ISO M8 x 1.0 bolt with an elliptical crack at the surface subjected to different loading conditions. The dimensions of the bolt are: Maximum diameter: 8 mm Minimum diameter: 6.77 mm Root radius: 0.125 mm Pitch: 1 mm Thread angle: 60º The bolt was modeled in parallel jointed threads, without taking into account the helical shape, to preserve the axial and transversal symmetries of the problem. A surface crack was considered in the open thread ground perpendicular to the bolt axis. The shape of the crack is semi-elliptical (Fig.1) with its center located on the surface of the inner -minimum diameter- cylinder and semi-axes a and b , corresponding to the crack depth and the transversal length of the crack. Two aspect ratios were considered: Slightly curved (SC) crack: a / b = 0.2 Circular (C) crack: a / b = 1.0 Five crack depths were used in the computations ( a / d = 0.1, 0.2, 0.3, 0.4 and 0.5), where d is the minimum (or net) diameter of the bolt. The bolt was considered to be loaded in tension.