ON OPTIMAL PATHS OF DEFORMATION AND FRACTURE IN CREEP

The problem of the determination of an optimal path of deformation in creep that leads to a given residual strain with minimal damage of the material is studied under constraints on the duration of the process and on the value of the equivalent stress. In contrast to a similar problem of [1], where in fact only viscous materials were considered (for which the strain at the instant of fracture in the long-time rupture strength tests under constant stress decreases as the stress increases), in the present paper brittle materials are also studied for which this stress-strain dependence is replaced by the inverse one. Moreover, among all simple deformation paths, the least favorable paths are indicated which lead to the maximum damage under the same conditions. This makes it possible to obtain upper and lower estimates for the damage of the material in terms of the known residual strains. The problem of optimal (in the sense of energy consumption) fracture of the material under the constraints indicated is also studied.