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 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.     

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.     

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.     

Numerical investigation of J-characterization of growing crack tips

Two different geometries, a centrally cracked panel and a three-point bend bar, are modelled with aid of the finite element program ABAQUS. Elastic-plastic behaviour with a realistic linear hardening modulus is assumed. By simulation of the growth with the aid of nodal relaxation, the J-value for a remote path around the growing tip is obtained for some different load-crack growth histories. This J_F-value is compared to the J_D-value that results if the crack tip is assumed to be stationary at the current length. It is found that the J_D- and J_F-values agree well for crack growth histories satisfying the criteria for J-characterization. However, after examination of the crack surface displacements it was found that the results for the bend geometry and the tension geometry, respectively, did not coincide for corresponding J-values, except at low load levels. This raises doubts about the abilities of J to characterize the state at a growing tip.     

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.     

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

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

Application of the J-integral concept to thermal shock loadings

In the frame of our analytical work the applicability of ductile fracture mechanical J-integral concept on mechanical and thermal shock loaded structures with flaws is investigated. By that the behaviour of possible flaws in components of power plants during accidents can be described (e.g. reactor pressure vessel and piping during emergency cooling).The analyses presented in this paper have been performed with a version of the finite element code ADINA [1] extended by fracture mechanical options. The postanalyses of the first series of pressurized thermal shock experiments (PTSE-1A, B, C) performed at ORNL show stress intensity factors (K_I) calculated from J-integrals which are about 10% lower than values of OCA programs [2] based on the linear elastic K-concept usually used for brittle materials. The discrepancy may be referred to different treatment of the influence of plasticity. The results assessed in the frame of the cleavage fracture concept coincide well with the measured times respectively crack tip temperatures at crack initiation and arrest.In the first thermal shock experiment (NKS-1) performed at the MPA-Stuttgart a circumferentially deep cracked test cylinder with overall upper shelf material conditions has been investigated. The postcalculations based on the J-integral with J_R-controlled crack growth show good coincidence between analytical determined and measured structure and fracture mechanical quantities but they are accompanied with numerical problems due to unloading and large plasticity effects.     

A critical survey on the application of plastic fracture mechanics to nuclear pressure vessels and piping

Plastic fracture mechanics techniques have been developed to treat the regime where extensive plastic deformation and stable crack growth occur prior to fracture instability in the tough ductile materials used in nuclear systems. As described in this paper, a large number of crack tip parameters can be used in a plastic fracture resistance curve approach. However, applications using the J-integral currently predominate. This parameter has significant advantages. It offers computational ease and can provide a lower bound estimate of the fracture condition. But, J also has a disadvantage in that only a limited amount of stable crack growth can be accommodated. The crack tip opening angle parameter, in contrast, can be valid for extensive stable crack growth. But, with it and most other realistic alternatives, the computational convenience associated with the J-integral is lost and finite element or other numerical methods must be employed. Other possibilities such as the two-criterion approach and the critical net section stress are also described in the paper. In addition, current research work focussed upon improving the theoretical basis for the subject is reviewed together with related areas such as dynamic plastic analyses for unstable crack propagation/arrest and creep crack growth at high temperatures. Finally, an application of plastic fracture mechanics to stress corrosion cracking of nuclear piping is made which indicates the possible anti-conservative nature of the current linear elastic assessments.     

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.     

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.     

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.     

In situ crack growth observation and fracture toughness measurement of hydrogen charged Zircaloy-4

The effect of hydrogen on the fracture behaviour of a Zircaloy-4 alloy was analysed performing simultaneous fracture mechanics tests of small SE(B) specimens and in situ observation of crack initiation and propagation inside the chamber of a scanning electron microscope. Load and displacement were continuously measured and J_IC, J-R curves and CTOD determinations were obtained. Detailed images of the zone close to the crack tip were taken and the resistance to crack growth was correlated with hydrogen content and hydride morphology. The size and orientation of hydride precipitates showed an important influence on the fracture process. A good agreement with results obtained using standard CT specimens was met.     

Analysis of stable crack growth across welded fusion line: Japanese round-robin

Bimaterial CT specimens are numerically analyzed in the elastic-plastic states. By changing the material constants and the distance between the crack tip and the phase boundary, the parametric analyses are conducted. J integral evaluated by the line integration is compared with that obtained by the empirical formula by Merkel-Corten. The effects of the inhomogeneities on the accuracy of the J integral evaluation are discussed. Next the stable crack growth analyses are conducted. Using the relation between a and load-load line displacement obtained experimentally, the generation phase analyses are carried out. J integral, T^* integral and CTOA are evaluated and the effects of the fusion line are discussed.     

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.     

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

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

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.     

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.     

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.     

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.