PSI - Issue 28

S.V. Suknev et al. / Procedia Structural Integrity 28 (2020) 903–909 Author name / Structural Integrity Procedia 00 (2019) 000–000

906

4

Thus, the condition for smallness of the fracture process zone, which limits the field of application of prevalent nonlocal criteria within the framework of the TCD, takes the form 0 L d e   . In this case, one can assume that const 0   d d . For the developed fracture process zone, the second term in Eq. (1) is not small with respect to 0 d , and it actually can be comparable or even exceed the characteristic size of the material microstructure, with const  d . This case is the subject of the consideration. In this case, it is assumed that the fracture process zone remains small with respect to the dimensions of a deformable body, and the material is deformed elastically outside this region. In the work by Suknev (2019), nonlocal criteria are used to predict the fracture of quasi-brittle materials under uniaxial compression. We now consider the application of the TCD to the problem of tensile crack initiation in a plate with a circular hole subjected to proportional biaxial loading by a tensile stress k p 1 1   along one axis and a compressive stress k p 2 2   along the other axis with account for the above-given ideas about the formation of the fracture process zone. 3. Formulae for the critical stresses Let's consider the application of the Theory of Critical Distances using the FFM method as an example. Applying the FFM to the problem under consideration yields the formula for the critical pressure:    

2 2 16 1 k J k k J k J   1 2 12 1 2 1 2

,

(2)

p C c  

0

2

where

2

0,5

0,5

1,5

2,5







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256

1408

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384

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242

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147

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320 1035

704

192

192

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12

Here 0 0 / C    , 0  is the uniaxial tensile strength, and 0 C is the uniaxial compressive strength. In order to describe the quasi-brittle fracture, d is determined from Eq. (1), in which the size of the stress concentration zone e e e L   grad  is calculated at the point of maximum stress. For the problem under consideration, d a / 1    ,

1 1 2 k k L a k k e    7 5 3

. For 1   , Eq. (2) yields the critical stress according to the traditional fracture criterion that does

2

not account for the size effect. The asymptotic (as  a ) value of the critical pressure:         s s s s s k J k k J k J k k T T     2 2 2 1 2 12 1 2 1 1 2 0 2 ) 16 1 (3      .

(3)

1 2 0 C  

1 1 2 k k k k  

and

is the asymptotic value of the critical stress for brittle material.

Here

1 3

T

   



0

s

3 k k

7 5

2