13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- Close observation of the micromechanisms of CL growth reveals that there is always formation of AZ first in a vicinity of a a micro defect or specially made notch. After some time of growth, AZ reaches a stationary state, at which its length does not visibly change. It implies that the thermodynamic force reciprocal to AZ length has vanished. During that time, however, we observe an increasing load point displacement. It can be noticed from the load point displacement records of discontinuous (stepwise) SCG (Figure 4). The increase of load point displacement during a stationary AZ size stems from the macroscopical creep of the bulk material accompanied by an increasing width of AZ. The later may result from either drawing of an additional material across AZ boundary or creep of the drawn material of AZ or both. The absence of a crack growth from a macroscopical view point means that the crack driving force XCR 0, i.e., 1 2 CR J . This inequality may change the sign after a certain time of creep and degradation of fibers within AZ, since the specific fracture energy decays due to degradation of microfibers. Then, the crack moves into AZ for the distance controlled by an interplay between 1 CR J and 2 ( , ) x t . The advancement of the crack into AZ reduces AZ length and thus violates the AZ equilibrium condition, giving rise to an increase of AZ force that result in the AZ growth. Thus, the role of AZ is in moderating high stress concentration caused by a crack. It is achieved by strain localization (displacement discontinuity) in form of cavitation and cold drawing. However, AZ can only delay the fracture propagation process: the creep and/or other types of degradation of the AZ material reduce its toughness with time and ultimately allow crack penetration into AZ. Such process of CL propagation continues by crack and AZ assisting mutual growth. The described scenarios of CL growth is formalized in the following system of coupled ordinary differential equations with respect to cr and AZ : 1 2 , 0, 0, 0 , 0, 0, 0 cr CR CR cr CR AZ AZ AZ AZ AZ k X if X and if X k X if X and if X . (16) The kinetic coefficients k1 and k2 in Eq. (16) as well as the parameters entering the CL driving forces XAZ and XCR are evaluated by matching the model predictions with observed CL evolution reflected by load point displacement vs. time plot like shown in Figure 4, side views and fracture surface micrographs similar to that shown in Figures 5, 6, and 7. The crack and AZ thermodynamic forces are non-linear functions of crack and AZ lengths. Thus, the system of Eq. (17) despite of its simple appearance is a nonlinear system of ODE, solution of which calls for numerical methods. An illustration of numerical simulation of CL growth in a CT specimen is presented in the accompanying paper [8]. 4. Conclusion The focus of the paper is brittle fracture resulting from SCG. The limitation of the conventional approach of lifetime assessment in brittle fracture originates from complexity of SCG process. Specifically, relatively new data on continuous vs. discontinuous modes of SCG is presented in details. Only continuous CL growth takes place for low enough load. Above that value, both continuous and discontinuous modes of SCG are possible at different temperature. The active zone of CL constituted by cold drawn microfibers and the energy dissipation associated with AZ formation play a major role in fracture process. A brittle fracture of microfibers in process
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