Transient analysis of blowdown thrust force under PWR LOCA

The analytical results of blowdown characteristics and thrust forces were compared with the experiments, which were performed as pipe whip and jet discharge tests under the PWR LOCA conditions. The blowdown thrust forces were obtained by Navier-Stokes momentum equation for a single-phase, homogeneous and separated two-phase flow, assuming critical pressure at the exit if a crifical flow condition was satisfied.The following results are obtained:

1. (1) The node-junction method is useful for both the analyses of the blowdown thrust force and of the water hammer phenomena.

2. (2) The Henry-Fauske model for subcooled critical flow is effective for the analysis of the maximum thrust force under the PWR LOCA conditions. The jet thrust parameter of the analysis and experiment is equal to 1.08.

3. (3) The thrust parameter of saturated blowdown has the same one with the value under pressurized condition when the stagnant pressure is chosen as the saturated one.

4. (4) The dominant terms of the blowdown thrust force in the momentum equation are the pressure and momentum terms except that the acceleration term has large contribution only just after the break.

Stress analysis of core support post in a very high-temperature reactor

A very high-temperature gas-cooled reactor (VHTR) has been developed by Japan Atomic Energy Research Institute and its core consists of so-called fuel blocks, removable reflector blocks and so on. These graphite blocks are supported by thin cylindrical graphite bars called support posts. These posts are in contact with the blocks through hemispherical seats to absorb the relative displacement of blocks by small inclination or rotation of the posts.Stress distributions and stress concentration coefficients of the support post under the reactor core weight are analysed by means of photoelastic experiment and compared with two-dimensional calculation by using the finite element method.

The following are the conclusions we have derived:

1. (1) Stress concentration coefficients of the post are expressed uniquely as a function of regardless of the shapes of model and material properties.

2. (2) Inclination of the post caused by small rotation has little effect on the stress concentration coefficients.

The structure of the hollandite type phase of synroc b in the temperature range 20–1060°c

The crystal structure of the hollandite type phase Ba_1.17Ti_5.04Al_2.10O₁₆ has been determined by neutron diffraction powder methods in the temperature range 20–1060°C. The lattice parameters, the positional parameters and the anisotropic thermal parameters of each atom have been determined at seven temperatures.The principal results are:

1. (1) the thermal expansion coefficients are almost isotropic, α_a = (10.40 ± 0.25) × 10⁻⁶, α_c = (11.17 ± 0.35) × 10⁻⁶;

2. (2) the fractional atomic coordinates do not change in this temperature range;

3. (3) the Debye temperature is (581 ± 15) K; and

4. (4) the amplitude of thermal vibration of the barium atoms is anomalously high at all temperatures.

Transferability of post yield fracture mechanics properties from small scale specimens to large scale specimens and components

This contribution describes a method for the determination of the J-integral as a function of the load-line displacement for arbitrary specimen geometries.A correspondence could be found between the approximation method and the results determining with the Rice integral by means of a FE-calculation. Using the initiation values of the J-integral as a fracture mechanics parameter determined from the J_R-curve, correspond with failure values of double-édged notched tensile specimens and circumferentially notched round tensile specimens of which crack initiation was tantamount to instability. Consequently, it could be proved that the J-integral is a transferable parameter that may be ascertained from simple determinable deformation values. The application to real components seems to be promising, due to these good results.     

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.     

Use of J–R curves in assessing the fracture behavior of low upper shelf toughness materials

The objective of this investigation was to evaluate the use of small specimen J–R curves in assessing the fracture resistance behavior of reactor vessels containing low upper shelf (LUS) toughness weldments. As required by the U.S. Code of Federal Regulations (10 CFR, Part 50), reactor vessel beltline materials must maintain an upper shelf Charpy V-Notch (CVN) energy of at least 50 ft-lbs (68 J) throughout vessel life. If CVN values from surveillance specimens fall below this value, the utility must demonstrate to the U.S. Nuclear Regulatory Commission (NRC) that the lower values will provide “margins of safety against fracture equivalent to those required by Appendix G of the ASME Boiler and Pressure Vessel Code”. This paper will present recommendations regarding the material fracture resistance aspects of this problem and outline an analysis procedure for demonstrating adequate fracture safety based on CVN values.It is recommended that the deformation formulation of the J-integral be used in the analysis described above. For cases where J-integral fracture toughness testing will be required, the ASTM E1152-87 procedure should be followed, however, data should be taken to 50% to 60% of the specimen remaining ligament. Extension of the crack growth validity limits for J–R curve testing, as described in E1152-87, can be justified on the basis of a “J-controlled crack growth zone” analysis which shows an engineering basis for J-control to 25% to 40% of the specimen remaining ligament. If J-R curve extrapolations are required for the analysis, a simple power law fit to data in the extended validity region should be used. The example analysis performed for low upper shelf weld material, showed required CVN values for a reactor vessel with a 7.8 inch (198 mm) thick wall ranging from 32 ft-lbs (43 J) to 48 ft-lbs (65 J), depending on the magnitude of the thermal stress component.     

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.     

Short circumferential through-wall cracked pipes subjected to stretch-bending load

The methods for assessment of elastic–plastic fracture behaviour of cracked components include the net section plastic collapse concept, the J-integral approach, and the two-parameter R-6 failure assessment diagram, Revision 3. These failure assessment methods are usually used to obtain fracture behaviour prediction with a reasonable degree of accuracy without carrying out complicated full-length numerical fracture analysis. In the current work, fracture experiments on stainless steel pipes with short circumferential through-wall cracks under stretch-bending load were conducted. Stretch-bending load refers to the loading situation where axial load is generated that is proportional or related to the applied bending load. The J-integral values derived from the experimental load-point load–displacement data under stretch-bending and pure bending conditions are compared to investigate the effect of axial load on the J–resistance curves. The results show clear dependence of crack resistance force on axial load for short circumferential cracks. Crack resistance force decreased noticeably for increased stretch-bending loading compared to pure bending loading.     

Pipe fracture safety analysis using limit load and J-integral techniques

J-integral fracture toughness tests were performed on full scale pipe specimens to assess the fracture safety performance of two reactor piping alloys. The two alloys investigated were ASTM A106 Grade B carbon steel and circumferentially welded Type 304 stainless steel.The full scale pipe fracture tests were performed on 1.2 m long, circumferentially cracked pipes loaded in four-point bending on a variably compliant test bed. Results of the experiments were analyzed using the limit load approach currently being considered for inclusion in Section XI of the ASME Code. The results were also evaluated using two tearing instability approaches. One approach assumed elastic-perfectly plastic material behavior and the other accounted for material hardening by requiring actual load and displacement data.The limit load analysis provided a good prediction of the maximum load carrying capacity of the pipe specimens in most cases. The results were especially good for the ASTM A106 steel pipes when the materials property data was used to calculate the flow stress. The J-integral tearing instability analysis was shown to accurately describe the ductile tearing instability behavior of the ASTM A106 steel pipe providing material hardening was taken into account.     

A comparison of the use of the modified J-integral and the deformation J-integral in procedures for estimating the critical crack length for CANDU pressure tubes

The paper presents the results of a theoretical investigation whose objective has been to see whether there are advantages to be gained from using the modified J-integral in procedures for estimating the critical crack length for CANDU pressure tubes. For typical operation conditions, and with irradiated tubes having critical crack lengths over a wide range, it is shown that the slope of the modified J-integral J_M-Δa crack growth resistance curve for a pressure tube crack is only marginally greater than the slope of the corresponding deformation J-integral J_D-Δa curve; the results are expressed in terms of the parameter Z_*, which is dJ_M/da − dJ_D/da and the parameter Q, which is the fractional difference between dJ_M/da and dJ_D/da. In the light of these findings, there would appear to be little advantage to be gained in using J_M, rather than J_D, as a characterizing parameter for crack growth in a CANDU pressure tube.     

Time dependence of J-integral

Tests performed within the framework of earlier RWTÜV projects together with results obtained elsewhere with regard to the time dependence of fracture mechanics data show that time effects reduced the toughness of materials, according to the nature of the test (extremely slow load rate or hold times with sustained load).

Reduction in toughness has an effect on the following:

• - decrease in critical material data (J₀, δ_i)

• - levelling off of the crack resistance curve J = J(Δa) and in consequence a decrease of tearing modulus.

This tendency is confirmed quantitatively by recent test results. These tests were performed with the material 15 Mn Ni 63 at room temperature with hold times under sustained load and according to the appropriate standards (without hold times). The tests show that hold times cause additional stable crack growth. The resulting J − Δa curve is lower and less sloping than the curve obtained in a standardized test. The time effect should be taken into account in a safety analysis.     

Damage, crack growth and fracture characteristics of nuclear grade graphite using the Double Torsion technique

The crack initiation and propagation characteristics of two medium grained polygranular graphites, nuclear block graphite (NBG10) and Gilsocarbon (GCMB grade) graphite, have been studied using the Double Torsion (DT) technique. The DT technique allows stable crack propagation and easy crack tip observation of such brittle materials. The linear elastic fracture mechanics (LEFM) methodology of the DT technique was adapted for elastic-plastic fracture mechanics (EPFM) in conjunction with a methodology for directly calculating the J-integral from in-plane displacement fields (JMAN) to account for the non-linearity of graphite deformation. The full field surface displacement measurement techniques of electronic speckle pattern interferometry (ESPI) and digital image correlation (DIC) were used to observe and measure crack initiation and propagation.Significant micro-cracking in the fracture process zone (FPZ) was observed as well as crack bridging in the wake of the crack tip. The R-curve behaviour was measured to determine the critical J-integral for crack propagation in both materials. Micro-cracks tended to nucleate at pores, causing deflection of the crack path. Rising R-curve behaviour was observed, which is attributed to the formation of the FPZ, while crack bridging and distributed micro-cracks are responsible for the increase in fracture resistance. Each contributes around 50% of the irreversible energy dissipation in both graphites.     

Predictions of non-steady asymptotic crack tip fields in power law creeping materials

The applicability of accepted engineering procedures to predict the amplitude of singular crack tip fields during the transitional regime prior to steady state has been investigated. Estimates of both transient and steady state values of the C(t)-integral for simplified geometries are compared with results obtained from detailed finite element analyses. Different creep exponents and both primary (mechanical) and secondary (displacement-controlled) loadings are considered.Estimates of the steady state value C^* were obtained from Nuclear Electric's high termperature assessment procedure, R5, which is based on reference stress concepts, and from the EPRI's fully plastic solutions for J-integrals. The transient behaviour of C(t) was estimated using approximations given by Ehlers and Riedel (Advances in Fracture Research, Proc. Fifth Int. Conf. on Fracture, Vol. 2, Pergamon, New York, 1981, pp. 691–698), Saxena (Fracture Mechanics: Seventeenth Volume, ASTM STP 905, ASTM, Philadelphia, 1986, pp. 185–201), and the R5 procedure (Ainsworth et al., Fatigue Fract. Eng. Struct. 10 (1987) 115–127). In most cases, the transient estimates given by the latter two were found to conservatively predict the finite element results, although some underpredictions were encountered in the planar geometries shortly after loading. The recommended use of plane stress reference stresses with the R5 procedure, however, provides overall conservatism in the values of C(t). Ehlers and Riedel estimates, though, are generally non-conservative, except for the lowest crack-tip constraint configuration analysed (i.e. centre cracked plate).     

Fracture mechanics analysis for inhomogeneous material behaviour

The J-integral is an important parameter for the ductile fracture mechanics assessment of components. With an appropriate modification it may even be applied to inhomogeneous materials where the material characteristics may depend strongly on the location, e.g. in welded joints. Experimental and numerical investigations on fracture mechanics specimens made from a welded joint including the heat affected zone show the influence of the different material parameters on the J-integral. Also, the influence of residual stress on the J-integral and on other fracture mechanics parameters is shown.     

On the dynamic fracture toughness and crack tip strain behavior of nuclear pressure vessel steel: Application of electromagnetic force

This paper is concerned with the application of the electromagnetic force to the determination of the dynamic fracture toughness of materials. Taken is an edge-cracked specimen which carries a transient electric current I and is simply supported in a steady magnetic field B. As a result of their interaction, the dynamic electromagnetic force occurs in the whole body of the specimen, which is then deformed to fracture in the opening mode of cracking.Using the electric potential and the J - R curve methods to determine the dynamic crack initiation point in the experiment, together with the finite element method to calculate the extended J-integral with the effects of the electromagnetic force and inertia, the dynamic fracture toughness values of nuclear pressure vessel steel A508 class 3 are evaluated over a wide temperature range from lower to upper shelves.The strain distribution near the crack tip in the dynamic process of fracture is also obtained by applying a computer picture processing.     

Allowable minimum upper shelf toughness for nuclear reactor pressure vessels

The paper develops methodology and procedure for determining the allowable minimum upper shelf toughness for continued safe operation of nuclear reactor pressure vessels. Elastic-plastic fracture mechanics analysis method based on the J-integral tearing modulus (J/T) approach is used. Closed from expressions for the applied J and tearing modulus are presented for finite length, part-throughwall axial flaw with aspect ratio of . Solutions are then presented for Section III, Appendix G flaw. A simple flaw evaluation procedure that can be applied quickly by utility engineers is presented. An attractive feature of the simple procedure is that tearing modulus calculations are not required by the user, and a solution for the slope of the applied J/T line is provided. Results for the allowable minimum upper shelf toughness are presented for a range of reactor pressure vessel thickness and heatup/cooldown rates.     

Transferability of results of small scale experiments to real structures

Numerical evaluations in combination with experiments on the basis of the J-integral methods are a necessary step in the chain of transferability from small specimens to real structures.For three cases, single-edge notched specimens of different thicknesses, flat plates under tension containing two through-cracks and side-grooved compact specimens of various steels, both finite element calculations including crack growth and experiments using the partial unloading technique were performed.The results show a good agreement of the experimental and numerical J-values and confirm the experimental procedure to evaluate J from the work done on the specimen.Moreover, for the single-edge notched specimen the strong influence of the angular stiffness of the loading system on the specimen behaviour is demonstrated.     

A parametric study on J-integral under pressurized thermal shock by using statically indeterminate fracture mechanics

The method of statically indeterminate fracture mechanics (SIFM) is application of elastic-plastic fracture mechanics to statically indeterminate problems. Application of SIFM has been developed for axially cracked cylinder problems under axisymmetric pressurized thermal shock, PTS loading. This method allows us to evaluate the J-integral in an explicit form and is efficient in clarifying the mechanical characteristics of the PTS event. This paper describes a parametric study of the J-integral under PTS loading by using SIFM.