The requirement (3) ensures the transition of the nonlocal to the traditional criterion in the case of the uniform stress state. The requirement (4) ensures the relation between the nonlocal criterion and linear elastic fracture mechanics (LEFM). A constant in expression (4) depends on the cracking resistance of a material and the crack size and shape. We present the critical size of the flaw in the form cl = + t c K l l β 1 0 , 0 ≥β , (5) where is the critical size of the crack and β is a numerical parameter. The physically consistent values of β lie in the domain 0l 0≥β . Since the local stress distribution in considered problem depends on the curvature radius of the concentrator to a large extent than on other geometrical parameters; therefore, in the first approximation, one can use the curvature radius of the concentrator ρ at a dangerous point to estimate . For estimation of , the critical size of the flaw l is used. We present the function eL 0L c , / ) ( 0 0 e f L L σ in the form ( / ) ( , / ) 0 0 0 ρ σ σ c e f l f L L = . (6) Bearing in mind that the stress concentration factor is an increasing function of ρ / l (l is the size of the concentrator) ( / )ρ f l K t t = , (7) it is easy to see that it suffices to use the function as tf ( / )ρ c f l to satisfy the requirements (3) and (4): ( / ) ( / ) ρ ρ t c c f l f l = . (8) The function given by Eqn. (8) is unique because 0 σ σ = c for l cl = , for any ρ. Thus, with allowance for Eqns. (6) and (8), the nonlocal fracture criterion takes the form ( / ) 0 ρ σ σ t c e f l = . (9) Therefore, the critical stress is determined by the expression ( / ) ( / ) 0 ρ ρ σ σ f l f l t t c c = , and the ratio ( / ) ( / ) ρ ρ t c t f l f l can be regarded as an effective stress concentration factor. EXAMPLES OF FRACTURE CRITERION APPLICATION A plate with an elliptic hole under tension The stress concentration factor can be presented in the form [10] ρ α / 1 l Kt = + , (10) where α is a numerical coefficient which depends on the elastic constants of a material and the dimensions of a plate. For an infinite isotropic plate α = 2 [10] and for an infinite orthotropic plate /(2 ) / 1 1 1 2 E E E G − + = ν α [11], where 1 2 1 , , ν E E and G are the elastic constants. The local-strength function ( ) ρ α σ σ / ( , / ) 1 0 0 0 c e l f L L = + . The critical stress has the form
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