CONTINUOUS MODELS OF FRACTURE OF SOLIDS SUBJECTED TO NONSTEADY LOADS. I

The description of processes of deformation and fracture of solids under the action ofnonsteady intensive loads is a complex problem of solid mechanics which is still unsolved. The essence of the problem is hidden in the variety of physical processes occurring on the microscopic level. This problem is distinguished also by the feature that it is hardly possible to establish quantitative laws governing the process of fracture of solids only on the basis of experimental data, without introduction of intuitive concepts and hypotheses. It is well known that fracture processes in solids are essentially based on the nucleation and development of various sort of microdefects such as dislocations, micropores and microcracks. Therefore, to establish the laws of the behavior of a medium with the fracture processes being taken into account, it is necessary, first of all, to establish laws governing the nucleation and development of microdefects. After that, when using the continuous approach lo the description of fracture, one should introduce the phase space of parameters identifying the stale of microdefects and the function of distribution of these microdefects in the phase space. Based on the laws of nucleation and development of microdefects, one should determine the equation for the distribution function. Once this function is known, one can introduce various average quantities which occur in the model on the microlevel and are the desired physical variables. Moreover, using the distribution function, one can establish constitutive equations if the distance between pores is much larger than their own size. If this condition is not satisfied and, hence, one cannot ignore the influence of the neighboring pores on the stress state in the vicinity of each pore, one has lo construct a more sophisticated model which is the subject matter of the micromechanics of fracture. In the present paper, we do not consider issues related to the micromechanics of fracture. In the phenomenological approach, one proceeds in another manner. Using intuitive considerations, one introduces various sorts of microscopic physical quantities into the model. Then, using some hypotheses, one postulates anecessary number of laws which must be satisfied by these quantities. Thus, although taking into account the local microdefects, the continuous model is formulated so that it is not necessary to study the behavior of an individual micropore. Asimilar case is for the statistical approach which implies introducing the function of distribution of microdefects. This function takes into account the processes occurring on the microlevel and describes the behavior of the entire assembly of defects. Over the last two decades, a lot of works have appeared devoted to both experimental and theoretical investigations of fracture processes in solids.