Issue 47

S. K. Kourkoulis et alii, Frattura ed Integrità Strutturale, 47 (2019) 247-265; DOI: 10.3221/IGF-ESIS.47.19

Adopting the above values the stress components at the two critical points of the configuration (namely points A( R 2 ,0) and B( R 1 ,0)) are calculated equal to: ‐ σ θ ( R 2 ,0)=39.97 MPa, σ θ ( R 1 ,0)= –75.98 MPa, for plane strain, ‐ σ θ ( R 2 ,0)=33.45 MPa, σ θ ( R 1 ,0)= –63.59 MPa, for plane stress. The ratio of the two stresses is equal to:     1 2 2 1 , 0 1.9, for 2 , 0 R R R R         (21) In other words, the ratio of the maximum compressive stress developed over the respective maximum tensile one, in a CSR with ρ =2, is less than 2. Compared to the respective ratio of the Brazilian disc test, which at the center of the disc is equal to 3, one of the major advantages of CSR-specimen is highlighted, since the CSR-test can be used in a broader variety of materials concerning the ratio of compressive over tensile strength. Regarding now the contribution of each one of the two constituent components (transverse forces and bending moments) of the overall stress field, it can be determined that for plane strain conditions it holds that: - Contribution of transverse forces, – P , P ( β -dislocation): σ θ ( β ) ( R 2 ,0)=30.62 MPa, σ θ ( β ) ( R 1 ,0)= –61.24 MPa, ‐ Contribution of couples, – Pc , Pc ( ε -dislocation): σ θ ( ε ) ( R 2 ,0)= 9.35 MPa, σ θ ( ε ) ( R 1 ,0)= –14.74 MPa, while for plane stress it holds that: ‐ Contribution of transverse forces, – P , P ( β -dislocation): σ θ ( β ) ( R 2 ,0)=25.62 MPa, σ θ ( β ) ( R 1 ,0)= –51.25 MPa, ‐ Contribution of couples, – Pc , Pc ( ε -dislocation): σ θ ( ε ) ( R 2 ,0)= 7.82 MPa, σ θ ( ε ) ( R 1 ,0)= –12.34 MPa. In both cases (plane strain - plane stress), it is determined that: - Point A: σ θ ( β ) ( R 2 ,0) =0.77 σ θ ( R 2 ,0), σ θ ( ε ) ( R 2 ,0)=0.23 σ θ ( R 2 ,0), - Point B: σ θ ( β ) ( R 2 ,0) =0.81 σ θ ( R 2 ,0), σ θ ( ε ) ( R 2 ,0)=0.19 σ θ ( R 2 ,0). In addition, for either plane strain or plane stress, it holds that:





( ) 

 

R R

, 0 , 0

R R



1

- Bending by transverse forces, – P , P ( β -dislocation):

2    , 2 





( ) 

1



2

R R R R

2 2   R R R

2 2 log

2





( ) 

 

R

, 0 , 0

2

1

2



1

1

- Bending by couples, – Pc , Pc ( ε -dislocation):





1.58

.





( ) 

2 R R R R   2 2

2 2 log

2



2

1

1

1

80

0.7 0.5 0.3 0.1 = 1.43 2.00 3.33 10.0

R 2

/ R 1

40

0

σ θ [MPa]

B B

-40

A

-80

0

10

20

30

40

50

r [mm]

Figure 6 : The distribution of the transverse normal stress along the axis of symmetry (locus AB) of the CSR for various ρ -values.

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