###### Abstract  
This paper aims to predict the damage and fracture behavior of thermoplastic fiber-reinforced metal laminates (TFMLs) under ballistic impact loadings. A dynamic metal constitutive model has been employed and implemented in Abaqus/Explicit through a vectorized user material subroutine (VUMAT). The effects of the Lode angle, temperature, and strain rate are considered in the strength model, while the effects of stress triaxiality, Lode angle, temperature, and strain rate are taken into account in the failure criteria. To assess the validity and superiority of the proposed model, the numerically predicted responses of polypropylene fiber-reinforced metal laminates subjected to varying impact energies were systematically compared with corresponding experimental results. Additionally, a comparative analysis was performed between the numerical simulation results predicted by the present model and those obtained using other constitutive models, such as the Johnson-Cook (JC) constitutive model and the elastoplastic constitutive model. Furthermore, the effect of projectile types on the ballistic performance of TFMLs have been systematically investigated. The findings demonstrate that the failure pattern predicted by the current model closely aligns with the experimental observations, while both the Johnson-Cook (JC) constitutive model and the elastoplastic constitutive model were unable to accurately replicate the experimentally observed failure behavior. This study also reveals that the projectile's nose shape plays a significant role in influencing the perforation behavior of TFMLs, affecting both the residual velocity and damage. thermoplastic FMLs; ballistic impact; damage; fracture; FE model +
Footnote †: journal: Applied Sciences  
1
Footnote 1: Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China;  
[EMAIL_ADDRESS], cgli@whrsm. deformation of aluminum sheets, fracture failure, damage to the composite material layer, as well as delamination [10]. [PERSON] et al. [11] observed that the aluminum alloy layer in FMLs exhibit a petal-like failure morphology based on experimental studies. Furthermore, experimental observations have demonstrated the strain-rate effect on FMLs subjected to impact loadings [12; 13]. [PERSON] et al. [14] performed a comprehensive numerical analysis to examine the behavior of polypropylene fiber-reinforced metal laminates under impact loadings. The composite layers in their study comprised woven polypropylene fiber-reinforced polypropylene matrix composites (PP/PP), widely used thermoplastic composite materials. Elastoplastic constitutive models were employed in the analysis of both metallic and composite materials. The numerical prediction of the maximum permanent displacement exhibits a high degree of concordance with the experimental results. However, there is a significant discrepancy between the predicted failure morphology of the target plate and the observed experimental results. [PERSON] et al. [15] also employed elastoplastic constitutive models for metals. Nevertheless, these models are overly simplistic and inadequate for capturing the complex responses of materials. Residual velocity and ballistic limit under high-speed impacts are primarily emphasized by current models [16], with the prediction of damage morphology for the target plate often being overlooked. The precise prediction of the dynamic response of the metal layer in FMLs subjected to impact loads depends critically on the selection of suitable metal constitutive models and failure criteria. The response of metals under impact loads is often modelled using the JC constitutive model and failure criteria, which frequently fail to accurately predict damage and fracture failure morphology [17; 18; 19]. [PERSON] et al. [20] evaluated the JC constitutive model and failure criteria, finding that the model's prediction results agree with experimental observations at low strain rates and temperatures.