atw - International Journal for Nuclear Power | 04.2019

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atw Vol. 64 (2019) | Issue 4 ı April

OPERATION AND NEW BUILD 218

| | Fig. 7.

Allowable size for axial crack.

4.1.2 Circumferential cracks

Fracture mechanics analysis (brittle

failure): The circumferential cracks in

all the risers of the jet pumps are under

tension and bending. Both loading

conditions have to be evaluated.

Tension: The allowable length of a

through thickness circumferential

crack was evaluated with equation 1.1,

vol. 1, pag 1-1 [16]. All the evaluation

was carried on with Matlab code. The

stress intensity factor was evaluated

with the following equation.

(12)

This relation is valid when 0 <

≤ 0.55, 10 ≤ ≤ 20 and .

The geo metrical factor is

(13)

(14)

K I is the stress intensity factor. σ is the

axial stress and depends on the mean

radius R. P is the axial load, t is the

thickness and θ is the mean angle of

the crack.

For the case of bending,

(15)

This relation is valid when 0 <

≤ 0.55, 10 ≤

≤ 20 and

(16)

(17)

K I is the mode I stress intensity factor,

σ b is the bending stress and it depends

on the mean radius, M is the bending

moment and t is the thickness. θ is the

mean angle of the crack and F b is a

geometric factor.

| | Fig. 8.

Allowable size for axial crack, limit load of collapse.

The maximum length of a circumferential

crack was evaluated with

loading conditions for the range of

operation considered. Two analyses

were carried out. In the first one, the

two circuits (normal operation) of the

Reactor Recirculation Core System

were operating. In the second, only

one of them was in operation (single

loop operation). The results are

summarized in the Figure 9. Again,

Matlab coupled with Excel are applied

to make the iterations.

The results showed that the allowable

crack length is reduced as the

core flow core is augmented. This

happens because of the hydraulic

forces exacerbate the vibration of the

riser and the jet pumps. As a result,

fatigue should be considered.

Limit load analysis (ductile failure):

In this case, the cross section of the

riser is under plastic collapse, the allowable

length of a through wall crack

is evaluated with the equation 1.2, Vol.

1, pag. 1-4 [16]. All the iterations were

done with Matlab coupled with Excel.

(18)

(19)

This equation is valid when ≤ 0.1

(20)

M is the limit moment for plastic

collapse, σ f is the flow stress, R is the

mean radius, t is the thickness and θ

is the mean angle of the crack. α is a

geometrical factor.

The results are summarized in

Figure 10. In this case, the maximum

allowable length of a circumferential

crack was evaluated with an analysis

of limit load under collapse conditions.

These evaluations were carried

out for a range of operations, which is

between 95 % and 107 % of the output

power. These evaluations considered

the operation of either, one or two

circuits of the Reactor Recirculation

Core system.

| | Fig. 9.

Allowable size for circumferential crack, LEFM.

| | Fig. 10.

Allowable size for circumferential crack,

limit load of collapse.

It can be observed that the allowable

circumferential crack length decreases

as the flow of water increases.

Under these conditions, the hydraulic

loads generate more vibrations and

fatigue.

5 Failure Assessment

Diagram R6

This is a methodology that is widely

used to evaluate the elasto-plastic

failures in structural components. In

general terms, the failure is determined

by the interaction between

ductile and brittle behavior of a

material. The first versions were based

on the “Strip-Yield” model. The Stress

Intensity Factor for an infinite plate

with a central crack through thickness

is a methodology that is widely used

to evaluate the elasto-plastic failures

in structural components. In general

terms, the failure is determined by

the interaction between ductile and

brittle behavior of a material. The

first versions were based on the

“ Strip-Yield” model. The Stress

Intensity Factor for an infinite

plate with a central crack through

thickness is

(21)

This equation is asymptotic with

respect to the yield strength of the

material; thus, it has to be modified. It

should be considered the flow stress,

instead the yield stress, and the effective

stress intensity factor has to be

obtained. An adimensional relation is

proposed for this purpose. The new

relation is divided by the Stress Intensity

Factor in mode I.

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

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