PSI - Issue 19

6

Okan Yılmaz et al. / Procedia Structural Integrity 19 (2019) 302 – 311 Yılmaz et al. / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 4. One-quarter finite-element model to simulate four-point bending test condition with a simplified bolt geometry (left). Maximum principal stress distribution (front view) to illustrate the highest tensile stress area under loading (right).

convergence study done for the bolted assembly analysis in [3]. Contact is defined between the plates, simplified bolt geometry, and rigid rollers. The friction coe ffi cient is taken as 0 . 7. The analysis starts with applying a preload of 62.5 kN in the form of a self-equilibrating concentrated load applied over the mid-cross-section of the bolt [17]. Then, the length of the bolt is fixed at the calculated value and the top rigid roller is displaced while the other roller is fixed. Figure 4 contours the obtained maximum principal stress distribution on the deformed view, clearly showing the tensile and compressive sides. Failure locus is estimated by a multiaxial fatigue crack initiation criterion with a critical plane implementation [18], which uses the stress-strain function suggested by Smith et al. [19]. There exists several multiaxial fatigue criteria [20], however a comparative study exceeds the scope of this study. Smith-Watson-Topper (SWT) parameter is expressed as follows: where σ max is the maximum stress and ∆ ε/ 2 is the amplitude of the strain both normal to the critical plane. The critical plane is the plane, in which SWT parameter is found to be maximum. The parameter can also be combined with Basquin’s law [21] to estimate the fatigue life. The distribution of SWT parameter is shown in Fig. 5 along with the contact status (at the minimum and maximum displacement values), and experimentally observed crack. We see that the crack and the area where SWT parameter is found to be maximum correspond well, however, the slip region changes considerably as the specimen take turns between the maximum and minimum load levels. The intensity of the fretting marks also hints the areas where continuous and alternating slip are observed. The discrepancy between the slip and high-SWT locations highlights a contest between the failure modes, which arise from the oscillatory motion between the surfaces and high tensile bending stresses at the flange edge respectively. This competition characterizes the cracking under out-of-plane bending mode, which occurs under the flange head, close to the outer flange diameter. Numerical analysis shows that the failure area can be limited to the region enclosed by the slip at the minimum loading level and the location where multiaxial fatigue crack initiation parameter is maximum. On the contrary, under in-plane shear loading, slip region and failure location simply overlap [3]. To be able to analyze complex designs and multi-bolt patterns, it is essential to increase the computational e ffi ciency as three-dimensional finite-element simulations of a single joint such as the one presented above have a substantial computational cost. Instead of using models, in which three-dimensional solid elements are used for all parts, it is possible to use simplified modeling strategies where plates and bolts can be replaced by two-dimensional shells and equivalent beam and coupling surfaces providing a drastic reduction in computational cost without compromising the accuracy of the results [22]. SWT = σ max ∆ ε 2 , (1)