Incubation time approach in rock fracture dynamics

  • V. Smirnov
  • Yuri V. PetrovEmail author
  • V. Bratov


The paper is summarizing latest results connected with application of the incubation time approach to problems of dynamic fracture of rock materials. Incubation time based fracture criteria for intact media and media with cracks are discussed. Available experimental data on high rate fracture of different rock materials and incubation time based fracture criteria are used in order to evaluate critical parameters of causing fracture in these materials. Previously discovered possibility to optimize (minimize) energy input for fracture is discussed in connection to industrial rock fracture processes. It is shown that optimal value of momentum associated with critical load in order to initialize fracture in rock media does strongly depend on the incubation time and the impact duration. Existence of optimal load shapes minimizing momentum for a single fracturing impact or a sequence of periodic fracturing impacts is demonstrated.


incubation time dynamic fracture rocks dynamic strength fracture toughness crack resistance energy and momentum input fracture process optimization 

List of main symbols






local coordinate


local time


incubation time of a fracture


characteristic size of a fracture process zone


normal stress


ultimate stress


stress intensity factor for mode I loading


quasistatic limit for stress intensity factor for mode I loading (critical stress intensity factor)


mass density


Lame constants


displacement in direction x i .


stress in direction ij


Kronecker delta


pressure (stress)


load amplitude


load duration


Heaviside step function


longitudinal wave speed


transversal wave speed


time to fracture


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© Science China Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.St.-Petersburg State Transport UniversitySt.-PetersburgRussia
  2. 2.St.-Petersburg State UniversitySt.-PetersburgRussia
  3. 3.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSt.-PetersburgRussia

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