Issue 52

J. Kasivitamnuay et alii, Frattura ed Integrità Strutturale, 52 (2020) 163-180; DOI: 10.3221/IGF-ESIS.52.14

Methodology

Region

Model

Reference temperature

Lower bound

Transition

ASME Section XI ASME Section VIII

Nil-ductility transition temperature, RT NDT Estimate from Charpy transition curve and ASME exemption curve

Charpy impact

Transition Upper shelf

Charpy V-notch transition curve Rolfe-Novak correlation Wallin J-integral correlation

- - -

Master curve

Transition

-

Master curve index temperature, T 0

Table 1: Fracture toughness estimation methodologies adopted in software development.

Calculation issues The standard provides definite steps to manipulate the input information for each type and level of assessment. Yet some issues require preparation and consideration before coding. The first issue was information preparation in the standard which appears as a graph (e.g., screening curve) or table and converting that into a suitable format for programming. The next issue was the SIF calculation when the origin of the local coordinate on the thickness direction of a cracked cylinder differs from the recommended residual stress profile, or from after crack recategorization. The final issue was related to fatigue crack growth analysis. Each screening curve was digitized and the coordinates obtained were stored in a text file. An array-type variable was prepared to store the data read from the opened text file while the program was running. A one-dimensional linear interpolation algorithm was used to determine a permissible crack length at an intermediate value of the independent variable, i.e. T – T ref + 56. The information from each table was stored in a text file. A one or three-dimensional linear interpolation algorithm was employed depending on the number of independent variables. The next issue was SIF calculation. Considering the CSCLE and CSCCE cracked cylinders with an external surface crack, shown respectively in Figs. 5(d) and 5(f), the origin of the local coordinate x was defined at the outer wall, whereas the recommended residual stress profiles were typically defined at the inner wall. Therefore, before computing the SIF of these two cracked cylinder geometries, the recommended residual stress profiles must be rewritten in the form of:

2

3

4

x

x

x

x

0  = +  − +  − +  − +  −                 1 2 3 4 1 1 1 1 t t t t            

(7)



( ) x

where  0 ,  1 ,  2 ,  3 and  4 are recommended coefficients given in the standard. A similar situation occurs when the CSCLE and CSCCE cracked cylinders with an external surface crack (Figs. 5(d) and 5(f)), are respectively recategorized as the CTCL (Fig. 5(a)) and CTCC (Fig. 5(b)) cracked cylinders. The user-defined stress profiles of any type (i.e. mechanical, thermal and residual) for the cases of CSCLE and CSCCE must be rewritten in the form of Eqn. (7) before computing the SIF for the CTCL and CTCC cases. For fatigue crack growth analysis, the standard does not provide guidance to incorporate the influence of residual stress on the FCGR. This software considered the residual stress as mean stress, thus the stress ratio, R in the Walker FCGR model was given by:

min K K K K + + max

res

=

(8)

R

res

where K min and K max are the minimum and maximum of mode-I SIF due to a cyclic nominal load, respectively. K res is mode-I SIF due to residual stress. A further consideration for crack growth analysis is the calculation of the remaining life of a cracked cylinder. As a compromise between accuracy and computational time, FCGR was calculated only at the representative locations on the crack front. In addition, the crack size was updated every allowable number of loading cycles, i.e. the FCGR was supposed to be constant during this interval. Herein, the allowable number of loading cycles was set to the number of cycles required to grow the crack by 1% of its previous dimensions. For a through-thickness crack, FCGRs were calculated at the inner and outer points on the crack front. The allowable number of loading cycles  N allow was determined from:

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