PSI - Issue 30

S.V. Suknev et al. / Procedia Structural Integrity 30 (2020) 179–185 S.V. Suknev / Structural Integrity Procedia 00 (2020) 000–000

183

5

4. Results and discussion The values of  and  are calculated by the finite element method at the center of the specimen with no hole, loaded via inserts of a given size. For the inserts used in the first series of tests, the value of  is 0.764 p and  = 0.187. According to Eq. (2) and the estimates for  and  , the critical pressure in a specimen with a circular hole can be written as        2 1 1 3 0 2 0.1431 2 0.764 1               p C c , (4) where 0 0 / C    and 0 C is the uniaxial compressive strength. The parameter  is determined by Eq. (3), where  = 0.187. The asymptotic (for  a ) value of the critical pressure is

       1      3 2 1 2(1 3 ) 

.

(5)

 s T T

 2





0



1





s s

s

s

 



0 0 0.838 C T   is the asymptotic value of the critical pressure for brittle material. For

and

Here

 5 7 1 1 3

   s



  1 / 2 0    T T s .

quasi-brittle materials with moderate plastic properties,

Figure 3 illustrates experimental data (dots) on the critical load at the instance of the initiation of tensile cracks at the hole as a function of its diameter 2 a , obtained in the first series of tests and the results of calculating the critical pressure using Eq. (4) for 0   (curve 1) and 0.6   (curve 2). The size 0 d is determined from the best match between the calculation results and the experimental data. Its value is 1.0 mm, which is comparable with the size of the largest pores in the material. In accordance with Eq. (5), the stress s T is equal to 0 T in the first case (dashed line) and 0 1.3 T T s  in the second case (solid line). Figure 3 shows a significant size effect, i.e., the effect of the hole diameter on the local strength of the material. As it decreases, the critical pressure increases, reaching the ultimate compressive strength, and, as it increases, it asymptotically approaches the stress 0 1.3 T T s  . This behavior of critical pressure is well described by modified nonlocal criterion.

Fig. 3. Dimensionless critical pressure versus the hole diameter.