PSI - Issue 28

Alla V. Balueva et al. / Procedia Structural Integrity 28 (2020) 873–885 Author name / Structural Integrity Procedia 00 (2019) 000–000

881

9

Table 2. Internal crack growth time in conditions of hydrogen embrittlement ( D = 10  6 mm 2 /sec) for real gas

H YDROGEN CONCENTRATION , c 0 , mol/mm 3

G ROWTH TIME , REAL GAS t

958 years

10  9

96 years

10  8

9.6 years

10  7

0.96 years

10  6

2.2. Model Calculations and Parametric Analysis The dimensionless graph of dependence of the radius of the delamination a ( t ) on time t is given in Figure 3a, and Figure 3b provides a comparison with the ideal gas model used in former work (Goldstein et. al., 1977; Balueva and Dashevsky, 1994). The purpose of this model calculation is to determine the feasibility of our model, and to gain insight into the general behaviour of our solution. A comparison of the above figures reveals a striking relationship between the models based on either of the real and ideal gas hypothesis. As time increases without bound, both models predict a steady-state in which the crack growth approaches linearity. Our model agrees with both our expectations and our previous work.

(a)

(b)

Fig. 3 (a) Normalized Crack Radius a / a * verses Normalized Time t / t * for Real Gas Model; (b) Normalized Real Gas and Ideal Gas Models Comparison - Crack Radius verses Time

For graphs 4 through 6, we allowed α to vary with fixed β, then allowed β to vary with fixed α, in order to provide insight into how the variables affect the overall behaviour of the model, and to provide a qualitative description of the functions sensitivity to these parameters.