PSI - Issue 13

H.E. Coules / Procedia Structural Integrity 13 (2018) 361–366 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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along the plate width and a function of through-thickness dimension only. The through-thickness distributions of stress are shown in Figure 2. The first case is simple uniform tension. The second stress distribution is given in (González Albuixech et al. 2016) and represents the stress distribution that would be caused by pressurized thermal shock of a Reactor Pressure Vessel (RPV) in a two-loop pressurized water reactor 399 seconds into a Medium Loss-Of-Coolant Accident (MLOCA), according to elastic FEA calculations.

Figure 1: Pairs of co-planar semi-elliptical surface cracks in a plate. a). Definition of deepest point, surface point and ellipse parametric angle, b.) Geometric parameters for a pair if identical cracks, c.) geometric parameters for a pair of dissimilar cracks.

Figure 2: Two different through-thickness distributions of stress applied to twin crack pairs – uniform tension and thermal shock of a reactor pressure vessel during MLOCA (predicted).

Elastic finite element models of the crack pair in a plate were constructed using Abaqus/CAE v6.12 and solved using Abaqus/Standard v6.12. The cracks had an aspect ratio = 0.5 , a separation = 0.125 and depths of = 0.125 , 0.25 , 0.5 and 0.75 . The results are shown in Figure 3. Comparing Figure 3a-b and Figure 3d-e, the increase in stress intensity factor caused by proximity of the cracks in both loading cases is apparent and the interaction factor depends strongly on the loading case (Figure 3c & f). For the interaction between a pair of identical co-planar cracks in an elastic material, subject to an arbitrary through wall distribution of stress, the degree of interaction can alternatively be calculated using a weight function method (Coules 2017). This method is based on the weight function analysis for single semi-elliptical flaws due to Shen & Glinka (Glinka & Shen 1991; Shen & Glinka 1991b; Shen & Glinka 1991a). Weight function coefficients were calculated from SIF results for single and interacting cracks calculated via elastic FEA for cracked plates subjected to different through-wall stress distributions. For the example stress distributions shown in Figure 2, interaction factor determination via the method of weight functions was compared with explicit calculation of interaction factors from the FEA results shown in Figure 3. Good agreement between the methods is seen for all crack sizes. 2.2. Identical flaws (elastic-plastic analysis) The effect that interaction of flaws has on elastic-plastic fracture and plastic collapse can be investigated by two methods. One method is to perform elastic-plastic finite element analysis deformation properties of the material in question and determine the increase in Strain Energy Release Rate (SERR) cause by flaw proximity. Results from this method are specific to the material, and the degree of interaction may also change with the applied load (and hence the cracks’ proximity to fracture initiation) (Coules 2018). Another method is to use a limit load analysis to determine the effect of the cracks on the structure’s Local Limit Load (LLL), and then use this information in a failure assessment diagram analysis (Bezensek & Coules 2018). To illustrate the effect that flaw interaction can have on elastic-plastic fracture, finite element modelling of a cracked tube was performed to determine the SERR as a function of position on the crack tip line and of internal pressurisation. The tube has an internal diameter of 400 mm and a wall thickness of 50 mm. It is closed at both ends