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.     

Crack growth pattern and threshold stress intensity factor, KIH, of Zr–2.5Nb alloy with the notch direction

The objective of this study is to obtain a better understanding of the threshold stress intensity factor for an initiation of delayed hydride cracking (DHC) in a Zr–2.5Nb pressure tube. By changing the crack propagation from the longitudinal direction to the circumferential direction, the threshold stress intensity factor, K_IH, and the crack growth pattern were investigated in the Zr–2.5Nb pressure tube with a strong circumferential texture. The threshold stress intensity factor, K_IH, was discussed phenomenologically based on the crack growth pattern and analytically as a function of the tilting angle of hydride habit planes to the cracking plane. A supplementary experiment was conducted to demonstrate a linear decrease of K_IH with an increase in the basal pole component in the cracking plane. Thus, it is concluded that the DHC is controlled by the nucleation and growth of the hydride precipitates on the habit plane.     

Some fractographic aspects of hydrogen-induced delayed cracking in Zr–2.5 wt% Nb alloys

The fractographic features after hydrogen-induced delayed cracking (HIDC) in Zr-2.5 wt% Nb pressure tube material have been studied as a function of stress intensity factor (K), temperature and hydride dispersion. The important observations were of regularly spaced ductile striations parallel to the main crack front, and brittle cleavage markings between the striations. The striations were cusped due to dimple formation, and individual cleavage regions were separated by ductile ridges or shear cliffs. The size and morphology of the cleavage regions was consistent with the size and preferred orientation of hydrides near the crack tip. The inter-striation spacing increased exponentially with temperature, but within the range of study, was essentially independent of K. Neither hydride content nor dispersion had a significant effect on the fracture morphology. The results are consistent with a discontinuous mechanism of crack propagation involving the accumulation of hydride at the crack tip, followed by fracture through this embrittled region and subsequent crack arrest. The observations support recent theoretical models for HIDC which interpret the inter-striation spacing as a critical hydride length for crack advance.     

Comparison of near threshold fatigue crack growth data by Kmax-constant method with the post-construction codes

In this paper we obtain near threshold fatigue crack growth (FCG) data for several carbon steels and type 304 stainless steel by the K_max-constant method. Since the FCG rate obtained by the K_max-constant method is considered to give the upper limit of the FCG data obtained by the stress ratio-constant method, this data was compared with the FCG evaluation diagrams given in the ASME and Japan Society of Mechanical Engineers (JSME) pressure vessel post-construction codes to ensure their validity. Though the FCG rate for carbon steel S55C was somewhat affected by the K_max value, the results show that the obtained near threshold FCG data is close to the upper bound of the JSME code diagram, which is an extrapolation of the ASME FCG diagram to the near threshold region.     

An empirical formula for L line X-ray production cross-section of elements from Ag to U for protons below 3.5 MeV

When computing element concentration from proton induced X-ray emission analysis, an important parameter is the X-ray production cross-section. There have been numerous experimental and theoretical works in this field. Nonetheless, although there is a simple analytical formula to compute K X-ray cross-sections, there is no such ones for the L lines. We present here analytical formulas for the cross-section of the three main X-ray lines L, L_β and L_γ based on experimental data. So far, nearly 3000 values of cross-sections for elements from Ag to U and proton energy ranging from 0.5 to 3.5 MeV have been collected from various references. This experimental data set has been fitted for each X-ray line with an exponential function depending on the proton energy and on the element atomic number. These fitted values have then been compared to the experimental data and with theoretical values obtained by the ECPSSR theory and Coster–Kronig fluorescence yields.     

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.     

Fatigue testing of metallurgically-bonded EBR-II superheater tubes

Fatigue crack growth tests were performed on 2¼Cr–1Mo steel specimens machined from ex-service experimental breeder reactor-II (EBR-II) superheater duplex tubes. The tubes had been metallurgically-bonded with a 100 μm thick Ni layer; the specimens incorporated this bond layer. Fatigue crack growth tests were performed at room temperature in air and at 400 °C in air and humid Ar; cracks were grown at varied levels of constant ΔK. In all conditions the presence of the Ni bond layer was found to result in a net retardation of growth as the crack passed through the layer. The mechanism of retardation was identified as a disruption of crack planarity and uniformity after passing through the porous bond layer. Full crack arrest was only observed in a single test performed at near-threshold ΔK level (12 MPa√m) at 400 °C. In this case the crack tip was blunted by oxidation of the base steel at the steel–nickel interface.     

A theoretical procedure for detection of simulated cracks in a pipe by the direct current–potential drop technique

Based on the direct current–potential drop (dc–pd) technique, an efficient theoretical detection procedure is developed to identify the existence of simulated cracks in a pipe. By this procedure, the electric potential on a ‘pseudo’ perfect pipe needs to be calculated in advance by finite element method. The proposed defect influence factor, which is defined as the ratio of the electric potential of the defective pipe divided by that of the ‘pseudo’ perfect one, is then employed to reveal the effect of cracks on the electric potential. By depicting the contours of the defect influence factor with sufficient resolution, not only the position, but also the shape and length size of cracks in the pipe can be identified accurately by the detection criterion devised in this work. The types of detectable through-wall cracks include circumferential crack, inclined crack, and multiple cracks. Good detection results show the merits of the procedure developed for the identification of the simulated cracks as described above in the pipe structure.     

Measurement of the mechanical properties of thermally-shocked zirconia-based simulated inert matrix fuel

The Vickers micro-hardness (H_V) was measured by an indentation technique of simulated ZrO₂-based Inert Matrix Fuel (IMF) material with a composition of Er_0.07Y_0.10Ce_0.15Zr_0.68O_1.915 in two different densities on sintered specimens and specimens thermally shocked with the quenching temperature differences (ΔTs) between 473 and 1673 K and compared with those of simulated MOX, namely, U_0.92Ce_0.08O₂. The H_V values obtained for two IMF materials were found higher, ranging from 6.37 GPa to about 7.84 GPa, depending on ΔT and the sintered density, than those obtained for the simulated MOX which are quasi-constant in the same range of ΔT with a mean value of 6.37 GPa. The fracture toughness (K_IC) was calculated from the measured H_V and the crack length, and it was found to exhibit a slight increase with increasing ΔT, ranging between 1.4 and 2.0 MPa m^1/2, while that of simulated MOX specimen is ranging between 0.8 and 1.1 MPa m^1/2. The thermally shocked specimens were observed with an optical microscope and analyzed in terms of microstructural changes and cracking patterns.     

Observation of the evanescent wave excited by proton beam

An exit angle dependence of the intensity of carbon K line during proton bombardment was measured to observe the evanescent wave. A Soller type spectrometer was used to measure the intensity of X-ray lines. A mirror polished Si (1 1 1) wafer was used as a substrate and carbon was deposited onto this surface. As a result a curious exit angle dependence which is similar to the evanescent wave of X-rays was found . The calculated transmission coefficient of X-ray evanescent wave is compared with measured exit angle dependence of X-ray emission. The experimental and theoretical values are in good agreement. Utilization of this phenomenon permits to enhance the surface sensitivity of the PIXE analysis method.     

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.     

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).     

Dynamic analysis of crack arrest properties in compact arrest tests

The transverse wedge-loaded compact crack arrest test is a widely used small scale test to evaluate the crack arrest toughness of nuclear pressure vessel steels. Crack arrest toughness is determined wholly on the basis of static analysis in this test method.The present study tried to clarify the dynamic features of this test. Crack extension and the opening displacement behavior were measured using a sensitive time scale. The crack attained a high velocity after initiation, then decelerated to a low velocity prior to arrest. The opening displacement remained constant during the crack propagation and began to increase several tens of microseconds after crack arrest.Numerical analysis of the dynamic stress intensity factor was also performed by a finite element code ADINA. Crack propagation was simulated by the elimination of truss elements which connected crack surfaces. Discussion is directed to the comparison between the conventional static approach and the present dynamic analysis.     

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 $\text{K}{}_{\mathrm{IC}}$.     

Effects of off-centered cracks and restraint of induced bending caused by pressure on the crack-opening-area analysis of pipes

Current models for the crack-opening-area analysis of pipes with circumferential through-wall cracks are based on various idealizations or assumptions which are often necessary to simplify the mathematical formulation and numerical calculation. This paper focuses on the validity of two such assumptions that involve off-centered cracks and the restraint of induced bending caused by pressure, and quantifies their effects on the crack-opening area analysis of pipes. Finite element and/or simple estimation methods were employed to compute the center-crack-opening displacement and crack-opening shape for a through-wall-cracked pipe, considering off-centered cracks and the restraint of induced bending caused by pressure. The results of the analyses show that, for both cases, the crack-opening area can be reduced significantly. For pipes with off-centered cracks, the crack-opening area can be evaluated from analyses of symmetrically centered cracks and assuming elliptical profile. For pipes with complete restraint of the induced bending caused by pressure, the reduction in crack-opening area depends on the crack size. When the crack size is small, the restraint effects can be ignored. However, when the crack size is large, the restrained crack opening can be significantly smaller than the unrestrained crack opening, depending on the length of pipe involved; hence, it may be important for the crack-opening-area and leak-rate analyses.     

Evaluation of effect of hydrogen on toughness of Zircaloy-2 by instrumented drop weight impact testing

Hydride-assisted degradation in fracture toughness of Zircaloy-2 was evaluated by carrying out instrumented drop-weight tests on curved Charpy specimens fabricated from virgin pressure tube. Samples were charged to 60 ppm and 225 ppm hydrogen. Ductile-to-brittle-transition behaviour was exhibited by as-received and hydrided samples. The onset of ductile-to-brittle-transition was at about 130 °C for hydrided samples, irrespective of their hydrogen content. Dynamic fracture toughness (K_ID) was estimated based on linear elastic fracture mechanics (LEFM) approach. For fractures occurring after general yielding, the fracture toughness was derived based on equivalent energy criterion. Results are supplemented with fractography. This simple procedure of impact testing appears to be promising for monitoring service-induced degradation in fracture toughness of pressure tubes.     

Use of the Master Curve methodology for real three dimensional cracks

At VTT, development work has been in progress for 15 years to develop and validate testing and analysis methods applicable for fracture resistance determination from small material samples. The VTT approach is a holistic approach by which to determine static, dynamic and crack arrest fracture toughness properties either directly or by correlations from small material samples. The development work has evolved a testing standard for fracture toughness testing in the transition region. The standard, known as the Master Curve standard is in a way “first of a kind”, since it includes guidelines on how to properly treat the test data for use in structural integrity assessment. No standard, so far, has done this. The standard is based on the VTT approach, but presently, the VTT approach goes beyond the standard. Key components in the standard are statistical expressions for describing the data scatter, and for predicting a specimens size (crack front length) effect and an expression (Master Curve) for the fracture toughness temperature dependence. The standard and the approach, it is based upon, can be considered to represent the state of the art of small specimen fracture toughness characterization. Normally, the Master Curve parameters are determined using test specimens with “straight” crack fronts and comparatively uniform stress state along the crack front. This enables the use of a single K_I value and single constraint value to describe the whole specimen. For a real crack in a structure, this is usually not the case. Normally, both K_I and constraint vary along the crack front and in the case of a thermal shock, even the temperature will vary along the crack front. A proper means of applying the Master Curve methodology for such cases is presented here.     

Fracture mechanics investigation regarding the effects of cracks on the structural integrity of a BWR-core shroud

As a consequence of core shroud intergranular stress corrosion cracking (IGSCC) detected in the course of inservice inspections, a fracture mechanics analysis was carried out to evaluate the effects of postulated cracks on the structural integrity. In this study, critical crack sizes and crack growth were calculated. Due to the comparatively low stress acting on the core shroud during normal operation, the residual stresses in the welds make up the major proportion of the tensile stresses responsible for IGSCC. In order to consider residual stresses of the lower core support ring welds, a finite element analysis was performed at MPA Stuttgart using the FE-code ANSYS. The crack growth computed on the basis of USNRC crack growth rates da/dt demonstrated that crack growth in depth direction increases quickly at first, then retards and finally comes almost to a standstill. The cause of this ‘quasi-standstill’ is the residual stress pattern across the wall, being characterized by tensile stresses in the outer areas of the wall and compressive stresses in the middle of the wall. Crack growth in circumferential direction remains more or less constant after a slow initial phase. As the calculation of stress intensity factors K_I of surface flaws under normal conditions demonstrated, a ‘lower bound’ fracture toughness value is only exceeded in the case of very long and deep surface flaws. It can be inferred from crack growth calculations that under the assumption of intergranular stress corrosion cracking, the occurrence of such deep and at the same time long flaws is unlikely, regardless of the initial crack length. Irrespective of the above, the calculated critical throughwall crack lengths, which were determined using a ‘lower bound’ fracture toughness value, demonstrated that even long throughwall cracks will not affect the component’s integrity under full load. Moreover, it can be concluded from the studies of crack growth that—assuming intergranular stress corrosion cracking—a sufficiently long period will elapse before a crack which has just been initiated reaches a relevant size. Therefore, it can be stated that these cracks will likely be detected during periodic inservice inspections.     

Hertzian indentation of advanced lmfbr fuels with simulated burn-up

Hertzian indentation fracture of advanced fast breeder reactor fuel materials [mixed carbonitrides, (U_0.8, Pu_0.2)C_0.8N_0.2, and nitrides (U_0.8Pu_0.2)N was evaluated to yield the fracture surface energy, γ, and the fracture toughness, K_Ic. Both technological grade fuels and fuels with added fission products to chemically simulate burn-up values of 3 and 10 at.% were used. As in previous self-diffusion studies on the same materials, identical behavior (identical critical loads, P_c for crack formation) was observed for 3 and 10% b.u. Simulated M(C, N), whereas the 10% b.u. Simulated MN showed a cracking behavior identical with that of the undoped MN. In contrast, the 3 at.% b.u. Simulated MN showed lower P_c values. This is compatible with differences in fission product solubilities in these materials. The effect of fission products on γ was < 20% whereas γ increased from (U, Pu)(C, N) to (U, Pu)N by up to 80 to 90%, depending on content in fission products.