Analysis of single-bolt joints

The joint stiffness was measured between 2 and 7 kN, for which the experimental load-displacement curves were essentially linear. Table 11.3 hsts the change in stiffness as the clearance is varied from neat-fit (Cl) to 240 pm (C4), for both the experiments and the finite element models. It is evident that as clearance increases, joint stiffness decreases, and it is also evident that the finite element models provide an accurate prediction of this loss in stiffness. 

Above 2 kN the joints begin to slip and the behaviour transitions to a new region of quasilinearity with a reduced slope Slope 2 ). In the transition region, the clearance is taken up in the 240 pm clearance joints because the bolts were initially centred in the holes, no bolt-hole contact is made imtil the end of the transition region. 

There is good repeatabihty between the tests with virtually no distinction between the initial slopes (Slope 1) in any test, while Slope 2 in the neat-fit clearance cases had an average value of 50.37 kN/mm with a standard deviation of 0.99 (2%) and in the 240 pm clearance cases had an average value of 37.06 kN/mm with a standard deviation of 1.74 (4.7%). The difference in Slope 2 for the two clearance cases was due to differences in the developing contact area between the bolt and the hole, as described in Section 11.3.1 above. 

As expected, the 240 pm clearance joints are particularly interesting because there are three distinct regions of behaviour, as the load increases the first dominated by static friction, then the transition region dominated by kinetic friction, then a final region in which the stiffness is due to bolt-hole contact forces as well as friction. 

The finite element model described in Section 11.2 was used here to model the friction experiments described above. However, to simulate the 16 Nm torque, a bolt pre-stress of 227 MPa was applied. This value was obtained experimentally from the axial gauges in the shank of a specially manufactured instmmented bolt, as discussed previously. For comparison, both the continuous and stick-slip [25] fiiction models (available in MSC Marc finite element code) was used to account for fiiction between the contacting interfaces. The fiiction coefficients were chosen to be 0.1, 0.3 and 0.45 between the bolt/laminate, washer/laminate and laminate/laminate interfaces, respectively. More details on fiiction coefficient selection can be found in [17]. 

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