Performance of low-upper-shelf material under pressurized-thermal-shock loading

The second pressurized-thermal-shock experiment (PTSE-2) of the Heavy-Section Steel Technology Program was conceived to investigate fracture behavior of steel with low ductile-tearing resistance. The experiment was performed in the pressurized-thermal-shock test facility at the Oak Ridge National Laboratory. PTSE-2 was designed primarily to reveal the interaction of ductile and brittle modes of fracture and secondarily to investigates the effects of warm prestressing, A test vessel was prepared by inserting a cracklike flaw of well-defined geometry on the outside surface of the vessel. The flaw was 1 m long by ≈ 15 mm deep. The instrumented vessel was placed in the test facility in which it was initially heated to a uniform temperature and was then concurrently cooled on the outside and pressurized on the inside. These actions produced an evolution of temperature, toughness, and stress gradients relative to the prepared flaw that was appropriate to the planned objectives. The experiment was conducted in twoseparate transients, each one starting with the vessel nearly isothermal. The first transient induced a warm-prestressed state, during which K_I, first exceeded K_Ic. This was followed by repressurization until a cleavage fracture propagated and arrested. The final transient was designed to produce and investigate a cleavage crack propagation followed by unstable tearing. During this transient, the fracture events occurred as had been planned.     

Some advances in fracture studies under the heavy-section steel technology program

Recent results are summarized from HSST studies in three major areas that relate to assessing nuclear reactor pressure vessel integrity under pressurized-thermal-shock (PTS) conditions. These areas are irradiation effects on the fracture properties of stainless steel cladding, crack run-arrest behavior under non-isothermal conditions, and fracture behavior of a thick-wall vessel under combined thermal and pressure loadings.Since a layer of tough stainless steel weld overlay cladding on the interior of a pressure vessel could assist in limiting surface crack extension under PTS conditions, its resistance to radiation embrittlement was examined. A stainless steel overlay cladding, applied by a submerged arc, single-wire, oscillating-electrode method, was irradiated to 2 × 10²³ neutrons/m² (> 1 MeV) at 288°C. Yield strength increases up to 27% and a slight increase in ductility were observed. Charpy V-Notch data showed a ductile-to-brittle transition behavior caused by temperature-dependent failure of the 8-ferrite phase. The type 308 cladding, microstructurally typical of that in reactor pressure vessels, showed very little degradation in either upper-shelf energy or transition temperature due to irradiation.Crack-arrest behavior of A533 grade B class 1 steel was examined for temperatures extending above the onset of Charpy upper-shelf. Crack-arrest experiments that use wide-plate specimens have shown crack arrest occurring prior to transition to tearing or tensile instability. High values of crack-arrest toughness have been recorded (static values above 400 MPa that are well above the maximum value that safety assessment criteria assume such materials can exhibit.A validation experiment was performed by exposing an intentionally flawed HSST intermediate test vessel to combined pressure and thermal transients. The experiment addressed warm-prestressing phenomena, crack propagation from brittle to ductile regions, and crack stabilization in ductile regions. Test and analysis results are summarized.     

European experiences of the proposed ASTM test method for crack arrest toughness of ferritic materials

The proposed ASTM test method for measuring the crack arrest toughness of ferritic materials using wedge-loaded, side-grooved, compact specimens was applied to three steels: A514 bridge steel tested at −30°C (CV30–50°C), A588 bridge steel tested at −30°C (CV30–65°C), and A533B pressure vessel steel tested at +10°C (CV30-12°C) and +24°C (CV30+2°C). Five sets of results from different laboratories are discussed here; in four cases FOX DUR 500 electrodes were used for notch preparation, in the remaining case HARDEX-N electrodes were used. In all cases, notches were prepared by spark erosion, although root radii varied from 0.1–1.5 mm. Although fast fractures were successfully initiated, arrest did not occur in a significant number of cases.The results showed no obvious dependence of crack arrest toughness, K_a, (determined by a static analysis) on crack initiation toughness, K₀. It was found that K_a decreases markedly with increasing crack jump distance, Δα/W. A limited amount of further work on smaller specimens of the A533B steel showed that lower K_a values tended to be recorded.It is concluded that a number of points relating to the proposed test method and notch preparation are worthy of further consideration. It is pointed out that the proposed validity criteria may screen out lower bound data. Nevertheless, for present practical purposes, K_a values may be regarded as useful in providing an estimate of arrest toughness — although not necessarily a conservative estimate.     

Conservatism of ASME KIR-reference curve with respect to crack arrest

The conservatism of the RT_NDT temperature indexing parameter and the ASME K_IR-reference curve with respect to crack arrest toughness, has been evaluated. Based on an analysis of the original ASME K_Ia data, it was established that inherently, the ASME K_IR-reference curve corresponds to an overall 5% lower bound curve with respect to crack arrest. It was shown that the scatter of crack arrest toughness is essentially material independent and has a standard deviation (S.D.) of 18% and the temperature dependence of K_Ia has the same form as predicted by the master curve for crack initiation toughness. The ‘built in’ offset between the mean 100 MPa√m crack arrest temperature, TK_Ia, and RT_NDT is 38°C (TK_Ia=RT_NDT+38°C) and the experimental relation between TK_Ia and NDT is, TK_Ia=NDT+28°C. The K_IR-reference curve using NDT as reference temperature will be conservative with respect to the general 5% lower bound K_Ia(5%)-curve, with a 75% confidence. The use of RT_NDT, instead of NDT, will generally increase the degree of conservatism, both for non-irradiated as well as irradiated materials, close to a 95% confidence level. This trend is pronounced for materials with Charpy-V upper shelf energies below 100 J. It is shown that the K_IR-curve effectively constitutes a deterministic lower bound curve for crack arrest The findings are valid both for nuclear pressure vessel plates, forgings and welds.     

Energy transformation during dynamic crack initiation and arrest

This contribution deals with the experimental determination of fracture mechanics parameters concerning dynamic crack initiation, crack propagation and crack arrest demonstrated on reactor pressure vessel steels 20 MnMoNi 5 5 and 22 NiMoCr 3 7. Appropriate measuring methods are available to determine the impact fracture toughness K_Id for CT specimens and CCP specimens. However, for small scale specimens there are still experimental and theoretical problems to be met with when determining the fracture heat of a propagating crack and ascertaining the parameters of arrest.     

The effect of ligaments on the reinitiation of fracture at the tip of a crack arrested during a hypothetical thermal shock event in a water-cooled reactor pressure vessel

During a hypothetical thermal shock event involving a water-cooled nuclear reactor pressure vessel, a crack can propagate deep into the reactor vessel thickness by a series of run-arrest-reinitiation events. Within the transition temperature regime, crack propagation and arrest in pressure vessel steels is associated with a combination of cleavage and dimpled rupture processes, the dimpled rupture regions being contained within ligaments that are normal to the crack plane and parallel to the direction of crack propagation. The present paper models the effect of ligaments on the reinitiation of fracture at the tip of an arrested crack, and the results of a theoretical analysis define the conditions under which ligaments might increase the reinitiation value above $\text{k}{}_{\mathrm{IC}}$, assuming that they fracture by a ductile rupture process. By comparing the predictions with experimental results for model vessels subject to thermal shock, it is shown that the ligaments, which are present at arrest, are unlikely to fail entirely by ductile rupture prior to the reinitiation of fracture at an arrested crack tip. Instead it is suggested that the ligaments fail by cleavage, whereupon they do not markedly affect the reinitiation $\text{K}$ value, which thus correlates with $\text{K}{}_{\mathrm{IC}}$.     

Micromechanisms and toughness for cleavage fracture of steel

A complete understanding of the fracture mechanisms of steel in the ductile/brittle transition region requires analysis not only of crack initiation, but also of crack propagation. This paper reviews micrographic and fractographic experiments that give insight into both phenomena, and suggests a frame-work through which both may be related.Unstable cleavage crack initiation can occur after some blunting of the original fatigue precrack or after some stable crack growth. In either event, instability appears to be triggered by the fracture of a brittle micro-constituent ahead of the precrack. The large scatter in reported K_Ic values within the transition region reflects the size distribution and relative scarcity of these “trigger” particles.While a large number of models have attempted to correlate toughness in the ductile/brittle transition regime to events occurring ahead of the crack tip, surprisingly little attention has been paid to events occurring behind the crack front. Fractographic evidence as well as metallographic sectioning of arrested cracks show that the mechanism of rapid crack propagation by cleavage is affected strongly by partial crack-plane deflection which leaves unbroken ligaments in its wake. The tearing of these ligaments by dimple-rupture is the dominant energy-absorbing mechanism. Etch-pit experiments using an Fe-Si alloy show that the crack-tip stress intensity based on plastic zone size is extremely low. It is suggested that the mechanism of crack arrest should be modeled using a sharp crack which is restrained by a distribution of discrete pinching forces along its faces. The same model is applied to crack initiation.     

Experimental and numerical investigations of the warm-prestressing (WPS) effect considering different load paths

The effect of warm prestressing has been investigated representative for the core weld metal of the RPV Stade. Model experiments on CT specimens show a significant rise of effective fracture toughness K_eff after warm prestressing and the conservative WPS hypothesis, ‘no failure, if ∂K_I/∂t≤0’, is verified. Partial unloading and reheating show no influence on the effective fracture toughness K_eff. The magnitude of the WPS effect as a function of warm prestress level and temperature, path of unloading and cooling can be predicted using a modified Beremin model with temperature dependent parameters. It is shown that the Weibull stress is an appropriate crack tip loading parameter for decreasing load paths.     

Application of statistical linear elastic fracture mechanics to pressure vessel reliability analysis

An evaluation of the failure probability for a pressure vessel is made on the basis of linear elastic fracture mechanics (LEFM). Failure is identified by actual crack length equal to critical crack length. The probability of failure is the joint probability that there exists a crack (i.e. K_I) greater than a given crack (i.e. K) and that the critical crack (i.e. K_IC) is smaller than that same crack, where K_I and K_IC are considered for same time and location. K_IC as well as K_I are treated as statistical variables with probability density functions (p.d.f.), which are functions of material, location and time. The variability of K_IC (that is the p.d.f. of K_IC) is a result primarily of the statistical nature of the material properties and to a lesser degree of the increasing neutron-done experienced by certain parts of the pressure vessel. The variability of K_I (that is the p.d.f. of K_I) is a result of the following parameters:

1. (1) initial distribution of cracks (that is the crack distribution at the start-up of the reactor) regarded as a statistical variable, because of the uncertainty in the non-destructive testing of the pressure vessel prior to start-up.

2. (2) stresses, regarded as a statistical variable because of the uncertainty in the stress analysis and the geometry of the vessel.

3. (3) crack growth by fatigue, which is a result of the normal (with probability equal to 1.0) and abnormal (with a p.d.f.) operational transients. The statistical nature of the crack growth is due to the statistical variation of the abnormal operational transients.

4. (4) material properties (that is K_IC, yield strength and the factors governing the fatigue crack growth) regarded as statistical variables.

The p.d.f.s of the abovementioned parameters are evaluated on the basis of the available literature. The integrated calculations of failure probability are performed by a computer program utilizing the Monte Carlo technique with importance sampling, which gives a greater freedom in selection of p.d.f.s. Calculations of failure probability for existing reactors are presented.     

Fracture initiation and propagation in a cylindrical shell containing an initial surface flaw

The paper deals with the problem of fracture initiation, propagation, and arrest in a pressurized cylindrical vessel which contains an initial surface flaw. It is assumed that the flaw has the most unfavorable geometry and orientation, namely, it is a relatively long part-through axial crack.First we consider the problem of a crack which is sufficiently ‘shallow’ so that the plastic deformations are confined to the neighborhood of the crack border and part of the net section near the inner wall is still elastic. The plasticity-corrected stress intensity factor obtained from this analysis is the controlling load factor in failure considerations related to fatigue crack propagation, stress corrosion cracking, and static fracture (with the use of fracture toughness, COD, or a K_R curvetype failure criterion).The problem of relatively deep crack with fully-yielded net ligament is then considered. Plastic deformations are also assumed to spread around the crack ends through the entire wall thickness. A perfectly plastic strip model (with an eight order shell theory) is used to calculate the plastic zone size and the crack opening displacement along the crack border. Previous studies indicate that for the analysis of the type of stable and subsequent unstable crack propagation problems under consideration, the crack opening displacement δ is a more suitable load factor than the stress intensity factor K, or the crack extension force G. Thus, in this paper a ‘crack opening stretch’ type material characterization will be used.After the rupture of the net ligament under the crack, the axial crack propagation is accompanied by the depressurization of the vessel caused by leakage. From this point on the fracture problem is coupled with the related fluid mechanics or gas dynamics problem where the primary unknowns are the pressure and the crack length as functions of time. In the present study it is assumed that the volume of the vessel is finite and the crack propagation is quasi-static (this assumption, which is necessary to keep the problem within manageable proportions, is justified by the relatively low crack velocities, i.e. v_c < 0.25 c₂, c₂ being the shear wave velocity).     

2D crack growth simulation with an energetic approach

It is well known that the tearing resistance curve J–Δa is not a material property. A recent approach, based on an energetic critical parameter to model ductile tearing propagation, is used to model 3D effects. The approach considered in this work aims to estimate the dissipated energy in the fracture process during ductile tearing represented by an intrinsic parameter G_fr. A fracture criterion, which accounts for the crack extension length, is defined and lies on a critical energy release rate, noted G_c, which is compared to G_fr. Previously, this parameter was obtained from a numerical local energy release rate, which handicaps the application field of the approach: a fine mesh for the whole propagation area was needed and the criterion allowed only to model 1D propagation. A new manner to estimate G_c is then proposed in this article, based on the J plastic part variation, which allows to model 2D propagation by defining a local criterion. This new calculation method is validated on a CT specimen made in Tu52b ferritic steel, by comparing the results obtained from the two methods of G_c calculation. Then, the 2D crack growth case is studied, by modelling the propagation in a ring, loaded in compression. It is shown that a 3D effect, such as tunnel effect, could be successfully represented with this approach.     

A combined ligament rupture-cleavage model for crack arrest in thick-section steel plate

In the transition regime, plane strain crack propagation in ferritic steels proceeds by a combination of cleavage and ductile rupture processes, the latter being confined to ligaments that are parallel to the direction of macroscopic crack propagation. The paper models crack propagation, and particularly the limiting case of crack arrest, when fracture proceeds via these two modes. An important theoretical result is that, because of the unfractured ligaments which remain behind the crack tip, the plastic zone size is much smaller than when it is predicted for the operative $\text{K}$ values and assuming that there are no ligaments. Linear elastic fracture mechanics procedures may therefore be used to describe the arrest phenomenon at $\text{K}$ values that exceed the normally accepted limits for their validity. The theoretical results are also used to speculate upon the effect of neutron irradiation on the arrest toughness.     

A practical method for computation of ductile crack growth by means of finite elements and parametric 3D-modelling

The present paper originates from a contribution to the safety assessment of a reactor pressure vessel (RPV). Investigations evaluating the safety against brittle fracture (exclosure of crack initiation and arrest assessments) are completed by calculations concerning ductile crack extension. Crack geometries including the expected crack extension are generated parametrically by a computer code and are used for further calculations with finite element programs. J-integrals of ductile growing cracks located between two comparative contours are determined by interpolation. The comparative contours are loaded by instationary temperature and pressure fields and are evaluated in advance. Taking the stability condition into consideration, the ductile crack extension is determined by pursuing the equilibrium between loading and crack resistance. The automatic modelling and a mathematical program processing the finite element results evaluate the crack growth of the finite element results very effectively.     

Application of the J-integral concept to thermal shock loadings

In the frame of our analytical work the applicability of ductile fracture mechanical J-integral concept on mechanical and thermal shock loaded structures with flaws is investigated. By that the behaviour of possible flaws in components of power plants during accidents can be described (e.g. reactor pressure vessel and piping during emergency cooling).The analyses presented in this paper have been performed with a version of the finite element code ADINA [1] extended by fracture mechanical options. The postanalyses of the first series of pressurized thermal shock experiments (PTSE-1A, B, C) performed at ORNL show stress intensity factors (K_I) calculated from J-integrals which are about 10% lower than values of OCA programs [2] based on the linear elastic K-concept usually used for brittle materials. The discrepancy may be referred to different treatment of the influence of plasticity. The results assessed in the frame of the cleavage fracture concept coincide well with the measured times respectively crack tip temperatures at crack initiation and arrest.In the first thermal shock experiment (NKS-1) performed at the MPA-Stuttgart a circumferentially deep cracked test cylinder with overall upper shelf material conditions has been investigated. The postcalculations based on the J-integral with J_R-controlled crack growth show good coincidence between analytical determined and measured structure and fracture mechanical quantities but they are accompanied with numerical problems due to unloading and large plasticity effects.     

Interpreting the high KIa values obtained in thermal shock tests

A theoretical analysis shows that, as regards the two crack arrest events in the Oak Ridge pressurised thermal shock event PTSE I, the measured arrest K values should not be significantly larger than the arrest K_Ia value expected for a deep crack, and could indeed be smaller than K_Ia. This is due to the arrest crack depths being small, and becuase ligaments are associated with crack arrest in the transition temperature regime.     

Significance of warm prestress to crack initiation during thermal shock

During a loss of coolant accident (LOCA) followed by operation of the emergency core cooling system, the inside wall of a nuclear pressure vessel is subjected to high thermal stresses that can cause extension of a pre-existing flaw. During this event the crack-tip stress intensity factor, K_I, may achieve its maximum value early in the transient, but the critical level for crack initiation, K_Ic, may not be reached until minutes later at which time the loading has decreased from its peak. It is shown that this phenomenon, termed warm prestress (WPS), can preclude crack extension when K_I equals or exceeds K_Ic.NRL has conducted an experimental study, employing three-point bend specimens, to investigate the potential for elevation in K_Ic by WPS, and to translate the significance of this behavior into structural terms in the sense of minimizing crack extension in a nuclear vessel during a LOCA. From the experiments it is concluded that the mechanisms associated with WPS act to elevate the K_Ic of the material at the crack tip and that this fact can greatly minimize crack extension that would have been predicted theoretically without consideration of WPS. The experiments demonstrated that failure never occurs during the unloading portion of the simulated LOCA path. This finding is of major significance to the integrity of a vessel. For example, with relatively deep cracks there is a combination of conditions wherein initiation ordinarily would be predicted as K_Ic is reached along a decreasing K_I path. For this set of conditions the present research studies have shown that the WPS phenomenon will preclude all such crack initiation.In terms of margin of safety against fracture it is shown that the elevation in K_Ic caused by WPS is not uniform but depends upon the WPS level, the degree of unloading, and the increment between the temperature of WPS and the failure temperature. For LOCA conditions, however, it is concluded that WPS can result in an effective elevation in K_Ic up to the WPS level assuming, of course, that metallurgically the material is capable of exhibiting this level of toughness.In terms of structural significance it is clear that WPS by itself cannot prevent the initiation of shallow cracks. Specifically, for a reference calculational vessel under the worst combination of conditions including a long, axial flaw and severe radiation embrittlement it is shown that a shallow crack can extend to a relative depth of 0.34 of the wall thickness; further crack extension is prevented by WPS. However, cracks having initial depths greater than 0.2 of the wall are prevented, by WPS, from extending any amount. Finally, it was observed that an elastic analysis of crack extension during a LOCA has predicted nearly complete penetration of the wall without consideration of WPS. Factoring WPS into the same analysis results in predicted crack extension of greatly reduced proportions such that complete penetration of the wall does not occur. Thus, WPS may form a key element upon which to base the assurance of vessel integrity during a LOCA.     

The effect of irradiation on the toughness of pressurized water reactor vessel steels under different service conditions

The different toughness tests performed on two pressure vessel steels with very different upper shelves served to make a number of observations concerning the shifts in the transition temperature due to the effect of irradiation, as well as changes in toughness with temperature in the ductile region.With respect to shifts in the transition temperature, the following was observed: the shift obtained with precracked charpy test specimens was narrower than with the others; the shift obtained with charpy V impact tests was substantially equal to that obtained with CT test specimens — wider in the case of steel A, but slightly narrower in that of steel H.With respect to toughness values in the ductile region: the toughness values obtained using precracked charpy test specimens are significantly higher than those obtained with CT test specimens for static tests; 25and 12.5 mm thick CT test specimens display comparable variations in J_1C and dJ/da, but with wide scattering; the effect of irradiation, if any, is of the same order of magnitude as the scattering of the results — however, a test temperature effect is observed; the variation in toughness with temperature is determined more easily by considering a J value corresponding to a stable crack propagation of 1 mm, so that ; this variation of J_Δal with temperature is substantially the same for both steels, or about −30% at 70 or 80°C, and −50% at 290°C.     

Crack arrest in pressure vessel steels in a K-gradient and at low KIa levels

A simple theoretical model is used to examine the effect of the gradient of the crack tip stress intensity K on crack arrest in a nuclear reactor pressure vessel which is subject to a hypothetical thermal transient. Attention is focussed on the case where arrest occurs at the lower end of the transition temperature regime, when crack propagation and arrest are not accompanied by the formation of ductile ligaments. The analysis shows that the arrest K values depend on the gradient of K, and this leads to variability in the arrest values. In particular the arrest K value should be lower when the K gradient is positive than when it is negative; this prediction is reconciled with recent experimental results on crack arrest in model vessel tests.     

Stable crack growth of axial flaws in pressure vessels

The ductile crack growth of axial through and part-through cracks in a vessel under internal pressure has been studied experimentally to contribute to the fundamental problem whether or not and under which conditions resistance curves obtained from specimens can be transferred to large scale components. The experiments and numerical analyses are part of a research program on fracture mechanics failure concepts for the safety assessment of nuclear components.Whereas only an averaged crack extension is determined in specimen tests, the local propagation of cracks may be of main importance for surface cracks in vessels and pipes. In the present experiments, the surface cracks revealed the well known canoe shape, i.e. a larger crack extension has occurred in the axial direction than in the wall thickness direction. Two of these tests have been analysed by finite element calculations to obtain the variation of the J-integral along the crack front and the stress and strain state in the vicinity of the crack. The local crack resistance appeared to depend on the local stress state. To Predict ductile crack extension correctly, J_R-curves have to account for the varying triaxiality of the stress state along the crack front.     

Elastodynamic fracture analysis of large crack-arrest experiments

Recent elastodynamic fracture analysis results are summarized from Heavy-Section Steel Technology (HSST) studies in two major areas that related to assessing nuclear reactor pressure vessel integrity under pressurized-thermal-shock (PTS) conditions. These areas are crack run-arrest behavior in wide plates under nonisothermal conditions and fracture behavior of a thick-wall vessel under combined thermal and pressure loadings.The WP-1 series of HSST wide-plate crack-arrest tests are being performed at the National Bureau of Standards (NBS), Gaithersburg, MD, using specimens from HSST Plate 13A of A533 grade B class 1 steel. The six tests in the WP-1 series are aimed at providing crack-arrest data at temperatures up to and above that corresponding to the onset of the Charpy upper-shelf, as well as providing information on dynamic fracture (run and arrest) processes for use in evaluating improved fracture analysis methods. Elastodynamic analyses have been completed for the actual test conditions of the four tests, WP-1.1 through WP-1.4, conducted thus far in the WP-1 series. In this paper, the computed results are compared with data for crackline strain-time response, crack-propagation speed, arrest location and post-arrest tearing. The paper includes a summary of the arrest toughness calculations compiled in the four tests at temperatures that range from transition to upper-shelf values for the wide-plate material.These same elastodynamic fracture analysis techniques have been applied to the analysis of the first pressurized-thermal-shock experiment (PTSE-1) performed at ORNL. The experiment addressed warm-prestressing phenomena, crack propagation from brittle to ductile regions, and crack stabilization in ductile regions. Test and analysis results are summarized in the paper.