A modified phase-field model for fracture is presented which includes the material strength and cleavage planes to quantitatively predict the crack propagation path and the mechanical response in polycrystalline brittle materials. To demonstrate the capability of this model, the crack initiation and propagation and the mechanical response in zirconium diboride bi-crystal and polycrystalline samples are investigated. Using a relationship analogous to the modified Read-Shockley model for grain boundaries with large misorientation angles, the fracture surface energy and the strength of the grain boundaries are made dependent on the misorientation angle of the adjacent grains. In general, the crack path inside each grain follows the orientation of the cleavage plane similar to the experimental observations. At the grain boundaries, a low fracture surface energy and/or a low material strength can result in intergranular crack propagation. Comparing the results of different models show that to have a reasonable mechanical response it is necessary to include the material strength and cleavage planes in the formulations of the model. The proposed phase-field model enables designing texture and engineering grain boundaries to control intergranular and transgranular crack propagations and the macroscopic mechanical response.