The J integral evaluation of a nozzle corner crack under thermal transient loading condition

This paper presents the results of the evaluation of the three dimensional J integral of a nozzle corner crack which is initiated by fatigue under thermal transient loading conditions of a BWR type reactor vessel. Analyses are carried out by using the finite element method in the following two cases. One case consideres the effect of the stainless steel cladding deposited over the inside surface of the reactor vessel, and the other neglects it. In both cases, the extended J integral concept, called integral, is used to obtain the path independent J value in the thermal stress fields.By changing the shapes and the dimensions of the crack, some elastic analyses are carried out in the two dimensional space. The effects of the cladding are studied qualitatively, and the integrals are compared with the critical J value, and discussed.Three dimensional values along the three dimensional crack front are evaluated for the embedded crack. The results are compared with those for two dimensional analysis.The nozzle corner crack is treated under thermal transient condition and distributions of values, and their change with time is obtained. The shapes and dimensions are changed by the assumption that the crack growth occurs at the point where the vector has its maximum, and the three dimensional shape of the propagating crack is estimated.     

Constraint effects on fracture toughness of impact-loaded, precracked Charpy specimens

Impact-loaded, precracked Charpy specimens often play a crucial role in irradiation surveillance programs for nuclear power plants. However, the small specimen size B = W = 10 mm limits the maximum value of cleavage fracture toughness J_c that can be measured under elastic—plastic conditions without loss of crack tip constraint. In this investigation, plane strain impact analyses provide detailed resolution of crack tip fields for impact-loaded specimens. Crack tip stress fields are characterized in terms of J—Q trajectories and the toughness-scaling model which is applicable for a cleavage fracture mechanism. Results of the analyses suggest deformation limits at fracture in the form of b > MJ_c/σ₀, where M approaches 25–30 for a strongly rate-sensitive material at impact velocities of 3–6 m s⁻¹. Based on direct comparison of the static and dynamic J values computed using a domain integral formulation, a new proposal emerges for the transition time, the time after impact at which interial effects diminish sufficiently for simple evaluation of J using the plastic η factor approach.     

Study on the effect of the crack length on the JIC value

The ductile fracture tests are carried out using compact type (CT) specimen, three point bend specimen and center cracked tension (CCT) specimens made of A533B steel and aluminum alloy with different crack lengths. The effect of the crack tip constraint on the microscopic fracture behavior is studied by the scanning electron microscope (SEM). It is shown that the apparent J_IC value increases due to the decrease of the crack tip constraint. It is pointed out that the increase of the apparent J_IC value is partly due to the error of the conventional equation to estimate the J value. Based on the FEM analyses, these apparent J_IC values are corrected and are compared with the valid J_IC values. The good co-relation between apparent J_IC value and the Q factor, proposed by O'Dowd and Shih, is shown for all the specimens. The FEM analyses based on the Gurson's constitutive equation is also carried out. The effect of the constraint on the crack tip field is discussed.     

Ontario hydro's leak before break approach: Application to the darlington (candu) nuclear generating station a

Ontario Hydro has developed a leak before break (LBB) approach for application to the large diameter heat transport piping for Darlington NGS A as an alternative to the provision of pipewhip restraints. This approach has been applied to pipe sizes which are equal to or greater than 530 mm (21 in. NPS). The proposed LBB approach incorporates assessments at several levels to provide assurance against catastrophic rupture. A comprehensive and systematic review of pipe failure mechanisms is considered the first important step in establishing role and applicability of the LBB concept. The elements integral to the approach are those related to demonstration of crack stability utilizing fracture mechanics methods and those related to leak rate predictions and leakage detection capability. For evaluation of crack stability the J-integral/tearing modulus (J/T) method has been selected. Results from an extensive material test program from actual heat transport piping, forgings, associated welds and heat affected zones as inpur to EPFM analyses provide the J-resistance and J—T curves. The details of EPFM analyses for a straight pipe with a circumferential crack and a piping elbow with a central longitudinal throughwall crack are presented here. Additionally, results of crack opening detail, the effects of crack face pressure, the predictions of LEAK RATE code and an assessment of the leakage detection capability are presented.     

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.     

Elastic-plastic analysis of small cracks in tubes under internal pressure and bending

Elastic-plastic finite element analyses were conducted to generate new solutions of J-integral and crack-opening displacement (COD) for short through-wall cracks in pipes subjected to combined bending and tension loads. The results are presented in terms of the well-known GE/EPRI influence functions to allow comparisons with some limited results in the literature. Two different pipe pressures with values of 7.24 MPa (1050 psi) and 15.51 MPa (2250 psi) simulating BWR and PWR operating conditions, respectively, were used to evaluate the effects of pressure on J and COD. Pipes with various radius-to-thickness ratios, crack sizes, and material parameters were analyzed. Limited analyses were also performed to evaluate the effects of hoop stresses in pipes under pure pressure loads. The results suggest that the fracture response parameters can be significantly increased by pressure-induced axial tension for larger crack size, material hardening constant, and radius-to-thickness ratio of the pipe. The presence of pressure-induced hoop stresses also increases the fracture response, but in low-hardening materials their effects are insignificant due to small plastic-zone size that was expected for the intensity of pipe pressure and crack size considered in this study. However, for high-hardening materials when the plastic-zone size is not negligible, the hoop stresses can moderately increase J and COD.     

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.     

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 use of acoustic emission to determine characteristic dynamic strength and toughness properties of steel

The dynamic J integral at crack initiation (J_id) and dynamic yield stress (σ_yd) are useful parameters to characterize elastic-plastic material behaviour under rapid loading rates. The critical step for evaluating J_id and σ_yd under the condition of the three point impact bending test is the detection of the crack initiation and of the yield point in the impact load–deflection curve, respectively. This paper presents an acoustic emission (AE) based method to determine the ductile crack initiation and additionally the beginning of yield. The experimental techniques used to evaluate σ_yd and J_id include both instrumented pendulum impact tests with the AE transducer within the striker (tup) and medium rate three point bend (TPB) tests with additional AE transducers on the specimen surface. Results obtained from the tests indicate that the AE method is capable of detecting general yielding and the onset of ductile crack growth (initiation). Different types of pulse shaped AE signals can be observed. They were connected with characteristic features during the loading process.     

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.     

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.     

Round-robin activities on finite element analyses of elastic-plastic fracture in Japan

The establishment of the leak-before-break (LBB) concept requires a method to evaluate the fracture characteristics. The finite element method can be used for this purpose but the solution is more or less influenced by the method employed. In this study, two round-robin analyses are performed for three-dimensional crack problems. The first problem is for surface crack growth in a carbon steel plate subjected to tension loading. Ten solutions are obtained by ten participants, and calculated results are compared with each other as to the applied load, displacement and J-integral. Though the relation between applied load and displacement is affected by modeling of the stress-strain curve, fairly good agreement is obtained between the solutions. The second problem is for a circumferential part-through crack in a carbon steel pipe subjected to a bending moment. Nine solutions are obtained by eight participants. The difference between the solutions is relatively significant as to the relation between J-integral and load-point displacement. A discussion is made about the sources of difference between each solution.     

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.     

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.     

Elastic-plastic fracture mechanics analysis of a pressure vessel with an axial outer surface flaw

The stress and strain state in pressure vessel containing an axial semi-elliptical surface flaw is analyzed by elastic-plastic finite element (FE) calculations. The variation of J along the crack front is presented. Stresses and strains in the vicinity of the surface flaw are compared with those of a compact specimen of the same material at a similar J level. The FE results are taken to examine the ductile crack growth obtained in a vessel test and to discuss the validity of J-controlled crack growth. It is shown that the local constraint of the component affects the crack resistance significantly and that, therefore, J_R-curves have to account for the varying triaxiality of the stress state. This improved two parameter approach yields a much better prediction of the stable crack growth and, especially, is able to describe the canoe shape of the surface crack.     

Elastic-plastic finite element analyses of stable crack growth and fracture instability in a girth welded pipe

Detailed elastic-plastic finite element fracture mechanics analyses were conducted on a 16 inch diameter Type 304 stainless steel pipe containing a circumferential through-wall crack located in a girth weld. Calculations were performed to analyze the welded pipe treated as (1) a monolithic pipe entirely composed of the base metal, and (2) a composite of base metal and weldment. In the latter, each constituent was assigned distinct mechanical and fracture properties. In both solutions applied J values were calculated for a fixed axial load combined with a monotonically increasing applied bending moment. The material J-resistance curves appropriate for the two problems were each used to initiate and grow the initial crack in a stable manner until fracture instability occurred under load control. It was found that the extent of stable crack growth and the applied loads at fracture instability are distinctly different in the two analyses. It is concluded that more precise fracture mechanics approaches than those now in current use are required for accurate assessments of weld cracking problems.     

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.     

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.     

Effect of loading rate upon fracture behavior of ferritic steel under large scaled yielding

Dynamic loading to ferromagnetic materials and large scaled yielding result in peak or valley and non-linear curve, respectively, on the Direct Current Potential Drop (DCPD) versus Crack Opening Displacement (COD) plots, which make it difficult to determine the crack initiation point. In this work high intensity of current up to 100 A was applied to the specimens of SA106Gr.C ferritic steel and the crack growth behavior was directly monitored by a high speed camera to obtain the crack initiation point. The effects of loading rate up to 1200 mm min⁻¹ upon the fracture resistance were explored. As the results, it has been shown that, although no substantial difference was seen in the load–COD plots, the crack initiation and then J_i and J–R curve were quite sensitive to the loading rate. That is, under the loading rate of 300 mm min⁻¹ the material showed the worst fracture resistance than under static loading and even under the higher loading rates of 600 and 1200 mm min⁻¹. Also applying the high speed camera and high current source have been proved to be an effective way to find out the accurate crack initiation point and to compensate the pulse of DCPD due to the ferromagnetic effect.     

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.