Rheological transitions from suspension flow to granular deformation and shear cracking are investigated in equiaxed-globular semi-solid alloys by combining synchrotron radiography experiments with coupled lattice Boltzmann method, discrete element method (LBM-DEM) simulations. The experiments enabled a deformation mechanism map to be plotted as a function of solid fraction and shear rate, including a rate dependence for the transition from net-contraction to net-dilation, and for the initiation of shear cracking. The LBM-DEM simulations are in quantitative agreement with the experiments, both in terms of the strain fields in individual experiments and the deformation mechanism map from all experiments. The simulations are used to explore the factors affecting the shear rate dependence of the volumetric strain and transitions. The simulations further show that shear cracking is caused by a local liquid pressure drop due to unfed dilatancy, and the cracking location and its solid fraction and shear rate dependence were reproduced in the simulations using a criterion that cracking occurs when the local liquid pressure drops below a critical value.