THE "BEAM" APPROACH TO CRACK PROPAGATION PROBLEMS

Most publications devoted to the crack propagation in elastobrittle solids deal with the analysis of conditions for initiation of cracks or their steady-state propagation. The nonstationary crack growth has been studied considerably less. Even for the simplest case where the speed and direction of the crack movement are given, the determination of the corresponding stress state leads to serious mathematical difficulties [1-6]. Forthis reason, when solving dynamical problems of crack mechanics, researchers widely use simplified models, in particular, the so-called "beam" approximations. This model is used both for the study of crack initiation conditions [7] and for the analysis of crack propagation processes [8-10]. In this case, an infinitedegree-of-freedom system, as a rule, is modelled by a single-degree-of-freedom one. The most consistent analysis of the dynamical problems of crack mechanics on the basis of the "beam" model was carried out in [8-9]. In the present paper, using the cantilever beam functions and Lagrange equations of the second kind, we modify the Guilman approach [7] preserving its fundamental idea. The solution obtained allows us to analyze the growth of the crack which has an initial length L at different rates and magnitudes of loading.