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.     

Damage, crack growth and fracture characteristics of nuclear grade graphite using the Double Torsion technique

The crack initiation and propagation characteristics of two medium grained polygranular graphites, nuclear block graphite (NBG10) and Gilsocarbon (GCMB grade) graphite, have been studied using the Double Torsion (DT) technique. The DT technique allows stable crack propagation and easy crack tip observation of such brittle materials. The linear elastic fracture mechanics (LEFM) methodology of the DT technique was adapted for elastic-plastic fracture mechanics (EPFM) in conjunction with a methodology for directly calculating the J-integral from in-plane displacement fields (JMAN) to account for the non-linearity of graphite deformation. The full field surface displacement measurement techniques of electronic speckle pattern interferometry (ESPI) and digital image correlation (DIC) were used to observe and measure crack initiation and propagation.Significant micro-cracking in the fracture process zone (FPZ) was observed as well as crack bridging in the wake of the crack tip. The R-curve behaviour was measured to determine the critical J-integral for crack propagation in both materials. Micro-cracks tended to nucleate at pores, causing deflection of the crack path. Rising R-curve behaviour was observed, which is attributed to the formation of the FPZ, while crack bridging and distributed micro-cracks are responsible for the increase in fracture resistance. Each contributes around 50% of the irreversible energy dissipation in both graphites.     

Transferability of post yield fracture mechanics properties from small scale specimens to large scale specimens and components

This contribution describes a method for the determination of the J-integral as a function of the load-line displacement for arbitrary specimen geometries.A correspondence could be found between the approximation method and the results determining with the Rice integral by means of a FE-calculation. Using the initiation values of the J-integral as a fracture mechanics parameter determined from the J_R-curve, correspond with failure values of double-édged notched tensile specimens and circumferentially notched round tensile specimens of which crack initiation was tantamount to instability. Consequently, it could be proved that the J-integral is a transferable parameter that may be ascertained from simple determinable deformation values. The application to real components seems to be promising, due to these good results.     

Fracture mechanics analysis for inhomogeneous material behaviour

The J-integral is an important parameter for the ductile fracture mechanics assessment of components. With an appropriate modification it may even be applied to inhomogeneous materials where the material characteristics may depend strongly on the location, e.g. in welded joints. Experimental and numerical investigations on fracture mechanics specimens made from a welded joint including the heat affected zone show the influence of the different material parameters on the J-integral. Also, the influence of residual stress on the J-integral and on other fracture mechanics parameters is shown.     

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.     

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.     

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.     

Charpy upper shelf energy and crack resistance

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

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.     

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.     

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.     

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.     

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.     

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.     

On the dynamic fracture toughness and crack tip strain behavior of nuclear pressure vessel steel: Application of electromagnetic force

This paper is concerned with the application of the electromagnetic force to the determination of the dynamic fracture toughness of materials. Taken is an edge-cracked specimen which carries a transient electric current I and is simply supported in a steady magnetic field B. As a result of their interaction, the dynamic electromagnetic force occurs in the whole body of the specimen, which is then deformed to fracture in the opening mode of cracking.Using the electric potential and the J - R curve methods to determine the dynamic crack initiation point in the experiment, together with the finite element method to calculate the extended J-integral with the effects of the electromagnetic force and inertia, the dynamic fracture toughness values of nuclear pressure vessel steel A508 class 3 are evaluated over a wide temperature range from lower to upper shelves.The strain distribution near the crack tip in the dynamic process of fracture is also obtained by applying a computer picture processing.     

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.     

The application of constraint based fracture mechanics to engineering structures

Elastic-plastic crack tip fields can be characterised by two parameters, J and T/Q which describes crack tip constraint. This forms the foundation of a constraint based fracture mechanics in which toughness is expressed as a function of constraint in the form of a J–(T/Q) locus. The enhanced toughness associated with shallow cracks and defects can be used in a systematic manner by constraint matching, and implemented through a simple modification to a failure assessment diagram. This methodology enables the conservatism associated with the use of deeply cracked fracture toughness measurements to be relaxed. In this work these methods have been applied to a tubular welded joint.     

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.     

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.