Issue 48

M. Laredj et alii, Frattura ed Integrità Strutturale, 48 (2019) 193-207; DOI: 10.3221/IGF-ESIS.48.21 194 I NTRODUCTION atigue cracks in mechanical structures primarily begin at stress concentration tips such as rivet holes and / or geometric discontinuities. Hole cold expansion process is a very useful technique to extend fatigue life of structural assemblies. Hence, in the case of crack detection, a hole in the front of the crack will be created to reduce the concentration of local stresses leading to a delay of the propagation. This improvement is explained by lower notch sharpness and the presence of residual stresses introduced by the plastic deformation at the edge of the hole [1, 2]. Hence, the role of compression residual stresses is to reduce the effective stress level. Cold Expansion hardening (CEH) is a process used in the aerospace industry to extend the life of riveted and bolted structures by applying a high field of tangential compressive residual stresses. Consequently, residual stresses have a major role for determining the surface micro-cracks growth rate and thus on fatigue lifetime. Therefore residual stress analysis is a mandatory step in the design and manufacture of components. Numerous studies based on experimental measurements [3, 4] or on numerical finite elements calculations [5, 6, 7, and 8] studied separately the influence of several factors on the technique of cold expansion hardening. J VOGVELL [2] simulated the expansion of a hole by a steel ball assumed undeformable on an aluminium 7075 T6 alloy plate. Numerical modelling is done using 3D finite elements. Three cases of plate thicknesses (2. 5and 10 mm) and three degrees of expansion (2, 4 and 6%) were studied. The authors concluded that, increasing the degree of expansion does not have a significant influence on fatigue life. Contrary, AMROUCHE and al [9] performed fatigue tests with the following degrees of expansion 1.7, 3.4 and 4.3% to study the influence of the number cycles leading to fatigue crack initiation for aluminium alloy 6082 T6 plate. The authors showed that the increase of the expansion degree leads to the retardation of crack initiation. In AT ÖZDEMIR’s work [10] fatigue tests were also carried out on aluminium alloy T651 8090 plates and aluminium alloy 7050 plate of thickness 1.6 and 5 mm respectively with 4% expansion degree in addition to aluminium alloy 7010 of 19 mm thickness and 3% of expansion degree to investigate the effect of the plate thickness. They showed that the 3% expansion for the 19 mm thick plate gives a greater compression stress comparing to thinner plates of 1.6 and 5 mm with the expansion of 4%. Salvati and all [11] proposed eigenstrain field to the evaluation of residual strain within an additively anufactured nickel superalloy compressor blade that was subsequently subjected to shot peening treatment. Eigenstrain variation is described by a continuous function of the distance from the boundary of the bject in a twodimensional model of its cross ‐ section. The authors showed that eigenstrain method for the in ‐ plane strain reconstruction was successfully applied to a real case study of compressor blade section. The eigenstrain profile induced by shot peening was assessed, and the predicted residual elastic strain distribution compared to experimental measurements. Acceptable overall agreement was found. DeWald and Hill [12] presents a methodology for predicting the residual stress within threedimensional parts caused by laser peening treatment. The eigenstrain is input into the finite element model in stated treatment areas where laser peening is applied. The authors concluded the model has a fair amount of agreement with the measurements over the range of geometry studied. But there is disagreement between the measurements and the predictions with respect to the relation between radius size and depth of compressive residual stress for the corner radius geometry. Renan and all [13] predict that the residual stresses arising from cold expansion by using two different finite element (FE) approaches and compare the obtained results to measurement data obtained by the contour method. The first FE approach considers process modeling, and includes elasticplastic behaviour. The second approach is based on the eigenstrain method and includes only elastic behavior. The results obtained from the FE models are in good agreement with one another as well as with the measurement data. The eigenstrain method was found to be very useful, providing generally predictions of residual stress. Both models were found to give reasonable residual stress estimates. Thus, the model results give confidence to estimate the residual stress. The residual stresses produced by cold expansion hardening depend on several intrinsic or extrinsic factors of the material which complicate and make the modelling of the stresses difficult. The present work deals with the influence of three factors that affect cold expansion hardening process and the distribution of stresses around a hole using 3D finite element model. The main parameters analyzed in this work are the thickness, the degree of expansion as well as the yield strength. The experimental design methodology is used for modelling and predicting residual stresses in the input face. The approach allows the determination of the values of these factors which ensure the improvement of the service life. F