Issue 46

A. Baltach et alii, Frattura ed Integrità Strutturale, 46 (2018) 252-265; DOI: 10.3221/IGF-ESIS.46.23 256 The material used in this study is an aluminum alloy 7075-T6 for the plate and En 24 grade steel for the pin. The mechanical properties of the plate and the mandrel are given in Tab. 2. According to Mahendra and coworkers [1], the process of the cold expansion is dynamic in nature, leading to large strains in at a relatively small volume element. Moreover, the behavior of the material is nonlinear during expansion. Thus, an isotropic elasto-plastic model with kinematic hardening behavior was used for the plate and elastic behavior for the pin. Kinematic hardening models are provided in Abaqus to model the cyclic loading of metals. The linear kinematic model approximates the hardening behavior with a constant rate of hardening. Isotropic hardening is defined by the yield stress which can be given as a tabular function of plastic strain. The yield stress at a given state is simply interpolated from this table of data, and it remains constant for plastic strains exceeding the last value given as tabular data (Tab. 2). Mechanical properties Aluminum alloy 7075-T6 En 24 grade steel Yong modulus E (GPa) 72 210 Stress yield  y (MPa) 500 - Poisson coefficient  0.33 0.3 Table 2 : Mechanical properties of aluminum alloy 7075-T6 and En 24 grade steel. The boundary conditions are presented in Fig. 6. These latter are chosen as reported in [12]. Figure 6 : Boundary conditions used in the finite element cold expansion simulation. So, displacement conditions are imposed on the outer face of the mandrel. This imposed displacement forces the mandrel to penetrate into the hole from one side (Entry) to the other side (Exit). The penetration of the mandrel into the hole causes an expansion of this latter. As a consequence, when the mandrel is removed, the material which is elastically deformed returns back from the expanded state and constrains the material in the elasto-plastic zone to contract. Friction coefficient μ = 0.1 is used taking into account the effect of the friction between contact surfaces during the cold expansion procedure. Practically, this simulates a solid mandrel that is larger than the hole and pulled through the hole using a hydraulic puller. When the larger mandrel slips through the hole, a process of plastic deformation happens and the material around the hole is stressed and strengthened. As a result, the hole has a zone of residual compressive stress around it. R ESULTS Validation of the model efore addressing the focused analysis, we first compared our results with those published by Chakherlou and vogwell [12]. These results relate to the expansion with a conical pin L = 3 mm (λ = 7.667 %). The residual circumferential stress resulted by cold expansion are presented in Fig. 7. It can be seen that the stress distribution is compressive near the hole but is tensile further from the hole edge. Figs. 7a, 7b and 7c present the actual results compared with those published in [12], for the entrance face, the exit face, and the mid-plane, respectively. From these curves, one can note the correlation between the results, particularly, the extent of the compression zone and the neighboring points to the hole edge. Thus, our model seems relevant, allowing us to approach the analysis of the effect of the mandrel shape on the residual stresses. B