The application of elastic-plastic fracture mechanics parameters in fracture safe design

The report summarizes some of the methods which are currently used for assessing the fracture toughness of materials under elastic and elastic-plastic conditions. The main parameters which are considered are (1) plane strain fracture toughness (K_Ic), (2) equivalent energy (K_Icd), (3) contour integral (J) and (4) crack opening displacement (COD). Gross strain crack tolerance and stress concentration methods are also discussed.It is concluded that of these parameters, the contour integral and the crack opening displacement have most potential for future development. These two parameters are shown to be equivalent, however, at the present stage of development the COD concept has several advantages over the J concept. Firstly, the COD concept is able to take into account, secondary stresses, such as welding residual stresses. Because these stresses are in equilibrium, they do not appear in energy measurements to evaluate J. Secondly, the COD value is a physical measure of the crack tip conditions which includes the effect of stress state and thickness. It is, therefore, possible to measure and calculate COD levels for cracks in real structures. It is not possible to evaluate J for real structures since J methods are appropriate only to in-plane problems. This also means that partial wall (thumbnail) flaws are better characterized by the COD concept.The COD concept has been developed to a stage where it is possible to estimate the significance of flaws in welded structures provided the toughness of the material and the acting stresses or strains are known. This development is described and the method used to analyze tests on model pressure vessels with 6″ thick walls. A comparison is made with other methods, and it is concluded that although the COD analysis gives conservative estimates of the flaw size to cause failure, further work is necessary to be able to predict vessel burst conditions when failure is preceded by extensive plasticity and stable ductile tearing. A simple nomogram to determine COD levels to ensure leak before break conditions is also developed.     

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.     

Assessment of cracks existing in the strain concentrated region from a viewpoint of brittle fracture

The significance of cracks existing in the strain concentrated region is discussed from a viewpoint of brittle fracture.In this study, the J-integral, of which the mathematical treatment is easier and stricter than that of COD (crack opening displacement) is considered as the fracture parameter. Also, averaged local strain, , in the strain concentrated region without a crack is considered as the mechanical parameter which characterizes the state of the elastic-plastic region generated near the stress raiser. The relation between the J-integral of the cracked body and the local strain is investigated experimentally and theoretically with the aid of the elastic-plastic finite element analysis.Brittle fracture tests on the strain concentration models of the four kinds of the structural steel (SM41, SM50, HT80 and A508 C1.3) show that a newly proposed J design curve provides a good estimation for the strength of brittle fracture from a crack existing in the stress/strain concentrated region.     

Probabilistic elastic-plastic fracture analysis of circumferentially cracked pipes with finite-length surface flaws

A probabilistic model was developed for predicting elastic-plastic fracture response and reliability of circumferentially cracked pipes with finite-length, constant-depth, internal surface cracks subject to remote bending loads. It involves engineering estimation of energy release rate, J-tearing theory for characterizing ductile fracture, and standard methods of structural reliability theory. The underlying J-estimation model is based on the deformation theory of plasticity, a constitutive law characterized by power law model for stress-strain curve, and an equivalence criterion incorporating reduced thickness analogy for simulating system compliance due to the presence of a crack. New analytical equations were developed to predict J-integral and are shown to be fairly accurate when compared with generally more accurate elastic-plastic finite-element results. Using this J-estimation method, fast probability integrators and simulation methods were formulated to determine the probabilistic characteristics of J. The same methods were used later to predict the probability of crack initiation and net-section collapse as a function of the applied load. Numerical examples are provided to illustrate the proposed methodology. The results show that probabilistic analysis based on net-section collapse (without any margin) may significantly overpredict the reliability of surface-cracked pipes.     

Failure assessment of RPV nozzle under loss of coolant accident

In case of a postulated loss of coolant accident (LOCA) of a reactor pressure vessel (RPV), the nozzle region experiences higher stresses and lower temperatures than the remaining part of the RPV. Thus, the nozzle is to be considered in the RPV safety assessment. For a LOCA event, three-dimensional elastic–plastic finite element calculations of stresses and strains in the intact RPV were performed. Using the substructure technique, fracture mechanics analyses were then carried out for several postulated cracks in the nozzle corner and in the circumferential weld below the nozzle. For different crack geometries and locations, the J-integral and the stress intensity factor were calculated as functions of the crack tip temperature. Based on the K_IC-reference curve and the J_R curve, both brittle and ductile instability of the postulated cracks were excluded. In order to reduce the expenses of three-dimensional finite element analyses for various crack geometries, an analytical procedure for calculating stress intensity factors of subclad cracks in cylindrical components was extended for cracks in the nozzle corner.     

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.     

Investigation on constraint effect of reactor pressure vessel under pressurized thermal shock

In recent years, the integrity of reactor pressure vessels (RPVs) under pressurized thermal shock (PTS) accident has been treated as one of the most critical issues. Under PTS condition, the combination of thermal stress due to a steep temperature gradient and mechanical stress due to internal pressure causes considerable tensile stress inside the RPV wall. As a result, cracks on the inner surface of RPVs can experience elastic-plastic behavior that can be explained using the J-integral. In such a case, however, the J-integral may possibly lose its validity due to the constraint effect. The degree of constraint effect is influenced by the loading mode, the crack geometry and the material properties. In this paper, three-dimensional finite element analyses are performed for various surface cracks to investigate the effect of clad thickness and crack geometry on the constraint effect. A total of 36 crack geometries are analyzed and results are presented by the two-parameter characterization based on the J-integral and the Q-stress.     

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.     

Investigation of the ductile fracture properties of type 304 stainless steel plate, welds, and 4-inch pipe

J-integral fracture toughness tests were performed on welded 304 stainless steel 2-inch plate and 4-inch diameter pipe. The 2-inch plate was welded using a hot-wire automatic gas tungsten arc process. This weldment was machined into 1T and 2T compact specimens for single specimen unloading compliance J-integral tests. The specimens were cut to measure the fracure toughness of the base metal, weld metal and the heat affected zone (HAZ). The tests were performed at 550°F, 300°F and room temperature. The results of the J-integral tests indicate that the J_Ic of the base plate ranged from 4400 to 6100 in lbs/in² at 550°F. The J_Ic values for the tests performed at 300°F and room temperature were beyond the measurement capacity of the specimens and appear to indicate that J_Ic was greater than 8000 in lb/in². The J-integral tests performed on the weld metal specimens indicate that the J_Ic values ranged from 930 to 2150 in lbs/in² at 550°F. The J_Ic values of the weld metal specimens tested at 300°F and room temperature were 2300 and 3000 in lbs/in² respectively. One HAZ specimen was tested at 550°F and found to have a J_Ic value of 2980 in lbs/in² which indicates that the HAZ is an average of the base metal and weld metal thoughness. These test results indicate that there is a significant reduction in the initiation fracture toughness as a result of welding.The second phase of this task dealt with the fracture toughness testing of 4-inch diameter 304 stainless steel pipes containing a gas tungsten arc weld. The pipes were tested at 550°F in four point bending. Three tests were performed, two with a through wall flaw growing circumferentially and the third pipe had a part through radial flaw in combination with the circumferential flaw. These tests were performed using unloading compliance and d.c. potential drop crack length estimate methods. The results of these test indicate that the presence of a complex crack (radial and circumferential) reduces in the initiation toughness and the tearing modulus of the pipe material compared to a pipe with only a circumferentially growing crack.     

Observations on the effect of post-weld heat treatment on J-resistance curves of sa-106b seamless piping welds

Ontario Hydro has developed a leak-before-break (LBB) methodology for application to large diameter piping (21, 22 and 24 inch) Schedule 100 SA106B heat transport (HT) piping as a design alternative to pipe whip restraints and in recognition of the questionable benefits of providing such devices. Ontario Hydro's LBB approach uses elastic-plastic fracture mechanics (EPFM).In order to assess the stability of HT piping in the presence of hypothetical flaws, the value of the material J-integral associated with crack extension (J— R curve) must be known. In a material test program J-resistance curves were determined from various pipe heats and four different welding procedures that were developed by Ontario Hydro for nuclear Class 1 piping. The test program was designed to investigate and quantify the effect of various factors such as test temperature, crack plane orientation and welding effects which have an influence on fracture properties. An acceptable lower bound J-resistance curve for the piping steels and welds were obtained by machining maximum thickness specimens from the pipes and weldments and by testing side-grooved compact tension specimens. This paper addresses the effect of test temperature and post-weld heat treatment on the J-resistance curves from the welds.The fracture toughness of all the welds at 250°C was lower than that at 20°C. Welds that were post-weld heat treated showed high crack initiation toughness, J_lc, rising J-resistance curves and stable and ductible crack extension. Non post-weld heat treated welds, while remaining tough and ductile, showed comparatively lower J_Ic, and J-resistance curves at 250°C. This drop in toughness is possibly due to a dynamic strain aging mechanism evidenced by serrated load-displacement curves. The fracture toughness of non post-weld heat treated welds increased significantly after a comparable post-weld heat treatment.The test procedure was validated by comparing three test results against independent tests conducted by Materials Engineering Associates (MEA) of Lanham, Maryland. The J_Ic and J-resistance curves obtained by Ontario Hydro and MEA were comparable.     

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.     

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.     

The effects of the stainless steel cladding in pressurized thermal shock evaluation

Fracture mechanics analysis is the key element of the integrity evaluation of the nuclear reactor pressure vessel (RPV), such as the pressurized thermal shock (PTS) analysis and P–T limit curve construction. However, the existence of stainless steel cladding, with different thermal, physical, and mechanical property at the inner surface of reactor pressure vessel complicates the fracture mechanics analysis. In this paper, the simple analytical treatment schemes to calculate the stress and resulting stress intensity factor at the tip of the flaws in the RPV with stainless steel cladding are introduced. For a reference thermal–hydraulic boundary condition, the effects of cladding thermal conductivity and thermal expansion coefficients on the stress intensity factor of surface flaws were examined. Also, the effects of cladding plasticity and thickness were quantitatively examined. The analysis results showed that the existence of the stainless cladding had significant impacts on the RPV failure probabilities.     

Evaluation of SCC crack behavior in zirconium and zircaloy-2 using nonlinear fracture mechanics parameters

Applicability of nonlinear fracture mechanics parameters, i.e. J-integral, crack tip opening displacement (CTOD), and crack tip opening angle (CTOA), to evaluation of stress corrosion crack (SCC) propagation rate was investigated using fully annealed zirconium plates and Zircaloy-2 tubing, both of which produce SCC with comparatively large plastic strain in an iodine environment at high temperatures.Tensile SCC tests were carried out at 300°C for center-notched zirconium plates and internal gas pressurization SCC tests at 350°C, for Zircaloy-2 tubing, to measure the SCC crack propagation rate. The J-integral around semi-elliptical SCC cracks produced in Zircaloy-2 tubing was calculated by a three-dimensional finite element method (FEM) code.The test results revealed that the SCC crack propagation rate dc/dt could be expressed as a function of the J-integral, which is the most frequently used parameter in nonlinear fracture mechanics, by the equation dc/dt = C · Jⁿ, where C and n were experimental constants.Among the other parameters, CTOD and CTOA, the latter appeared to be useful for assessing the crack propagation rate, because it had a tendency to hold a constant value at various crack depths.     

Pressure Recovery in Diffuser for Discharge Flows from Gas Centrifuges Rotating at High Mach Numbers

This paper deals with the irradiation effects on the thermal shock resistance Δ = σ_tk/Eα (σ_t : tensile strength, k: thermal conductivity, E: Young's modulus, α: thermal expansivity) and the thermal shock fracture toughness ?=K_Ick/Eα (K_Ic : fracture toughness value of mode I) in addition to other mechanical properties such as the diametral compressive strength and fracture toughness of two kinds of near isotropic graphite neutron irradiated at 750～1,000°C to a dose of (1.1 ～ 1.5)10²¹ n/cm² (>29 fJ). One of the graphite specimen is an isostatically molded graphite IG-11 with fine grain petroleum coke and the other is a binderless molded graphite HCB-18 which was prepared using mesophase pitch carbon with very fine grain size. These measurements are carried out by means of disk testing method developed by us. Results show that both the thermal shock resistance and the thermal shock fracture toughness of the two kinds of graphite after irradiation decrease considerably in contrast with increasing trends of the usual mechanical strengths.     

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.

A critical survey on the application of plastic fracture mechanics to nuclear pressure vessels and piping

Plastic fracture mechanics techniques have been developed to treat the regime where extensive plastic deformation and stable crack growth occur prior to fracture instability in the tough ductile materials used in nuclear systems. As described in this paper, a large number of crack tip parameters can be used in a plastic fracture resistance curve approach. However, applications using the J-integral currently predominate. This parameter has significant advantages. It offers computational ease and can provide a lower bound estimate of the fracture condition. But, J also has a disadvantage in that only a limited amount of stable crack growth can be accommodated. The crack tip opening angle parameter, in contrast, can be valid for extensive stable crack growth. But, with it and most other realistic alternatives, the computational convenience associated with the J-integral is lost and finite element or other numerical methods must be employed. Other possibilities such as the two-criterion approach and the critical net section stress are also described in the paper. In addition, current research work focussed upon improving the theoretical basis for the subject is reviewed together with related areas such as dynamic plastic analyses for unstable crack propagation/arrest and creep crack growth at high temperatures. Finally, an application of plastic fracture mechanics to stress corrosion cracking of nuclear piping is made which indicates the possible anti-conservative nature of the current linear elastic assessments.     

Thermal stress initiated fracture as a fragmentation mechanism in the UO2-sodium fuel-coolant interaction

An analytic study was carried out to determine the applicability of the concept of thermal stress fragmentation to the UO₂-Na fuel-coolant interaction. Major emphasis was put on the fracture mechanics approach to assess whether or not the solidifying UO₂ would fracture under the thermally-induced stresses. It was found that the stress levels were sufficient to generate K_I values substantially in excess of the UO₂ fracture toughness K_IC. Thus, rapid instantaneous propagation of inherent flaws is anticipated.     

Large stable crack growth in fracture mechanics specimens

According to the J concept, information is reported about the crack resistance behaviour up to 8 mm crack growth of side-grooved CT-25 as well as CCT-25 specimens made from German standard steel StE 460. Numerical simulations controlled by J_R curves make the calculation of J from the stresses and strains of specimen models during large crack growth feasible. These data allow a comparison to standards and rules describing the evaluation of J from experiments. Using stress, strain and displacement fields from a plane-strain finite-element analysis, the extended J concept is discussed concerning larger ductile crack growth. Additionally, the distribution of other fracture mechanics parameters such as the crack tip opening displacement (CTOD) and the crack tip opening angle (CTOA) are presented for larger crack growth.     

The importance of the triaxiality modified J concept for the assessment of pressurized components with surface flaws

With the progress of stable crack growth of surface flaws observed in panels or pressure vessels a canoe-shaped crack front is formed. The crack propagation in the longitudinal direction is more pronounced that in the wall thickness direction. Therefore, the canoe effect is important with respect to a leak-before-break assessment because the actual through crack length is influenced by this effect. Based on the J integral concept crack initiation and crack propagation in ductile materials are described by J resistance curves which were found to be dependent on the constraint effect of the specimen geometry. Prediction of local crack growth by taking a conservative (flat) J_R-curve into account results in a nonconservative estimate of the axial extension of the surface crack [W. Brocks, H. Veith and K. Wobst, in K. Kussmaul (ed.), Fracture Mechanics Verification by Large Scale Testing, Mech. Eng. Publication Limited, London, 1991]. This means that the influence of local constraint effects on crack resistance has to be considered.Ductile crack growth of semi-elliptical surface cracks in side-grooved specimens F(SCTsg) under tension made from German standard steel StE 460 will be reported on. The development of the canoe effect of an SCTsg specimen was also analysed by a finite element simulation of ductile crack growth which was modelled by using the node shift and node release technique and controlled by crack mouth opening displacement versus crack growth curves from the experiment. The simulation allows the determination of local J_R-curves in dependence on the local multiaxility of the stress state to verify the constraint modified J concept. It is demonstrate that the slope of the J_R-curves decreases with increasing multiaxiality of the stress state near by the crack front.