PSI - Issue 2_B

J. Toribio et al. / Procedia Structural Integrity 2 (2016) 626–631

629

4

Author name / Structural Integrity Procedia 00 (2016) 000–000

1000

0.35

1 = 7º 1 = 9º

2 = 5º 2 = 5º

1 = 7º, 1 = 9º,

2 = 5º 2 = 5º

 

 

 

 

500

0.3

0

P



 (MPa)

0.25

-500

-1000

0.2

0

1

2

3

4

5

0

1

2

3

4

5

r (mm)

r (mm)

(a)

(b)

Fig. 3. Radial distribution of hydrostatic stress (a) and equivalent plastic strain (b) after two drawing processes with different varying die angle.

2.4. Drawing straining path Toribio et al. (2012) studied the effect of the straining path on the HE susceptibility of prestressing steel wires by means of a numerical simulation of two drawing processes: one of them with a heavy first reduction step (wire A) and the other one with a heavy last reduction step (wire B). The distribution of both hydrostatic stress and equivalent plastic strain after these two whole drawing procedures is plotted in Fig. 4, showing that: (i) hydrostatic distributions generated in wire B exhibit a positive gradient in the surface while in wire A the gradient is negative; (ii) a heavy reduction at the first step produces a smoother plastic strain profile than in wire B (heavy reduction at the last step).

2

1000

Heavy red. (1st step) Heavy red. (last step)

Heavy red. (1st step) Heavy red. (last step)

1.8

500

1.6

0

P



1.4

 (MPa)

-500

1.2

1

-1000

0 0.5 1 1.5 2 2.5 3 3.5

0 0.5 1 1.5 2 2.5 3 3.5

r (mm)

r (mm)

(a)

(b)

Fig. 4. Radial distribution of hydrostatic stress (a) and equivalent plastic strain (b) after two drawing processes with different straining path.

3. Hydrogen embrittlement susceptibility HE phenomena can be analyzed in terms of hydrogen diffusion assisted by stress and strain, as discussed by Toribio et al. (2010). The stress-and-strain assisted diffusion equation (1) includes two key terms: (i) the inwards gradient of hydrostatic stress and (ii) the inwards gradient of strain-dependent hydrogen solubility , as follows:

  

     

  

( )

t C

   S P ε K K



(1)

  RT D C DC V H

( ) S P ε

  

 



R being the universal gases constant, V H the partial volume of hydrogen, T the absolute temperature and K s  the hydrogen solubility which is linearly dependent on equivalent plastic strains according to K s   p .