PSI - Issue 14

L. Chikmath et al. / Procedia Structural Integrity 14 (2019) 922–929 Chikmath/ Structural Integrity Procedia 00 (2018) 000–000

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Fig 3: Cold working cycle and insertion of interference fit

Fig 4: Separation/contact regions in interference fit

2.2 Inverse formulation and Fatigue loading In inverse formulation the load required to cause various extents of separation/contact on the pin-hole interface are estimated in case of interference fits and this is described in Fig.5. Assume that the separation region of 2α 0 is to be caused. The region of contact is to be identified with zero radial pressure at the ends of the region. This is achieved as shown in figure below. For a load P 1 applied on the pin, let R 1 be the reaction at the transition point (T) (Fig.5a). For the same separation angle, let the reactions at the transition points be R 2 for a pin load of P 2 . (Fig.5b). Since the problem is linear between P 1 and P 2 (due to same separation/contact regions), the load to be applied to make the reaction to be zero at transition point can be obtained by linear interpolation/extrapolation (Fig.5c). This actual load (P s ) is given in Eqn. 1. On these cold worked holes with interference fit pins, stress analysis is carried out and the critical locations are identified. On these locations, the fatigue analysis is carried out for the pin load ratio (Rp=0) and fatigue crack initiation analysis is conducted using the Basquin's equation with Morrow's mean stress effect and Miner's rule given in Eqns. 2&3. The typical fatigue load cycles for which the analysis is carried out is shown in Fig. 6. � = � � − � � � − � … (1) 2 � = [ � � � − � ] � � � � … (2) = � � � � ��� … (3)

Fig 5: Inverse formulation for interference fits

Fig 6: Fatigue load cycles

2.3 Boundary conditions During insertion of the mandrel, the boundary conditions on the hole are given in Eqn.4 (Fig.7a). Later when the interference fit is pin is introduced without application of load, boundary conditions are described in Eqn.5 (Fig.7b). Few of these boundary conditions depend on the mode of application of the load. It is not possible to analyse with any prescribed load, P on the pin geometry since its distribution on the pin – lug interface is not known. With the application of pin load, The boundary conditions can be reworked in a similar way without affecting the stress and strain distributions. A rigid body displacement U 0 is superposed on the whole lug joint in such a way that the displacement of the rigid pin is zero which enforces the reference point for displacements to be the centre of the rigid pin. This redefines the boundary conditions at the far end edges of the lug to have rigid body displacement U 0 in negative x-direction for Pin load. A typical interference fit with this approach for is shown in Fig.7c. Material properties of the material are also shown in the same Fig.7. The separation/contact regions are checked by the inequality constraints. Necessary boundary conditions are defined from Eqns.(4-10).