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In this work we have studied transgranular cleavage and the fracture toughness of titanium hydrides by means of quantum mechanical calculations based on density functional theory. The calculations show that the surface energy decreases and the unstable stacking fault energy increases with increasing hydrogen content. This is consistent with experimental findings of brittle behaviour of titanium hydrides at low temperatures. Based on Griffith-Irwin theory we estimate the fracture toughness of the hydrides to be of the order of 1 MPa⋅m1/2, which concurs well with experimental data. To investigate the cleavage energetics, we analyse the decohesion at various crystallographic planes and determine the traction-separation laws based on the Rose's extended universal binding energy relation. The calculations predict that the peak stresses do not depend on the hydrogen content of the phases, but it is rather dependent on the crystallographic cleavage direction. However, it is found that the work of fracture decreases with increasing hydrogen content, which is an indication of hydrogen induced bond weakening in the material.