PSI - Issue 48

Štěpán Major / Procedia Structural Integrity 48 (2023) 230 – 237 Major / Structural Integrity Procedia 00 (2019) 000 – 000

233

4

(3)

L L L C Y N  

Where Y L is the occupancy of lattice sites and N L the number of lattice sites per unit volume. Hydrogen concentration at trap sites can be expressed as a function of the hydrogen concentration in lattice sites in the case of equilibrium:



 1 1





 

(4)

1 T T T C N K N    T

Where trap equilibrium constant is

E



T K e 

(5)

RT

In this expression the ∆ E is the trap binding energy with respect to the lattice site; R is the universal gas constant and T the absolute temperature. The number of trap sites can be expressed as a function of equivalent plastic strain ε P is given equation

T C C C C dN t C t           T L

T N d t     T P T P

(6)

L

This equation was conceived under the assumption that the number of lattice sites is a constant and the temperature will be kept constant, i.e the partial derivative of the hydrogen concentration in trap sites with respect to time. From this equation we can obtain so called "plastic- strain rate factor“ , and finally we get a relationship for hydrogen concentration in trap sites, which is quadratic equation:

  

 

N K

2

0

(7)

C

tot T T C N C N C   T tot

L   



T

T

Where C tot = C T + C L is total hydrogen concentration.

Fig. 1. (a) Geometry of sub-surface crack. (b) Crack plane in weld. The crack occurs on the middle plane marked in the picture as "Crack plane". The crack has the shape of an ellipse in the center of which there is an inclusion. The picture also shows the load with which the model works.

2.3. Crack growth from the perspective of fracture mechanics For analysis of crack propagation phase is necessarily calculate the stress intensity factor around the inclusion, respectively at the forehead of crack. In order, to calculate the stress-strain characteristics in the vicinity of the inclusion, it is necessary to first analyze the geometry of its location relative to the fracture plane. In the following Fig. 1, we see a subsurface crack of an elliptical shape in the weld that joins the two parts. This is a model of a weld that could, for example, connect two cylinders (pipes or elements of a pressure vessel). Inclusion assumed in the plane