Application to Integrity Assessments

4.14.3.1 Transferability of Test Data

The statistical size adjustment enables one to extend the fracture toughness estimation to specimens and structures with different crack front lengths. A longer crack front means that a larger volume of material is exposed to tensile stress ahead of the crack tip, which increases the probability that a crack exceed­ing the critical size will exist in this volume leading, according to the weakest link theory, to brittle frac­ture. This size effect is addressed in a conservative way by the size adjustment formula (eqn [15]). Generally, the size adjustment is made for all test specimens so that a single reference thickness (nor­mally 1 in.) is used for the Master Curve. As described earlier, when approaching the lower shelf, the size effect diminishes to zero for both EPFM Kjc data and LEFM KIc data; note that KIc data are often characterized as being size independent, but as pre­viously described in the transition region, a size cor­rection appears to be applicable. An example is presented in Figure 20, which shows LEFM fracture toughness values (including both KIc and Kq) from a

image464

Eb0sys

30(1-v2)

 

Lower tail MML estimate

 

Minimum value estimate

image550

T (°C)

 

Step 3 used only when n <10

 

Step 2

 

Figure 18 Data censoring in SINTAP Steps 1 and 2 and the T0 determination in Step 3.

 

image548image549

image551

Figure 19 Flow chart for the SINTAP procedure.

 

A533B Cl. 1 (HSST 02) oy = 480MPa center A533B Cl. 1 (HSST 02) oy=480MPa center

image552

Figure 20 Fracture toughness data (KIc and KQ) from the heavy-section steel technology program measured with different size specimens showing the data before (left) and after (right) the size adjustment. Material: A533B Cl.1 steel of HSST 02 (sys = 480 MPa). Modified from Sattari-Far, I.; Wallin, K. Application of Master Curve Methodology for Structural Integrity Assessments of Nuclear Components; SKI Report 2005:55; Swedish Nuclear Power Inspectorate: Stockholm, 2005; p 178.

 

T (°C) T (°C)

large dataset measured in the heavy-section steel technology (HSST) program with different size spe­cimens ranging from 25.4 up to 152 mm (6 in.) thick­ness.23 The data from different specimen sizes follow the same Master Curve prediction after the size adjustment as shown in the second plot in Figure 20.

Another example of applying the size adjustment is presented in Figure 21, showing LEFM Kic data measured by MPA (Materialpriifungsanstalt Universitat Stuttgart, Germany) with different size
specimens, including two very large ones (B = 500 mm).24 A distinct size effect is visible in the uncor­rected data (Figure 21, plot on the left), but not in the data size adjusted to the 25.4 mm specimen thickness (plot on the right in Figure 21).

The above transferability principle also applies for a structure when the size adjustment is made for a real or postulated crack front length, if the material and load conditions remain constant over the whole crack length. If they do not, their variation has to

20 MnMoNi 5 5 (KS 15) sy = 602MPa B =25-500mm 20 MnMoNi 5 5 (KS 15) o-y = 602MPa B =25-500mm

image553

Figure 21 Fracture toughness data measured on steel 20MnMoNi55 (KS 15, sys = 602 MPa) by MPA without size adjustment (left) and size adjusted to specimen thickness 25 mm (right). Modified from Sattari-Far, I.; Wallin, K. Application of Master Curve Methodology for Structural Integrity Assessments of Nuclear Components; SKI Report 2005:55; Swedish Nuclear Power Inspectorate: Stockholm, 2005; p 178.

 

be taken into account. This situation is typical in a thick-wall structure, where the crack front is not usually straight and the temperature and loading may significantly vary along the crack length.

By combining the three-parameter Weibull distri­bution (eqn [13]) and the formula for the statistical size adjustment (eqn [15]), one can derive a formula for the cumulative failure probability of the form:

 

image554

Figure 22 Definition of quantities along the surface crack front.

 

B k — Kmin 4

B0 K0 — Kmin

 

Pf = 1 — exp

 

[31]

 

general expression for the cumulative failure proba­bility can thus be expressed in the form25:

 

where B is the specimen thickness, B0 is the normaliza­tion thickness (usually 1 in. or 25 mm), Kmin is the mini­mum fracture toughness (20 MPa Vm), Kj is the stress — intensity factor, and K0 is the scaling fracture toughness corresponding to 63.2% failure probability.

In this formula, Kj represents the crack driving force, whereas K0 is specific for the material, and B for the specimen or geometry of the structure or component. In test configurations with simple and small specimen geometry, both KI and K0 can be taken to be constants over the whole crack length with sufficient accuracy.

In a real structure, where a real three-dimensional surface crack is possible, both KI and K0 may vary depending on the location (F) along the crack front and should be treated as variables (Figure 22). Note in Figure 22 the designation of the surface crack depth (a), the crack length on the surface (2 c), the total surface crack front length (s), the angle f along the crack front, and the wall thickness (t). A more

 

X

 

4

KIF Kmin ds

K0F — Kmin B0

 

Pf = 1 — exp

 

[32]

 

0

 

By defining an effective stress-intensity factor (Kj eff) corresponding to a specific reference temperature (Tref), which can be the minimum temperature along the crack front, eqns [31] and [32] can be combined to determine the effective stress intensity corresponding to the same failure probability as eqn [32]:

 

X

 

^ІФ Kmin ds

K0F — Kmin B0

 

KIeff T, ef

 

0

 

[33]

 

(K0Tref Kmin) T Amin

 

Kj F is obtained from a stress analysis as a function of location (F). K0r[ef is the standard, high constraint

 

Подпись: 0.019 T-TПодпись: expПодпись: [35]Подпись: Figure 23 Comparison of Master Curve analysis of real flaws (5% curve) and the ASME Code Case N-629 - curve. Reproduced from Sattari-Far, I.; Wallin, K. Application of Master Curve Methodology for Structural Integrity Assessments of Nuclear Components; SKI Report 2005:55; Swedish Nuclear Power Inspectorate: Stockholm, 2005; p 178. image555

Master Curve K0, corresponding to the reference temperature (Tref) along the crack front and has the form for 63.2% failure probability of:

K0T[ef = 31 + 77 exp{0.019(Tref — T>)} [34]

K0 F is the local K0 value, based on local temperature and constraint and can be expressed in the form:

K0 F = K0T, т„[… = 31 + 77

Tst

0deep 10 MPa °С-1

Equation [35] is directly applicable with the ASME Code Case N-629 fracture toughness reference curve,26 since it is written in terms of the standard deep specimen T0.11(ASME Code Case N-629 and N-631 allow the determination of RTt0 when T0 is measured, see Section 4.14.4.2) Equations [33]—[35] give the effective crack driving force, normalized to represent a standard Master Curve 25.4 mm crack front (B0) and the minimum temperature along the crack front.

It should be noted that the area of applicability of the constraint correction based on the Tstress has not yet been fully established.19 The Tm:ess actually is a LEFM concept that does not work when excessive plasticity is present. In this case, a more advanced concept should be used, such as the Q-parameter or a local approach.27 The Х/геж equation (eqn [26] as applied in eqn [35]) works well for the negative values of Tstress, but the effect saturates at higher values. However, in actual components, the Х/геж is generally negative. The new Tstress equation [27] is expected to be valid up to the Tstress value of 300 MPa.2

The fracture toughness can be expressed either with the 5% lower bound Master Curve, which can be expressed in the form:

K5% ,Trf = 25.2 + 36.6 exp{°.°19( Tref — T0 deep) }

[36]

or by using the fracture toughness reference curve from ASME Code Case N-629 or N-631.26,28 Details on these Code Cases are presented in Section

4.14.4.2. The following expressions are derived:

Kic-ASME. Tref = 36.5 + 11.4

exp{0.036(Tref — T) deep) } [37]

or

Kic-ASME, Tref = 36.5 + 3.083

exp{0.036(Tref — RTt0 + 56 °C)}

The curves are compared in Figure 23. Note that the fracture toughness curve is not directly com­pared to the crack driving force estimated from stress analysis. Instead, the fracture toughness is compared to an effective driving force, which accounts for the local stress and constraint state and temperature along the crack front, as well as the crack front length. In this way, it is possible to combine the classical fracture mechanics and Master Curve analyses, and to present the comparison in a conventional format. One should remember, how­ever, that postulated flaws often contain unrealisti­cally long crack fronts. An assumed quarter thickness elliptical surface flaw (а/t = 1/4; c/ a = 3), as used in the ASME Code for pressure-temperature operating curves for RPVs, may be used from a conservative deterministic driving force perspective (as was the intention), but from a statistical size adjustment point of view, this assumption is too conservative. If such postulated flaws are analyzed using KIeff, an additional size adjustment to the Master Curve is recommended. Note that s for a 200-mm thick RPV would correspond to an a of 50 mm, 2 c of 300 mm, and an s of about 400 mm. A more realistic maxi­mum crack front length (s) is 150 mm or less. This value of s is also consistent with much of the original KIc data for the ASME Code KIc curve and therefore justifiable in terms of the functional equivalence principle. The form of KIeff for an excessively large postulated flaw (s > 150 mm) becomes11: