Numerical simulation of post yield fracture mechanics experiments as a basis for the transferability to components

As a necessary step in the chain of transferability from small specimens to actual structures the numerical evaluations of two crack-growth resistance experiments on the basis of the J-integral and utilising sidegrooved compact specimens of different sizes, tested at room temperature and at 285°C are discussed. The necessary experimental and numerical techniques are presented:

• -The partial unloading technique as applied in the IWM is applicable with high accuracy and reproducability in the relevant temperature range up to operating temperature.

• -The J-evaluation combined with a node shifting and releasing technique as implemented in the IWM-version of ADINA proved to be a powerful and economic tool even for parameter studies.

The results of the experiments and of the numerical evaluations are presented as force-displacement diagrams and as J-integral vs. crack extension curves. The good qualitative and quantitative agreement supports the experimental evaluation of J from the force-displacement diagram and validitates the numerical procedures to be applied and extended to real structues.

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.     

Fracture mechanics investigations on cylindrical large scale specimens under thermal shock loading

To investigate the crack growth and crack arrest behaviour of primary circuit materials large scale experiments were conducted on component-like specimens under pressurized thermal shock loading at MPA Stuttgart. The material characteristics varied from high tough material to low tough material with higher nil ductility transition temperature to simulate EOL or beyond EOL-state. All tests started from in-service conditions and were cooled down to room temperature. The specimens showed both stable and unstable crack growth and partly crack arrest. The crack growth behaviour was verified by post test calculations and could be explained with the help of the multiaxiality of the stress state.     

Applications of probabilistic fracture mechanics to FBR components

A probabilistic fracture mechanics code which evaluates fracture probability of a plate model with an elliptical surface crack caused by creep-fatigue crack growth has been developed. The code named PCCF (Probabilistic Fracture Mechanics Code for Creep-Fatigue Crack Growth) uses simplified methods of C^* and J-integral for evaluation of creep-fatigue crack growth and a stratified sampling method for two input variables to improve the solution convergency. According to the test analyses focused on an applied stress level using PCCF code, leak probability is sensitive to a stress level and increases rapidly when an applied stress is close to a yield stress level.     

The influence of the material toughness and the state of stress on fracture of large scale specimens

The influence of the material toughness on fracture behaviour of large scale tensile specimens is being described in this report. Selected large scale specimens show that the amount of stable crack growth prior to instability is affected by the constraint in the specimen. The constraint depends on the specimen geometry, the specimen size, and in the case of elastic plastic material behaviour on the ductility of the material. A possibility of estimating these influences is presented by quantifying the constraint with the multi-axiality quotient q.     

Fatigue crack propagation properties from small sized rod specimens

Mechanical properties characterization is needed in many industrial applications yet sufficient amount of material for fabricating standard-sized testing specimens is often not available. Techniques for testing miniaturized specimen must be adopted. Much effort has been made to develop techniques for impact, fracture toughness and tensile properties of sub-sized specimens. Work on the testing of fatigue properties is more limited. In this study, fatigue crack propagation behavior is evaluated from the growth of surface crack in a cylindrical rod under tension. Rods of various lengths and diameters were tested. As the size of the rod specimen is reduced, the fatigue crack growth rate tends to increase when correlated using the stress intensity factor range. This increase is explained largely by the decrease in the degree of premature crack closure in the small specimens. Valid fatigue crack growth data can be obtained among the specimens examined except on the crack growth on the surface of the smallest specimen, which has a length of 26 mm and diameter of 8 mm. Even so, valid data can still be elucidated on the latter specimen if the interior growth is considered. The dimensions of the latter specimen allow fatigue properties to be evaluated using broken remnants from impact or other test specimens.     

Probabilistic fracture mechanics of nuclear structural components: consideration of transition from embedded crack to surface crack

This paper describes a probabilistic fracture mechanics (PFM) analysis of aged nuclear reactor pressure vessel (RPV) material. New interpolation formulas of three-dimensional stress intensity factors are presented for both embedded elliptical surface cracks and semi-elliptical surface cracks. To investigate effects of transition from embedded crack to surface crack in PFM analyses, one of the PFM round-robin problems set by JSME-RC111 committee (i.e. aged RPV under normal and upset operating conditions) is solved, employing the interpolation formulas.     

Acoustic emission measurements on large scale tensile specimens within the FKS-program (research program integrity of components)

Within the FKS-Program (Research Program Integrity of Components) acoustic emission measurements, mostly done in the new 100 MN-machine at the MPA Stuttgart, were carried out on large flat and cylindrical specimens manufactured from partly modified reactor steels with the following purposes (1) to distinguish the different origins of acoustic emission, (2) to recognize the onset of subcritical crack growth and (3) to predict fracture.     

Degradation of fracture mechanics properties of reactor graphite due to burn-off

This paper evaluates the change in various mechanical and fracture mechanics properties of two kinds of graphite for high temperature gas-cooled reactors due to burn-off by air oxidation. Thermal shock resistance and thermal shock fracture toughness of the burn-off graphite are also quantitatively determined by using an arc discharge heating method. These results are expressed as a function of burn-off, B, by an empirical formula of the form; S = S₀exp(−nB), where S₀ and n denote respectively the initial value and the degradation exponent of the material. The empirical formulas for thermal shock are found to agree reasonably well with those calculated from the results of individually examining the effect of burn-off on the associated properties.     

Validation of simplified fracture mechanics methods by testing of real components

The evaluation of integrity of structural components is often based on the proof of leak-before-break (LBB). Leak-before-break behaviour in piping constitutes a fail-safe condition. Which means that, during multiplied loading conditions, a defect results at first in a leakage. The crack length which leads to the leakage is smaller than the critical through-wall crack length. Simplified fracture mechanics concepts are used for the demonstration of LBB. For this the conservative, safe calculation of the critical through-wall crack length for ductile failure is necessary. To validate simplified calculation methods for circumferential cracks (flow stress concept (FSC); plastic limit load (PLL)) and for axial cracks (Battelle approach (BMI); Ruiz approach (RUIZ)) all available experiments on real structural components, especially on pipes, were analysed and evaluated by the mentioned simplified methods (approximately 460 experiments). The methods were adapted by application of correction factors, mainly on the flow stress, to result in conservative (safe) and realistic (as near as possible to the experiments) predictions. Depending on method (FSC, PLL, BMI, RUIZ), crack orientation (circumferential and axial cracks) and type of material (ferritic and austenitic material) different definitions of flow stresses were established.     

Stress analysis incorporating fracture mechanics and materials aspects for components under complex loading

The title deals with a complex subject. Stress analysis with consideration of fracture mechanics and material properties is subject to research and development worldwide. A final answer is not possible. This is only an attempt to discuss the problem.In the following, three examples are discussed. Due to the size of the problems, extensive use of references (with more detailed information) is made. The examples are: a pressure vessel nozzle, a disc with crack, and a thick walled vessel.     

Application of fracture mechanics methods in safety analysis of piping components in subcreep and creep behavior

A survey and review program for the application of fracture mechanics methods in elevated temperature design analysis and safety evaluation was initiated in December 1976. The first report [1] surveyed and assembled the material for a critical review of the theories of fracture and the application of fracture mechanics methods to life prediction and safety analysis of piping components. The second report [2] provided the basic concepts and a review of the problem areas associated with the development of analytical and experimental programs for a systematic evaluation and comparison of the currently available fracture mechanics theories. The basis for such an evaluation was described in terms of a series of benchmark problems which accurately specify conditions of geometry, loading and environment characteristic of large diameter piping systems in nuclear service.The objective of this third report is to establish a data base and detail the additional analytical techniques needed to confirm the validity of existing analytical methods and improve the state of the art in current problematic areas effecting the interpretation and extension of safety evaluation methods. The need for such a program in the elevated temperature field has been demonstrated by a number of independent surveys on various safety aspects of LMFBR related structural analysis methods and matetials problems. The results of this program, however, will be applicable not only to reactor plants operating at elevated temperatures, but will also lead to improvements of light water reactor evaluation methods for operating and accident conditions.The current state of elevated temperature reactor design technology is embodied in the standards and codes which provide guidance and minimum requirements for systematic design and evaluation procedures. These, however, do not necessarily provide specific absolute values which, if satisfied in the course of design, will guarantee thirty to forty years of uninterrupted life. There are numerous assumptions and approximations embodied in these standards concerning materials behavior, damage mechanisms, and failure modes at elevated temperature. There are also numerous areas of uncertainty and conflicting opinion in the interpretation of the existing test data and in the analysis and evaluation methods. Furthermore, the standards and codes leave some areas to the judgement of the designer, some of which require explicit justifications, but no standards or rules are provided.The overall safety therefore lies, at the present time, in the combination of rigorous enforcement of current standards, judicious application of experience with high temperature equipment even if not in nuclear service, and the surveillance of actual operating conditions. In the past, one criterion proposed for elevated temperature design has been that the time for crack initiation should exceed the design life. However, due to the complexities of the piping structures and the nature of the stress history during service, the evaluation of initiation times is difficult and often leads to uneconomical designs. In addition defects may exist in the component before it enters service. Hence, the knowledge of the growth rates of cracks and the residual strength of the components containing cracks is important in a realistic design evaluation. For more brittle materials and lower temperature applications where plasticity is restricted, linear elastic fracture mechanics methods have been developed. For more ductile materials where the plastic zones near the cracks are larger, linear fracture mechanics methods are not directly applicable, but in these nonelastic cases the opening displacement and J integral methods of assessment have been proposed. In the complex situation encountered in nuclear power plant design, the analysis must also account for cyclic thermal strains, time dependent creep, and the effect of harmful environments which are not explicitly treated in the above-mentioned methods. In this report an in-depth review is presented in sufficient detail to illustrate the degree of agreement between the theoretical and empirical methods available in the literature and indicate the scope of the additional analyses and experimental work needed for the development of reliable safety evaluation methodology.For pure cylindrical bending, cracks perpendicular to the load start to grow when reaches a critical value which is generally larger than the corresponding critical uniaxial tension value. There appears to be a thickness effect in the bending case which is probably due to interference from the compressive sides of the crack.For a circular plate with lateral pressure and small lateral displacements, results agree with the bending data when using the nominal bending stress . For larger displacements when bulging occurs, the results agree with the tensile data when the nominal tensile stress is used.For curves surfaces, such as a cylinder under internal pressure, the data agree with the expression developed by Folias both for axial cracks under hoop stress σ and for circumferential cracks under axial stress σ Generally, the expressions were accurate up to , showing a tendency to be lower than the experimental data at higher values of the parameter. The parameter is a promising one.To study the influence of cracks at different angles to the applied load, analysis and data are available including the stress component parallel to the crack in the stress field around a crack tip. This, together with the concept of a critical circumferential stress at a critical distance (α = 0.1) ahead of the crack provides improved correlation with fracture predictions for both the angle of fracture and the critical stress intensity factor for the angled cracks in flat plates.For a hollow cylinder under torsion with angled cracks, the best correlation was given by the same analysis although the results were not as conclusive as for the flat plate. From elastic theory useful curves for the variation of K₁, K₂, and K₃ around the border of an elliptically shaped crack are available.In a plane stress fracture the addition of a biaxial stress produces an increase in the apparent fracture toughness compared with the uniaxial case. However, there is as yet no evidence to show that there would be the same increase in a plane strain situation. Hence, in the absence of biaxial information the uniaxial fracture data may be the most conservative for flat plates. However, for shells there will also be a curvature effect.In an analogous manner, fatigue crack propagation rates appear to be less rapid under biaxial stresses than under uniaxial stress. However, this shift is not great and generallly will be masked by other effects such as environment and temperature service situations.The analysis of cracks in weldments with residual stress effects are also available. In the case of a crack in a weld the estimated residual stress distribution agreed reasonably well with some experimental data for elastic conditions. Results indicate that there can be a tensile stress intensity factor even when the original residual stress distribution has changed to compressive. A point to remember is that residual stresses near welds can be beyond yield.An analysis based on Lagrangean mechanics is useful for indicating the different effects of liquids and gases as pressurizing media in hollow pipes. The results show that whereas gases maintain their pressure as a crack begins to propagate, the pressure in the liquid can quickly decrease so that subsequent catastrophic failure is less likely even in large diameter piping.     

Probabilistic fracture mechanics analysis of nuclear structural components: a review of recent Japanese activities

This paper describes a review of recent Japanese activities on probabilistic fracture mechanics (PFM) analyses. Japan Atomic Energy Research Institute (JAERI) has sponsored research committees on PFM organized by Japan Society of Mechanical Engineers (JSME) and Japan Welding Engineering Society (JWES) for more than 10 years. The purpose of the continuous activity is to establish standard procedures for evaluating failure probabilities of Japanese nuclear structural components such as PV&P and steam generator tube, combining the state-of-the-art knowledge on structural integrity of nuclear structural components and modern computer technology such as parallel processing. This paper shows two topics of the newest results of JWES committee, PFM analysis of aged reactor pressure vessel considering embedded cracks and PFM analysis of piping considering seismic loading, and one topic by JAERI itself, development of PTS analysis code for transient loading (PASCAL).     

Coupled phenomenological and fracture mechanics approach to assess the fracture behaviour of TWC piping component

The present study demonstrates the numerical prediction of experimental specimen J-R curve using Gurson-Tvergaard-Needleman phenomenologically based material model. The predicted specimen J-R curve is used to determine the geometric independent initiation fracture toughness (J_SZWc) value that compares well with experimental result. Using the experimentally determined and numerically predicted J_SZWc values and specimen J-R curves, the accuracy of predicting the fracture behaviour of the cracked component is judged. Thus the present study proposed a coupled phenomenological and fracture mechanics approach to predict the crack initiation and instability stages in cracked piping components using numerically predicted specimen J-R curve obtained from tensile specimens testing data.     

Comparison of fracture toughness measurements from ferritic steel compact and surface-flawed specimens

Comparisons are made between predicted values of stress for initiation of crack growth in surface-flawed specimens and experimentally determined values. The comparisons are made for test temperatures corresponding to the lower shelf and the lower transition region which have elastic and elastic-plastic conditions, respectively. Predictions of stress levels for initiation of crack growth are based on Appendix A, Section XI of the ASME Boiler and Pressure Vessel Code and on an approach developed by Newman-Raju. The experimental results are based on acoustic emission techniques used to detect loads corresponding to crack initiation; their use in the comparison involved both the measured elastic-plastic stress value and an “equivalent” elastic stress.Evaluation of the analytical approaches showed that neither method was consistently more conservative over the full range of input dimensions. For tests conducted at lower-shelf temperatures (where very little plastic deformation occurs), the predicted stresses were lower than experimental values. At higher temperatures (where increasing amounts of plastic deformation occurs), some nonconservative predictions were made.A correlation is noted between the predicted-to-experimental stress ratio and a parameter used to quantify the severity of the surface flaw. This correlation may provide a basis for an empirical method for predicting the stress required to initiate crack growth.     

Application and evaluation of fracture mechanics failure concepts to precracked vessels

The elastic-plastic fracture mechanics concepts R-curve method, Two Criteria Approach, COD concept and Battelle formula were applied on three tested vessels made of low and high tough and fine grained structural steel and X 8 Ni 9 with an axial notch on the outer surface. Apart from the R-curve method for the vessel made of low tough material, failure loads were conservatively calculated. The COD concept could not be applied to these vessels and failure geometries using the well known design curve. A modification of the COD concept by means of FE-calculations was made so that a correlation between the displacement at the crack tip and at the vessel surface could be determined. With this procedure, the calculated load at fracture was only 8% below the experimental result.     

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.     

The application of constraint based fracture mechanics to engineering structures

Elastic-plastic crack tip fields can be characterised by two parameters, J and T/Q which describes crack tip constraint. This forms the foundation of a constraint based fracture mechanics in which toughness is expressed as a function of constraint in the form of a J–(T/Q) locus. The enhanced toughness associated with shallow cracks and defects can be used in a systematic manner by constraint matching, and implemented through a simple modification to a failure assessment diagram. This methodology enables the conservatism associated with the use of deeply cracked fracture toughness measurements to be relaxed. In this work these methods have been applied to a tubular welded joint.     

Three-dimensional interpretation of cleavage fracture tests of cladded specimens with local approach to cleavage fracture

Electricité de France has conducted during these last years an experimental and numerical research programme in order to evaluate fracture mechanics analyses used in nuclear reactor pressure vessels integrity assessment, regarding the risk of brittle fracture. Two cladded specimens made of ferritic steel A508 Cl3 with stainless steel cladding, and containing shallow subclad flaws, have been tested in four point bending at very low temperature to obtain cleavage failure. The crack instability was obtained in base metal by cleavage fracture, without crack arrest. The tests have been interpreted by local approach to cleavage fracture (Beremin model) using three-dimensional finite element computations. After the elastic–plastic computation of stress intensity factor K_J along the crack front, the probability of cleavage failure of each specimen is evaluated using m, σ_u Beremin model parameters identified on the same material. The failure of two specimens is conservatively predicted by both analyses. The elastic–plastic stress intensity factor K_J in base metal is always greater than base metal fracture toughness K_1c. The calculated probabilities of cleavage failure are in agreement with experimental results. The sensitivity of Beremin model to numerical aspects is finally exposed.