Erfahrungs- und Forschungsbericht 2012 - Ensi

Erfahrungs- und Forschungsbericht 2012 - Ensi

Figure 1a:

Comparison of K I and

K IC of the RPV subjected

to the MLOCA, The

Chell model is used to

consider the WPS effect

on K IC.

Figure 1b:

Comparison of K I and

K IC of the RPV subjected

to the MLOCA. The

Wallin model is used

to consider the WPS

effect on K IC.

3.1.3. Application of Chell and Wallin

models in WPS analysis

In this section we compare the K IC of a RPV subjected

to a MLOCA transient when applying the

Chell and Wallin models, respectively, to quantify

the WPS effect.

Figure1 shows the history of K I and K IC of the RPV

for the MLOCA transient. Without considering

the WPS effect, it shows that K I exceeds K IC for a

certain time period, which means that crack initiation

occurs in this period. However, by considering

the WPS effect either with the Chell or the

Wallin model, it is shown that K IC is significantly

increased, excluding most of the crack initiation.

However, since there is only a beneficial effect

of WPS after the maximum preloading, the WPS

effect decreases the initiation and failure probability,

but is not able to completely exclude the crack

initiation and failure if K I > K IC occurs not only in

the falling part of SIF-temperature curve but also

in the rising part.

3.2 SP 2: Study of transients with


The concerning documents were studied and

open questions were identified. The RELAP5 input

deck (previously used for LOCA analysis) has been

reviewed, and the possibly necessary modifications

as well as the additional information required for

the transients relevant for PTS studies have been

listed. The questions related to input parameters

and modeling approaches with both codes need

to be clarified in the ongoing discussions.

3.3. SP 3: 3D fracture mechanics

calculations (deterministic)

3.3.1. Finite element modeling

In PISA-I, the integrity of an example reference

case RPV is analyzed by assuming a semi-elliptical

surface crack (shallow crack) with axial orientation

in the beltline region of the RPV. The depth of the

crack is two times the nondestructive testing limit,

according to the German standard KTA 3201.2.

Probabilistic fracture mechanics analyses in PISA-I

have shown that shallow cracks contribute more

than deep cracks to the initiation probability of the

RPV, due to the fact that the neutron irradiation

and PTS loading are more severe at the surface.

However, in fracture toughness testing standards

the use of highly constrained test specimens with

deep cracks is required to guarantee conservative

fracture toughness data. The effective toughness

for the deeper cracks (high constraint) is lower

than that for shallow cracks (low constraint) due to

the higher hydrostatic stress at the crack tip. If this

data from deep cracks is directly used in a vessel

with low constraint, it may lead to over-conservative

results and a too early decommissioning of the

vessel. Thus, the crack tip constraint effect on the

integrity of the RPV was quantified.

For linear elastic analysis, the K-T method provides

a two-parameter fracture mechanics theory to

describe crack-tip stresses and deformation and

is used for the integrity analysis of structures by

considering the constraint effect. K I is calculated

based on the actual deformation field to measure

the scale of the crack-tip deformation (crack driving

force) and the T-stress is calculated based on

the load level, linear elastic material properties and

component geometry to characterize the triaxiality

of the crack-tip stress state. Positive T-stress

strengthens the level of crack tip triaxiality and


ENSI Erfahrungs- und Forschungsbericht 2012

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