Analysis of crack arrest event in NESC-1 spinning cylinder experiment

W Xu, J B Wintle, C S Wiesner and D G Turner+

Paper published in International Journal of Pressure Vessels & Piping, Volume 79, Issue 11, November 2002, pp. 777-787. by Elsevier www.elsevier.com/locate/ijpvp

⁺ Current address: MBDA (UK) Ltd, Six Hills Way, Stevenage, UK

Abstract

In the NESC-1 Spinning Cylinder test, a large surface-breaking flaw in a thick steel cylinder component was subjected to high primary and secondary stresses produced by combined rotation and thermal shock loading. The crack arrestedafter relatively small amounts of ductile tearing and cleavage crack extension. Finite element analyses have been carried out to obtain static elastic stress intensity factors for the initial and arrested crack under constant load andconstant displacement boundary conditions. Applied static elastic stress intensity factors for the arrested crack have been compared with the plane strain crack arrest toughness values measured using small-scale Compact Crack Arrestspecimens. The present analyses of the crack arrest event in the NESC-1 Spinning Cylinder test have concluded that ⁽¹⁾ Applied static elastic stress intensity factors are reduced significantly for the lobe-shaped arrested crack which developed from the initial semi-elliptical surface crack as a result of the localised cleavage crack propagation.This reduction in crack driving force is likely to be the main reason for crack arrest. ⁽²⁾ The analysis carried out and the comparison with the full-scale experiment confirm the prevailing approach to the assessment of crack arrest that brittle propagation will stop if the applied crack driving force falls below thecrack arrest toughness. ⁽³⁾ The results justify the use of the static elastic stress intensity factor as the crack propagation driving force parameter and the static plane strain crack arrest toughness as the resistance parameter for crack arrest evaluationfor small relative crack jump dimensions. ⁽⁴⁾ The small-scale Compact Crack Arrest (CCA) crack arrest tests can be employed to evaluate crack arrest in a large cylinder of the same material.

1. Introduction

In the NESC-1 Spinning Cylinder test, ^[1] a large surface-breaking flaw in a thick steel cylinder component was subjected to high primary and secondary stresses, produced by combined rotation and thermal shock loading. After the test, destructive examination of thecylinder showed that the flaw (hereafter referred to as flaw R) had grown initially by ductile tearing before extending by cleavage at one end. Cleavage crack propagation stopped after 13.5mm of sideways extension and the lobe-shapedcleavage region was contained within 30mm of the inside surface (see Fig.1).

Fig.7. Static elastic stress intensity factors for the initial crack at 217s after the water quench

A curve is drawn through all the discrete points representing K _I values in Fig.7 to indicate trends of the stress intensity factors. The KI values computed by the FE analysis seem to drop as the inner surface is approached, but it is not certain how K _I values actually vary within a small distance of about 2mm at the inner surface because no reliable K _I values have been obtained there in the present work. There are oscillations of K _I values in a band of about 8mm near the inner surface. Similar oscillations were also found in the ONRL analyses ^[13] and are likely to be a computational effect due to influences of free surface and of material in-homogeneity, and, to a less extent, FE mesh design on calculated stresses and strains. The oscillations of the stress intensityfactor do not, however, occur in the region of actual interest, which is the band of base material at a distance of 10 to 30mm from the inner surface. Checks undertaken using analytical K _I solutions show that the FE model gives accurate results at the deepest point for the stresses produced by centrifugal loading.

Arrested flaw

It was not the intention of this work to explain the shape of the arrested crack. For this it would have been necessary to undertake an incremental viscoplastic dynamic analysis of the propagating crack and changing stress field,computing the stress intensity factor at each increment. An example of this complex type of analysis is given in Ref. ^[4] . Instead, the present analysis has been made using the shape of the arrested crack (slightly idealised), where the objective is to show that the use of compact crack arrest toughness data with statically determined elasticcrack driving force is a sufficient condition for crack arrest.

The computed K _I values for the arrested defect are shown in Fig.8 (open symbols). The minimum K _I at about 15 to 25mm from the inner surface coincides with the position of the arrested cleavage growth. It can be seen from Fig.8 that K _I values oscillate both at the free surface and at the positions of the arrested crack. The oscillations at the position of the arrested crack are believed to be the effects of the non-smooth crack frontconsisting of segments of straight lines. A smoother crack front would have reduced the oscillations significantly. Lin and Smith ^[14] have investigated the effects of a non-smooth crack front on K values. They have shown ^[14] that for a crack front modelled with multiple segments of straight lines with corners at the joining points between two adjacent segments, similar to the one in the present paper, K values from the joining points are lower,which is consistent with the present results. They also show ^[14] that the K values from the non-joining points of the crack front are closer to the K values obtained for the same crack front modelled with smooth splines. This suggests that the oscillations in K values would be real if thecorners in the crack front were real geometry features. It is worth pointing out, therefore, that the variations of the K values due to a non-smooth crack front and the oscillations of K values at the free surface should not beconfused. Causes of oscillations of K _I values at the free surface are more complex than the non-smoothness in the crack front, but the conclusions of the present work are not affected by this position.

Fig.8. Static elastic stress intensity factors for the arrested crack

Comparison of results for the initial and arrested defect

The elastic K _I values for the initial and arrested crack are compared in Fig.9. It is evident that the K _I values are significantly reduced in the region of the arrested cleavage growth, 11 to 28.5mm from inner surface (see Fig.1), where the K _I values are about 50%-60% of those of the initial crack. Post-test destructive examination showed that a lobe-shaped crack developed from the cleavage fracture initiation site, about 16.5mm from inner surface(see Fig.1). The crack grew away from the initial semi-elliptical defect boundary predominantly in the direction of the cylinder axis. Since the applied stresses hardly vary in the axial direction, it is the change in the crackfront shape that has caused the reduction in K _I values, leading to arrest.

Fig.9. Comparison of static elastic stress intensity factors obtained under constant load for the initial and arrested crack

Elastic stress intensity factors under constant displacement

The constant displacement analyses described next were intended to check the significance of dynamic effects on crack driving forces.

Figure 10 includes both results of applied K _I values obtained under constant load and constant displacement boundary conditions for the arrested crack. For the sake of clarity, the curves in Fig.10 have been drawn through K _I values obtained from the mid-nodes of the crack front elements, where the crack front curvatures are continuous locally. It can be seen from Fig.10 that the two sets of results are almost identical. Figure 10 implies that dynamic effects on K _I values of the run-and-arrest event of flaw R are negligible in the NESC-1 test. This is because the cylinder is stiff and its stiffness is hardly changed by the small amounts of crack extension. The newlycreated crack surface area is, in fact, merely 0.2 to 0.3 % of the un-cracked area.

Fig.10. Comparison of static elastic stress intensity factors obtained under constant load or constant displacement boundary conditions for the arrested crack

If crack extension is large, dynamic effects on K _I values are more important. This is illustrated by carrying out a constant displacement analysis on a crack of the same size as the initial flaw R which was assumed to have developed from an un-cracked cylinderof exact dimensions as the NESC-1 spinning cylinder. Applied loads were the same as those in the NESC-1 test and appropriate displacement boundary conditions were imposed on cylinder outer surface in the constant displacementanalysis.

Figure 11 shows K _I results under constant load and constant displacement for this hypothetical crack. As pointed out before, for the sake of clarity, the curves in Fig.11 have been drawn through K _I values obtained from the mid-nodes of the crack front elements. KI values under constant displacement are 10% lower than K _I values under constant load at 20mm from inner surface and 20% lower at 76.5mm (the deepest point). The cracked area in this hypothetical case is about 6% of the un-cracked area, which seems to be big enough tocause dynamic effects.

Fig.11. Comparison of static elastic stress intensity factors obtained under constant load or constant displacement boundary conditions for a hypothetical large crack

3. Comparison of stress intensity factors with crack arrest toughness

Previous review work ^[3,15] has led to the conclusion that in terms of fracture mechanics, sustained crack arrest will take place if the applied crack driving force falls below the crack arrest toughness and if the dynamic crack driving force peak shortly after arrest does not exceed the dynamic initiation toughness. It was also concluded that standardised Compact Crack Arrest (CCA) tests give conservative estimatesfor both crack arrest and dynamic initiation toughness. These principles of crack arrest assessment are now applied to flaw R. As dynamic effects have been shown to be negligible in this case, the crack driving force shortly afterarrest is not considered further.

Figure 12 shows a comparison of the computed elastic stress intensity factors K _I and the measured crack arrest fracture toughness (K _Ia ) of the base material. Clearly, the relevant K _I values fall inside the range of measured crack arrest toughness. Fig.12 therefore explains crack arrest, as observed experimentally. It can be speculated with some confidence that if further crack driving force calculations were carried out modelling larger (along the axial crackpropagation direction) arrested crack dimensions, even lower elastic K _I value would be obtained. If a series of such calculations were carried out, the crack dimensions where the measured arrest toughness first exceeds the applied K _I value would then predict the arrested crack shape and size. Given the current coincidence of elastic crack driving force and arrest toughness, the predicted arrested crack shape thus obtained would be verysimilar to the actual arrested crack shape.

In the present study, evaluation of the experimentally observed crack arrest behaviour of the large NESC-1 spinning cylinder (1296mm length x 1045mm inner diameter x 175mm thickness) uses crack arrest toughness data obtained fromsmall scale CCA specimens of 152x150x25mm. The current analysis of the NESC-1 test results shows that the small-scale CCA crack arrest tests are able to explain the crack arrest behaviour of the large cylinder. Good correlation ofcrack arrest between small-scale CCA specimens and large-scale structural components has also been demonstrated in the past (a review of recent work is given in Ref. [16]

).

Whereas the stress intensity factor for the arrested crack shape reduces from that of the initial defect between 10mm and 30mm from the inner surface, Fig.9 shows that below 10mm the SIF for the arrested crack exceeds that for the initial defect and rises towards the surface, before it finally reduces. With an apparently rising stress intensity factor, it may be asked whythe arrested crack did not re-initiate and propagate in this region.

Firstly, it must be pointed out that the total stress consists of a relative low primary stress ( <50% of yield strength) due to spinning and a high secondary self-balancing thermal stress. The thermal stress will be relaxed tosome extent in elastic-plastic materials due to the presence of the crack and plastic yielding. The stress intensity factors for both initial and arrested defects were derived from elastic finite element stress analyses. Figs.5 and 6 show the elastic stresses and the effect on the stress distribution of plasticity. In Fig.6, the stainless steel cladding has yielded and the stresses in the ferritic cylinder are reduced, although still shown in excess of uni-axial yield due to hydrostatic constraint. Tunnelling of the arrested crack under thesurface produces very high elastic stresses in the ligament of material between the crack and the surface that would have yielded and redistributed. Between 0 and 10mm the elastic stress intensity factor for the arrested crack shown inFig.8 is therefore considered to be an over-estimate of the SIF in the true elastic plastic stress field.

There are other reasons apart from a possible over-estimation of the stress why the crack did not propagate in the 10mm near surface region. This region consists of approximately 4mm of stainless steel cladding and 6.5mm of heataffected zone ferritic material from the deposition of the cladding. The toughness of these materials are both higher than that of the parent ferritic. In addition, tests on deeply and shallow cracked specimens showed a significantincrease in toughness for shallow cracks with less constraint. Thus, propagation would not be expected in the cladding or HAZ until high values of stress intensity factor were reached.

If one looks at Fig.1, a small cleavage facet in the HAZ is evident. This detail was too small to be modelled in the finite element analysis but would not be expected to influence the stress and stress intensity factor around the main part ofthe arrested crack. The small facet may, however, be a result of re-initiation within the HAZ after arrest. As it has not propagated significantly, it may be concluded that the observation is consistent with it being an effectcontrolled by variations in the local microstructure.

4. Conclusions

Finite element analyses have been carried out to obtain static, elastic stress intensity factors for the initial and arrested crack in the large NESC-1 cylinder specimen under constant load and constant displacement boundaryconditions. The computed static, elastic stress intensity factors have been compared with the plane strain crack arrest toughness measured using small-scale Compact Crack Arrest (CCA) specimens. The present work supports the followingconclusions:

(1) Applied static elastic stress intensity factors are reduced significantly for the lobe-shaped arrested crack which developed from the initial semi-elliptical surface crack as a result of the localisedcleavage crack propagation. This reduction in crack driving force is likely to be the main reason for crack arrest.

(2) The analysis carried out and the comparison with the full-scale experiment confirm the prevailing approach to the assessment of crack arrest that brittle propagation will stop if the applied crackdriving force falls below the crack arrest toughness.

(3) The results justify the use of the static elastic stress intensity factor as the crack propagation driving force parameter and the static plane strain crack arrest toughness as the resistance parameterfor crack arrest evaluation for small relative crack jump dimensions.

(4) The small-scale Compact Crack Arrest (CCA) crack arrest tests can be employed to evaluate crack arrest in a large cylinder of the same material.

5. Acknowledgement

Financial support from HM the Nuclear Installations Inspectorate of the UK Health & Safety Executive (Mr F M D Boydon) is gratefully acknowledged.

Table 1: Material properties used in thermal analyses (from Ref. ^[7] )

Table 2: Material properties used in stress analyses (from Ref. [7]

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