Perforation of metal plates due to through-thickness shearing and cracking. Optimum toughness/strength ratios, deformation transitions and scaling

The mechanics of punching and plugging are re-examined and it is argued that fracture toughness, as well as ‘strength’ must be an important material property that controls the ease, or otherwise, of perforation. It is shown that the toughness/yield strength ratio (R/k) in shear for a given thickness plate determines the amount of energy absorbed. Because the rates of energy absorption in the initial plasticity-only phase, and in the subsequent crack propagation phase, are different there appears to be an optimum (R/k) for greatest energy absorption. The peak normalised energy absorbed Utotal/πDkt2 is about 0.7, where t is plate thickness and D is punch/projectile diameter, precise values depending upon (i) the normalised depth δtrans/t = Δtrans at which the initial mode of plastic shear changes to cracking plus plasticity; and (ii) the relative speeds of the punch/projectile and the free-standing crack running ahead into the remaining ligament. Calculations based on different ways of predicting the length of the free-standing crack, including a new algebraic calculation given in the present paper, as well as damage mechanics and FEM, all lead to a similar conclusion of a peak normalised energy. Experiments show that (R/kt) is constant so that R in shear must vary with target thickness, a result that is surprising but appears to be connected with changing relative clearance between punch and die. The result is nevertheless compatible with damage mechanics criteria for fracture in terms of a critical shear strain, or critical work/volume, both dependent on hydrostatic stress. The analysis predicts the well-known experimental observation that the projectile travel δf at which plugging is complete is proportional to t; the constant of proportionality depends on δtrans = (R/k), thus explaining different behaviour in targets having different thermomechanical treatments. The scaling relations (including toughness as well as strength) between results for scaled models and prototypes undergoing ductile shear fracture are derived (including non-proportional scaling). They agree with experimental results, and give a theoretical foundation for empirical relations that say that the ballistic limit velocity Vlim depends directly on target thickness. Again, the constant of proportionality depends on the toughness/strength ratio, showing that the different slopes in Vlim vs t plots are attributable to different thermomechanical treatments.