PSI - Issue 25

Ch.F. Markides et al. / Procedia Structural Integrity 25 (2020) 214–225

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8

Ch. F. Markides et al., Structural Integrity Procedia 00 (2019) 000 – 000

Fig. 4. The variation of stresses along an arbitrary radius with θ=30 ο due to problems I and II, for CSRc and CSRt.

Fig. 5. The variation of stresses along AB, due to problems I and II, for CSRc and CSRt.



     2





  2 R 



2

  





2

 

2 2  

2       2  1 1

2

2 1 4 log

2

2log 1

1 log

c



 

 



 





CSRt

P P



 

f

K





(21)









CSRc



   





  2 R 



  

2





2

 

2 2 2 log 1 c         2 2

2       2 1 1 

2

2 1 4 log

1 log



 



 

f

 

It holds that K <1, thus, the fracture load for the CSRt is always lower than that for the CSRc. In Fig.6, the variation of K according to Eq.(21) is plotted against ρ . As it is seen, in the case, for example, ρ =2, considered, also, in drawing Figs.4 and 5, P f (CSRt) is only 53% of P f (CSRc) , thus reducing further when CSRt is used, the possibility of fracturing at the supported parts of the specimen. In addition, using the notation D =2 R 2 , Eqs.(18, 19) may be put in the form:

         

    

    

   

















CSRc

BD

2 2  

2   

2log 1 

1

c



 

2

P

P

  t





  CSRc BD 

CSRc

f

f

k







t 

(22)

 





 BD P R 





Dh

  

  

2

2 

2  

1 log

1



 





2

2 

2 1 4 log

 

 

f

2

    

    

   



 2













CSRt

BD

2 2 2 log 1       2

2    

4

2 

1

c



2

P

P

  t





  



CSRt

CSRt

BD

f

f

k







(23)

 





 BD P R 

t





Dh

  

  

2

2 

2  

1 log

1

 





2 

2 1 4 log

 

 

f

2