**atw** Vol. 64 (2019) | Issue 4 ı April

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In this equation, the square root of

the semi-length is eliminated. In this

way, it is independent of the geometry,

as the strip model. In order to

use an adimesional **for**m, the following

parameters have to be established.

and

The new equation is

(23)

This curve is the boundary between

the safe and unsafe zones (Fig. 9).

Fracture would take place when the

Effective Stress Intensity Factor is

bigger than the Fracture Toughness,

K r > 1 On the other hand, ductile

failure is expected if S r > 1. Also, it is

important to observe that in the

elastoplastic analysis, fracture and

collapse are in interaction. The points

defined by K r and S r have to be

localized in the failure diagram so as

to determine if they are in the safe or

unsafe zones.

The material hardening has not

been considered in the “Strip-Yield”

model. There**for**e, this situation

can be included in an elastoplastic

analysis with the J-integral. The

equation proposed by the British

Standard BS 7910 is

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The Failure Diagram shown in Figure

11 compares different failure

curves. This was used in the evaluations,

which were carried out in this

paper.

6 Cases of analyses

The allowable horizontal and vertical

projections of a helicoidal crack in the

riser were determined in the previous

section. In this section, some cases

have been postulated, as an example,

in order to show the application of the

evaluation of the structural integrity

of the riser.

6.1 Circumferential cracks

As an example, a circumferential

crack at the weld of the riser was

postulated. Its length was 4 inches.

The reactor is in operation with the

two loops of recirculation and 107 %

| | Fig. 11.

Diagram of evaluation of failure by plastic

de**for**mation.

| | Fig. 12.

Postulated case circumferential length

of crack.

| | Fig. 13.

Failure Diagram R6.

of the flow of the water flowing

through the core.

Initially, the evaluation was done

in accordance with linear elastic

fracture mechanics. The allowable

crack length is 4.9 inches (Figure 9).

The length of the actual crack is

lower than this limit. So, this crack is

acceptable.

After this, the evaluation was done

under the scope of the Collapse Limit

Load analysis (Figure 10). The allowable

crack length is 16.36 inches. The

length of the actual crack is lower.

There**for**e, it can be accepted.

This evaluation was complemented

with the Failure Assessment Diagram.

The following parameters were

calculated:

and

. As this point is located

within the safe zone. It is considered

safe. However, this point is located

close to the vertical axis in the zone in

which a brittle failure can take place.

So, this is the dominant failure mechanism,

it is recommended to increase

the inspection and to determine the

remaining life because a brittle failure

is undesirable (Figure 11 and 12).

| | Fig. 14.

Failure diagram, postulated case

circumferential projection of crack.

| | Fig. 15.

Failure Assessment Diagram, Postulated case

axial projection of crack.

| | Fig. 16.

Failure Assessment Diagram, Postulated case

circumferential projection of crack.

6.2 Safe helical crack

In this case, a helical crack close to the

weld of the riser brace is postulated. Its

length is 4 inches. Its projections along

the circumferential and the axial axis

are 3.5 inches and 1.94 inches, respectively.

The output power of the reactor

is 100 % and the two circuits of the

RRC system have been in operation.

Initially, the axial projection of the

crack was evaluated. In accordance

with Linear Elastic Fracture Mechanics,

brittle fracture is developed, when

the allowable crack length is greater

than 11.689 inches (Figure 7). Regarding

the ductile failure, the evaluation

was done with the Collapse Limit Load

analysis. The allowable crack length is

11.11 inches (Figure 8). It is greater

than the axial pro jection of the crack.

These results were evaluated with the

Failure Diagram R6. The following

parameters were calculated too.

and ,

then they are localized in the diagram,

Figure 13.

In the case of the circumferential

projection of the helical crack, it was

evaluated against the brittle fracture

with linear elastic fracture mechanics

OPERATION AND NEW BUILD 219

Operation and New Build

Failure Analysis of the Jet Pumps Riser in a Boiling Water Reactor-5

ı Pablo Ruiz-López, Luis Héctor Hernández-Gómez, Juan Cruz-Castro, Gilberto Soto-Mendoza, Juan Alfonso Beltrán-Fernánde and Guillermo Manuel Urriolagoitia-Calderón