PSI - Issue 20

S.V. Suknev / Procedia Structural Integrity 20 (2019) 30–36 S.V. Suknev / Structural Integrity Procedia 00 (2019) 000 – 000

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3

In the experiment, both cases of brittle and quasi-brittle fracture are characterized, as a rule, by the sudden appearance and rapid growth of a crack (if necessary conditions for the propagation of an unstable crack are satisfied). Therefore, in practice, it is difficult to determine the d egree of “brittleness” or “quasi - brittleness” of fracture of notched specimens. Below, quasi-brittle fracture is understood as a rapid propagation of an unstable crack, accompanied by the formation of relatively large FPZ. The size of the FPZ d is not related to the length of the crack, as is customary in fracture mechanics, but to the characteristic length of the material microstructure 0 d . If 0 d d  , then it is brittle fracture; if 0 d d  , it is quasi-brittle fracture, which transitions to ductile fracture in the range 0 d d  . The redistribution of stresses within the limits of 0 d is not related with the plastic (in the macroscopic sense) deformation of the material. The plastic properties of the material begin to appear when 0 d d  , and the larger d with respect to 0 d , the more they manifest themselves. Taking this into account, we represent d in the following form: e d d L    0 . (1) 1   . In the case where  ~ 1, the material is characterized by moderate plastic properties. The first term in Eq. (1) characterizes the microstructure of the material itself, while the second one reflects the contribution of inelastic deformations. For ductile material, the fracture load does not depend on the size of the stress riser, so the size of the FPZ is proportional to the size of the stress riser and, accordingly, to the size of the stress concentration zone e L (under unchanged boundary conditions). In brittle fracture, on the contrary, the size of the FPZ does not depend on the size of the stress riser and is determined by the microstructure of the material. Based on the proposed approach, a set of new (modified) nonlocal fracture criteria is developed. 3. Quasi-Brittle Fracture Criteria The possibility of application of nonlocal criteria in the problems of the fracture of plane samples with a circular hole in uniaxial tension and compression is considered with account for the above-given concepts of the FPZ formation. 3.1. Average Stress Criterion The most well-known nonlocal criterion is the average stress criterion (ASC), or the line method in the TCD, which has the form 0    e d , where e d  is the equivalent stress averaged at the distance d along the dangerous cross section. Equivalent stress is determined using the theory of the maximum tensile stress. Under uniaxial tension and in accordance with the known solution of the Kirsch problem given by Timoshenko and Goodier (1970), the normal stress distribution y  along the dangerous cross section has the following form: For brittle materials, 0   ; for ductile materials,

       2 2 2 2 x a 

4 4

   

x a

.

(2)

3



y

In view of Eq. (2), the following formula for the critical stress is obtained:

 1 /( 2 ) 2 2 l l d    



0

.

(3)





 2

c

2

/( 2 ) l d

l  