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.     

Prediction of fatigue crack growth and experimental result on overlaod retardation

The phenomena of crack growth retardation are frequently observed under variable amplitude or irregular loading fatigue tests. This paper describes a prediction method on crack growth retardation caused by an overload during fatigue loads.The prediction reported in this paper is performed by the following procedure using the yield strength and vs. ΔK relationship of the material.

1. (1) Determination of the residual stress distribution caused by cyclic load and overload based on the Dugdale model.

2. (2) Determination of the effective residual stress intensity factor and effective stress intensity range (ΔK_eff).

3. (3) Prediction of the crack growth rate using ΔK_eff and vs. ΔK relationship of the material.

From the viewpoint to apply the prediction to a structural component, experiments have been carried out on steel pipes with an axial through thickness crack, which are subject to an overpressure during cyclic pressure. In the paper, the experimental results are compared with the prediction.     

Analytical evaluation method of J-integral in creep-fatigue fracture for type 304 stainless steel

Creep-fatigue crack growth at the operating temperature of LMFBR can be characterized by ΔJ_F and J′ (same as C^*). Type 304 stainless steel, the main structural material of the Japanese LMFBR, shows notable cyclic hardening at elevated temperatures. Evaluation of these J-integrals with the finite-element method is strongly affected by the reference strain range when the cyclic hysteresis' is used as the stress-strain relation.In this paper, an evaluation method for ΔJ_F and J′ with a cyclic stress-strain curve (Δσ – Δ relation) is proposed and verified by experimental results. The evaluation method proposed here does not require cyclic calculations but is monotonic and the effect of the reference strain range is relatively small.     

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.     

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.     

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.     

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.     

Part-through cracks in pipes under cyclic bending

The propagation of a circumferential external surface crack in a metallic round pipe under cyclic bending loading is examined through a two-parameter theoretical model. A finite element analysis is carried out to determine the stress-intensity factor distribution along the front of the flaw, which is assumed to present an elliptical-arc shape with aspect ratio α=a_el/b_el (a_el, b_el=ellipse semi-axes). The relative depth ξ of the deepest point on the front is equal to the ratio between the maximum crack depth, a, and the pipe wall thickness, t. The parameter R/t, with R=internal radius of the pipe, is made to vary from 1 to 10. The fatigue growth of the surface flaw occurs according to preferred paths in the diagram of α against ξ.     

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.     

Application of a local approach to ductile-brittle transition in a low-alloyed steel

Both tensile tests on notched specimens and fracture mechanics experiments on axisymmetrically cracked specimens were performed on one heat of A508 steel (AFNOR: 16MND5). Tensile tests on notched geometries were made to determine the characteristic parameters used in a statistical analysis of cleavage fracture proposed previously [1]. Tests on cracked specimens were carried out between −80°C and −20°C to investigate the critical values of stable crack growth, Δa_c, occurring before unstable cleavage fracture. At a given temperature a large scatter in the values of critical crack growth, Δa_c, was observed.To interpret these results a model derived previously for cleavage crack initiation [1] is used. In this model the Weibull stress is calculated by the finite element method for three different initial crack lengths covering stable growth increments observed experimentally. It is shown that this model accounts reasonably well for the observed effects.     

Creep and creep-fatigue cracking behaviour of two structural steels

The present study deals with crack initiation and crack growth, not only under creep and creep-fatigue conditions but also under more complex thermomechanical cyclic loadings, in both 316L and 1Cr-1Mo-0.25V steel.In these creep ductile materials, most studies have focused on the creep crack growth rates, da/dt and load-geometry parameter C* correlations. In this paper, the creep crack initiation time is defined as the time T_i necessary for a defect to grow by a small critical distance X_c (X_c ≈ 50 μm for example). This initiation stage may represent a large part of the rupture life of a cracked component. The importance of such studies is discussed in the first part.In the second part, an attempt is made to present a simplified method based on the fracture mechanics of creeping solids to define the relevant load-geometry parameters for crack initiation and crack growth under creep-fatigue loadings. In particular, it is shown that da/dN-ΔK correlations apply only when the hold time t_h is smaller than the transition time t_tr between small-scale and large-scale viscoplasticity. Conversely, for long hold times, it is suggested that the T_i-C* correlation be used to predict the fatigue.     

European experiences of the proposed ASTM test method for crack arrest toughness of ferritic materials

The proposed ASTM test method for measuring the crack arrest toughness of ferritic materials using wedge-loaded, side-grooved, compact specimens was applied to three steels: A514 bridge steel tested at −30°C (CV30–50°C), A588 bridge steel tested at −30°C (CV30–65°C), and A533B pressure vessel steel tested at +10°C (CV30-12°C) and +24°C (CV30+2°C). Five sets of results from different laboratories are discussed here; in four cases FOX DUR 500 electrodes were used for notch preparation, in the remaining case HARDEX-N electrodes were used. In all cases, notches were prepared by spark erosion, although root radii varied from 0.1–1.5 mm. Although fast fractures were successfully initiated, arrest did not occur in a significant number of cases.The results showed no obvious dependence of crack arrest toughness, K_a, (determined by a static analysis) on crack initiation toughness, K₀. It was found that K_a decreases markedly with increasing crack jump distance, Δα/W. A limited amount of further work on smaller specimens of the A533B steel showed that lower K_a values tended to be recorded.It is concluded that a number of points relating to the proposed test method and notch preparation are worthy of further consideration. It is pointed out that the proposed validity criteria may screen out lower bound data. Nevertheless, for present practical purposes, K_a values may be regarded as useful in providing an estimate of arrest toughness — although not necessarily a conservative estimate.     

Elastic–plastic analysis of an elbow with a through-wall axial crack at crown under in-plane bending

Piping elbows under bending moment are vulnerable to cracking at crown. The structural integrity assessment requires knowledge of the J-integral. The J-integral values for axially through-wall cracked thick elbows under in-plane bending moment are not available in open literature. This paper presents the J-integral results for 90°, long radius elbows subjected to in-plane opening bending moment based on a large number of finite element analyses covering a wide range of standard geometries. The non-linear elastic–plastic finite element analyses were performed using WARP3D software. Both geometric and material non-linearity were considered in the study. The geometry considered were for R_m/t = 5, 6, 7.5, 9, 12, 15, 20 and 25 with crack angles of 9°, 18°, 27° and 36° and strain hardening exponent, ‘n’ varied for 2, 3, 5, 7 and 10.     

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.     

The growth of fatigue cracks in the creep range from the point of view of ductile fracture

This paper deals with experimental and numerical investigations of crack growth in 1% CrMoV steels in the creep temperature range. For the load and displacement controlled fatigue tests with predominantly plastic deformation amplitudes, centre cracked panels and CT-specimens of different thicknesses were used.For describing the crack growth per load cycle the crack tip displacement δ_t and the J-integral were applied, whereby the question arises whether the various fracture concepts are applicable unrestrictedly or where they meet their limits of validity.Detailed theoretical-numerical calculations using the finite element method were expected to yield information about the path independence of the J-integral. Special importance was therefore attached to investigate the J-integral, both cyclical and with reference to the instantaneous state of deformation, by comparing the different J-integral values (ΔJ, J) with the experimental method of Dowling/Begley.     

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.     

Fatigue crack growth under residual stress field in low-carbon steel

The influence of residual stress on fatigue crack growth was experimentally and analytically investigated for surface crack. Fatigue tests were performed on straight pipe components of low-carbon steel having a circumferential inner surface crack in laboratory air environment. Some of the test pipes had been subjected to special heat treatments so as to have compressive or tensile residual stresses along the inner surface.The results show that the compressive residual stress remarkably suppresses the surface crack growth while the tensile residual stress doesn't accelerate the crack growth very much.The crack growth analyses were conducted by the application of power relationship between ΔK and . The stress intensity factors due to the non-linear stress field were calculated by the weight function method. The analyses resulted in a confirmation of the behavior of the crack growth observed in the experiments.     

The effect of irradiation on the toughness of pressurized water reactor vessel steels under different service conditions

The different toughness tests performed on two pressure vessel steels with very different upper shelves served to make a number of observations concerning the shifts in the transition temperature due to the effect of irradiation, as well as changes in toughness with temperature in the ductile region.With respect to shifts in the transition temperature, the following was observed: the shift obtained with precracked charpy test specimens was narrower than with the others; the shift obtained with charpy V impact tests was substantially equal to that obtained with CT test specimens — wider in the case of steel A, but slightly narrower in that of steel H.With respect to toughness values in the ductile region: the toughness values obtained using precracked charpy test specimens are significantly higher than those obtained with CT test specimens for static tests; 25and 12.5 mm thick CT test specimens display comparable variations in J_1C and dJ/da, but with wide scattering; the effect of irradiation, if any, is of the same order of magnitude as the scattering of the results — however, a test temperature effect is observed; the variation in toughness with temperature is determined more easily by considering a J value corresponding to a stable crack propagation of 1 mm, so that ; this variation of J_Δal with temperature is substantially the same for both steels, or about −30% at 70 or 80°C, and −50% at 290°C.     

A comparison of the use of the modified J-integral and the deformation J-integral in procedures for estimating the critical crack length for CANDU pressure tubes

The paper presents the results of a theoretical investigation whose objective has been to see whether there are advantages to be gained from using the modified J-integral in procedures for estimating the critical crack length for CANDU pressure tubes. For typical operation conditions, and with irradiated tubes having critical crack lengths over a wide range, it is shown that the slope of the modified J-integral J_M-Δa crack growth resistance curve for a pressure tube crack is only marginally greater than the slope of the corresponding deformation J-integral J_D-Δa curve; the results are expressed in terms of the parameter Z_*, which is dJ_M/da − dJ_D/da and the parameter Q, which is the fractional difference between dJ_M/da and dJ_D/da. In the light of these findings, there would appear to be little advantage to be gained in using J_M, rather than J_D, as a characterizing parameter for crack growth in a CANDU pressure tube.     

Mechanical integrity analysis of TMI-1 OTSG unplugged tubes

Small I.D. circumferential defects have been identified in many steam generator tubes. The origin of the cracks is known to be chemical, not mechanical. A fracture mechanics evaluation has been conducted to ascertain the stability of tube cracks under steady-state and anticipated transient conditions. A spectrum of hypothetical crack sizes was interacted with tube stresses derived from the load evaluation using the methods of linear elastic fracture mechanics (LEFM). Stress intensities were calculated for part-through wall cracks in cylinders combining components due to membrane stress, bending stress, and stresses due to internal pressure acting on the parting crack faces as the loads are cycled.The LEFM computational code, “BIGIF”, developed for EPRI, was used to integrate over a range of stress intensities following the model to describe crack growth in INCO 600 at operating temperature using the equation (ΔK)^3.5.The code was modified by applying ΔK_Th, the threshold stress intensity range. Below ΔK_Th small cracks will not propagate at all. Appropriate R ratio values were employed when calculating crack propagation due to high cycle or low cycle loading.Cracks that may have escaped detection by ECT will not jeopardize tube integrity during normal cooldown unless these cracks are greater than 180° in extent. Large non-through-wall cracks that would jeopardize tube integrity are not expected to evolve because in axi-symmetric tensile stress fields, cracks propagate preferentially through the tube wall rather than around the circumference. Tube integrity can be demonstrated for mid-span tube regions and for the transition region as well.The as-repaired transition geometry is a design no less adequate than the original. The as-repaired condition represents an improvement in the state of stress due to mechanical and thermal loads as compared to the original.