Issue 35

O. Plekhov et alii, Frattura ed Integrità Strutturale, 35 (2016) 414-423; DOI: 10.3221/IGF-ESIS.35.47 420 The Fig. 7 presents the evolution of Young`s modulus of the sample П1 versus dilatation caused by the decrease of the sample diameter. We can observe the expected decrease of Young`s modulus versus dilatation. The evolution of the decrement is not so evident and requests an additional analysis. D ISCUSSION ( SAMPLE SURFACE EFFECT ON LOCATION OF DAMAGE TO FRACTURE TRANSITION POINT ) he experimental results show the important role of dilatation in the failure process under VHCF regime. To describe the evolution of void type defects we can use a statistical approach for the description of the defect evolution proposed in [14]. Under high cycle and VHCF regimes we can assume a weak interaction of defect accumulation and microplastisity processes. Based on Onsager reciprocal relations between defect density rate p  and corresponding thermodynamic force               p F D p x x we can write in one dimensional case                p p F p l D p x x  , (1) where p l - Onsager coefficient,  - applied stress, F - part of free energy of the system which depends on p only, D - the coefficient of self-diffusion which is known to obey the Arrenius law,   0 exp /   sd D D E T ( sd E is the activation energy of self-diffusion) and largely depends on the defect concentration. In order to illustrate the effect of the sample surface we consider two representative material volumes sur V , bulk V located near the specimen surface (part of the surface volume coincides with the specimen surface) and into specimen volume, respectively. If we introduce a mean strain induced by the defect initiation in the considering volume as 1   i m i v p pdv v we can rewrite the Eq. (1) as            p m m p m h l F p p l V p  , (2) where we used the following boundary conditions       i p S v p h D pdv x V . (3) The Eq. (3) requests an approximation of     F p function which determined the equilibrium states of material with defects. Taking into account the solution of statistical problem of defect evolution [2] we can propose the following approximation for defect evolution law   2 2 0 2 0            p m m p m m h l n p p l p p a p V n E  , (4) where n is initial defect concentration,  is the mean stress for the considered volume, 0 , , p p l a are material constants, h -the constant which determines the boundary conditions for considered volumes. To explain the different mechanisms of crack initiation on specimen surface and in volume we need to consider a surface as a physical object with high concentration of incomplete atomic planes and other defects of different nature. T