Effect of reverse cyclic loading on the fracture resistance curve in C(T) specimen

Fracture resistance (J–R) curves, which are used for elastic–plastic fracture mechanics analyses, are known to be dependent on the cyclic loading history. The objective of this paper is to investigate the effect of reverse cyclic loading on the J–R curves in C(T) specimens. The effect of two parameters was observed on the J–R curves during the reverse cyclic loading. One was the minimum-to-maximum load ratio (R) and the other was the incremental plastic displacement (δ_cycle/δ_i), which is related to the amount of crack growth that occurs in a cycle. Fracture resistance tests on C(T) specimens with varying the load ratio and the incremental plastic displacement were performed, and the test results showed that the J–R curves were decreased with decreasing the load ratio and decreasing the incremental plastic displacement. Direct current potential drop (DCPD) method was used for the detection of crack initiation and crack growth in typical laboratory J–R tests. The values of crack initiation J-integral (J_I) and crack initiation displacement (δ_i) were also obtained by using the DCPD method.     

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.     

Low cycle fatigue and ductile fracture for Japanese carbon steel piping under dynamic loadings

Dynamic fracture behavior of circumferentially cracked pipe is important to evaluate the structural integrity of nuclear piping from the viewpoint of the LBB concept under seismic conditions. Fracture tests have been conducted for Japanese carbon steel (STS410) circumferentially through-wall cracked pipes that are subjected to monotonic or cyclic bending loads at room temperature. In the monotonic-loading tests, the maximum load to failure increases slightly with increasing loading rate. The failure cycles can be expressed simply by ratio of the load amplitude to the plastic collapse load. Fracture analysis has been also conducted to model the pipe tests. A new equation for calculating ΔJ for a circumferentially through-wall cracked pipe subjected to bending has been proposed. The failure cycles under cyclic loads are satisfactorily evaluated using an elastic-plastic fracture mechanics parameter ΔJ.     

Stable crack growth of axial flaws in pressure vessels

The ductile crack growth of axial through and part-through cracks in a vessel under internal pressure has been studied experimentally to contribute to the fundamental problem whether or not and under which conditions resistance curves obtained from specimens can be transferred to large scale components. The experiments and numerical analyses are part of a research program on fracture mechanics failure concepts for the safety assessment of nuclear components.Whereas only an averaged crack extension is determined in specimen tests, the local propagation of cracks may be of main importance for surface cracks in vessels and pipes. In the present experiments, the surface cracks revealed the well known canoe shape, i.e. a larger crack extension has occurred in the axial direction than in the wall thickness direction. Two of these tests have been analysed by finite element calculations to obtain the variation of the J-integral along the crack front and the stress and strain state in the vicinity of the crack. The local crack resistance appeared to depend on the local stress state. To Predict ductile crack extension correctly, J_R-curves have to account for the varying triaxiality of the stress state along the crack front.     

Leak-before-break and plastic collapse behaviour of statically indeterminate pipe system with circumferential crack

Much research has been carried out on Leak-Before-Break (LBB) behavior of pipes with cracks. However, most studies have been made on statically determinate pipe systems. Few studies have been made on LBB behavior of statically indeterminate pipe systems. Most pipe systems in nuclear power plants have supports and restraints, thus they can be considered as statically indeterminate pipe systems. From above points of view, LBB and plastic collapse behaviors of statically indeterminate pipe with circumferential crack and compliance were studied in this paper. A new method is proposed to analyze and evaluate the LBB and plastic collapse behavior of a statically indeterminate structure. The pipe system of which one end is clamped and the other is supported with compliance was analyzed. The main results obtained are as follows: (1) By combining the limit analysis theory and elastic–plastic fracture mechanics, the effects of crack size, compliance and fracture toughness on load deflection behaviors to failure and structural integrity of statically indeterminate pipe system have been analyzed quantitatively and easily. (2) When a crack grows in a statically indeterminate pipe before plastic collapse, load drop conditions can be derived quantitatively, as a function of J_IC, dJ/da, flow stress, crack size, pipe span length, compliance and flexural rigidity of the pipe. (3) The analytic method developed in this research is useful and convenient to evaluate the LBB and tearing instability behavior of a statically indeterminate pipe system. (4) LBB resolves easily for statically indeterminate pipes with a crack, even when it does not resolve for statically determinate pipes with the same crack. That results from the fact that bending moment redistribution during the fracture process occurs easily for statically indeterminate pipe systems, and its redistribution restrains plastic deformation of the cracked weak section.     

Development of simplified evaluation method for creep-fatigue crack propagation

In the design assessment of fast reactor plant components, prevention of crack initiation from defect-free structures is a main concern. However, existence of initial defects such as weld defects cannot be entirely excluded and this potential cracks are to be evaluated to determine if initiated cracks do not lead to component failure instantly. Therefore, evaluation of structural integrity in the presence of crack-like defects is also important to complement the formal design assessment. The authors have been developing a guideline for assessing long-term structural integrity of fast reactor components using detailed inelastic analysis and nonlinear fracture mechanics. This guideline consists of two parts, evaluation of defect-free structures and flaw evaluation. In the latter, creep-fatigue is considered to be one of the most essential driving force for crack propagation at high operating temperature exceeding 500 °C. The uses of J-integral-type parameters (fatigue J-integral range and creep J-integral) are recommended to describe creep-fatigue crack propagation behavior in the guideline. This paper gives an outline of the simplified evaluation method for creep-fatigue crack propagation.     

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.     

Pipe fracture safety analysis using limit load and J-integral techniques

J-integral fracture toughness tests were performed on full scale pipe specimens to assess the fracture safety performance of two reactor piping alloys. The two alloys investigated were ASTM A106 Grade B carbon steel and circumferentially welded Type 304 stainless steel.The full scale pipe fracture tests were performed on 1.2 m long, circumferentially cracked pipes loaded in four-point bending on a variably compliant test bed. Results of the experiments were analyzed using the limit load approach currently being considered for inclusion in Section XI of the ASME Code. The results were also evaluated using two tearing instability approaches. One approach assumed elastic-perfectly plastic material behavior and the other accounted for material hardening by requiring actual load and displacement data.The limit load analysis provided a good prediction of the maximum load carrying capacity of the pipe specimens in most cases. The results were especially good for the ASTM A106 steel pipes when the materials property data was used to calculate the flow stress. The J-integral tearing instability analysis was shown to accurately describe the ductile tearing instability behavior of the ASTM A106 steel pipe providing material hardening was taken into account.     

A unified time dependent model for low cycle fatigue and ratchetting failure based on microcrack growth

In this paper, a unified time dependent model for low cycle fatigue and ratchetting failure has been developed based on the microcrack growth. The model utilized fracture mechanics theory using J-integral under creep–fatigue loading and assumed that the microcrack propagation determines the failure life. The microcrack rates are separated into three parts: (1) the time independent fatigue crack growth, (2) the time dependent fatigue crack growth and (3) the time dependent ratchetting crack growth. The cyclic failure criteria under different loading conditions were derived from the microcrack growth. Some simplified models were obtained and they can characterize the time dependent low cycle and ratchetting failure lives with hold time and loading frequency effects.     

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.     

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.     

Evaluation of throughwall crack pipes under displacement controlled loading

Tearing modulus solutions are developed for flawed throughwall pipes subjected to displacement controlled loading. Two cases of loading were considered: (1) a displacement controlled bending loading, and (2) a displacement controlled axial tension loading. A revised version of the EPRI J-integral estimation scheme is used in the development of the solutions. These solutions can be used for the entire range of elastic-plastic loading, from linear elastic, contained yielding, to large scale yielding of the crack section. Experimental data from pipes in bending were used to assess the accuracy of the compliant loading solutions. The evaluations were performed using elastic plastic J-integral (J) and tearing modulus (T) analysis methods. These solutions are shown to have good accuracy when used to predict the experimental results. The methodology and procedure can also be applied to part-throughwall cracks. These solutions have application to the leak before break fracture mechanics analyses.     

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.     

Estimation of crack driving forces on strength-mismatched bimaterial interfaces

This paper presents a framework to estimate crack driving forces in terms of crack-tip opening displacement and J-integral for mismatched dissimilar joints with interface cracks. The mismatch in elastic, thermal, and plastic hardening properties is not considered, but the mismatch in plastic yield strengths is emphasized here. The main outcome of the present work is that the existing methods to estimate crack driving forces for homogeneous materials can be used with slight modification. Such modification includes: (i) mismatch-corrected limit load solutions; and (ii) evaluating the contribution of each material in dissimilar joints to the total crack driving force, which depends on the strength mismatch of the dissimilar joints.     

Dynamic fracture analysis of a transverse wedge-loaded compact specimen

The J-integral method cannot be applied to the elastic plastic dynamic crack propagation, because unloading and inertia force may take place. From this point of view dynamic elastic plastic scheme using J-integral is developed.Using this dynamic finite element program an MRL type specimen is analyzed. As the result, the property of path-independence of the J-integral under the existence of inertia force and unloading is confirmed. Dynamic effects are considerably small in the MRL type specimen. Also the influence of plastic zone on the crack arrest toughness is shown.Finally the present result is compared with the request of ASTM 2nd round robin test program for crack arrest toughness.     

Characteristics relevant to ductile failure of bimetallic welds and evaluation of transferability of fracture properties

Life management and structural integrity assessment of bimetallic welds in its state-of-the-art form relies on practical methods derived on the basis of years of experience in operation and simplistic strength of materials analyses. The complex conditions and properties of the weldment, as resulting from the elaborate interaction of different microstructures with gradients in material properties, have limited the ability of currently existing methods to construct the assessment on the basis of actual failure mechanisms of bimetallic welds. Current work addresses the assessment procedure by combining experimental and numerical fracture mechanics comprising a micro-mechanical evaluation of the relevant damage mechanisms. The studied dissimilar ferrite (SA508)–austenite (AISI 304) circumferencial weld is one with a Ni-enriched buttering layer.The experimental work comprises tensile and fracture mechanical characterization of the different microstructural zones of the bimetallic weld. Tensile properties are determined with microstructure specific flat bar specimens as well as round bar specimens enabling better inference of true stress–strain curves. Fracture resistance curves are established by applying small-specimen testing techniques. Different crack configurations are modeled by finite element analysis (FEA) to assess the relationships between fracture types, toughness and local near crack tip constraint parameters. Transferability and characterization question are considered by determining J–Q-trajectories and employing small-scale yielding corrections (SSYCs). On the basis of the experimental and numerical results and a fractographical investigation, the micromechanics of fracture are interpreted. Differences in strain hardening capacities of microstructural zones are found to most severely affect the toughness transitions of the weld and the associated failure modes. Two prime failure types are noted, one for cracks located at outer heat affected zone (HAZ) resulting in an unstable crack deflection towards the fusion line (FL) and another type associated with cracks positioned near the fusion line, wherein a low-toughness ductile fracture process results. Small fracture mechanics specimen is found applicable for fracture resistance determination of bimetallic weldments.     

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.     

Influence of the specimen configuration and the insert material on fracture toughness characterisation with reconstituted specimens

Specimen reconstitution techniques offer the possibility to obtain fracture toughness measurements when only small amounts of material are available. In order to obtain extra information from charpy specimens, an electron-beam weld reconstitution method is established to obtain compact tension specimens (CT) from the broken halves of the charpy ones. Three types of reconstituted CT specimens with different weld configurations are tested in order to analyse the influence of specimen configuration on fracture toughness evaluation. The validity of the fracture toughness characterisation is analysed by comparing J-integral resistance curves (J–R curves) of specimens with insert and those of reference specimens without insert.     

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.