13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- A single cantilever was presented as a beam of elementary cantilevers (mini-cantilevers) of infinitesimal thickness dx. As seen from Fig. 1, length of the elementary cantilever at a distance of х from the specimen axis is equal to l(x) = l0 + x⋅ctg(α/2), where l0 is the minimum distance from the load application point to the chevron notch boundary, α is the angle at the end of the chevron notch (Fig. 1). The known formula from the elasticity theory is valid for each cantilever in the beam [9-11]: 3 4 ( ) ( ) , λ dP x l x E dx b ⎛ ⎞ = ⎜ ⎟ ′ ⎝ ⎠ (1) Fig. 1. Scheme of the chevron-notched specimen. where b is the cantilever thickness, dP is the load that provides cantilever deflection in width of dx by the value of λ’. Displacement of load application points λ for a double-cantilever design exceeds λ’ twice, i.е. λ = 2λ’. Accordingly, from the equation (1) we derive the dependence of elementary load dP, applied to the mini-cantilever’s end on the variable x: 3 λ ( ) . 8 ( ) E b dP x dx l x ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ (2) Integration of elementary forces (2) affecting each mini-cantilever along the full width of the specimen а, determines the actual load Р, to which the displacement of load application points by the value of λ corresponds: 3 2 3 3 2 0 0 0 0 2 λ λ ctg 4 ctg 2 ctg , 8 2 4 2 2 a a E b E a b a a P l x dx l l l α α α − − − ⎛ ⎞ ⎡ ⎤⎡ ⎤ ⎛ ⎛ ⎞⎞ ⎛ ⎞ ⎛ ⎞ = + ⋅ = + + ⎜ ⎟ ⎢ ⎥⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦⎣ ⎦ ∫ where а is the specimen width (Fig. 1). Hence we derive the working formula to determine the Young’s modulus: 2 1 3 0 0 0 8 2 ctg 4 ctg . 2 2 M l a a E a b l l α α − ⎡ ⎤ ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ = + + ⎢ ⎥ ⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎣ ⎦ (3) The value of М = P/λ characterizes the specimen rigidity at the initial stage of elastic loading. According to the formula (3), the Young’s modulus calculations for commercial titanium VТ1-0 and titanium alloy VТ6 were conducted. For the VТ6-alloy with coarse-grained (CG) structure (grain size
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