Multiscale modelling of precipitation hardening: a review

Precipitation hardening, a cornerstone of alloy strengthening, finds widespread application in engineering materials. Comprehending the underlying mechanisms and formulating models bear crucial significance for engineering applications. While classical macroscopic theoretical models based on the line tension model have historically guided research efforts, their reliance on simplifications, assumptions, and parameter adjustments limits their predictability and expansibility. Moreover, the challenge of understanding the intricate coupling effects among various hardening mechanisms persists. One fundamental question to achieve the transition of material design paradigms from empirical trial-and-error methods to predictive-and-design approaches is to develop more physics-based multiscale modelling methods. This review aims to elucidate the physical mechanisms governing precipitation hardening and establish a tailored bottom-up multiscale modelling framework to steer the design of new alloys. The physical scenarios of precipitation hardening are firstly summarized, including particle shearing, Orowan bypass, and dislocation cross-slip and climb. Afterwards, an in-depth discussion is given regarding the application of macroscopic models and their correlation with the mechanisms and precipitation characteristics. As for the multiscale modelling methods, we categorize them into three main types: slip resistance based approaches, misfit stress field based approaches, and energy based approaches. By integrating multiscale modelling with the physical scenarios, we systematically addressed the key idea of the multiscale coupling framework, and their scale transfer procedure, applicability, advantages, and limitations. Some examples of coupling different types of multiscale methods and considering precipitates with complicated shapes are also presented. This study not only furnishes insightful comprehension of precipitation hardening, but also guides the development of multiscale modelling methodologies for other types of hardening effects in alloys.