Issue 46

A. Baltach et alii, Frattura ed Integrità Strutturale, 46 (2018) 252-265; DOI: 10.3221/IGF-ESIS.46.23 263 of taper increases the compressive radial stresses. Since, one can note a tensile stresses near the hole edge induced by the passage of the conical mandrel with taper λ = 11.5% and less with λ = 7.667%. For the exit face, the effect of the mandrel is not obvious, so the effect is not considerable (Fig. 18b). At the mid-thickness of the hole, the radial stresses have similar distribution trends for any taper, except for the case of the ball mandrel, where the compressive radial stresses are lower (Fig. 18 c). Fig. 19 illustrates the distribution of the circumferential residual stress along the thickness of the hole, for the two types of mandrels and for different tapered pins λ. All comments discussed above are clearly identified in this figure. So, one can note that the expansion with a ball mandrel in a thick plate leads positive stresses on the vicinity of both sides of the hole (the inlet and the outlet). However, residual stresses in mid-thickness of the hole are relatively compressive. Better yet, Fig. 19 shows that the circumferential residual stresses along the thickness are slightly uniformly distributed for lower taper. This confirms the hypothesis of the severity of the high taper on the lateral deformations of the material around the hole. Figure 19 : Comparison of Distribution of the circumferential residual stresses along the thickness for different mandrel shapes The FEM simulation yielded the results that, with lower taper, as 3.83%, 2.875 % and 2.3 %, a significant gain in circumferential residual stresses is obtained. C ONCLUSION numerical analysis of residual stress distribution around a cold expanded hole was conducted in this work. Special attention was made on the mandrel shape used for the expansion procedure. Thus, common types of mandrels were modeled, such as the ball and the conical mandrel. For the latter, it was varied its taper degree defined by the relation (2). According to the length of the conical part, the degrees of taper used are: 11.5%, 6.667%, 3.833%, 2.875% and 2.3%. So, a study of the effect of the geometric shape for the same type of tool is described here including a distribution of residual stresses along the plate thickness is also discussed. Following the studied cases, the obtained results allow us to make the following conclusions:  The residual stresses around the expanded hole are not uniformly distributed. And this regardless the type of the oversized tool used for the expansion,  The cold expansion with a ball results in tensile residual stresses around the hole edge.  In any way, the ball mandrel technique is unsuitable for thicker plates. However, it remains useful in the case where the load direction coincides with the radial direction.  The tapered pin is more suitable for the cold expansion, especially for thick plates.  The residual stresses distribution along the hole thickness can be broadly optimized, by using appropriate geometry of the mandrel. In fact, low taper degree is more suitable than the high taper degree.  Taper degrees lower than 7.667% leads to higher values of compressive circumferential stresses around the entrance face of the hole edge. Especially, taper of 3.83 % is recommended. A