PSI - Issue 59

Jesús Toribio et al. / Procedia Structural Integrity 59 (2024) 206–213 Jesús Toribio / Procedia Structural Integrity 00 ( 2024) 000 – 000

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concentration at each point of the sample. The computational program provides the nodal concentrations at each step of calculation. By using an interpolation both in space and time, it is possible to determine the hydrogen concentration at all points and instants. Fracture will take place in an instant t c (time to failure or critical time) at which the critical concentration c c is reached over a critical distance x c . For a given applied stress  ap , the critical depth x c and the dimensionless critical concentration c c /c o * are introduced into the computational results of the diffusion program (concentration at all points of the sample for any time). Firstly, the dimensionless hydrogen concentration at the xc depth point at any instant is calculated; later, the time t c for which such a dimensionless concentration reaches the value c c /c o * is obtained, as sketched in Fig. 3, Apart from the case of the wire free of residual stresses, two opposite residual stress laws (tensile and compressive) were considered, as sketched in Fig. 3 (where x is the depth from the wire surface). Their levels are very realistic and typical of commercial prestressing steel wires.

c/c o *

c/c o *

+100 MPa

c c /c o *

t 3

300

200

100

x( m)

t 2

t 1

t

t

x

x c

-100 MPa

c

(a)

(b)

(c)

Fig. 3. Hydrogen concentration evolution at any point (a) and at the critical point (b), together with the residual stress distributions used in the numerical computations. The data used in the computations were: two test temperatures of 35ºC and 50ºC; V* = 2 cm 3 /mol (Hirth, 1980), D = 4.99 x 10 – 12 m 2 /s (Doig and Jones, 1977); c c /c o = 1.24 and K IHE = 0.27 K IC (Toribio and Elices, 1991), where K IC is the conventional fracture toughness in the absence of hydrogen, i.e., in air (inert) environment. The SIF was calculated by Astiz (1986) for a semi-elliptical crack in a cylinder. As a matter of fact, the zone damaged by hydrogen in high-strength steel bars frequently has a thumbnail shape that may be assumed to be semi-elliptical. For a small ratio of the crack depth to the cylinder diameter — the most common case in hydrogen environments — and for a crack aspect ratio or relationship between the crack depth (minor axis) and the crack transverse length of 0.5, the dimensionless SIF is M=0.94. Nevertheless, the SIF, cf. Astiz (1986), is not very sensitive to the crack aspect ratio for the range of values found in the experiments. 5. Results and discussion The computational results — in the form of curves applied stress vs. time to failure — for the material with zero, tensile and compressive residual stresses are shown in Fig. 4 (35ºC and 50ºC), together with the boundaries of the experimental scatter area. The agreement between model predictions and experimental results is excellent, because the curve for the material free of residual stresses exactly fits the central tendency of the experimental results, whereas curves for tensile and compressive residual stresses approach the boundaries of the experimental scatter area, which demonstrates the goodness of the proposed computer model to estimate the wire life in the ATT and thus to analyze the role of surface residual stresses in the HE susceptibility of prestressing steel wires. Tensile residual stresses enhance the hydrogen penetration into the critical area, thus decreasing the life of the wire, whereas compressive residual stresses delay the hydrogen ingress, thereby extending the wire life. The explanation for these assertions lies in the fact that hydrogen diffusion is governed not only by the concentration gradient, but also by the hydrostatic stress field in the material that is itself influenced by the residual stress