Dynamic fragmentation is a fast and catastrophic failure that takes place when an extreme load is applied to a material. During this process complex crack patterns develop. Cracks initiate at internal micro-defects, they propagate, eventually branch, and finally coalesce by forming fragments. This complex phenomenon was initially mainly studied with experimental and analytical methods, with particular emphasis on fragment sizes and shapes distributions. However, in the last decades the rapid development of computer capabilities led to an increasing number of numerical studies. In this work a numerical analysis of dynamic fragmentation is presented. Simulations are based on the finite-element method with dynamic insertion of cohesive elements. This method lets elastic waves spread unaltered and at the same time lets cracks initiate, propagate, branch and coalesce freely at any element borders. In order to use fine 3D meshes with several hundreds thousands of elements, all the algorithms have been coded in parallel. The presented numerical analysis constitutes one of the first applications of this new method in the fragmentation modeling of brittle materials. The studied model consists of a hollow sphere of aluminum oxide subjected to uniform radial expansion. Material defects are reproduced by imposing random stress thresholds around the model following a Weibull distribution. Several strain rates and radial thicknesses are considered, and statistics about fragment sizes and shapes are computed. For a small thickness, fragmentation is similar to that of a 2D plate in expansion. However, in thicker spheres, cracks can branch and merge also in the radial direction. They ultimately develop more complex patterns, transitioning to a mixed 2D/3D regime or pure 3D regime.