Dynamic void growth in a non-linear viscous solid

When a ductile material is subjected to high strain-rate deformation, rapid growth of the voids occurs in a very short time. Here, the problem of void growth has been investigated to study the mechanisms of void growth in ductile metals and to evaluate the growth rate of the void under axisymmetric loading condition. Experimentally, both plate impact tests on Cu-SiO{dollar}sb2{dollar} and split Hopkinson pressure bar tests on Al-Si alloy and Al-SiC{dollar}sb{lcub}rm w{rcub}{dollar} composite are conducted to generate the high strain-rate deformation. After the test, specimens are sectioned and observed by scanning electron microscope to investigate the void growth mechanism and to determine the final volume fraction of voids. It is found that both the applied strain and stress triaxiality affect the void density in the specimen. Analytically, the problem of dynamic void growth based on this micro-mechanical model is solved by the use of the variational method. The theoretical model consists of numerous spherical voids of the same size in a matrix considered to be a non-linear viscous material. The velocity fields are assumed to be the sum of the volumetric expansion velocity and the shape changing velocity. Two integral equations reduced from variational equations are solved by the use of a numerical method. The velocity at a void surface is obtained, and thus the actual size and the actual volume fraction of the voids can be evaluated. An analytical solution is found when the shape change of the voids can be ignored. The model developed can include all the existing analytical solutions as special cases. A non-dimensional parameter {dollar}ysb{lcub}o{rcub}{dollar} is found to play an important role on void growth along with the stress triaxiality; the effect of inertia reduces the growth rate when {dollar}ysb{lcub}o{rcub}{dollar} is large. However, dynamic void growth can be approximated by the static growth model as long as {dollar}ysb{lcub}o{rcub}{dollar} remains small. Material non-linearity is shown to play a less important role in dynamic void growth than in static void growth. Moreover, it can be ignored at small strain for large {dollar}ysb{lcub}o{rcub}{dollar}. Finally, comparison between experimental results and analytical results shows that the proposed model predicts reasonably well void growth in its early stages.