13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- d ranges from 7 to 10 µm), the value of Е equal to 110±8 GPa was obtained. For the same material with UFG structure, the value of Е is equal to 114±8 GPa. These values agree with reference data [7]. The Young’s moduli of commercial titanium VТ1-0 in CG and UFG states appeared equal to 111±8 GPa and 113±8 GPa, respectively, that slightly differs from the value of Е equal to 110 GPa for commercial titanium by reference data [12, 13]. Thus, the conducted calculations with use of experimental data have shown the following: - equation (3) can be used for approximate Young’s modulus calculation for materials by test data of the chevron-notched specimens; - grain structure refinement by SPD methods does not lead to essential change in elastic behavior of the studied specimens. 3. Definition of specific fracture energy under crack propagation Gs Energy approach is reasonable when determining condition of unstable crack propagation. The gist of energy fracture criterion can be defined as follows: crack growth takes place if system can release energy to start crack propagation at elementary distance dl. Energy necessary for crack growth appears entirely due to elastic strain energy occurring in bulk of the material under the action of external applied force. Let us consider a double-cantilever beam specimen with a narrow straight-through notch (Fig. 2) to begin with. Distance from load application points to the notch boundary is a crack in length of l0. It was shown in the papers [6, 14] for this case that a necessary condition for crack propagation obeys the equation 2 η , P d G dS = (4) where Р is the load applied to the specimen, dS = 2a ⋅dl is the doubled area swept by the crack when propagating to the short distance dl (Fig. 2), η = λе/P is the specimen ductility (value reverse to rigidity М = λе/P). The value of G determines elastic energy release rate under crack propagation. Further we shall call the characteristics of G a specific fracture energy. Fig. 2. Straight-through notched specimen. According to [6], displacement of load application points λе for the specimen in width of a with crack length l is provided by load: 3 eλ . 8 E a b P l ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ (5)
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