Prediction of Elastic-Plastic Boundary Around Cold-Expanded Holes Using Elastic Strain Measurement

The cold-expansion process is used routinely for improving the fatigue life of holes in a variety of components. The expansion process involves drawing a slightly oversized tapered mandrel through the hole. Upon expansion, the material near the hole deforms plastically while material away from the hole undergoes elastic deformation. Upon removal of the mandrel, the ensuing elastic recovery of the surrounding material results in the development of a compressive residual stress field around the hole. Since the magnitude of plastic deformation sustained by the material near the hole depends on the severity of the expansion, the elastic-plastic boundary radius (EPBR) during the expansion process can be used to characterize the extent of cold expansion. The elastic-plastic boundary is an important parameter in characterizing the residual stress distribution around cold-expanded holes, as well as in determining required spacing between successively expanded holes. This paper presents a new method for determining the EPBR using strain measurements within the elastic region. Analytical equations are developed relating elastic strains measured away from the hole to EPBR. A methodology is presented for employing strain data (obtained via miniature resistance strain gauges located away from the hole and within the elastic region) to be used as an input variable into the developed equations for determining EPBR. Using the method described in this paper, an average normalized EPBR of 2.38 (normalized with respect to the initial hole radius) was calculated utilizing elastic strain measurements during 4.0% cold expansion of a set of 4.826 mm thick 7075-T6 aluminum specimens containing a 6.0 mm diameter hole. The results showed excellent agreement with numerical simulations using a nonlinear elastic-plastic finite element code (ABAQUS). The deviation between the average EPBR determined by the analytical-experimental method and the finite element analysis was about 4.0%. The proposed method for using elastic strain measurements away from the hole provides improvement over earlier methods that rely on fringe observations or strain measurements within the relatively narrow plastic zone that has an uneven surface near the hole.