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.     

Effect of hydrogen and neutron irradiation on the failure of flawed Zircaloy-2 pressure tubes

Experiments were made with Zircaloy-2 tubes containing axial slits. Failure stress at 20 and 300 °C is increased by neutron irradiation: hydride precipitates reduce failure stress at 20 °C but not at 300 °C. There is evidence that stress applied during irradiation, and neutron dose, affect failure stress.

Crack opening displacement measurements on notched bend specimens predicted within 20% the critical crack lengths measured on full size tubes.     

Load-carrying capacity and crack resistance of a cladding by the Sigma-oscillating wire technique

If cracks are postulated in the ferritic base material beneath the austenitic cladding, their initiation and propagation under hypothetical loading cases is influenced by the load carrying capacity of the cladding. The toughness of the KKS-RPV cladding was assessed by means of elastic-plastic fracture mechanics methods. Sub-sized tensile and bend specimens were fabricated by reconstitution technique from broken halves of standard ISO-V Charpy specimens, representing crack extension in radial and circumferential direction. They were tested and evaluated and further analyzed with the Gurson model. For temperatures relevant to the loss of coolant and upset conditions analyzed, a sufficient toughness of the cladding in terms of J and CTOD resistance curves could be shown.     

Ductile crack growth simulation from near crack tip dissipated energy

A method to calculate ductile tearing in both small scale fracture mechanics specimens and cracked components is presented. This method is based on an estimation of the dissipated energy calculated near the crack tip. Firstly, the method is presented. It is shown that a characteristic parameter G_fr can be obtained, relevant to the dissipated energy in the fracture process. The application of the method to the calculation of side grooved crack tip (CT) specimens of different sizes is examined. The value of G_fr is identified by comparing the calculated and experimental load line displacement versus crack extension curve for the smallest CT specimen. With this identified value, it is possible to calculate the global behaviour of the largest specimen. The method is then applied to the calculation of a pipe containing a through-wall thickness crack subjected to a bending moment. This pipe is made of the same material as the CT specimens. It is shown that it is possible to simulate the global behaviour of the structure including the prediction of up to 90-mm crack extension. Local terms such as the equivalent stress or the crack tip opening angle are found to be constant during the crack extension process. This supports the view that G_fr controls the fields in the vicinity near the crack tip.     

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.     

Hydrogen embrittlement of ASTM A 203 D nuclear structural steel

The influence of hydrogen on the mechanical properties of ASTM A 203 D nuclear structural steel has been studied by tension, bend and delayed-failure tests at room temperature. While the tension tests of hydrogen charged unnotched specimens reveal no change in ultimate strength and ductility, the effect of hydrogen is manifested in notched specimens (tensile and bend) as a decrease in ultimate strength (maximum load in bend test) and ductility; the effect increases with increasing hydrogen content. It is observed that for a given hydrogen concentration, the decrease in bend ductility is remarkably large compared to that in tensile ductility.Hydrogen charging does not cause any delayed-failure upto 200 h under an applied tensile stress, 0.85 times the notch tensile strength. However delayed failure occurs in hydrogen charged bend samples in less than 10 h under an applied bending load of about 0.80 times of the uncharged maximum load.Fractographs of hydrogen charged unnotched specimens show ductile dimple fracture, while those of notched tension and bend specimens under hydrogen-charged conditions show a mixture of ductile dimple and quasi-cleavage cracking. The proportion of quasi-cleavage cracking increases with increasing hydrogen content and this fracture mode is more predominant in bend specimens.The changes in tensile properties and fracture modes can reasonably be explained by existing theories of hydrogen embrittlement. An attempt is made to explain the significant difference in the embrittlement susceptibility of bend and tensile specimens in the light of difference in triaxiality and plastic zone size near the notch tip.     

Experimental investigation on ductile stable crack growth emanating from wire-cut notch in AISI 4340 steel

An experimental investigation on the stable crack growth (SCG) behaviour in AISI 4340 using CT type specimen with a sharp slit (0.05 mm) under mode I and mixed modes (I and II) loading is presented. The slit was made in the specimen through wire cutting technique. Different combinations of loading angle and ratio of original crack length to specimen width (a₀/W) are examined. Data concerned with direction of initial crack extension, load–load line displacement (L–LLD) diagrams, initiation and maximum loads, range of stable crack growth, crack tip blunting, crack front geometry, fracture surfaces and their scanning electron micrographs are obtained. A noticeable blunting effect is observed prior to crack initiation. Although the crack initiates from a straight front, a considerable front tunnelling effect occurs as the crack extends. Under mixed mode, the crack extension takes place initially almost along a straight path, inclined with the main crack. The loading angle and initial crack length affect the initiation (P_i) and maximum (P_max) loads significantly, but the ratio between P_max and P_i remains almost constant. The direction of initial stable crack extension due to mixed mode loading is determined throughout an elastic finite element analysis. There is a good agreement between the experimental and predicted results.     

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.     

Tests on large scale LMFR piping Part I: crack resistance properties of through-cracked straight 700 mm nominal diameter pipes tested under bending at ambient temperature and 550°C

Knowing the crack resistance properties of a structure is essential for fracture mechanics safety analyses. Considerable attention has to be given in many cases to the through-wall case, since this is generally believed to be the controlling case with regard to complete pipe failure. Within a cooperative fracture mechanics programme of Electricite de France (EdF), Novatome and Siemens/KWU, bending tests with monotonously increasing load on circumferentially cracked straight pipes of typical liquid metal fast reactor (LMFR) main piping dimensions were performed. In this paper a summary report is given on crack resistance curves based on the crack tip parameters S, J and JM. The data are compared with those of C(T) specimens. The experiments have demonstrated an enormous potential for stable crack extension under global bending which is a typical loading for LMFR piping structures. The results of checking the transferability of laboratory specimen crack growth characteristics to the cracked pipes on the austenitic stainless steel 316 L demonstrate that the fracture mechanics concept for a reliable transfer of crack resistance data from small specimen geometries to large structures needs further qualification for high toughness materials.     

Fatigue studies on carbon steel piping materials and components: Indian PHWRs

This paper describes the results of fatigue studies on carbon steel piping materials and components of Indian Pressurized Heavy Water Reactors (PHWRs). The piping components include pipes and elbows, of outer diameter 219 mm, 324 mm and 406 mm, made of carbon steel (SA333 Gr.6 grade) material. Tests on actual pipes and elbows with part through notch were carried out to study the behaviour of crack growth under cyclic loading for different pipe sizes, notch aspect ratios, stress ratios, etc. During the tests, numbers of cycles for crack initiation from blunt notch were recorded with an accuracy of 0.1 mm. In conjunction with component tests, the experimental studies were also conducted on standard specimens to understand the effect of different variables such as size (thickness), type of specimen and components (elbow and pipe), welding, stress ratio, notch orientation on fatigue crack growth rate. The fatigue crack growth curve (da/dN versus ΔK) obtained from three-point bend specimen and pipe was compared with that given in ASME Section XI. The comparison shows that da/dN versus ΔK curves obtained from the specimen and pipe tests are nearly same. The analytical predictions for crack initiation and crack growth for the tested components were compared with experimental results. Such comparisons validate the modeling procedure for crack initiation and growth.     

Effect of biaxial loading on the fracture behaviour of a ferritic steel component

The effect of biaxial loading on the ductile behaviour of a through-wall crack in a ferritic steel structure under contained yield is of particular interest to the structural integrity argument for reactor pressure vessels. This results from the fact that there are many instances in practice (for example a crack in a circumferential weld), where a significant applied stress is present in the direction parallel to the crack as well as in the perpendicular direction. Two large plate ductile tearing tests have been performed on centre through-crack specimens (75 mm by 2 m by 2 m) manufactured from a ferritic steel. The first test specimen was loaded in uniaxial tension and the second test specimen was loaded biaxially. This paper presents experimental details and results of the two plate tests and describes the analysis work undertaken to interpret the experiments satisfactorily.     

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.     

Elastic-plastic analysis of local and integral straining behaviour in a cracked plate

For components of the primary coolant system of the German LMFBR prototype reactor SNR-300, integrity against anticipated accidents (Bethe-Tait) has to be shown for a cracked structure. Within this programme a number of tests with cracked wide plate specimens yielding overall limit strains of approximately 15% have been run; finite element calculations have been initiated for the wide plate geometry. The paper discusses the straining behaviour of a cracked plate by considering the numerical simulation of structures strained up to such high levels.The stress-strain diagram of the weldment of the austenitic stainless steel X6 CrNi 18 11 at 450°C has been used. Plane strain and stress conditions have been prescribed. The original plate dimensions (t=thickness=40 mm; h=height=400 mm) have been used as well as a similar, but smaller plate of t=8.8 mm width. The crack length is defined as 0.1t.The results show that for a cracked plate under high plastic strain the near-crack-tip-field values still govern the structural mechanical behaviour. Concerning the absolute dimensions the effects known for elasticity retain their influence in the plastic regime; however, the crack location becomes more unimportant with increasing strain, i.e. the appropriate pure geometry factor tends to unity in the plastic regime. The center-crack, defined as 2a=0.1t, corresponds to an equivalent edge crack of depth a=0.05t in the elastic case. It can be shown that for high plastic strains this correspondence remains fully valid.     

Fracture initiation and propagation in a cylindrical shell containing an initial surface flaw

The paper deals with the problem of fracture initiation, propagation, and arrest in a pressurized cylindrical vessel which contains an initial surface flaw. It is assumed that the flaw has the most unfavorable geometry and orientation, namely, it is a relatively long part-through axial crack.First we consider the problem of a crack which is sufficiently ‘shallow’ so that the plastic deformations are confined to the neighborhood of the crack border and part of the net section near the inner wall is still elastic. The plasticity-corrected stress intensity factor obtained from this analysis is the controlling load factor in failure considerations related to fatigue crack propagation, stress corrosion cracking, and static fracture (with the use of fracture toughness, COD, or a K_R curvetype failure criterion).The problem of relatively deep crack with fully-yielded net ligament is then considered. Plastic deformations are also assumed to spread around the crack ends through the entire wall thickness. A perfectly plastic strip model (with an eight order shell theory) is used to calculate the plastic zone size and the crack opening displacement along the crack border. Previous studies indicate that for the analysis of the type of stable and subsequent unstable crack propagation problems under consideration, the crack opening displacement δ is a more suitable load factor than the stress intensity factor K, or the crack extension force G. Thus, in this paper a ‘crack opening stretch’ type material characterization will be used.After the rupture of the net ligament under the crack, the axial crack propagation is accompanied by the depressurization of the vessel caused by leakage. From this point on the fracture problem is coupled with the related fluid mechanics or gas dynamics problem where the primary unknowns are the pressure and the crack length as functions of time. In the present study it is assumed that the volume of the vessel is finite and the crack propagation is quasi-static (this assumption, which is necessary to keep the problem within manageable proportions, is justified by the relatively low crack velocities, i.e. v_c < 0.25 c₂, c₂ being the shear wave velocity).     

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.     

Characterization of stable crack growth through AISI 4340 steel using cohesive zone modeling and CTOD/CTOA criterion

The criteria based on cohesive zone model (CZM) and CTOD/CTOA have been employed for analysis of stable crack growth (SCG) through AISI 4340 steel. Investigations have been reported first concerning characterization of mode I SCG using the CZM and a particular crack size in a CT specimen 8 mm thick. The characteristic data is then verified considering other mode I crack sizes and the same specimen geometry. Similar verifications have also been done considering cracks under mixed mode (I and II) loading. The same mode I cases have been studied later considering some variations of crack tip opening displacement/angle (CTOD/CTOA) with crack extension. Load-load-line displacement (LLD) predictions based on these two approaches have been compared with experimental results reported in the literature. The predictions based on the CZM are found to be closer to the experimental results. The results include the traction-separation law suitable for characterization of SCG through AISI 4340 steel under mode I and mixed mode (I and II). Similarly a CTOD/CTOA variation with crack extension for the similar purpose under only mode I loadings has been reported. Other observations on modeling of crack tip constraint effects by mixed (plane strain core plus plane stress outer domain) discretisation scheme, crack tip element size and J integral, are presented.     

Stress corrosion cracking of low-alloy, reactor-pressure-vessel steels in oxygenated, high-temperature water

The stress corrosion cracking (SCC) behaviour of low-alloy, reactor-pressure-vessel (RPV) steels in oxygenated, high-temperature water and its relevance to boiling water reactor (BWR) power operation, in particular its possible effect on both RPV structural integrity and safety, has been a subject of controversial discussions for many years. This paper presents the results of an experimental study on crack growth through SCC in three, nuclear-grade, steels (SA 533 B Cl.1, SA 508 Cl.2, 20 MnMoNi 5 5) under simulated, BWR water-chemistry conditions. Modern, high-temperature water loops, on-line crack-growth monitoring and fractographic analysis in the scanning electron microscope were used to quantify the cracking response of pre-cracked, fracture-mechanics specimens under a variety of mechanical and environmental conditions. Corrosion-assisted crack advance could be only initiated by active loading within the environment. If SCC crack advance at constant load was observed, initiation of crack growth had always occurred while increasing the load to the intended value for subsequent, static-load testing. During the constant load period the rate of SCC crack advance rapidly decayed and crack arrest occurred within a period of <100 h (for tests with K_I60 MPa m^1/2). Supplementary experiments with slowly increasing loading revealed that the initiation of crack growth, and the extent of further crack advance, are crucially dependent upon maintaining both a positive crack-tip strain rate and a high sulphur-anion activity in the crack-tip environment. It is concluded that there is no sustainable susceptibility to SCC crack growth under purely static loading, as long as small-scale-yielding conditions prevail at the crack-tip and the water chemistry is maintained within current BWR/NWC operational practice (EPRI water chemistry guidelines). However, sustained, fast SCC (with respect to operational time scales) cannot be excluded for faulted water-chemistry conditions (>EPRI action level 3) and/or for highly stressed specimens either loaded near to K_IJ or with a high degree of plasticity in the remaining ligament.     

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.     

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.