Stress relaxation analysis and irradiation creep and swelling in pressure tubes

An analysis is presented of slit width test information on two pressure tubes that had been irradiated in test reactors. The analysis showed that differential swelling stresses and thermal stresses undergo relaxation. The mechanism responsible for the stress relaxation at temperatures less than 700 K was irradiation creep. Irradiation creep in thermal test reactor pressure tubes is evidently greater than it would be at equivalent conditions in fast reactors. The residual stresses observed in the slit width tests varied between 30 and 257 MPa and would act to reduce the operating stresses, thus allowing for increased service life of the tubes as compared with no stress relaxation.     

Creep fracture mechanics parameters for internal axial surface cracks in pressurized cylinders and creep crack growth analysis

In the present study, a low alloy Cr–Mo steel cylinder subjected to internal pressure at high temperature with a semi-elliptical crack located at the inner surface is considered. The creep crack driving force parameter C1-integrals calculated by finite element (FE) method, are compared with results from previous studies, which indicates that empirical equations may be inaccurate under some conditions. A total of 96 cases for wide practical ranges of geometry and material parameters are performed to obtain systematic FE results of C1-integral, which are tabulated and formulated in this paper. It is observed that the maximum C1-integral may occur neither at the deepest point nor at the surface point when the aspect ratio is large enough and the value of C1-integral is significantly sensitive to the crack depth ratio. Furthermore, based on the proposed equations for estimating C1-integrals and a step-by-step analysis procedure, crack profile development, crack depth, crack length and remaining life prediction are obtained for surface cracks with various initial aspect ratios. It is found that when the crack depth ratio is increased, there is no obvious convergence of crack aspect ratio observed. The magnitude of half crack length increment is always minor compared with the crack depth increment. In addition, the remaining life is much more dependent on the surface crack depth than on the surface crack length.     

Damage assessment method of P91 steel welded tube under internal pressure creep based on void growth simulation

Development of creep damage assessment methods for longitudinal welded piping of P91 steel is important and an urgent subject to maintain reliable operation of boilers in ultra super critical thermal power plants. Internal pressure creep tests were conducted on P91 steel longitudinal welded tubes to characterize the evolution of creep damage in a heat-affected zone (HAZ) of the longitudinal welded pipe. Failure occurred at a heat-affected zone without significant macroscopic deformation. It was found that initiation of creep voids had concentrated at mid-thickness region rather than surface. Three-dimensional finite element (FE) creep analysis of the creep tested specimens was conducted to identify stress and creep strain distribution within the specimen during creep. Finite element creep analysis results indicated that triaxial tensile stress yielded at the mid-thickness region of the HAZ. It was suggested that the triaxial stress state caused acceleration of the creep damage evolution in the heat-affected zone resulting in internal failure of the tube specimens. Void growth behavior in the heat-affected zone was well predicted with the previously proposed void growth simulation method by introducing void initiation function to the method. A “limited strain” was defined as rupture criterion and dependency of the maximum stress and multiaxiality on the “limited strain” was derived by the void growth simulation. Creep damage distribution in the HAZ under the internal creep test was calculated by proposed damage assessment method.     

Fatigue crack growth calculations for a vessel internal corner crack under repeated thermal transients

A problem of current fundamental and industrial interest is the structural integrity of pressure vessels containing defects when subjected to repeated thermal shock at constant internal pressure. The component considered is a nozzle to a hemispherical pressure vessel intersection containing a defect at the internal corner. A range of 12 cases of thermal shock loads characterised in severity by two dimensionless parameters, the Biot (B) and Fourier (F) numbers, were applied. Estimation of remaining life for each case was carried out based on the PD6493 procedure. Numerical modelling of the crack growth from the quadrant shaped crack showed that more severe shocks accelerate crack growth while less severe shock leads to slow growth or eventual crack arrest. The effect of the Biot and Fourier parameters on the remaining life of the component was quantified. A methodology that comprises of heat transfer, thermal stress and fracture mechanics of defect assessment is applied to a problem of industrial interest.     

Influence of reference stress formulae on creep and creep-fatigue crack initiation and growth prediction in plate components

Creep and creep-fatigue crack growth in pre-cracked plates of 316L(N) austenitic stainless steel, containing a semi-elliptical surface defect and tested at 650 °C under combined axial and bending loading, are investigated. The results have been interpreted in terms of the creep fracture mechanics parameter C^∗ and compared with data obtained on standard compact tension (CT) specimens of the same material and batch. In making the assessments, the reference stress method has been used to determine C^∗. Several formulae exist for calculating the reference stress depending on whether it is based on a ‘global’ or a ‘local’ collapse mechanism and the assessment procedure adopted. When using this approach, it has been found that the most satisfactory comparison of crack growth rates with standard CT specimen data is obtained when the ‘global’ reference stress solution is used in conjunction with mean uniaxial creep properties. It has been found that the main effect of changing the fatigue cycle range from 0.1 to −1.0 is to cause an acceleration in the early stage of cracking.     

A damage mechanics approach to the prediction of creep crack growth

Based upon the local damage hypothesis and utilizing similarity solutions, a theoretical equation for the calculation of creep crack growth rate has been derived in this paper. Creep crack growth tests under constant load and constant load-pin-displacement-rate have been carried out at 550°C and 565°C in a 2·25Cr-1Mo steel. It has been shown that the prediction of creep crack growth rate using the local damage model would be on the safe side, as the prediction line ties in with the upper limit of the experimental data. In this paper, the validity of the C* parameter in the case of a small damage zone has been examined and confirmed. An empirical formula for the evaluation of the ‘creep constraint factor’ has been established to meet the needs of calculation of creep crack growth using the local damage model.     

The effect of residual stress on the creep deformation of welded pipe

The finite element method has been used to study the creep deformation of pipe butt welds in the presence of an initial residual stress distribution. The study has used values for pipe dimensions, temperature (575°C) and internal pressure (70 bar) which correspond to the conditions being used in a pressure vessel testing programme which is investigating transverse weld metal cracking in CrMoV reheat pipe welds. Two sets of steady state creep data for the weld metal have been used, one to represent a weld weaker than the parent and the other one that was stronger. A residual stress distribution, consistent with experimental data, has been generated as àn initial condition for the analysis. The results are presented, discussing the effects of residual stress on both the total and creep strain accumulations for the two weld properties. The steady state creep laws used in the analysis do not allow for damage accumulation, but the possibility of such an effect is discussed using the Kachanov model. The results of the finite element analysis are compared with the experimental creep strain data from the pressure vessel testing programme.     

Comparison of creep crack initiation and growth in four steels tested in HIDA

In power generation plants and the chemical industries there is a need to assess the significance of defects which may exist in high temperature equipment operating in the creep range. For the life prediction methodology for cracked components developed under the HIDA (High Temperature Defect Assessment) Brite/Euram project, it is necessary to have a verifiable data-base of crack initiation and growth data in order to obtain relevant material properties for use in calculations. This paper examines the methods of analysis used. Four types of steels were tested in the programme. These were P22, 1CMV, 316LN and P91 in the parent, as welded and overaged conditions. The data have been obtained from seven participating laboratories. All the results were analysed in the same way using a programme called zrate developed to follow the ASTM E1457-98 testing standard. The results are compared with other crack initiation and creep crack growth data in the literature and with predictions produced from creep data using a model of the cracking process. It has been found that in all cases the scatter in the data is less than for the generic data in the literature. It has also been found that creep crack initiation and growth data can be correlated most satisfactorily in terms of the creep fracture mechanics parameter C¹.     

Modeling for ductile-to-brittle transition under ductile crack growth for reactor pressure vessel steels

The local stress–strain state (SSS) near the crack tip is investigated by the finite element method in the finite strain statement (with regard to a change of the crack tip blunting) for both stationary cracks and crack growing by a ductile mechanism. Using the revealed particularities of SSS near the stationary and growing crack tips and the local cleavage fracture criterion the phenomenon of the ductile-to-brittle transition is explained for reactor pressure vessel steels. The model is proposed to predict the amount of ductile crack extension preceding the ductile-to-brittle transition as a function of the test temperature. The procedure for calculation of the cleavage fracture toughness is also elaborated with regard to ductile crack extensions. Analysis of the obtained calculated results and available experimental data is made. Alternative approaches for the interpretation of the ductile-to-brittle transition are discussed.     

A phenomenological theory of subcritical creep crack growth in a cylindrical vessel weakened by an axial part-through crack

A phenomenological theory of subcritical creep crack growth is formulated for materials with large creep exponent. The subcritical crack growth is shown to be mainly controlled by the average net section stress and the plastic deformations in the vicinity of the crack tip. Plastic zone size is evaluated by considering the effects of relaxation on the plastic stress singularity at the crack tip for a power hardening material. The theory has been applied to a cylindrical vessel weakened by an axial part-through crack. The predicted rupture behaviour compares favourably with published creep rupture tests on 9Cr 1Mo steel tubing pressurised at 550°C. The concept of flaw size stress is introduced and is used in failure mode prediction. Failure will be by breakage or leakage, depending on the relative values of flaw size stress and material yield stress.     

Ductile crack growth of semi-elliptical surface flaws in pressure vessels

Experiments on ductile crack growth of some axial surface flaws in a pressure vessel have 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 tests have been analyzed 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 depended 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.     

Difficulties in interpreting data from creep crack growth tests on type 316H weldments

Abstract

Experimental creep crack growth data are generally obtained by following standard methods such as ASTM E1457-07 and subsequently characterised using the C* parameter. These data are then used in assessment procedures, such as R5, together with reference stress estimates of C* in the component, to predict creep crack growth behaviour. Some modifications to the ASTM E1457 creep crack growth testing and analysis methods have already been proposed following a previous analysis of data from long term creep crack growth tests on type 316H parent material. This paper reports the results of creep crack growth tests on type 316H heat affected zone material at 550°C using compact tension (CT) specimens manufactured from non-stress relieved thick section butt welds. It is shown that interpretation of the data from these weldment tests is complicated by both the discontinuous nature of the cracking process and the presence of significant residual stresses in the CT specimens. Further modifications to creep crack growth testing and analysis methods are proposed to address difficulties arising from the discontinuous nature of the cracking process, and further work is identified to investigate the influence of the residual stresses present in the specimens on the observed crack growth behaviour.     

Effect of thermal stress on crack growth in inhomogeneous cylindrical superconductor

The effect of thermal stress on the growth of central cracks in inhomogeneous cylindrical superconductors is investigated assuming that the material properties vary linearly with the radial coordinate and temperature differences. General expressions for the temperature distribution and thermal stress in terms of a Bessel equation and the plane strain approach are derived. The results indicate that the distributions and variations in the radial and hoop thermal stresses in an inhomogeneous superconductor differ from those in homogeneous superconductors. However, thermal stress affects the crack growth similarly in both superconductor types. The thermal-stress analysis should be useful for the crack growth prediction regarding inhomogeneous superconductors.     

Statistical analysis of fatigue crack growth for 16MnR steel under constant amplitude loads

A statistical investigation of the fatigue crack propagation process has been carried out. Twenty-one pre-cracked specimens obtained from the same sheet of Chinese steel 16MnR were subjected to identical load and environmental conditions. Tests were conducted under constant amplitude loads in order to study the effect of material property randomness. From the experimental data, the distribution of the crack size at any given number of cumulative load cycles, or the distribution of the number of load cycles to reach any given crack size, is determined. The statistical distribution of the crack growth rate at any given number of load cycles or at any given crack size is also discussed. The statistical investigation methods of the fatigue crack propagation process, proposed by this article, were also found to be suitable for other materials.     

Failure pressure of straight pipe with wall thinning under internal pressure

The failure pressure of pipe with wall thinning was investigated by using three-dimensional elastic–plastic finite element analyses (FEA). With careful modeling of the pipe and flaw geometry in addition to a proper stress–strain relation of the material, FEA could estimate the precise burst pressure obtained by the tests. FEA was conducted by assuming three kinds of materials: line pipe steel, carbon steel, and stainless steel. The failure pressure obtained using line pipe steel was the lowest under the same flaw size condition, when the failure pressure was normalized by the value of unflawed pipe defined using the flow stress. On the other hand, when the failure pressure was normalized by the results of FEA obtained for unflawed pipe under various flaw and pipe configurations, the failure pressures of carbon steel and line pipe steel were almost the same and lower than that of stainless steel. This suggests that the existing assessment criteria developed for line pipe steel can be applied to make a conservative assessment of carbon steel and stainless steel.     

Development of probabilistic fracture mechanics analysis codes for reactor pressure vessels and piping considering welding residual stress

Probabilistic fracture mechanics (PFM) analysis codes for reactor pressure vessels (RPVs) and piping, called as PASCAL (PFM Analysis of Structural Components in Aging LWRs) series, have been developed. The PASCAL2 (PASCAL version 2) evaluates the conditional probability of fracture of an RPV under transient conditions including pressurized thermal shock (PTS) considering neutron irradiation embrittlement of the vessels. Recent improvements to PASCAL2 are related to the treatment of weld–overlay cladding. The results using the improved code indicate that the residual stress by weld–overlay cladding affects the fracture probability to some extent. The PASCAL-SP (PASCAL – Stress corrosion cracking at welding joints for Piping) evaluates the probabilities of failures including leakage and breaks of safety-related piping complying with Japanese regulation and rules. Effects of welding residual stress distribution as well as inspection accuracy are focused in this study. Residual stress distributions have been determined by parametric FEM analyses and incorporated into the code.     

A local approach to creep fracture by slow crack growth in an MDPE: Damage modelling

Slow crack growth (SCG) behaviour has been investigated under creep conditions in a medium density ethylene–butene copolymer (MDPE) on both axisymmetrical Full Notched Creep Tensile (FNCT) and Double Edge Notched Tensile (DENT) samples tested at 60 °C. An attempt is made to predict the long-term failure of a component under creep loading conditions, using an incremental damage law. The experimental creep damage observations were compared to the creep stress–strain distributions calculated by finite element method. Such comparison can provide a damage evolution law as a function of the maximum principal stress and the creep strain. The failure criterion is expressed in terms of a critical creep damage over a critical distance. This model is applied to creep crack growth on the FNCT and DENT samples.     

Statistical analysis of residual stress determinations using neutron diffraction

Within Task Group 1 (TG1) of the European Network on Neutron Techniques standardization for Structural Integrity (NeT), residual stress determinations by neutron diffraction were performed on a single weld bead on a plate (BoP) specimen by several laboratories. By following a pre-defined protocol, residual stress distributions have been estimated in the plate. Each residual strain/stress instrument at each institute have their own characteristics and their own methods by which the data is analyzed; however, the final estimate of the stress distributions are expected to be ‘the same’ to within the quoted uncertainty. This implies that this quoted uncertainty for each stress determination should be realistic.For specific measurement locations in the BoP specimen a modified Bayesian approach was used to obtain an average stress. This special approach is less affected by outliers, although care must be taken as it has been observed that in the case where there are few data points in the average, a strong bias can occur towards data points with a relatively small quoted uncertainty. In the data analyses used here, a ‘fairer average’ less influenced by such bias is implemented.Presented here is an overview of the main features that influence the stress and associated uncertainty determination, such as reference values, choice of moduli values, grain size effects and positioning etc.     

Convective heat transfer and pressure drop of annular tubes with three different internal longitudinal fins

Pressure drop and heat transfer characteristics of air in three annular tubes with different internal longitudinal fins were investigated experimentally at uniform wall heat flux. The tested tubes have a double‐pipe structure with the inner blocked tube as an insertion. Three different kinds of fins, plain rectangle fin, plain rectangle fin with periodical ridges and wave‐like fin, were located peripherally in the annulus. The friction factor and Nusselt number can be corrected by a power‐law correction in the Reynolds number range tested. It was found that the tube with periodical ridges on the plain fin or with wave‐like fin could augment heat transfer; however, the pressure drop was increased simultaneously. In order to evaluate the comprehensive heat transfer characteristics of the tested tubes, two criteria for evaluating the comprehensive thermal performance of tested tubes were adopted. They are: 1) evaluating the comprehensive heat transfer performance under three conditions: identical mass flow, identical pumping power, and identical pressure drop; 2) the second law of thermodynamics, i.e., the entropy generation. According to the two different evaluating methods, it was found that the tube with wave‐like fins provided the most excellent comprehensive heat transfer performance among the three tubes, especially when it was used under higher Reynolds number conditions. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(1): 29–40, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20186