13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Ductility of such specimen is equal to: 3 eλ 8 η = . l P Ea b ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ Considering that dS is equal to 2a ⋅dl, we shall find the derivative dη/dS in the equation (4): 2 2 3 η η 12 = . 2 d d l dS adl Ea b = Substituting the given expression into (4), we shall obtain: 2 2 2 2 3 η 12 . d P l G P dS Ea b = = (6) Equation (6) determines specific fracture energy along the crack length l and external load value Р, wherein the crack starts to propagate. Substituting expression (5) into this equation, we shall derive an equation for Gs, which allow us to calculate specific fracture energy based on crack length l and the value of λе: 2 3 e 4 λ 3 . 16 E b G l = (7) It is seen that in the given presentation the value of G does not depend on the specimen width а. Let us apply these considerations to the chevron-notched specimen. Assume that in the process of loading of the given specimen, the material lost discontinuity in segment of Δl (Fig. 3). Crack front is presented as a straight line. It is easy to find from geometrical constructions that length of this line is equal to х = 2Δl⋅tg(α/2). An equation (7) can be applied to the middle part of the specimen in width of х , wherein crack length l makes l0 + Δl. Using the equation (7), a specific fracture energy G can be found, if increment Δl is known. Moreover, it is necessary to know displacement of force application point λе, caused by enhancement in specimen ductility when increasing the crack length by Δl. Fig. 3. Determination of the specific fracture energy Gs. It should be noted that the experimentally measured value of λ (Fig. 3), in addition λе, includes the contribution due to plastic deformation of the material at the mouth of the crack, and in the volume of sample as a whole.
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