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.     

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.     

Analytical evaluation method of J-integral in creep-fatigue fracture for type 304 stainless steel

Creep-fatigue crack growth at the operating temperature of LMFBR can be characterized by ΔJ_F and J′ (same as C^*). Type 304 stainless steel, the main structural material of the Japanese LMFBR, shows notable cyclic hardening at elevated temperatures. Evaluation of these J-integrals with the finite-element method is strongly affected by the reference strain range when the cyclic hysteresis' is used as the stress-strain relation.In this paper, an evaluation method for ΔJ_F and J′ with a cyclic stress-strain curve (Δσ – Δ relation) is proposed and verified by experimental results. The evaluation method proposed here does not require cyclic calculations but is monotonic and the effect of the reference strain range is relatively small.     

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.     

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.     

Evaluation of different fracture-mechanical J-integral initiation values with regard to their usability in the safety assessment of components

Determining fracture-mechanical material characteristic values on the basis of the J-integral is described and stipulated in a variety of standards and guidelines. The individual specifications differ in terms of procedure when determining the characteristic values and, therefore, also in terms of the meaningfulness of the results. This paper presents the different procedures, suggested in the course of the development of test methods in the field of elastic—plastic fracture mechanics, used to characterize crack initiation behaviour with regard to their features as material characteristic values and their usability in the safety assessment of components.     

J integral estimation fracture analysis for circumferentially cracked carbon steel piping

The three-segment fitting method is presented to describe the material stress-strain curves with yield plateaus. A J integral estimation approach for carbon steel piping with circumferential through-wall cracks was developed. Failure assessment curves obtained using three options in the CEGB R6 approach were proposed for GB20 carbon steel piping under bending. The initiation and maximum moments predicted by the J estimation approach presented in this paper are quite close to the experimental values.     

Plastic limit load analysis for steam generator tubes with local wall-thinning

This paper introduces the study of experimental and numerical analysis for plastic limit loads of Inconel 690 steam generators (SG) tubes with local wall-thinning defects. Meanwhile, the effect of the three dimensions of a local wall-thinning defect on the plastic limit load of SG tubes is analyzed.A test facility which can test both burst pressure and plastic limit load of SG tubes was established and SG tubes with 3 typical types of defects were tested by using the facility. A regularization method for local wall-thinning defect is proposed and the finite element method was used to analyze the plastic limit load of SG tubes with defects. Compared with the experimental results of SG tubes with real defects, the calculated values of plastic limit load for SG tubes with regularized defects are conservative.Based on finite element method, the effect of the three dimensions of local wall-thinning defects on plastic limit loads of defected Inconel 690 SG tubes has been got. The studied results show that the defect depth of a local wall-thinning defect is the main factor influencing the plastic limit load of SG tubes, on the other hand, both the longitudinal length and the circumferential length of a defect have effect on the plastic limit load of SG tubes.It is found that in some cases, when the longitudinal length and the circumferential angle of a local wall-thinning defect exceed some extent, the effect of the longitudinal length and the circumferential angle on plastic limit load can be ignored.     

Use of load path dependent material fracture toughness values (WPS) in the safety analysis of RPV stade

The effect of warm prestressing (WPS) has been investigated for the specific material and loading conditions of the central circumferential weld of the reactor pressure vessel of KKS under emergency core cooling. Warm prestressing results in a significant rise of effective fracture toughness. The magnitude of the WPS-effect as a function of warm prestressing, path of unloading, amount of cooling (e.g. change of yield stress) can be predicted on the basis of a theoretical model of Chell et al.. Crack initiation can be excluded for emergency core cooling (ECC)-loading and for material conditions beyond end of life for the central circumferential weld of the pressure vessel of KKS.     

The calculation of dynamic JR-curves from the finite element analysis of a Charpy test using a rate-dependent damage model

A two-dimensional analysis of the Charpy V-notch specimen subjected to impact loading, according to the standard DIN EN 10045-1, is carried out, using a transient explicit dynamic finite element program. An elastic-viscoplastic, temperature dependent, constitutive relation for a porous plastic solid based on the Gurson damage model is developed. Ductile fracture of the matrix material will be described by the nucleation and subsequent growth of voids to coalescence. An updated Lagrange–Jaumann formulation is employed accounting for large strain and rotation. The discretization is based on four-node plane strain solid elements with one Gauss point. The equations of motion are integrated numerically by an explicit integration algorithm utilising a lumped mass matrix. The predictions of the numerical analysis in terms of force deflection response, crack resistance behaviour and deformation energy absorbtion are compared with results from Charpy tests which were carried out according to the low-blow technique.     

Materials analysis using ion beam techniques

Basic concepts of ion beam analysis techniques for the study of the composition and structure of surfaces, interfaces and thin layers are reviewed. For surface characterization the use of low-energy (1–20 keV) ions is compared with the use of medium-energy (50–200 keV) and high-energy (200 keV-several MeV) ions. Thin-layer analysis with Rutherford backscattering (RBS) and nuclear reaction analysis in combination with channeling is described in detail. Requirements, including the necessary precision demands, for the instrumentation are discussed. The analysis via computer simulations of channeling data, in particular of data for the determination of lattice sites of solute atoms in single crystals, will be treated. As an illustration of the potential of ion beam techniques for structure analysis, a number of examples of lattice site locations is presented.     

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.     

Development of safety analysis and constraint detection techniques for process interaction errors

Among the new failure modes introduced by computer into safety systems, the process interaction error is the most unpredictable and complicated failure mode, which may cause disastrous consequences. This paper presents safety analysis and constraint detection techniques for process interaction errors among hardware, software, and human processes. Among interaction errors, the most dreadful ones are those that involve run-time misinterpretation from a logic process. We call them the “semantic interaction errors”. Such abnormal interaction is not adequately emphasized in current research. In our static analysis, we provide a fault tree template focusing on semantic interaction errors by checking conflicting pre-conditions and post-conditions among interacting processes. Thus, far-fetched, but highly risky, interaction scenarios involve interpretation errors can be identified. For run-time monitoring, a range of constraint types is proposed for checking abnormal signs at run time. We extend current constraints to a broader relational level and a global level, considering process/device dependencies and physical conservation rules in order to detect process interaction errors. The proposed techniques can reduce abnormal interactions; they can also be used to assist in safety-case construction.     

Characterization of natural and modified zeolites using ion beam analysis techniques

Zeolites are very important materials in catalytic and industrial processes. Natural, modified and synthetic zeolites have a wide range of uses because of their good adsorption, ion exchange capacity and catalytic properties. Mexico is an import source of natural zeolites, however their utilization in the natural form is limited due to the presence of trace metallic impurities. For example, metals such as vanadium and chromium inhibit the elimination of sulfur in hydrocarbons. Therefore, it is important to know the precise composition of the zeolite material. In this work, we report the elemental characterization of zeolites using various IBA techniques. ³He⁺ and ²H⁺ beams were used to measure the major element concentrations (Si, Al, O, C) by RBS and NRA. PIXE and SEM-EDS were used to measure the total trace element content (V, Cr, Fe, Ni, Cu, Zn, Rb, Sr, Zr, Pb, etc). Additionally, XRD was used to study the zeolite crystal structure.     

Influences of the dynamic strain aging on the J–R fracture characteristics of the ferritic steels for reactor coolant piping system

The leak-before-break (LBB) design of the piping system for nuclear power plants has been based on the premise that the leakage due to the through-wall crack can be detected by using leak detection systems before a catastrophic break. The piping materials are required to have excellent J–R fracture characteristics. However, where ferritic steels for reactor coolant piping systems operate at the temperatures where dynamic strain aging (DSA) could occur, the fracture resistance could be reduced with the influence of DSA under dynamic loading. Therefore, in order to apply the LBB design concept to the piping system under seismic loading, both static and dynamic J–R characteristics must be evaluated.Materials used in this study are SA516 Gr.70 for the elbow pipe and SA508 Cl.1a for the main pipe and their welding joints. The crack extension during the dynamic and the static J–R tests was measured by the direct current potential drop (DCPD) and the compliance method, respectively. This paper describes the influences of the dynamic strain aging on the J–R fracture characteristics with the loading rate of the pipe materials and their welding joints.     

Computational techniques for inelastic stress and fracture analyses

Details of a unified creep—plasticity theory, based on the concept of an internal time, are presented, and a geometric interpretation of such a theory is given. A ‘tangent-stiffness’ formulation, for the finite-element/boundary-element calculation of weak solutions of the strain-history in the structure, is presented. An implicit algorithm of generalized mid-point radial mapping for computing the stress-history at a material point for a given strain-history is given. Appropriate crack-tip parameters that may be used to correlate the creep-crack-growth data for single—dominate-flaws in structures operating at elevated temperatures are discussed.     

Physical properties of nodular cast iron for shipping containers and safety analysis by fracture mechanics

Recently, the dry-storage technique for storing spent fuels or radioactive wastes in shipping containers has been improved as one of the new technologies in the nuclear-fuel cycle. Mitsui Engineering and Shipbuilding has engaged for 5 years in the development of a radioactive waste container made of modular cast iron. This paper describes the physical properties of nodular cast iron and a fracture mechanical study of the container made of this material.The material is equivalent to FCD 37 in the JIS Standard. Many tests were carried out to obtain the mechanical properties, the fracture toughness and other characteristics using specimens machined from a thick-walled casting block.Then, the structural integrity of the cubic-type container made of this material was estimated on the basis of fracture mechanics. The critical flaw sizes regarding stresses occurred during a 9-meter drop test and a 1-meter punch-drop test were calculated. The results indicate that these sizes can be determined by a nondestructive inspection.Consequently, it has been analytically confirmed that nodular cast iron containers are strong enough to withstand an impact load during drop tests if the applied stresses are less than the yield stress.     

An application of systems analysis techniques to the study of reactor seismic safety

Systems analysis is being used in conjunction with structural analysis to study the conservatisms and to provide insights into aspects of reactor seismic safety. An event-tree/fault-tree model of a commercial nuclear power plant is being constructed to determine the probability of release and probabilities of system and component failures caused by possible seismic events. The event-tree/fault-tree model is evaluated using failure data generated by applying the response a component sees to the component's fragility function. The responses are calculated by a structural analysis code using earthquake time histories as forcing functions. The quantification of the event-tree/fault-tree model is done conditional on a given seismic event and the conditional probabilities thus calculated unconditioned by integrating the results over the seismic hazard curve. In this way, most of the dependencies between event failures resulting from the seismic event itself are removed making known fault-tree analysis quentification techniques applicable. The outputs from the computations will be used in sensitivity studies to determine the key calculations and variables involved in seismic analyses of nuclear power plants.     

Characterization of silicon oxynitride films using ion beam analysis techniques

Heavy-ion elastic recoil detection analysis (HIERDA) is the ideal technique for quantitative analysis of silicon oxynitride films on silicon because of its unique ability to measure simultaneously all elements of interest (i.e., H, C, N, O and Si), thereby permitting key parameters such as the O/N-ratio to be determined in a single measurement. However, high-energy accelerators suitable for such HIERDA measurements are becoming much less readily available. Hence, the present paper investigates and calibrates an alternative IBA technique for simultaneous O, N and C analysis – namely, the use of (d,p) and (d,) nuclear reactions. Under optimum analysis conditions (850 keV deuterons and 150° detector angle), the Si background level sets a lower detection limit of 1×10¹⁶ nitrogen atoms/cm² and 3×10¹⁵ oxygen atoms/cm². H analysis is carried out separately, using low-energy ERDA and a 2 MeV ⁴He beam. Absolute cross-sections have been obtained for each of the (d,p) and (d,) groups. Comparison with data in the recent Handbook of Modern Ion Beam Materials Analysis shows reasonable agreement (10–15%) for the (d,p) reactions on oxygen and carbon. However, in the case of nitrogen, the measured cross-section values are 70% larger than the Handbook data. Several silicon oxynitride samples have been analyzed, first at UWO using 850 keV deuterons, and subsequently at ANU using HIERDA and a 200 MeV Au beam. The resulting O/N-ratios agree to within 10%. The relative importance of radiation damage effects is briefly discussed.     

PWR safety/relief valve blowdown analysis experience

The paper describes the difficulties encountered in analyzing a PWR primary loop pressurizer safety relief valve and power operated relief valve discharge system, as well as their resolution. The experience is based on the use of RELAP5/MOD1 and TPIPE computer programs as the tools for fluid transient analysis and piping dynamic analysis, respectively.General approaches for generating forcing functions from thermalfluid analysis solution to be used in the dynamic analysis of piping are reviewed. The paper demonstrates that the “acceleration or wave force” method may have numerical difficulties leading to unrealistic, large amplitude, highly oscillatory forcing functions in the vicinity of severe flow area discontinuities or choking junctions when low temperature loop seal water is discharged. To avoid this problem, an alternate computational method based on the direct force method may be used. The simplicity and superiority in numerical stability of the forcing function computation method as well as its drawback are discussed.Additionally, RELAP modeling for piping, valve, reducer, and sparger is discussed. The effects of loop seal temperature on SRV and PORV discharge line blowdown forces, pressure and temperature distributions are examined. Finally, the effects of including support stiffness and support eccentricity in piping analysis models, method and modeling relief tank connections, minimization of tank nozzle loads, use of damping factors, and selection of solution time steps are discussed.