In 1971 there was developed in collaboration with G. S. Pisarenko a model [19] of fracture of materials representing this process as a successive series of acts of origin of a microcrack at the tip of the main crack and their subsequent merging. In [20] the proposal was made for determination of the ductile-to-brittle transition temperature as the temperature corresponding to the appearance at the crack tip at the moment of fracture of a plastic zone of maximum size in which plane strain conditions are still satisfied. In it on the basis of the earlier proposed model there was obtained a determining relationship relating the transition temperature to the basic parameters influencing it, specimen dimensions, loading rate, and structure of the material. As the result of fruitful collaboration with Professor D. Francois and the presentation by him of broad experimental data on the scale effect in the ductile brittle transition in various steels it was possible to experimentally base the relationships obtained and to propose certain relationships useful for practical purposes [7]. Since [7] is not yet known to Soviet readers, it was appropriate to first give it a brief presentation and then to develop some of its proposals to other cases not touched upon in this work.