Issue 46

A. Baltach et alii, Frattura ed Integrità Strutturale, 46 (2018) 252-265; DOI: 10.3221/IGF-ESIS.46.23 261 D ISCUSSION he FEM results obtained in this work are in good agreement with the published literature results regarding the distribution of residual stresses around the cold expanded hole. In fact, all models simulated in this work indicate that the circumferential residual stresses are higher around the mid-thickness location of the expanded hole. To simulate the effect of the mandrel on the distribution of the residual stresses around the hole from the entrance to the exit face, it has been modelized two types of mandrel: a ball mandrel and tapered mandrels defined by different degrees of taper  Figs. 16a, 16b and 16c summarize the results of the circumferential residual stresses distribution for the studied cases, since this latter play a key role in the strength of fastener joints according to the tensile loading direction. An important result of the present analysis is the fact that, the residual compressive stress, which is responsible for the reduction of the stress concentration at the hole edge, varies along the plate thickness. This effect may be minimized using an adequate tapered pin. Effectively, it is revealed that, the lower taper the higher residual stress are obtained to entrance side (Fig. 16a). Thus, as shown in Fig. 16a and 16b, lower taper λ enhance the residual stress induced by the cold expansion, particularly at the inlet side of the mandrel (Fig. 16a). Moreover, the degree of taper strongly influences the extent of the compressive zone around the hole edge and far from it. From the moment where, a low taper degree gives better results by matching the circumferential residual stress around the inlet side with those around the exit side of the mandrel. Figure 16 : Comparison of the resulted circumferential stresses obtained by different mandrel shapes for: a) Entrance face, b) exit face and c) Mid-thickness plane. This makes sense, because a substantial taper (λ greater) results in greater gradual axial forces during penetration of the mandrel, as illustrated by Fig. 17. In fact, Fig. 17 clearly indicates the axial force decreases as the taper decreases. This is verified by measuring the force exerted by the mandrel during penetration into the hole. Indeed, it is found that the increment of force applied by the mandrel is greater as the taper is greater (Fig. 17). This will result in higher pressure on the edge of the hole and thus, significant lateral deformations are generated (in the direction of expansion). Therefore, a low taper allows a graduation of the deformation of the successive layers during the expansion process and facilitates the sliding of the mandrel through the hole, particularly during the penetration of the a) b) c)