A Computational Constitutive Model for Glass Subjected to Large Strains, High Strain Rates and High Pressures

This article presents a computational constitutive model for glass subjected to large strains, high strain rates and high pressures. The model has similarities to a previously developed model for brittle materials by Johnson, Holmquist and Beissel (JHB model), but there are significant differences. This new glass model, presented in Fig. 1, provides a material strength that is dependent on the location and/or condition of the material. Provisions are made for the strength to be dependent on whether it is in the interior, on the surface (different surface finishes can be accommodated), adjacent to failed material, or if it is failed. The intact and failed strengths are also dependent on the pressure and the strain rate. Thermal softening, damage softening, timedependent softening, and the effect of the third invariant are also included. The shear modulus can be constant or variable. The pressure-volume relationship includes permanent densification and bulking. Damage is accumulated based on plastic strain, pressure and strain rate. Significant features of the model are the ability to compute size effects (small scales are stronger than large scales), surface effects (smooth surfaces are stronger than rough surfaces), and high internal tensile strength (as demonstrated by spall plate-impact experiments). Simple (single-element) examples are presented to illustrate the capabilities of the model. Several example computations are presented in Figs. 2-4 to demonstrate the ability to compute more complex, high-velocity-impact conditions. Figure 2 presents computed results for a gold projectile impacting a borosilicate target with a copper buffer attached to the impact surface. The computed results produce interface defeat (no glass penetration) at Vs = 800 m/s and prompt penetration at Vs = 900 m/s. This is consistent with the test results provided by Anderson et al. [1]. Behner et al. [2] performed experiments using no buffer (gold rod impacting bare glass) which produced penetration at much lower impact velocities. For these experiments the penetration velocities were determined using a series of flash x-rays and are presented as a function of impact velocity in the lower protion of Fig. 3. Also shown are the computed penetration velocities for Vs = 900 m/s and Vs = 2400 m/s. The computed results are in good agreement with the experiments. Anderson et al. [3] also performed experiments using a pointed steel projectile impacting thin plates of borosilicate glass at three different scales. The smaller scale targets were stronger than the larger scale targets. Figure 4 demonstrates the capability to compute size effects. Computed results are presented for the 0.50-cal (scale = 1.0) and the 0.22cal (scale = 0.44) projectile for Vs = 300 m/s and Vs = 400 m/s. At 300 m/s the 0.50-cal projectile exits the target at Vr = 22 m/s but the smaller scale 0.22-cal projectile is stopped. As the impact veloicty is increased the computed size effect diminshes as shown at Vs = 400 m/s. The ability for the computations to produce size effects is due to the time-dependent features in the model.