Advances in analytical and numerical models for ballistic limits of fiber-reinforced composites
In recent years,fiber-reinforced polymer(FRP)composites have become increasingly popular in protective design and engineering due to their low specific gravity,high specific strength and stiffness,and exceptional impact resistance.A comprehensive understanding of the energy absorption of the FRP composites during the impact and penetration and precise prediction of the ballistic threshold would provide helpful guidance for the construction of sophisticated bulletproof composites.The main characteristics of impact and penetration of the FRP composites are high loading intensity and short action time.High stress is distributed over the contact area of the projectile and FRP composite target during the impact and penetration process,leading to the plastic deformation and failure of the target.The impact and penetration of the FRP composites are complex dynamic processes,in which the deformation and failure modes of composite targets are influenced by various internal and external factors.The ballistic response of the FRP composites subjected to a ballistic impact mostly depends on a combination of internal and external factors in a synchronous manner.Therefore,accurately forecasting the ballistic limits of FRP composites is challenging.This challenge poses a substantial obstacle to the development of advanced bulletproof composites.This paper reviews the analytical and numerical models for the ballistic limit prediction for FRP composites and summarizes the associated energy absorption mechanisms,expecting to provide a reference for the modeling of the ballistic limits of FRP composites and the design of bulletproof composites.Besides,the effects of target component characteristic,target structure,and projectile characteristic are discussed.The early research on the ballistic limits of FRP composites was mainly focused on proposing semi-empirical models.The semi-empirical models can provide simple and highly applicable formulas for predicting the ballistic limit of FRP composites.However,the accuracy of the obtained formulas depends on the completeness of the collected data.Since the early 2000s,researchers established energy analysis models for high-speed impact problems by analyzing various energy-absorbing mechanisms of FRP composites during the ballistic impact,thereafter,analytical research on the ballistic limits of FRP composites rapidly grew.Further efforts are needed to develop theoretical analysis models that include more comprehensive energy-absorbing mechanisms.Also,most theoretical research focuses on exploring the effects of target characteristics,while there is limited research on the effects of external factors.The finite element method is currently the mainstream numerical method for the ballistic performance of FRP composite.In addition,several researchers are committed to developing novel methods,such as the combined finite element method/artificial neural networks methodology and meshless methods for predicting the ballistic limit of FRP composites.The development of these novel methods for accurately predicting the ballistic limit of FRP composites is one of the most important directions in the future.