A possible explanation of the experimentally observed field-induced crossover of the irreversibility line T(c)(H) in deoxygenated high-T(c) superconductors is proposed via a new model of granular superconductor with dislocation-mediated grain boundary weak links. The model predicts magnetic field and oxygen deficiency dependence of the irreversibility line power exponent q(delta, H). It is shown that for an intermediate field region and small deficiency (delta approximately 0.01) the model leads to the transition from a de Almeida-Thouless-like line (with q = 2/3) to a Gabay-Toulouse-like one (with q = 2) with increasing the field, whereas for high enough deficiency (delta approximately 0.5) the system chooses another path in the H-T plane from H2/3 to H1/4, practically within the same field interval.