Modelling of Dislocation Evolution in Nickel-Based Single Crystal Superalloy Under Shot Peening

Shot peening is a surface treatment technique that can improve the fatigue performance of metallic materials by introducing compressive residual stresses and modifying the microstructure via grain refinement, phase transformation, texture and/or dislocation structure changes. In this study, a multi-scale modelling framework is developed to understand the evolution of dislocation structures during shot peening of a nickel-based single crystal superalloy. Firstly, explicit finite-element (FE) simulations of the shot peening process are carried out using a Johnson–Cook model calibrated on reported mechanical properties of PWA1484 (Walston et al. In Superalloys 2004 (Tenth International Symposium). TMS, pp 15–24 [1], Cetel and Duhl In Superalloys 1988 (Sixth International Symposium). TMS, pp 235–244 [2]). Instead of using a systematically pre-defined distribution of shots, a random distribution of shot is adopted for these simulations. An Avrami-type equation is used to relate the surface coverage to the necessary peening time and corresponding number of shots (Kirk and Abyaneh in Shot Peen 9:28–30 [3], Pham et al. in Surf Eng 33:687–695 [4]). Various shot peening coverage is modeled by identifying the peening time required for 100%, then using a linear relationship between peening time and coverage. In order to study the effect of shot peening intensity, the initial velocities of shot are chosen according to experimentally measured average shot velocities applied at varying levels of intensity. Figure 1 shows the von Mises stress distribution on shot-peened surface with intensity of 0.15 mmA. During the shot peening process, specimens experience large plastic strain and strain gradient, which induced localized dislocation activity and complex dislocation pattern near the surface. A significant gradient in Geometrically Necessary Dislocations (GND) induced by shot peening from the surface to the bulk has been widely reported (Breumier et al. in Mater Sci Eng A 816 [5]), which is usually correlated to experimentally measured hardening gradient. Thus, in this study, the discrete dislocation plasticity (DDP) model (Giessen and Needleman in Model Simul Mater Sci Eng 3:689 [6]) is adopted in order to explicitly model the activities of individual dislocations in the region of substrate near the peened surface. The DDP model is coupled to the FE simulations of the shot peening process by applying boundary conditions corresponding to the displacement on the top surface, as shown in Fig. 2. The surface strengthening mechanisms of the nickel-based single crystal superalloy under different shot peening conditions are investigated by analyzing the resultant dislocation structures (i.e. Figure 3), dislocation density, slip field and lattice orientations.