R5 and British Standards defect assessment procedures

In this paper, a basic high temperature defect assessment procedure is first described. This is common to the Nuclear Electric R5 procedure and the British Standards Document PD6539. Then the paper provides some details of the PD6539 method and the R5 procedure. The latter procedure covers a number of situations beyond the scope of the basic procedure, such as crack growth in dissimilar metal welds and creep-fatigue crack growth, and these are discussed.     

Use of R5 in plant defect assessment

The R5 defect assessment procedures are widely used to assess components in Nuclear Electric's Advanced Gas-Cooled Reactor plant. In this paper, the use of R5 is illustrated by calculating the creep- fatigue crack growth in a specific component. The resulting crack size is compared with the limiting crack size calculated using R6. The implications of considering ductile tearing in the latter calculation, the possible interaction of tearing with creep crack growth, and the use of leak before break arguments are discussed.     

Comparison of different approaches for estimation of creep crack initiation

In large components such as rotors defects due to manufacturing processes have to be taken into account and crack assessments based on findings of non-destructive evaluation are necessary. Approaches are used in remaining life estimations, for example:

• Time Dependent Failure Assessment Diagram (TDFAD),

• Two Criteria Diagram (2CD) and

• Nikbin–Smith–Webster-Model (NSW-Model).

The TDFAD approach is currently being developed within the R5 procedures as an alternative to conventional methods for predicting incubation and the early stages of Creep Crack growth. A key requirement of TDFAD approaches is the evaluation of a time dependent creep toughness, denoted K_c mat. The 2CD approach has been developed independently in Germany to assess Creep crack incubation in ferritic steels. This approach uses crack tip and ligament damage parameters, R_K and R_σ, respectively. Furthermore the NSW-Model is employed for the estimation of creep crack initiation by using the creep fracture mechanics parameter C^*. Calculations and used parameters were compared for a ferritic 1CrMoV-steel.     

SOME IMPLICATIONS OF THE USE OF THE PD6493 LEVEL 3 FAILURE ASSESSMENT PROCEDURE

Abstract— Under a natural mapping between the standard R-curve analysis diagram and the failure assessment diagrams of R6 and PD6493 Level 3 the R-curve becomes the RCI (R-curve image). It follows that whenever the assessment point moves along the failure assessment line during ductile crack growth, the implication is that the failure assessment line is the RCI. This result is used to test the conservatism of a specific PD6493 Level 3 analysis by two methods. The first calculates the variation during crack growth of the applied elastic-plastic crack tip opening displacement (CTOD) parameter (or‘driving force') which is implied by the PD6493 analysis and then compares this variation with an independent estimate of it. The second uses an assumed driving force to deduce the CTOD resistance curve implied by the failure assessment line. It is shown by both methods and also by a direct R-curve analysis that this particular PD6493 analysis is conservative relative to an R-curve analysis which uses a crack driving force estimated by the EPRI (Electric Power Research Institute) procedures. However there is inconsistency between standard R-curve analysis and PD6493 Level 3 analysis in that the latter implies a material resistance which, for a given material, depends on the geometry of the structure. A similar inconsistency arises in any failure assessment procedures like the Options 1 and 2 with Category 3 of R6, which require the assessment point to move on a geometry independent failure assessment line during crack growth; indeed, even when the failure assessment line is geometry dependent there is full agreement with R-curve analysis only if the correct RCI is used as the failure assessment line. In a brief discussion it is noted that the new failure assessment diagram studies involving multi-parameter fracture mechanics may help to ameliorate these problems.     

THE USE OF A FAILURE ASSESSMENT DIAGRAM FOR INITIATION AND PROPAGATION OF DEFECTS AT HIGH TEMPERATURES

The use of a failure assessment diagram, of the type in the R 6 defect assessment procedure, is investigated for creep crack growth under steady loading. While a detailed approach based on C* remains attractive for appreciable creep crack growth, it is shown that a simplified approach can be formulated for limited crack extension. A failure assessment diagram is derived based on the option 2 curve of R 6 using isochronous stress-strain data. The inclusion of elastic strains in the isochronous data covers stress redistribution effects. Equations are given which enable a toughness, K_mat, for assessments at temperatures in the creep range to be evaluated from creep crack incubation and growth data presented in terms of C*. The toughness, K_mat, replaces the fracture toughness used in low temperature R 6 assessments. Thermal stresses can be included in assessments by evaluating the stress intensity factor for the combined thermal and mechanical loading. A formula is given which enables the effect of thermal stresses to be reduced when creep strains are sufficient to relax out part or all of the thermal stress.     

A new method for assessing high-temperature crack growth

Experimental creep crack growth (CCG) test data are obtained by following standards that characterize CCG rates using the C* parameter. Such data are then used in high‐temperature failure assessment procedures. An alternative approach to defect assessment at high‐temperature failure is an extension of the R6 failure assessment diagram (FAD). At high temperature, creep toughness, K^c_mat, can be estimated from CCG tests and replaces low‐temperature toughness in R6. This approach has the advantage that it is not necessary to establish a creep fracture regime, such as small‐scale, primary or widespread creep. Also, a new strain‐based FAD has been developed, potentially allowing variations of stress and temperature to be accommodated. In this paper, the results of a series of crack growth tests performed on ex‐service 316H stainless steel at 550 °C are examined in the light of the limitations imposed by ASTM for CCG testing. The results are then explored in terms of toughness and presented in FADs.     

Method of analysis and prediction for variable amplitude fatigue crack growth

Fatigue crack growth behavior of structure subjected to variable amplitude loading is very complex. Both the truncation and the load sequence have been shown to have a significant influence on the test results because of the load level interaction effects. To understand these interaction effects and the possible influence they can have on the results obtained a test program was performed. Fatigue crack growth tests were conducted on the program using 7075-T6 and 2024-T3 aluminum and titanium 6A1-4V mill anneal.

Using the test data, an analysis method was developed. In this analysis method the crack growth rate is evaluated for each load cycle using a modification of the fracture mechanics correlation technique. The crack growth for each cycle was evaluated as a function of the stress intensity factor excursion with a correction factor for the maximum and minimum peak stress levels in the test spectrum. The fatigue crack growth correction for the peak stresses in the spectrum is given as a growth rate correction factor r. The relationship for r, is termed the ‘fatigue crack growth rate interaction model’.

For verification, the interaction model was applied to test data from spectrum loading tests. The correlation obtained for the example, indicated that the model properly predicts the interaction effects and its use could significantly improve the accuracy of crack growth life calculations for programmed spectrum tests.     

A fatigue crack growth model for interacting cracks in a plate of arbitrary thickness

Fatigue and fracture assessment of structures weakened by multiple site damage, such as two or more interacting cracks, represents a very challenging problem. A proper analysis of this problem often requires advanced modelling approaches. The objective of this paper is to develop a general theoretical approach and investigate the fatigue behaviour of two interacting cracks. The developed approach is based on the classical strip yield model and plasticity induced crack closure concept. It also utilises the 3D fundamental solution for an edge dislocation. The crack advance scheme adopts the cycle‐by‐cycle calculations of the effective stress intensity factors and crack increments. The modelling results were validated against experimental data available in the literature. Further, the nonlinear effects of the crack interaction and plate thickness on the crack opening stresses and crack growth rates were studied with the new approach for the problem geometry. It was demonstrated that the both effects could have a significant influence on fatigue life and cannot be disregarded in life and integrity assessments of structural components with multiple site damage.     

A comparison of the simplified probabilistic method in R6 with the partial safety factor approach

Probabilistic assessments are a useful aid to decision making in areas such as safety analysis, design studies and the deployment of resources on maintenance, inspection and repair. In principle, a full probabilistic assessment requires a complete knowledge of the relevant failure models and the distributions for each of the input quantities. However, in practice, these requirements cannot normally be met in full and it is necessary to employ various simplifying assumptions and approximations in order to make the analysis tractable. The partial factor method and the simplified approach in R6 provide two relatively simple and independent methods of assessing failure probabilities using R6.The two methods have been applied to a set of test cases and the results compared. In the case of the partial safety factor method target reliabilities in the range 10⁻³–10⁻⁵ were considered. Sets of partial safety factors for load, defect size, fracture toughness and yield stress were taken from BS 7910 and used for assessments covering different regions on the R6 failure assessment diagram. A calculation of the assessed failure probability was also carried out for each of these sets of conditions using a simplified probabilistic approach developed for the R6 procedure.The assessed failure probabilities were compared with the corresponding target reliability assumed for the partial safety factor calculation. It was found that the partial safety factor assessments were generally conservative compared to the simplified approach. However, in many instances the assessed probabilities were several orders of magnitude smaller than the target reliabilities suggesting that the recommended values of partial safety factors in BS7910 were excessively conservative for some of these conditions.     

High temperature fatigue crack growth in Inconel 718

Abstract

The nickel base superalloys are extensively used in high temperature applications, so it is important to know their behaviour under conditions of high-temperature fatigue. This paper studies the influence of ΔK, loading frequency, stress ratio and temperature on the high temperature fatigue crack growth rate of nickel base superalloys. This study is based on fatigue tests carried out in corner crack specimens of Inconel 718 at 600°C and at room temperature. Three stress ratios (R = 0.05, 0.5 and 0.8) and loading frequencies ranging from 0.0017 to 15 Hz were considered in the tests. For frequencies below 0.25 Hz, the load wave shape was trapezoidal with different dwell times at maximum load. At relatively high frequencies the propagation is cycle dependent, while for lower frequencies it is time dependent. At intermediate frequencies a mixed crack growth occurs. The transition frequencies from cycle dependent to mixed regime and from mixed to time dependent regime were obtained for each R. The increase of R increases the transition frequencies, i.e., extends the time dependent crack growth to higher frequencies. The increase of R also produces an increase of cyclic crack growth rate for all regimes of crack growth. In the time dependent regime, a higher variation is observed, that can be explained by an acceleration of oxidation damage promoted by the increase of maximum stress. An approach for modelling the high-temperature fatigue crack growth in nickel base superalloys is presented. A good agreement was observed between time dependent fatigue results and mathematical models based on static load results.     

Fracture experiments on through wall cracked elbows under in-plane bending moment: Test results and theoretical/numerical analyses

Fracture assessment of pipe bends or elbows with postulated through wall crack is very essential for leak-before-break qualification of primary heat transport system piping of nuclear power plants. The methodology for fracture assessment of cracked elbows is still in developing stage. Any new development in theoretical aspect requires experimental validation. However, fracture test data on cracked elbows is not so abundant as straight pipes. The earlier experiments on cracked elbows were focused mainly on the determination of limit load. Other fracture parameters e.g. crack growth, crack initiation load or crack opening displacement were not reported in the open literature. Against this backdrop, a comprehensive experimental and theoretical program on component integrity has been initiated at Reactor Safety Division (RSD) of Bhabha Atomic Research Center (BARC), India. Under this program, a number of fracture tests have been carried out on elbows with through wall circumferential/axial cracks subjected to in-plane closing/opening bending moment. These test data are then thoroughly analysed numerically through non-linear finite element analyses, analytically through limit load comparison and also through comparison of crack initiation loads by finite element and R6 methods. These test data may be utilized in future for validation of new theoretical developments in the integrity assessment of through wall cracked elbows.     

A new model for characterizing primary creep damage

Primary creep damage may occur at a crack tip in steel at room temperature and below. The effect of this time-dependent damage is generally neglected. Recently developed experimental data clearly show that, for some materials, neglecting time-dependent deformation and damage may be quite nonconservative and dangerous in certain practical applications.In this paper, a new theory is developed which incorporates the effects of time-dependent damage into the crack growth and failure process. The predictive ability of the model is verified first by finite element analyses and then by comparison to experimental data. It is clearly shown that, for the material considered here, time-dependent damage effects must be considered or the crack growth process is not adequately accounted for.     

SMALL CRACK GROWTH AND FATIGUE LIFE PREDICTIONS FOR HIGH-STRENGTH ALUMINIUM ALLOYS: PART I—EXPERIMENTAL AND FRACTURE MECHANICS ANALYSIS

The small crack effect was investigated in two high-strength aluminium alloys: 7075-T6 bare and LC9cs clad alloy. Both experimental and analytical investigations were conducted to study crack initiation and growth of small cracks. In the experimental program, fatigue tests, small crack and large crack tests were conducted under constant amplitude and Mini-TWIST spectrum loading conditions. A pronounced small crack effect was observed in both materials, especially for the negative stress ratios. For all loading conditions, most of the fatigue life of the SENT specimens was shown to be crack propagation from initial material defects or from the cladding layer. In the analysis program, three-dimensional finite element and weight function methods were used to determine stress intensity factors and to develop SIF equations for surface and corner cracks at the notch in the SENT specimens. A plasticity-induced crack-closure model was used to correlate small and large crack data, and to make fatigue life predictions. Predicted crack-growth rates and fatigue lives agreed well with experiments. A total fatigue life prediction method for the aluminium alloys was developed and demonstrated using the crack-closure model.     

Q345R钢多个过载作用下疲劳裂纹扩展行为研究

单一过载使得疲劳裂纹扩展速率减缓,可以提高疲劳寿命,但对于多个过载作用下疲劳裂纹扩展仍未明确,有待于进一步研究。针对Q345R标准紧凑拉伸试样,在常幅循环加载条件下引入多个拉伸过载,研究多个过载作用对疲劳裂纹扩展行为的影响。研究结果表明:在保持应力比、过载位置和过载比不变的情况下,随着过载间距增加,迟滞效应先增加后减小;过载间距循环数是单一过载迟滞循环数的一半时,da/dN_min达到最小,迟滞效应最明显。采用含有过载交互作用参数Ø_I的修正Wheeler模型对不同的过载间距疲劳裂纹扩展行为试验结果进行预测,预测的结果与试验结果能够很好的吻合。     

Untersuchungen zum Ermüdungs-Rißwachstumsverhalten des austenitischen Stahles X 6CrNi 18 11 (1.4948)

Investigations of the Fatigue Crack Growth Behaviour of the Austenitic Stainless Steel X 6CrNi 18 11 (1.4948) The fatigue crack growth behaviour of the heat resistant austenitic stainless steel X 6CrNi 18 11 (material number 1.4948), which is used as the structural material for the primary and secondary heat transfer systems of the liquid metal fast breeder reactor SNR 300, is described. The parameters under consideration are the temperature in the range from 308 K up to 973 K, the frequency from 0.5 Hz up to 20 Hz, the stress ratio R as well as the heat-to-heat variation. The minimum ligament size criterion as well as the influence of the test technique on crack propagation are discussed. For the various test parameters the constants C and n of the Paris equation are calculated. The test results demonstrate a small influence of the heat-to-heat variation on the crack growth. At low stress ratios and at room temperature the influence of frequency is very small. A strong influence of the stress ratio R on the crack growth rate is observed. For higher R-values and high temperatures a distinct influence of the frequency on the fatigue crack propagation is shown.     

Analysis of fatigue crack propagation in the frame of a hydraulic press

Within this paper the fatigue crack growth in the frame of a hydraulic press will be discussed. The crack growth started at a shrink hole in a notch in the middle part of the frame. The state of stress of the crack is predominantly influenced by the notch, which induces a Mixed-Mode-loading during the crack growth. The propagation of the crack will be analyzed with the crack simulation program ADAPCRACK3D, which has been developed at the Institute of Applied Mechanics at Universität Paderborn. This program is able to calculate fully automatic the stress intensities along a 3D-crack front as well as the crack path and the lifetime of a structure.     

Propagation of microcracks at stress amplitudes below the conventional fatigue limit in Ti–6Al–4V

Fatigue crack growth below the conventional fatigue limit was examined in Ti–6Al–4V in two different microstructural conditions, bi-modal and fully lamellar. Tests conducted at R = −1, at room temperature and in air showed that there is a stress dependency in the d a /d N –Δ K behaviour in both microstructures. The increasing crack front roughness associated with increasing crack size results in a decrease in the crack growth rate relative to the crack growth rate in a single grain. The d a /d N vs. Δ K lines were drawn for each crack size and a 'threshold'Δ K was determined using the intercept of the lines with d a /d N = 10⁻¹⁰ m cycle⁻¹. These values were used to construct modified Takahashi–Kitagawa diagrams to predict microcrack growth below the fatigue limit for each microstructure. A comparison of the two microstructures indicated differences in behaviour in microcrack and macrocrack growth that were explained by differences in crack front roughness at a given crack size.     

Thermomechanical coupling effects on fractured solids

An analytical model is presented to predict the temperature field induced in a fractured solid by mechanical loadings. The heat conduction equation used to compute the temperature field consists of three separate terms that account for the coupling effects. These are the thermoelastic, thermoplastic and thermofracture coupling terms. Finite element formulations were used for the numerical solutions of a case study. This case study involved experimental assessments of temperature rises near the tip of a stationary crack when subjected to an impact load that attempted to open the crack surfaces. Good correlations of analytical and experimental results were obtained. The measurable temperature rises in a fractured solid suggested that the coupling effect may be significant enough to influence the fracture characteristics of a solid; in particular, if the bulk temperature of the solid is close to the transition temperature from the brittle to ductile fracture mode or vice versa.     

ELASTIC-PLASTIC FRACTURE MECHANICS FOR PRESSURE VESSEL DESIGN

The project has been concerned with the verification of the J-philosophy for initiation and growth of cracks on laboratory type specimens as well as on larger surface cracked plates. The analysis of the experiments involved extensive fully three-dimensional finite element calculations. It was found that the initiation events for the six surface cracked plates occurred at approximately the same J-value. A corresponding relation to the laboratory type specimen was less successful, mainly because of the short-comings of current methods for J_IC-evaluations. A somewhat puzzling feature of the surface crack experiments was that unstable crack growth occurred immediately after crack growth initiation in four out of six tests, while some amount of stable crack growth was evident in the remaining two and in all of the laboratory type specimens. An evaluation of the surface experiments by a type of R6-analysis was also performed. Using as K_cr the mean value from the surface crack experiments, it was found that the R6-method yielded conservative predictions.