*Article* **Study on Mass Erosion and Surface Temperature during High-Speed Penetration of Concrete by Projectile Considering Heat Conduction and Thermal Softening**

**Kai Dong, Kun Jiang \*, Chunlei Jiang, Hao Wang and Ling Tao**

School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China; dongkai@njust.edu.cn (K.D.)

**\*** Correspondence: jkeddy@163.com

**Abstract:** The mass erosion of the kinetic energy of projectiles penetrating concrete targets at high speed is an important reason for the reduction in penetration efficiency. The heat generation and heat conduction in the projectile are important parts of the theoretical calculation of mass loss. In this paper, theoretical models are established to calculate the mass erosion and heat conduction of projectile noses, including models of cutting, melting, the heat conduction of flash temperature, and the conversion of plastic work into heat. The friction cutting model is modified considering the heat softening of metal, and a model of non-adiabatic processes for the nose was established based on the heat conduction theory to calculate the surface temperature. The coupling numerical calculation of the erosion and heat conduction of the projectile nose shows that melting erosion is the main factor of mass loss at high-speed penetration, and the mass erosion ratio of melting and cutting is related to the initial velocity. Critical velocity without melting erosion and a constant ratio of melting and cutting erosion exists, and the critical velocities are closely related to the melting temperature. In the process of penetration, the thickness of the heat affected zone (HAZ) gradually increases, and the entire heat conduction zone (EHZ) is about 5~6 times the thickness of the HAZ.

**Keywords:** concrete; penetration; melting and cutting erosion; temperature; heat conduction; coupling numerical calculation
