Moment modified compact tension specimen for measuring crack arrest toughness

Crack arrest toughness in reactor vessel steels in the transition and Charpy upper shelf energy temperature range are of particular interest to the nuclear industry to aid with the analysis of the phenomenon known as pressurized thermal shock (PTS). A test specimen and analysis technique have been developed to measure crack arrest toughness at temperatures from the transition region up to and beyond the Charpy upper shelf energy level. The moment modified compact tension (MMCT) specimen combines a thermal gradient with mechanical loadings to initiate a crack in brittle material below NDT and then have arrest take place in hot, ductile material. A finite element model was used to help design the specimen and fixturing geometry as well as calculate the arrest toughness. Tests have been conducted on ASME SA533 Grade B Class 1 steel plate with a variety of loadings confirming the veracity of the technique and developing valuable data. Crack arrest toughness has been measured from 0°F to 110°F (−18°C to 43°C). This work has been part of a research program performed by C-E, Windsor and funded by the Electric Power Research Institute.     

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.     

Dynamic fracture analysis of a transverse wedge-loaded compact specimen

The J-integral method cannot be applied to the elastic plastic dynamic crack propagation, because unloading and inertia force may take place. From this point of view dynamic elastic plastic scheme using J-integral is developed.Using this dynamic finite element program an MRL type specimen is analyzed. As the result, the property of path-independence of the J-integral under the existence of inertia force and unloading is confirmed. Dynamic effects are considerably small in the MRL type specimen. Also the influence of plastic zone on the crack arrest toughness is shown.Finally the present result is compared with the request of ASTM 2nd round robin test program for crack arrest toughness.     

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Abstract

The focus of the investigations on ferritic nodular cast iron with varying graphite morphology was the determination of fracture mechanical characteristics and crack resistance curves of the J-integral and Crack Tip Opening Displacement (CTOD) concept under static and dynamic load. The experiments were performed at various temperatures down to 40 degrees below zero. The results show a close correlation between static crack initiation toughness values as well as crack resistance curves and quantitative graphite morphology parameters. The practised low-blow technique allowed the reproducible detennination of dynamic R curves of the J-integral and CTOD concept. First results of the R curve investigations under dynamic load draw attention to a correlation between crack initiation toughness and graphite morphology that is comparable to the results under static load. A comparison of static and dynamic crack initiation toughness data shows a loss of toughness with the dynamic values due to the higher loading rate. An influence of temperature on the static fracture mechanical crack resistance data in the investigated range of temperatures was found to depend on the size of the graphite nodules.     

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).     

The viablility of the KIa procedure for predicting the arrest of a crack in a nuclear reactor steel pressure vessel

The current ASME Code procedure for predicting crack arrest in a nuclear reactor steel pressure vessel is based on a static linear elastic fracture mechanics analysis: a crack is presumed to arrest when the crack tip stress intensity factor K_I^ST falls below K_Ia, which is assumed to be a material property and is referred to as the arrest toughness. The viability of this procedure has been questioned since the theoretical justification, in the strictest sense, for this very simple K_Ia approach is based on the behaviour of a semi-infinite crack propagating in an unbounded solid due to the application of time-independent loads. Against this background, the present paper examines the effects of initial crack size and crack jump length on the viability of the K_Ia procedure. A theoretical analysis shows that the procedure should give accurate predictions of the crack length at arrest certainly if the crack jump length is less than twice the initial crack size.     

Results and conclusions from the first pressurized-thermal-shock experiment

The first pressurized-thermal-shock test of a 148 mm thick steel pressure vessel with a 1 m long flaw was performed to investigate fracture behavior of a vessel under conditions relevant to a flawed nuclear reactor pressure vessel during an overcooling accident. The objectives were to observe crack arrest and stability on the ductile upper shelf and the effects of warm prestressing on crack initiation. Three coordinated pressure and thermal transients were imposed on the vessel, which was preheated to 290°C. Two episodes of crack propagation and arrest occurred. The thermal transients were induced by coolant at −29 to 15°C. Pressure transients were as high as 94.4 MPa. The experimental objectives were attained. The inhibiting effects of warm prestressing were definitely demonstrated. Crack propagation was nearly pure cleavage, and arrest at 30 K above the onset of the Charpy upper-shelf was experienced in a positive K₁ gradient and with K₁ = 300 MPa√m. Fracture-mechanics analysis of brittle fracture based on small-specimen toughness measurements was reasonably accurate. Flaw evaluation by procedures of the ASME Boiler and Pressure Vessel Code conservatively predicted vessel failure, which did not occur. No ductile tearing occurred after each crack arrest, although some stable tearing had been predicted on the basis of tearing resistance data.     

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.     

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.     

Wide plate crack arrest testing

Five wide-plate crack arrest tests have been performed between September 1984 and December 1985 on an ASTM A533B quenched and tempered steel. These tests were done in the 26 MN Universal Testing Machine located at the National Bureau of Standards. The specimens were fractured in a thermal gradient to make the crack initiate at a preexisting notch in a cold, brittle region, and arrest in a hot, tough region. To obtain a great deal of information from these tests, each specimen was thoroughly instrumented with thermocouples, strain gages, crack-mouth-opening displacement gages, timing wires, and/or acoustic emission transducers. Fast data response was obtained from these sensors during the run-arrest events, which generally lasted for less than 10 ms. Estimates of two types of important data were obtained: (1) crack velocity as a function of time, and (2) initiation and arrest toughness. Thus, a successful data collecting system was developed for acquiring the basic data required for the prediction of the behavior of nuclear pressure vessels subjected to pressurized thermal shock.     

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.     

Dynamic analysis of a crack-arrest specimen

Under pressurized thermal shock (PTS) loading conditions arrest of running cracks at temperatures that range up to or above those corresponding to the onset of Charpy upper shelf is of particular interest. Only few crack arrest toughness (K_Ia) data above 200 MPa√m obtained from rather expensive PTS-experiments and wide-plate tests are available. In the present paper the capabilities of a relatively small panel crack arrest specimen for yielding K_Ia data in excess of 200 MPa√m under conditions of a rising K_I-field are investigated. For this purpose static and dynamic finite element analyses are performed. It is shown that dynamic effects cannot be neglected for this specimen type and K_Ia-values up to about 300 MPa√m can be expected from measurements in suitably conducted experiments.     

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.     

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.     

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.     

Crack arrest in high cycle thermal fatigue crazing

Thermal crazing in high cycle thermal fatigue due to thermal fluctuation in residual heat removal (RHR) system of some nuclear power plants is explained by crack arrest in the depth due to a decreasing stress intensity factor. This is related to high frequencies of thermal loading. An attempt has been made through a parametric study to acquire some knowledge about the loading, knowing the crack depth. For this purpose, analytical as well as finite element simulations of crack propagation in 2D- and 3D-semi-elliptical cracks have been performed. In periodic loading, bounds for the number of cycles to fatigue life are proposed. Moreover, it is shown that in the absence of mean stress, fatigue damage in RHR may be produced in the macroscopic elastic-plastic regime. Finally, it is shown by FE simulations that for a semi-elliptical crack, a small error on stress intensity factor may result in significant error on crack length at high number of cycles, due to error accumulation cycle by cycle. Moreover in this paper is given the reason as to why shielding effect has not been taken into account in the study of crack arrest in RHR.     

Time dependent ductile crack extension in A533B class I steel

Four wide plate specimens manufactured in A533B Class I, 90 mm thick by 500 mm wide containing through-thickness or semi-elliptical surface fatigue cracks were tested at +70°C. These specimens were subjected to a series of increasing applied loads, each of 100 h duration, until failure. Testing was performed using a computer interactive 40 MN load controlled tensile testing rig. Values of the fracture toughness parameters J and crack tip opening displacement (CTOD) were derived from the recorded values of applied load, plate extension and crack mouth opening displacement.The influence of loading rate, degree of yield containment and crack orientation on the time dependent behaviour is assessed and compared with data obtained from wide plate and bend tests under monotonic loading and from bend tests conducted with a variable loading rate, with hold periods, under crack mouth opening control. Interpretation of the results provides a clearer understanding of low temperature time dependent ductile crack extension and enables the identification of the conditions under which this phenomenon is apparent, to allow the necessary adjustments to failure assessments.     

TiN颗粒增韧Si_3N_4复合材料增韧机制的研究

加入 TiN 颗粒可显著提高 Si3N4陶瓷的断裂韧性,实验结果分析表明可能有几种增韧机制起作用:由于第二相与基体热膨胀系数和弹性模量的差异,复合材料烧结后从高温到室温的冷却过程中产生残余应力,由于残余应力场的作用发生裂纹分岔;通过对复合材料的压痕裂纹扩展路径观察,证实了裂纹偏转和弯曲的存在;对复合材料的磨面进行 SEM 观察,发现了微裂纹。提出了对 TiN 颗粒增韧Si3N4复合材料应采用残余应力场增韧、裂纹偏转增韧、微裂纹增韧三种增韧机制联合作用的增韧机制,使得复合材料增韧值的计算值和实测值符合得较好。     

Crack opening behavior of penetrated crack under cyclic or monotonic loading

Crack opening displacements (CODs) were examined experimentally at room temperature for both plate and pipe specimens containing a surface crack. Application of COD solutions from plate specimens, as proposed by the present authors, to pipe specimens were investigated. COD after penetration could be satisfactorily determined regardless of a type of load using the COD, solutions proposed by the authors.