Calculation of fatigue growth of internal cracks

A method for analysis of internal cracks using finite elements is presented. The analysis is based on the potential energy release rate which is determined as a function of the crack shape. For an elliptic crack subjected to a cyclical loading the crack-growth is found by integrating the energy release rates associated with incremental extensions of the half axes.As examples, internal elliptical cracks located centrically and eccentrically in a thick plate are analyzed. The plate is modelled by 20-node isoparametric solid elements. A condensation of degrees of freedom is performed so that only the freedoms necessary for defining the geometry of the growing crack are retained. Elliptic shapes with only one axis of symmetry are allowed to develop. The potential energy is calculated for different crack shapes and a least square smoothing technique is used for finding the energy release rates associated with growth of the half axes of the ellipse. The results obtained for a centric crack are compared with analytical expressions for a through centercrack and for an elliptic crack in an infinite body under uniaxial tension. In general good agreement between the different methods is observed.The energy release rates are integrated according to Paris's crack growth formula, and the geometry of the growing crack is visualized by plots of the crack periphery for prescribed numbers of load cycles.     

Theory of irradiation induced growth of fatigue cracks

A new type of irradiation damage is considered. It is proposed that the localized stresses that fluctuate both with time and with position in solids subjected to bombardment by energetic neutrons (or ions) can cause pre-existing cracks to grow in the same manner that fatigue cracks grow. Using a suitably modified Paris equation for fatigue crack growth it is calculated that cracks in niobium subjected to bombardment by 14 MeV neutrons grow at a rate of about 5 × 10^?10 m per stress pulse exerted at the crack tip. This growth rate is at the threshold level measured in conventional fatigue crack growth experiments. Thus it is not certain whether indeed cracks in irradiated solids will grow. If cracks do grow by the proposed fatigue mechanism they may seriously limit the life of the first wall material of fusion reactors. The crack growth mechanism cannot explain the chunk formation observed in the experiments of Kaminsky et al. but they might explain chunk formation under fluences many orders of magnitude greater than used by them.     

Estimation of crack growth in the creep range during plastic cyclic loading

Crack growth investigations were performed on the creep-resistant steel 13 CrMo 4 4 in the fatigue and the creep fatigue regime, especially regarding the influence of creep damage on crack growth. To this effect, 2% creep strain was applied to the material at a temperature of 560°C. The crack propagation rate was determined as a function of the specimen shape, temperature, test frequency and hold times. In the case of compact tension (CT-)specimens, creep pretreatment does not affect crack growth. For center-cracked tension (CCT-)specimens, however, the creep pretreatment results in a considerable increase in the crack propagation rate. Hold times of 90 minutes at maximum loading cause an increase in da/dN due to further cavity nucleation. The hold time at which cavity nucleation might occur is evaluated. The dependency on frequency of crack growth may be evaluated by means of a linear superposition of creep and fatigue crack growth. The transition frequency above which pure fatigue crack growth occurs is calculated and the regimes of fatigue, creep and creep—fatigue interaction with environmental influences are characterized.     

Fatigue growth and fracture risk from postulated cracks in pressurized-water reactor piping welds

The necessity of taking quick corrective action when a crack indication is discovered in a nuclear piping weld, has led Framatome to evaluate beforehand the potential risk of such a situation by investigating postulated cracks. Considering pessimistic loading conditions to act on a postulated crack of a given shape and orientation enables the determination of the critical size of such a defect. Introduction of fatigue crack growth then yields the maximum crack size that can be tolerated, given the remaining lifetime of the unit. Additionally, detailed analysis of the scenario that leads to these results contributes to the understanding of the potential risk and helps in alleviating it. In this paper, a review of the basic principles and the application to the case of a branch connection weld are presented.     

IFMIF specifications from the users point of view

This paper summarizes the proposals and findings of the IFMIF Specification Working Group established to update the users requirements and top level specifications for the facility. Special attention is given to the different roadmaps of fusion pathway towards power plants, of materials R&D and of facilities and their interactions. The materials development and validation activities on structural materials, blanket functional materials and non-metallic materials are analyzed and specific objectives and requirements to be implemented in IFMIF are proposed. Emphasis is made in additional potential validation activities that can be developed in IFMIF for ITER TBM qualification as well as for DEMO-oriented mock-up testing.     

Estimation of manufacturing defects in the creep range

Various concepts are available for the estimation of crack-like manufacturing defects of components operated in the creep regime. All these methods raise questions as to their practicable application respectively transferability to the component. Discussing these problems resulted in the demand for the development of a “Two-Criteria-Diagram” which can represent practicable load conditions and make statements on the failure modus.     

On the Donnell's equations in the creep range

This paper is concerned with assessing the accuracy of Donnell's approximation when employed in the creep analysis of a class of circular cylindrical shells. Basic formulation of a general method describing the creep behaviour of two-dimensional cylindrical shells is first presented. The terms affected by Donnell's approximation are then pointed out. The solution of governing equations is obtained through coupling the ‘extended Newton's method’ and finite difference technique in an iterative procedure. A number of examples having geometries falling within the shallow shell definition, around the limit, and beyond the range of applicability, are solved using both theories. It has been noted that the parameter α, representing the shell geometry, has a pronounced effect on the accuracy of Donnell's simplification. As α increases the deviation between the two theories decreases. It is concluded that for the class of circular cylindrical shells considered herein Donnell's approximations yield accurate results for creep analysis, particularly for higher values of creep exponent n. Of course, employing Donnell's approximations results in simpler formulation and a reduction in computational time.     

Crack initiation and growth under creep and fatigue loading of an austenitic stainless steel

Both the initiation and the propagation of macroscopic cracks have been studied in a creep ductile 316L type stainless steel at 575–650°C using various fracture mechanics specimens and a wide range of test conditions including steady load at constant or varying temperatures, varying loads at constant temperature. It is shown that, even for isothermal tests, the C^* parameter is unable to provide unique correlations for all the stages of both creep crack initiation and growth. A unique correlation nevertheless exists between C^* and the time to initiation, T_i. Large differences – either conservative or not – from a simplified linear damage cumulation rule are found when the tests are performed at two successive temperatures or two loads. Very detrimental effects of creep-fatigue loadings are shown.A simplified global approach to creep crack initiation under isothermal conditions, based on reference stress and length concept is developed. A local approach to creep cracking, in which an intergranular physical damage law determined experimentally on notched bars, and stress-strain fields obtained by analytical results is shown to provide crack growth results in good agreement with experiment.     

Determination of the fatigue crack growth threshold in cold-worked Zr-2.5 wt% Nb in the acoustic frequency range

Using infrared analysis, we found that the reaction rate of gaseous uranium hexafluoride and tritium is determined solely by the rate at which energy from the radioactive decay of tritium is absorbed in the reaction mixture. Because uranium hexafluoride and tritium absorb β-energy with different efficiencies, the reaction rate is somewhat dependent on the initial reactant concentrations. Reaction products include uranium subfluorides and tritium fluoride. A radiochemistry model has been developed that includes β-energy production and absorption in the gas phase to allow calculation of the reaction yield per ion pair formed. With this model it was found that the reaction mechanism does not include lengthy chain propagation steps-only about 10 uranium hexafluoride molecules are consumed for each ion-pair formed in the gas phase. Many possible reaction steps are suggested that could contribute to the observed overall mechanism.     

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.     

The role of ductile ligaments and warm prestress on the re-initiation of fracture from a crack arrested during thermal shock

The protection offered by warm prestress can be important for preserving a nuclear pressure vessel's integrity during a postulated emergency condition involving a loss of coolant, when the emergency core cooling water subjects the pressure vessel to a thermal shock. There are two aspects to the problem: (a) the initial extension of a defect into the vessel wall, and (b) the subsequent re-initiation of fracture at an arrested crack tip. This note considers the effect of warm prestress on the re-initiation of fracture from an arrested crack, and emphasizes the role of ductile ligaments. It is argued that the warm prestress concept is applicable, thus complementing the limited experimental results provided by the HSST Thermal Shock experimental programme.     

Fatigue cracks in Eurofer 97 steel: Part II. Comparison of small and long fatigue crack growth

The fatigue crack growth rate in the Eurofer 97 steel at room temperature was measured by two different methodologies. Small crack growth data were obtained using cylindrical specimens with a shallow notch and no artificial crack starters. The growth of semicircular cracks of length between 10-2000 μm was followed in symmetrical cycling with constant strain amplitude (R_ε = −1). Long crack data were measured using standard CT specimen and ASTM methodology, i.e. R = 0.1. The growth of cracks having the length in the range of 10-30 mm was measured. It is shown that the crack growth rates of both types of cracks are in a very good agreement if J-integral representation is used and usual assumptions of the crack closure effects are taken into account.     

A phenomenological approach for the analysis of combined fatigue and creep

An approach is proposed for the life prediction, under cumulative damage conditions, for fatigue and for creep. An interaction effect is introduced to account for a modification in the material behavior due to previous loading. A predictive technique is then developed which is applied to several materials for fatigue and which could potentially be used for creep.With due consideration to the similarity of the formulation for both phenomena, the analysis for the combination of fatigue and creep is then carried out through a straightforward sequential use of the two damage functions. Several patterns are studied without and with an interaction effect.     

Deformation bounds for elastic-plastic solids within and out of the creep range

A bounding principle for elastic-perfectly plastic creeping and noncreeping structures subjected to mechanical and/or thermal loads varying below or above the shakedown limit is presented. This principle contains some free “perturbation functions” which, suitably chosen, enable it to specialize, so generating bounds on a variety of deformation measures (such as inelastic work dissipated within any portion of the body, inelastic strains and displacements), some of which are new results, others recover or generalize known results. The resulting bounding technique possesses a quite unified character which is useful for computational purposes. The concept of “pseudo-plastic” strain is shown to be crucial for the derivation of bounds applicable above the shakedown limit.     

Crack growth initiation in concrete-like materials in the presence of creep

A numerical procedure that employs the finite element method and the state variables approach is proposed to analyse the critical condition of a crack in an aging viscoelastic body under sustained load. A far field solution proposed by Schapery is used. An example shows how a crack can become critical after some finite time that depends on the characteristics of the concrete.     

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.