Crack Arrest Event in NESC-1 Spinning Cylinder Experiment

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 arrested after 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 and constant 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 Arrest specimens. 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 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 parameter for 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.

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 the cylinder 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-shaped cleavage region was contained within 30mm of the inside surface (see Fig.1).

The arrest of a significant pre-existing flaw after a relatively small amount of ductile tearing and cleavage crack extension in a large-scale component test has potentially beneficial implications for safety cases of nuclear reactor plant under comparable conditions. It is important, therefore, that the reasons for crack arrest in this case are fully understood, so that the general theory can be applied with more confidence elsewhere.

The currently accepted theory of crack arrest has been summarised by Gillot and Wiesner ^[2] for the NESC-1 project. In essence, a cleaving crack will arrest when the crack driving force of the growing crack front falls below the crack arrest toughness of the material. Strictly speaking, a dynamic analysis is required, but for small relative dimensions, static computations of crack driving force have been shown to be appropriate. ^[3] Furthermore, whilst elastic-plastic analyses may appear appropriate for the analysis of the severe loading conditions experienced by the NESC-1 cylinder, viscoplastic constitutive equation would have to be used [e.g. ^[4,5] ]. The effort of such analyses was not considered appropriate for the present paper which aimed at checking whether the currently accepted crack arrest analysis method, which is based on elastic calculations, is applicable to the NESC experiment. The results from the spinning cylinder test have thus been used to verify this static, elastic crack arrest concept.

The approach is to compare the applied elastic stress intensity factor along the front of both the initial and the extended (arrested) flaw with the measured crack arrest toughness at the appropriate temperature. The crack arrest toughness of the NESC cylinder base material at different temperatures was measured within the NESC project by MPA Stuttgart, Germany, using compact crack arrest test specimens according to ASTM E1221 procedure. Finite element computations of stress intensity factors for the initial and arrested crack and subsequent analyses of the crack arrest event are the subject of this paper.

It is not the intention of the paper to give an accurate prediction of the initiation event nor to model, other than qualitatively, the shape of the arrested crack. Rather, a contribution is made to the validation of the currently accepted crack arrest analysis approach, which has also been included in the R6 procedure; ^[6] and also to add to the understanding of a particular feature of the behaviour of the NESC-1 spinning cylinder test, namely the fact that a brittle crack, which initiated under severe loading conditions, arrested after only a very limited amount of cleavage crack propagation.

2. Finite element analyses

Analysis procedures

Finite element analysis procedures were chosen on the basis of the following considerations. Although the rotational speed was increasing at the time of cleavage initiation, the averaged angular acceleration ^[7] was only 0.6 rpm/s. Inertial forces due to this low acceleration were considered negligible. Quasi-static constant load analysis was therefore considered appropriate for analysing flaw R in its initial state before the cleavage crack extension.

The cleavage run-and-arrest of flaw R in the cylinder is a dynamic phenomenon. Ideally, a full dynamic analysis should be carried out. However, it has been demonstrated in previous work [e.g. ^[8] ] that an analysis where the static boundary displacements prior to crack growth are imposed on the geometry containing the arrested crack dimensions can produce K _I results similar to those obtained from a full dynamic analysis. The argument for this constant displacement approach is that the crack propagation happens so quickly that the remote boundaries of the component remain the same during the short period of time between initiation and arrest. In order to find out if dynamic effects were significant in the NESC-1 Spinning cylinder test, finite element analyses of the arrested flaw R were carried out under both constant load and constant displacement conditions, respectively. The centrifugal forces and thermal strains for the constant load analysis are defined later. These loads were applied to the models of flaw R in its initial and arrested condition. For the constant displacement analysis, these loads were applied to the cylinder along with imposed displacements on the cylinder outer surface so that the outer surface remained at the exact positions as before the cleavage crack extension. These displacements were taken from the analysis of flaw R in its initial conditions.

Finite element mesh and crack geometry

A finite element (FE) model of the NESC-1 cylinder was developed with an inner diameter of 1045mm and a total wall thickness of 175mm. The thickness dimension includes the 4mm thick layer of stainless steel cladding on the inner surface and the 10mm layer of heat affected zone (HAZ) in the base material resulting from the deposition of the cladding. The assumption of the HAZ thickness in the present paper was made according to Ref. ^[7] so that the present analyses could be checked against Ref. ^[7] on the basis of identical geometry dimensions. It is recognised that the HAZ assumed here is somewhat thicker than the best estimate thickness 6.5mm from post-test metallography, but this difference will have no effects on elastic calculations in the present work.

The finite element model of the cylinder was generated in three dimensions using a commercial mesh generation package. Symmetry boundary conditions were taken into account so that it was only necessary to model one quarter of the cylinder. Two separate models were generated to include flaw R in its initial and arrested shape. The initial model was used to benchmark the results with previous analyses and obtain the boundary displacements for the constant displacement analysis of the arrested crack.

Flaw R was estimated to have a depth of 76.5mm and a length of 205mm at the start of the test after manufacture and pre-fatiguing on the basis of Ref. ^[9] , before the officially quoted dimensions 74x208mm ^[1] were available to the authors. They are broadly in agreement with those used by other parties involved in the NESC-1 project. For example, a depth of 74mm and a length of 200mm were used in Ref. ^[7] . Since the assumed crack was only 3.4% deeper and 1.4% longer than the officially quoted dimensions, this will not have a significant impact on the implications of the analysis.

A close approximation of the crack front geometry was obtained by using a semi-circle with a radius of 106.9mm with an offset centre 30.4mm from the cylinder inner surface. Fig.2 shows the finite element mesh for the cylinder with the initial crack.

The second model included flaw R after growth by ductile tearing and extension by cleavage crack propagation. This lobe-shape could not be easily represented by an analytic function, and therefore piece-wise linear interpolation of measured positions around the defect was used to model the crack front. Fig.3 shows the finite element mesh. It can be seen from Fig.3 that the crack front in the FE model, which is represented by a series of segments of straight lines for the reasons mentioned, is not smooth at positions of the arrested crack. Corners, where curvatures change discontinuously, exist at the joining points between two adjacent segments of straight lines. The effects of this non-smoothness on the K values are discussed later in the paper.

Material properties

Material properties were required for three aspects of the analysis:

1. FE thermal analysis: thermal conductivity, specific heat, density, heat transfer coefficient.
2. FE stress/fracture analysis: thermal expansion coefficient, Young's modulus, Poisson's ratio and stress strain curve.
3. Evaluation of crack arrest: crack arrest toughness.

The thermal and mechanical properties at discrete temperatures or as a continuous function of temperature were as those used by ORNL. ^[7,10] They are reproduced in this paper for completeness in Tables 1 and 2. The thermal coefficients used in the present calculations are mean data. The crack arrest fracture toughness properties were obtained from the final report of Materials Task Group (TG2) ^[11] of the NESC-1 Spinning Cylinder test project.

Loading conditions

The NESC-1 cylinder was subject to centrifugal forces and transient temperature distributions during the 12 minute period of the test when the cylinder was quenched. In the present finite element work the loading and temperature conditions 217s after the water quench had started were applied in a single computational step. It was at that moment that the NESC-1 cylinder is believed to have experienced cleavage crack propagation (a step change in strain was recorded by the three gauges beyond the end of flaw R).

This simplified approach did not therefore follow the entire transient loading history from the start of the test. If the materials were assumed to behave elastically, this would not affect the stress, strain or fracture parameters. Load path dependence would affect the plastic deformation of the materials, but its significance could be judged by comparison with analyses where the entire loading history had been modelled.

The angular speed at 217s was taken as 2247rpm, using the information presented in Ref. ^[7] (see figure 2 of Ref. ^[7] ). The corresponding centrifugal forces and stresses were determined by finite element analysis. As expected, there was good agreement with the results of other analyses.

The transient temperature distribution through the cylinder wall was determined from a simple 2D finite element model. The cylinder internal heat transfer was modelled by conduction. The heat flow from the inner surface of the cylinder to the quench water was quantified by the following equation:

q = HA(T - T ₀ )

where A is the area (m ² ), T is the temperature of the cylinder inner surface, T ₀ is the water temperature = 5°C, and H is the heat transfer coefficient [10,000W/(°C-m ² )].

The predicted temperature distribution through the cylinder wall at the assumed time of crack initiation is shown in Fig.4. Measurements during the test showed that temperature also varied slightly along the cylinder length and the circumference, but these variations were not considered significant to influence the thermal stress or crack front temperatures. This through-wall temperature distribution was therefore applied throughout the 3D finite element model.

In the finite element calculations, an initial temperature of 290°C was assumed. As a result, ABAQUS assumes that the finite element model is stress free at 290°C. In reality, there will be stresses in the cylinder at any uniform temperature because of the difference in thermal expansion coefficients between the stainless steel and the ferritic steel. However, because the cladding is only 4mm in a thick section of 175mm, neglecting those stresses is considered acceptable.

Stress results

Figure 5 shows the various hoop stress components through the cylinder wall in a part remote from the defect (479mm from crack position), 217s after the water quench, as computed from an elastic analysis. The hoop stress due to centrifugal forces at the angular speed of 2247rpm is about 200MPa in the base material. The thermal stress is in self-equilibrium and varies from just over 800MPa at the inner surface to just under -200MPa at 90mm from inner surface, and then increases slightly towards the outer surface.

Figure 6 shows the results from an elastic-plastic analysis mainly for the purpose of comparisons with the elastic results and the results in Ref. ^[7] . Compared with the elastic analysis results, plastic yielding reduces the magnitudes of hoop stresses in the cladding, HAZ and near-surface base material. The effect of the different yield and work hardening properties of the three materials can be clearly seen in the near surface regions, but throughout the remaining part of the cylinder, the hoop stresses are similar to those from the elastic analyses. The hoop stress results obtained by ORNL in Ref. ^[7] are also included in Fig.6 for comparison. Both the TWI and ORNL results follow the same trends, especially at the inner surface. ORNL predicted stresses higher than those of the present work at distances greater than about 15mm from inner surface, and this is likely to be due to differences in finite element mesh refinement.

Elastic stress intensity factors under constant load

Elastic fracture mechanics analyses were carried out to obtain J-integral values at discrete points along the crack front using the contour integral calculation scheme in ABAQUS. ^[12] Stress intensity factors, K, were calculated from J using the following equation (assuming plane strain conditions):

Where E is 206GPa and ν is 0.28.

Initial flaw

Figure 7 shows elastic stress intensity factors along the front of flaw R as a function of the distance normal to the inner surface of the cylinder. The stress intensity factors (K _I) obtained from the finite element analyses are shown as discrete points (open symbols). Each point in the figure represents a point along the crack front and its associated K _I value. The point right on the inner surface has not been included because of numerical instability. At the deepest point of the defect, 76.5mm from the surface, the value of K _I is 140MPa √m. The K _I value at 10mm from inner surface is about 300MPa √m, more than twice that at the deepest point, because the water quench generates very high thermal stresses near the inner surface (as shown in Fig.5 and Fig.6). Between these two positions, K _I decreases almost linearly from 300 to 140MPa √m.

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 intensity factor 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 elastic crack 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 front consisting 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 the corners 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 be confused. 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.

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 crack front shape that has caused the reduction in K _I values, leading to arrest.

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 newly created crack surface area is, in fact, merely 0.2 to 0.3 % of the un-cracked area.

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 cylinder of 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 displacement analysis.

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 to cause dynamic effects.

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 estimates for 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 after arrest 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 crack propagation 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 very similar 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 from small 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 of crack 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 why the 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 to some 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 the surface 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 in Fig.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 heat affected 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 significant increase 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 of the 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 effect controlled 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 boundary conditions. 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 following conclusions:

(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 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 parameter for 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] )

6. References

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