Modeling the competition between solid solution and precipitate strengthening of alloys in a 3D space

Abstract Until now, the nature of the competitive and cooperative correlation between solid solution strengthening and precipitate hardening is still uncovered, and then brings great challenges in designing the high-performance alloys. Here, a unified model has been developed to establish the quantitative relationships among the aging process, microstructure, and yielding strength for a model nickel-based superalloy in a three-dimensional (3D) space, which agglomerates the three independent variables of aging temperature, cooling time, and matrix composition, and these variables dominated the size and volume fraction of precipitates, and anti-phase boundary (APB) energy. Our experiments clearly suggest the competitive and cooperative correlation of solid solution and precipitate hardening exits in a 3D space. The size and volume fraction of precipitates, and the composition of matrix after the aging process can be predicted, and then integrated into the physical model to obtain the yielding strength of alloys. On average, the deviation of the yielding strength is 4%, which is far better than 15% with the existing strength model without considering the heat treatment, significantly reducing the development cycle. The size and volume fraction of precipitates decrease with the increased cooling rate, leading to that the precipitate strengthening firstly increases and then decreases. Meanwhile, this trend would result in enhancing solid solution strengthening monotonously. Especially, the critical cooling rate coordinates the relationship between the competition and cooperation owing to the obvious change of the APB energy together with the matrix composition, and a maximum yielding strength occurs at 166 ℃/min. The present work can provide a key theoretical guidance for designing advanced alloys with the excellent performance in a 3D space.