Kamran Nikbin

Finite element based plastic limit loads for cylinders with part-through surface cracks under combined loading

This paper provides detailed plastic limit load solutions for cylinders containing part-through surface cracks under combined axial tension, internal pressure and global bending. Such solutions are developed based on detailed three-dimensional (3D) finite element (FE) limit analyses using elastic-perfectly-plastic material behaviour, together with analytical solutions based on equilibrium stress fields. For the crack location, both circumferential and axial cracks, and for each case, both external and internal cracks are considered. Furthermore, in terms of the crack shape, calculations are presented for both semi-elliptical and constant-depth surface cracks. The resulting limit load solutions are given in a closed form, and thus can be simply used in practical situations and defect assessment documents. In general, differences between analytical solutions based on equilibrium stress fields and the proposed solutions are more significant for axial cracks than for circumferential cracks. Since the calculations are based on detailed 3D FE limit analysis no assumption is needed concerning the state of stress. The present solutions, therefore, are an accurate estimate of the limit loads of the geometries that have been considered and are thus very useful information for assessing the integrity of pressurised piping.

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

Abstract 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 C ∗ .

Experimental Evaluation of the J or C * Parameter for a Range of Cracked Geometries

In the current ASTM Standard Test Method for Measurement of Creep Crack Growth Rates in Metals (E 1457) the experimental C* parameter is related to the load and creep load line displacement rate through the geometry related η factor. In this work η factors for a range of geometries are presented. The geometries examined are the compact tension specimen, C(T), single edge notch specimen in tension, SEN(T), and bending, SEN(B), double edge notch specimen in tension, DEN(T), middle crack specimen in tension, M(T) and the C-shaped specimen in tension CS(T). Calculations have been performed for a linear elastic-power law hardening material but the resulting η factors are applicable to either power law plastic or power law creeping materials. Values for ηLLD and ηCMOD, based on the load line displacement and crack mouth opening displacement, respectively, have been determined. A wide range of crack depths, 0.1⩽a/W⩽0.7, where a is crack length and W is specimen width, and hardening exponents, 3 ⩽N ⩽10, under plane stress and plane strain conditions have been examined using the finite element method. The influence of specimen length, crack length, material properties and out of plane stress state on the η factor has also been considered. It has been found that for shallow cracks the value of η depends quite strongly on the exponent, N in the material power law, regardless of whether η is defined based on the load line displacement or crack mouth opening displacement. The ηLLD factor has also been found to be strongly sensitive to plane stress/strain conditions imposed, a/W and specimen length, whereas ηCMOD depends more weakly on a/W and is almost independent of specimen length for the cases examined. There is, however, no clear trend in these variations over the range of specimen geometries and a/W examined. These results are found to be consistent with those in the literature. Recommendations are made regarding the most appropriate values for η, depending on the specimen type and geometry while taking into account the variability due to the material properties, out of plane stress state and variations between the numerical analyses.

Creep crack growth rate predictions in 316H steel using stress dependent creep ductility

Abstract Short and long term trends in creep crack growth (CCG) rate data over test times of 500–30 000 h are available for Austenitic Type 316H stainless steel at 550°C using compact tension, C(T), specimens. The relationship between CCG rate and its dependence on creep ductility, strain rate and plastic strain levels has been examined. Uniaxial creep data from a number of batches of 316H stainless steel, over the temperature range 550–750°C, have been collected and analysed. Power-law correlations have been determined between the creep ductility, creep rupture times and average creep strain rate data with stress σ normalised by flow stress σ0·2 over the range 0·2<σ/σ0·2<3 for uniaxial creep tests times between 100 and 100 000 h. Creep ductility exhibits upper shelf and lower shelf values which are joined by a stress dependent transition region. The creep strain rate and creep rupture exponents have been correlated with stress using a two-stage power-law fit over the stress range 0·2<σ/σ0·2<3 for temperatures between 550 and 750°C, where it is known that power-law creep dominates. For temperature and stress ranges where no data are currently available, the data trend lines have been extrapolated to provide predictions over the full stress range. A stress dependent creep ductility and strain rate model has been implemented in a ductility exhaustion constraint based damage model using finite element (FE) analysis to predict CCG rates in 316H stainless steel at 550°C. The predicted CCG results are compared to analytical constant creep ductility CCG models (termed NSW models), assuming both plane stress and plane strain conditions, and validated against long and short term CCG test data at 550°C. Good agreement has been found between the FE predicted CCG trends and the available experimental data over a wide stress range although it has been shown that upper-bound NSW plane strain predictions for long term tests are overly conservative.

Effect of low transformation temperature weld filler metal on welding residual stress

Abstract The effect of weld filler metal austenite to acicular ferrite transformation temperature on the residual stresses that arise during the gas metal arc welding of a low carbon steel has been examined using a finite element model. It was found that the stress levels in the weld can be tailored by the appropriate selection of the filler metal and compressive, near zero or tensile residual stresses produced. Reasonable agreement was obtained between the model and the stresses measured using neutron diffraction both in welds using conventional and low transformation temperature filler metal.

Creep crack initiation and growth in thick section steel pipes under internal pressure

Abstract In this study, creep crack growth in pre-cracked straight and bent pipes of a 9% Cr-steel, containing multiple cracks and tested at 625 °C under static and slow cyclic pressure loading, is 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, reference stress methods have been used to determine C ∗ for the pipes. Several formulae can be employed for calculating reference stress depending on whether it is based on a ‘global’ or a ‘local’ collapse mechanism. When using this approach, it is shown that the values obtained for C ∗ are sensitive to the material properties, geometric dimensions and crack lengths chosen in the analysis. However, 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 the nominal thickness of a pipe and the mean parent uniaxial creep properties. Also, no difference has been observed between the crack growth rates measured in the straight and bent pipes. The main effect of the slow pressure cycling was to cause an acceleration in the early stages of cracking.

Two Parameter Characterisation of Crack Tip Fields under Creep Conditions

In this work the effect of constraint, i.e. specimen size and geometry, on the high temperature crack tip fields is studied. The approach extends the two parameter method developed for elastic-plastic fracture mechanics to the creep regime. Finite element distributions of crack tip stress and creep strain under transient and steady state conditions are presented and the results interpreted in terms of the Q stress. The variation of the Q value from short to long term conditions is also examined for elastic-creep materials.

Probabilistic analysis of creep crack initiation and growth in pipe components

Abstract In this paper creep data have been collected on uniaxial specimens of a carbon manganese (C–Mn) steel and a 9% Cr steel, designated P91, at 360 and 625 °C, respectively. Additional tests have been performed at these temperatures on precracked compact tension (CT) specimens and pressurized pipes and tubes containing axial cracks to measure the creep crack initiation (CCI) and creep crack growth (CCG) rate properties of these steels. All the data have been analysed statistically assuming log–normal distributions in properties. The results of this analysis have been incorporated into a Monte-Carlo simulation to predict the cracking behaviour of the pressurized pipes from the uniaxial and ‘benchmark’ CT specimen data. Good agreement has been obtained for the P91 steel but not for the C–Mn steel. The discrepancy observed for the C–Mn steel has been attributed to constraint effects, possible extensive plasticity which occurred on loading and to uncertainties in the determination of the creep fracture mechanics parameter C ∗ used for characterising the cracking behaviour. Further comparisons have been made with deterministic calculations involving different combinations of material properties in a sensitivity study to establish probabilities of failure in the pipes based on the ‘benchmark’ CT specimen.

A comparison of high temperature defect assessment methods

Cracked high temperature components which are subjected to creep or creep-fatigue loading may fail by crack growth, net section rupture or a combination of both processes. In this paper, models are presented for describing these modes of failure in terms of fracture mechanics concepts, limit analysis methods and cumulative damage laws. It is shown that these models form the basis of a number of high temperature defect assessment procedures that are available for plant. These procedures are then applied to a semi-elliptical defect in a plate which is subjected to creep-fatigue loading. It is found that the predictions are sensitive to the crack initiation criteria assumed and the limit analysis solutions adopted.

Probabilistic Prediction of Crack Growth Based on Creep/Fatigue Damage Accumulation Mechanism

In this paper a deterministic creep/fatigue accumulation model from simple sequential and repetitive creep and fatigue crack growth mechanisms for creep-brittle materials is developed. In the model the maximum stress intensity factor and stress intensity factor range can be used to describe, respectively, the creep and fatigue crack growth behaviors. The probabilistic behavior of the combined creep-fatigue can be calculated by direct integration of a joint log-normal probability density function or other methods. The Monte Carlo simulation method is used in this paper to analyze the probabilistic behavior of the derived deterministic creep-fatigue model and to estimate the reliability of a creep-fatigue correlation as introduced by the uncertainties in both creep and fatigue lives. Predicted results from this new crack growth method are compared with the bi-linear creep-fatigue interaction models as adopted by ASME Code Case N-47 and API579/ASME FFS, and the results are discussed.