###### Abstract  
To investigate the plastic deformation (PD) response of a liner material during the shaped-charge jet (SCJ) formation process, the state of motion of liner material and the pattern of change in its deformation environment under explosive loading were theoretically analyzed and modeled. The distribution patterns of the characteristic PD parameters (that is, strain, strain rate, temperature, and flow stress) of the jet at any given time were theoretically predicted. The distribution patterns of the characteristic PD parameters of jets formed from two materials, namely, oxygen-free high-thermal-conductivity copper (OFHC-Cu) and molybdenum (Mo), during their formation process were theoretically analyzed. A series of experimental and numerical simulation studies were conducted to examine the accuracy of the theoretical predictions. As per the results, the developed theoretical model is effective in predicting the one-dimensional distribution of the characteristic PD parameters in the direction of jet formation. At any given time, the distribution of the characteristic PD parameters varies considerably between different parts of the jet. There is no significant difference in the distribution of the strain and strain rate between the jets formed from the two materials in the presence of the same warhead structure. A theoretical analysis predicted average temperatures of 804 and 2277.8 K and average flow stresses of 193.1 and 344.3 MPa for the OFHC-Cu and Mo jets, respectively. A hardness analysis of the jet fragments revealed average strengths of 144.32 and 286.66 MPa for the OFHC-Cu and Mo jets during their formation process, respectively. These results differed by 34% and 20% from the corresponding theoretical predictions. s +
Footnote †: journal: Applied Sciences  
**Citation:** [PERSON]; [PERSON]. addition, numerous studies have shown [7; 8; 9] that tungsten (W)-Cu alloys have approximately 30% higher penetration power than red Cu at small standoff distances; however, at a standoff distance of more than three times the caliber, W-Cu jet fracture considerably, resulting in a significantly smaller penetration depth. In fact, the fracture behavior of the SCJ is primarily affected by its morphology (diameter) and flow stress (strength). Many researchers have investigated the plastic deformation (PD) and fracture behavior of a jet [10; 11; 12; 13; 14; 15; 16; 17] and established a large number of engineering and semiempirical models to predict jet fracture times. However, most of these models use the initial strength of the liner material as a substitute for the jet strength, neglecting the effects of the collapse of the liner and the PD history of the jet during the stretching process on the strength of the liner material. Moreover, when driven by a blast pressure as high as 29 GPa, metallic material collapses rapidly at a deformation rate as high as \(1\times 10^{5}\)-\(1\times 10^{6}\) s-1, leading to marked differences in the distribution of its strain rate, strain, and temperature between different parts of the jet. Therefore, modeling the distribution of the characteristic PD parameters (for example, the strain rate and temperature) of the SCJ is essential for better guiding the design and application of new liner materials and further revealing the intrinsic connections among the warhead structure, material properties, and jet-formation performance. In this study, based on theories related to the one-dimensional (1D) tensile deformation of SCJ, the distribution of the characteristic plastic flow parameters of the liner material in different parts of a jet at any given time during its deformation process was theoretically modeled. Two materials, namely, oxygen-free high-thermal-conductivity Cu (OFHC-Cu) and Mo, were compared in terms of the distribution patterns of the plastic strain, deformation strain rate, temperature, and flow stress under jet-formation conditions. Experiments and numerical simulations were conducted to examine the accuracy of the theoretical model.