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.     

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.     

Numerical investigation of ductile crack growth behavior in a dissimilar metal welded joint

In this paper, the finite element method (FEM) based on GTN model is used to investigate the ductile crack growth behavior in single edge-notched bend (SENB) specimens of a dissimilar metal welded joint (DMWJ) composed of four materials in the primary systems of nuclear power plants. The J-Δa resistance curves, crack growth paths and local stress-strain distributions in front of crack tips are calculated for eight initial cracks with different locations in the DMWJ and four cracks in the four homogenous materials. The results show that the initial cracks with different locations in the DMWJ have different crack growth resistances and growth paths. When the initial crack lies in the centers of the weld Alloy182 and buttering Alloy82, the crack-tip plastic and damage zones are symmetrical, and the crack grow path is nearly straight along the initial crack plane. But for the interface cracks between materials and near interface cracks, the crack-tip plastic and damage zones are asymmetric, and the crack growth path has significant deviation phenomenon. The crack growth tends to deviate into the material whose yield stress is lower between the two materials on both sides of the interface. The different initial crack locations and mismatches in yield stress and work hardening between different materials in the DMWJ affect the local stress triaxiality and plastic strain distributions in front of crack tips, and lead to different ductile crack growth resistances and growth paths. For the accurate integrity assessment for the DMWJ, the fracture toughness data and resistance curves for the initial cracks with different locations in the DMWJ need to be obtained.     

A practical method for computation of ductile crack growth by means of finite elements and parametric 3D-modelling

The present paper originates from a contribution to the safety assessment of a reactor pressure vessel (RPV). Investigations evaluating the safety against brittle fracture (exclosure of crack initiation and arrest assessments) are completed by calculations concerning ductile crack extension. Crack geometries including the expected crack extension are generated parametrically by a computer code and are used for further calculations with finite element programs. J-integrals of ductile growing cracks located between two comparative contours are determined by interpolation. The comparative contours are loaded by instationary temperature and pressure fields and are evaluated in advance. Taking the stability condition into consideration, the ductile crack extension is determined by pursuing the equilibrium between loading and crack resistance. The automatic modelling and a mathematical program processing the finite element results evaluate the crack growth of the finite element results very effectively.     

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.     

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.     

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.     

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.     

Time dependent ductile crack extension in A533B class I steel

Four wide plate specimens manufactured in A533B Class I, 90 mm thick by 500 mm wide containing through-thickness or semi-elliptical surface fatigue cracks were tested at +70°C. These specimens were subjected to a series of increasing applied loads, each of 100 h duration, until failure. Testing was performed using a computer interactive 40 MN load controlled tensile testing rig. Values of the fracture toughness parameters J and crack tip opening displacement (CTOD) were derived from the recorded values of applied load, plate extension and crack mouth opening displacement.The influence of loading rate, degree of yield containment and crack orientation on the time dependent behaviour is assessed and compared with data obtained from wide plate and bend tests under monotonic loading and from bend tests conducted with a variable loading rate, with hold periods, under crack mouth opening control. Interpretation of the results provides a clearer understanding of low temperature time dependent ductile crack extension and enables the identification of the conditions under which this phenomenon is apparent, to allow the necessary adjustments to failure assessments.     

Creep-fatigue crack propagation behavior in a surface cracked plate

A series of experiments were performed in order to clarify the surface crack growth behavior under creep-fatigue condition. Type 304 stainless steel was tested at 550°C and 650°C. Specimens were plates with a surface notch. Loading patterns were axial fatigue, bending fatigue, axial creep-fatigue and bending creep-fatigue. As results were obtained: (1) the beach mark method was available to measure the changes of the crack front shape after the test; (2) the electrical potential method was available to measure the changes of the crack front shape in real time; (3) the crack front shape was affected by the loading mode; and (4) ΔJ and ΔJ_c calculated from the proposed simplified method could characterize the surface crack growth rate.     

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.     

Charpy upper shelf energy and crack resistance

The correlation between Charpy upper shelf energy and crack resistance was investigated by means of instrumented impact tests (ISO-V specimens) and fracture mechanics tests (CT specimens) using four different steels. The strict definition of the Rice J-integral was not applied to the ISO-V specimens. Defining J as the first derivative of deformation energy, it was possible to obtain crack resistance curves of ISO-V specimens and CT specimens. This correlation has been obtained in steels of yield strength between 365 and 480 N/mm² and is independent of the material. The mechanical basis of this relation can be understood in terms of the criterion for ductile fracture. 60 to 80% of the upper shelf energy is consumed by stable crack growth according to these experiments. The upper shelf energy is useful as a screening test for crack resistance curves. More definite crack resistance values can be estimated from instrumented impact test carried out in dependence on temperature. It seems to be possible to estimate the required upper shelf energy to be specified in regulations with respect to ductile failure safety on the basis of materials mechanics.     

Analysis of stable crack growth of a semi-elliptical surface crack by numerical simulation

In the present paper, the canoeing effect during stable crack growth of a semi-elliptical surface crack in a side-grooved panel under tension was investigated by means of a three-dimensional elastic-plastic finite element analysis. The numerical crack growth simulation was performed by using crack mouth opening displacement resistance curves obtained from experiment on panels by the multi-specimen procedure. The influence of the crack tip constraint and the stress triaxiality on the ductile crack resistance property was studied. It is shown that the tearing modulus T_JR increases proportionally with decreasing stress triaxiality implying constraint dependent J_R-curves.     

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.     

Micromechanisms and toughness for cleavage fracture of steel

A complete understanding of the fracture mechanisms of steel in the ductile/brittle transition region requires analysis not only of crack initiation, but also of crack propagation. This paper reviews micrographic and fractographic experiments that give insight into both phenomena, and suggests a frame-work through which both may be related.Unstable cleavage crack initiation can occur after some blunting of the original fatigue precrack or after some stable crack growth. In either event, instability appears to be triggered by the fracture of a brittle micro-constituent ahead of the precrack. The large scatter in reported K_Ic values within the transition region reflects the size distribution and relative scarcity of these “trigger” particles.While a large number of models have attempted to correlate toughness in the ductile/brittle transition regime to events occurring ahead of the crack tip, surprisingly little attention has been paid to events occurring behind the crack front. Fractographic evidence as well as metallographic sectioning of arrested cracks show that the mechanism of rapid crack propagation by cleavage is affected strongly by partial crack-plane deflection which leaves unbroken ligaments in its wake. The tearing of these ligaments by dimple-rupture is the dominant energy-absorbing mechanism. Etch-pit experiments using an Fe-Si alloy show that the crack-tip stress intensity based on plastic zone size is extremely low. It is suggested that the mechanism of crack arrest should be modeled using a sharp crack which is restrained by a distribution of discrete pinching forces along its faces. The same model is applied to crack initiation.     

First spinning cylinder test analysis using a local approach to fracture

In recent years, several experimental programmes on large-scale specimens have been organized to evaluate the capabilities of the fracture mechanics concepts employed in structural integrity assessment of pressurized water reactor pressure vessels. During the first spinning cylinder test, a geometry effect was revealed experimentally showing the difficulties of transferring toughness data from small-scale to large-scale specimens. An original analysis of this test, by means of a local approach to fracture, is presented in this paper. Both compact tension specimen and spinning cylinder fracture behaviour were computed using a continuum damage mechanics model developed at EDF. We confirmed by numerical analysis that the cylinder's resistance to ductile tearing was considerably larger than in small-scale fracture mechanics specimen tests, about 50%. The final crack growth predicted by the model was close to the experimental value. Discrepancies in J R curves seemed to be due to an effect of stress triaxiality and plastic zone evolution. The geometry effect inducing differences in resistance to ductile tearing of the material involved in the specimens can be investigated and explained using a local approach to fracture methodology.     

Calculation of stress intensity factors of surface cracks in complex structures: Application of efficient computer program EPAS-J1

A finite element computer program EPAS-J1 was developed to calculate the stress intensity factors of three-dimensional cracks. In this program, the stress intensity factor is determined by the virtual crack extension method together with the distorted elements allocated along the crack front. The program also includes the connection elements based on the Lagrange multiplier concept to connect such different kinds of elements as the solid and shell elements, or the shell and beam elements. For the structure including the three-dimensional surface cracks, the solid elements are employed only at the neighborhood of the surface crack, while the remainder of the structure is modeled by the shell or beam elements since the crack singularity is very local. Computer storage and computational time can be highly reduced with the application of the above modeling for calculation of the stress intensity factors of the three-dimensional surface cracks, because the three-dimensional solid elements are required only around the crack front.Several numerical analyses were performed by the EPAS-J1 program. At first, the accuracies of the connection element and the virtual crack extension method were confirmed using the simple structures. Compared with other techniques of connecting different kinds of elements such as the tying method or the method using an anisotropic plate element, it is found that the present connection element provides better results than the others. It is also found that the virtual crack extension method provided the accurate stress intensity factor. Furthermore, the results are also presented for the stress intensity factor analyses of cylinders with longitudinal or circumferential surface cracks using the combination of various kinds of elements together with the connection elements.     

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.     

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.     

Boundary element analysis on interaction of external surface crack and embedded crack in a pressurized cylinder

This paper analyzes the interaction of external semi-elliptical surface crack and embedded elliptical crack in a longitudinal plane of a pressurized cylinder. No numerical solution appears to be available in the literature so far. The analyzed ratios of the crack depth to crack length (b_S/a_S and b_E/a_E) are 0.25 and 1.0; the distance between both cracks (s₁/b_min) ranges from 0.5 to 2.0. In total 24 crack configurations are analyzed and the stress intensity factors along the crack front are presented. The numerical results show that the interaction makes the stress intensity factors along the crack fronts increased for both the surface crack and the embedded crack, compared with the single surface crack and single embedded crack. For the given crack sizes, the stress intensity factors for both the surface crack and embedded crack increase with the decrease of the distance between two cracks. The numerical analyses are carried out by the hybrid boundary element method.