Simulation of Shock-Induced Fracture of a Plate Made of a Functionally Graded Material Based on Steel and Titanium

A numerical model was developed and implemented to describe the dynamic fracture of a plate made of a functionally graded material based on St.3 steel and VT8 titanium alloy under shock-wave loading. Numerical simulation was performed by a three-dimensional finite element using the EFES software. To describe the properties of the functionally graded material, a mixing parameter is introduced that ensures a smooth transition between the materials across the plate thickness. A numerical test similar to the Taylor test and a simulation of the impact of an aluminum projectile on a continuously functionally graded target were performed to evaluate residual strains, pressure profiles, and the conditions for the onset of spall fracture. It is found that the St.3 \( \to \) VT8 gradient provides effective shock-wave dissipation and suppression of spall fracture and the opposite gradient leads to the localization of tensile stresses and the formation of a spall fragment. The numerically obtained values of the spall thickness are in good agreement with the experimental data, which confirms that the proposed model adequately predicts the dynamic strength of functionally graded structures under high-velocity loads.