PSI - Issue 23

Nikitin I.S. et al. / Procedia Structural Integrity 23 (2019) 119–124 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

123 5

1 k

k  

( 1)( 

) 

( 1)( 

) 

 

( 1 2 ) k   

1

1









d

and 12 d

arcsin

arcsin









.

13

k

k

k

k

k

1

1

1

1











1 k    the coefficients are

1 k  and

While 12 0 S  ,

k

k

(1 )(

)

(1 )(

)

1 k     

   

(2 1) k   

1









d

and 12 d

arccos 1 1

arccos









.

13

k

k

k

k

1

1

1









While    . Thus, the formulas (2-3) describe the constitutive equations of the resulting plastic model. The plastic deformation condition is 13 1 0 S   and is similar with the Tresca condition. If we take the yield function       4 13 12 12 1 1 ij F S S S     and take it as a potential of plasticity then equations (2) express the associated law of plastic flow p ij ij kl kl h F F          ,   0 13 1 p h c S    , 0 kl kl F      and 0 F  . 1 k  13 12 d d 4

4. Comparison with experimental results

Examples of calculations of various loading trajectories taken from Mokhel et al. (1983) are shown in Fig. 2-4. On each figure on the left-hand side (Figs. 2-a to 4-a) a biaxial loading diagram is shown and on the right-hand side (Figs. 2-b to 4-b) a calculated 1 1    stress-strain diagram is shown.

(a)

(b) Fig. 2. (a) biaxial loading diagram; (b) stress-strain diagram