Understanding fracture behaviour of PGA reactor core graphite: perspective

Abstract

Magnox reactors are cooled by carbon dioxide gas. The pile grade A (PGA) graphite moderator bricks in the reactor core loose mass and become more porous during service due to the radiolytic oxidation caused by energy deposition, mainly gamma radiation. In addition, neutron irradiation brings about strengthening by irradiation hardening and dimensional change. In this perspective, experimental data related to the attendant microstructural changes and the associated initiation and propagation of cracks within the graphite are revisited. These results are compared with the predictions of multiscale finite element modelling based upon an idealised microstructure. The discussion considers the quasi-brittle characteristics of the PGA graphite over a range of service exposure conditions.     

Limit loads and fracture mechanics parameters for thick-walled pipes

In this paper, information on plastic limit loads and both elastic and elastic-plastic fracture mechanics parameters is given for cracked thick-walled pipes with mean radius-to-thickness ratios ranging from two to five. It is found that existing limit load expressions for thin-walled pipes can be applied to thick-walled pipes, provided that they are normalized with respect to the corresponding un-cracked thick-walled pipe values. For elastic fracture mechanics parameters, FE values of the influence functions for the stress intensity factor and the crack opening displacement are tabulated. For elastic-plastic J, it is shown that existing reference stress based J estimates can be applied, provided that a proper limit load for thick-walled pipes is used.     

Finite element calculation of contour integral parameters for cracked P91 pipe weld

Abstract

This paper reports the results of elastic–creep finite element (FE) analyses of a P91 steel pipe weld with two external ‘type IV’ circumferential cracks, subjected to internal pressure and end (system) load using creep properties obtained at 650°C. Numerical contour integral calculations have been performed to obtain both transient and stationary high temperature fracture mechanics parameters. A mesh sensitivity analysis was performed in order to ensure the accuracy of FE analyses in the transient creep stage. The effects of load magnitude, the material mismatch near the crack surfaces and the crack depth on the stationary creep C* contour integrals have been investigated, and corresponding analytical correlations are presented.     

Fracture toughness of spun cast SG iron pipe

The fracture toughness properties of two spun cast, ferritic SG iron pipe samples have been investigated and the results compared with previous work. It was found that the COD at fibrous crack initiation ($\text{δ}{}_{\mathrm{<mtext>i</mtext>}}$) was independent of: (a) specimen size; (b) machined or fatigue precracking and (c) graphite nodule number and spacing. This is discussed with respect to the fracture initiation mechanism which was found to be independent of graphite nodules. The maximum load COD values and COD transition were similar for fatigue cracked and machined slit specimens. The COD values and COD transition temperature obtained from spun cast pipe are lower than those obtained in previous work on SG iron and it has been shown that the maximum load COD decreases with decrease in graphite nodule spacing. The effect of graphite nodule spacing on the ductile fracture propagation energy is discussed.     

Mechanical behavior of electrochemically hydrogenated electron beam melting (EBM) and wrought Ti–6Al–4V using small punch test

The influence of electrochemical charging of hydrogen at j = ?5 mA/cm² for 6, 12, 48 and 96 h on the structural and the mechanical behavior of wrought and electron beam melting (EBM) Ti–6Al–4V alloys containing 6 wt% β and similar impurities level was investigated. The length of the α/β interphase boundaries in the EBM alloy was larger by 34% compared to that in the wrought alloy. The small punch test (SPT) technique was used to characterize the mechanical behavior of the non-hydrogenated and hydrogenated specimens. It was found that the maximum load and the displacement at maximum load of the wrought alloy remained nearly stable after 6 h of charging, showing a maximum decrease of ～32% and 11%, respectively. Similarly, hydrogenation of the EBM alloy resulted in a gradual degradation in mechanical properties with charging time, up to ～81% and 86% in pop-in load and displacement at the “pop-in” load, respectively. The mode of fracture of the wrought alloy changed from ductile to semi-brittle with mud-cracking in all hydrogenated specimens. In contrast, the mode of fracture of the EBM alloy changed from a mixed mode ductile-brittle fracture to brittle fracture with star-like morphology. The degraded mechanical properties of the EBM alloy are attributed to its α/β lamellar microstructure which acted as a short-circuit path and enhanced hydrogen diffusion into the bulk as well as δ_a and δ_b hydride formation on the surface. In contrast, a surface layer with higher concentration of δ_a and δ_b hydrides in the wrought alloy served as a barrier to hydrogen uptake into the bulk and increased the alloy resistivity to hydrogen embrittlement (HE). This study shows that EBM Ti–6Al–4V alloy is more susceptible to mechanical degradation due to HE than wrought Ti–6Al–4V alloy.     

Tearing–fatigue interactions in 316L(N) austenitic stainless steel

This paper presents the results from a programme of tearing, fatigue and tearing–fatigue tests performed on specimens from a 316L(N) stainless steel plate. All tests were carried out at ambient temperature. The experimental results have been compared with assessments performed using current guidance within the R6 defect assessment method. The work has shown that there is some evidence that fatigue cycling modifies the JR-curve behaviour of this material. In most cases, the data lie approximately 20–30% above the base-line JR-curve. However, whilst there may be a modest influence of fatigue crack growth on the ductile tearing characteristics, it is difficult to separate this from experimental scatter. In tearing–fatigue tests performed at a stress ratio, R=0.2, ductile tearing reduces the fatigue crack growth rates by up to 50%. This is likely to result from the presence of a residual compressive zone at the crack-tip, and increased crack closure due to the irregular and non-matching fracture surfaces generated by the ductile crack growth mechanisms. For R=0.1 tearing–fatigue tests, fatigue crack growth rates are apparently enhanced by a factor up to of 10, particularly during the latter stages of the tests when ΔK>60 MPam. This is likely to result from: (i) loading being in the elastic–plastic regime where the J-integral (rather than K) characterises the crack-tip fields, (ii) increments of ductile tearing which may occur during each fatigue cycle, and (iii) crack blunting which reduces crack closure effects. For the R=0.2 tearing–fatigue tests, the linear summation approach described in R6 provides a consistently conservative prediction of ductile, fatigue and total crack growth during the tests. However, for the R=0.1 tearing–fatigue tests, the Paris law under-predicts fatigue crack growth rates. This may be corrected by using the Kaiser equation, which acknowledges loading in the elastic–plastic regime and incorporates incremental growth due to tearing as well as fatigue. R6 provides conservative predictions of instability for the CT specimen geometry tested in the current programme, both in terms of the critical crack growth and load required for instability to occur.     

The effect of microstructure on fracture mechanisms of 2·25Cr1Mo low alloy steel, part A: the influence of non-metallic inclusions

The effect of variations in the size and distribution of non-metallic inclusions on the fracture behaviour of 2·25 Cr1Mo low alloy steel has been studied by undertaking a programme of disk bend testing at temperatures between 20°C and −196°C. Analysis of load/displacement data in combination with detailed fractographic evaluation indicates that inclusions greater than about 4 μm in diameter significantly increase the susceptibility for the formation of ductile voids. The ease with which ductile voids form then has a direct effect on the load and strain to failure. In contrast, inclusions do not appear to influence behaviour when fracture occurs by cleavage.     

Thermal stress and magnetic effects on nonlinear vibration of nanobeams embedded in nonlinear elastic medium

Abstract

Nonlinear vibration of nanobeams embedded in the linear and nonlinear elastic materials under magnetic and temperature effects is investigated in this study. Von Karman’s strain–displacement relation is applied to a nonlocal Euler–Bernoulli beam model. Equation of motion is derived using Hamilton’s principle. Galerkin’s method is applied to decompose the nonlinear partial differential equation into a nonlinear ordinary differential equation (NODE). The NODE is solved using He’s method. The nanobeams are embedded in the Winkler, Pasternak, and nonlinear elastic media. The effects of low and high temperatures, nonlocal parameter, magnetic force, amplitude, and linear and nonlinear elastic materials are examined.     

Finite element analysis on relationships between the J-integral and CTOD for stationary cracks in welded tensile specimens

In this study the effects of weld strength mismatching and geometry parameters on the relationship between the J-integral and the crack tip opening displacement (CTOD) are investigated. Numerical analysis was carried out by an ABAQUS two-dimensional elastic–plastic analysis mode. The work was performed for center-cracked welded specimens with uniform tensile load. In the specimens the weld strength mismatch, M, was from 0.8 to 1.2, the crack length, a/W, from 0.1 to 0.5, the weld width, h/c, from 0.1 to 0.5. The main results indicate that weld strength mismatching has only a weak influence on the relationship between the J-integral and CTOD at low load levels, but there is a strong effect at high load levels. The yield strength of weld metal may be used for low load levels and the yield strength of base metal may be used for high load levels, when the basic relationship of J-integral versus CTOD is utilized to treat the problem of welded joints. The results also show that the crack size and weld width have an influence on the relationship between the J-integral and CTOD at high load levels. Because the equivalence between the J-integral and CTOD breaks down at high load levels, the relationship between J-integral and CTOD becomes more complex, and the weld strength and geometry mismatching factors must be included.     

On anisotropy of ferritic ODS alloys

Abstract

Ferritic oxide dispersion strengthened (ODS) alloys are candidate materials to be used as cladding for long term fast reactors, due to their high strength at high temperature and good swelling and irradiation resistances. The fabrication of cladding tubes is usually made by a succession of cold deformation steps where a deformation induced anisotropic microstructure could take place, which would affect the mechanical behaviour of the tube. The characterisation of this microstructural anisotropy is one of the key issues in the development of cladding ODS tubes. In this paper, the microstructural anisotropy of a Fe–14Cr–ODS extruded bar and a Fe–12Cr–ODS plate is characterised and its effect on the mechanical properties is analysed by tensile, impact and small punch testing. In both materials, a reduction of the ductility is observed in the transverse specimens. In addition, the fracture behaviour seems to be strongly dependent on the location of the crack plane regarding the elongated grained microstructure.     

An investigation on strain and temperature rate-dependent thermoelasticity and its infinite speed behavior

Abstract

The present work is aimed at a mathematical analysis of the newly proposed strain and temperature rate-dependent thermoelasticity theory, also called a modified Green–Lindsay model (MGL) theory, given by Yu et al. (2018). This model is also an attempt to remove the discontinuity in the displacement field observed under temperature rate-dependent thermoelasticity theory proposed by Green and Lindsay. We study thermoelastic interactions in an infinite homogeneous, isotropic elastic medium with a cylindrical cavity based on this model when the surface of the cavity is subjected to thermal shock. The solutions for the distribution of displacement, temperature, and stress components are obtained by using the Laplace transform technique. The inversion of the Laplace transform is carried out by short-time approximation. A detailed comparison of the analytical results predicted by the MGL model with the corresponding predictions by the Lord–Shulman model and the Green–Lindsay model is performed. It is observed that strain rate terms in the constitutive equation avoid the prediction of discontinuity in the displacement field and other significant effects are noted. However, the new theory predicts the infinite speed of disturbance like the classical theory. Variations of field variables at different time are graphically displayed for different models and compared by using a numerical method.     

Analysis of fracture tests on large bend beams containing an embedded flaw

As part of a collaborative project to investigate the transferability of Master Curve technology to shallow flaws in reactor pressure vessel applications, a series of fracture tests were performed on large scale bend beams, which were fabricated from a reactor pressure vessel steel and contained simulated sub-surface defects. A 2-dimensional finite element model was used to simulate the behaviour of the test pieces and to study the variation in crack tip constraint at both the near surface and deep crack tips with increasing load. Wallin's two-parameter model, which uses the Master Curve representation of the fracture toughness transition curve together with the elastic crack tip T_stress parameter to estimate the shift in the T₀ reference temperature due to constraint loss, has been applied to arrive at estimates of fracture initiation probability. These are found to be consistent with the experimental results.     

Analysis of cyclic creep and rupture. Part 1: bounding theorems and cyclic reference stresses

Cyclic loading on structures can produce failures not readily predicted by conventional static analysis. Ratcheting or incremental distortion leads to structural failure, and complicates the problems of creep and fatigue prediction. Predicting shakedown, ratcheting, accelerated creep and rupture, for cyclic loading, are the objectives of cyclic stress analysis.Limit load, shakedown and ratcheting analyses provide a comprehensive basis to understand static structural behaviour for ductile inelastic materials, subject to variable loading but excluding inertial dynamic effects. From them we can predict the following failure modes:

• –Plastic collapse.
• –Failure to shakedown.
• –Ratcheting.
• –Accelerated creep and rupture.

This is achieved with a generalisation of the reference stress concept. Conventionally, and for steady loading, the limit load reference stress is the lowest yield stress for which the structure does not collapse. For cyclic loading two definitions are available. The more conservative is the lowest yield stress for which the structure shakes down (behaves elastically). The less conservative is the lowest yield stress for which the structure does not ratchet. They have different meanings and uses.Explaining and justifying the use of cyclic reference stresses to bound creep and rupture is the objective of Part 1. Part 2 gives examples illustrating a range of structural behaviours. The methodology of these papers involves so-called approximate methods at one level, that of inferring limiting or conservative time-dependent behaviour from time-independent elastic–plastic cyclic analyses. The elastic–plastic cyclic analyses themselves are straightforward if tedious. Some ideas and a new analysis technique are available to reduce the trial-and-error.     

Transferability of fracture parameters from specimens to component level

The structural integrity of components is usually performed using the specimen fracture resistance curve. However, the specimen fracture resistance curve significantly differs from the component fracture resistance. This is the most serious limitation of classical fracture mechanics. To address this issue, several tests have been carried out on fractured specimens and piping components under an Indo-German bilateral project. Two approaches, namely, two-parameter fracture mechanics and micro-mechanical models are considered to investigate the feasibility of transferability. For the two-parameter fracture mechanics approach, the J-integral has been used as the crack driving force and q is used as a measure of stress triaxiality. The triaxiality quotient q is proportional to the ratio of the hydrostatic stress and the von Mises effective stress and is an additional parameter to make a decision about the initiation value of the J-integral for the failure behaviour of a component. It is shown that if the triaxial conditions match for any two arbitrary geometries, it is feasible to transfer the fracture parameters. The difficulty in transferability is largely overcome by damage mechanics, which models the drop in load carrying capacity of a material with increase in plastic strain. Such modeling is done considering nucleation, growth and coalescence of voids in a material following large-scale plasticity. The Gurson–Tvergaard–Needleman and Rousselier models are used. Some of the results obtained by these models and comparisons with experimental results are presented in this paper to demonstrate the usefulness of damage mechanics in analyzing components with flaws.     

The effect of microstructure on the fracture toughness of structural steels

Comprehensive research has demonstrated that fracture toughness, K_IC, may be uniquely related to the mechanical properties describing a material's crack tip behaviour and microstructure. In the work described in the present paper the behaviour of cracks in seven weldable low alloy structural steels with tensile strengths, σ_TS, in the range 455–765 MPa was investigated by measurement and observation of plane-strain fracture toughness, tensile properties and the microstructure. The information so obtained was used to establish a sophisticated K_IC calculation model. It is shown that the process zone size is the dominant microstructural factor controlling the fracture toughness and that it varies from two to six grain sizes, depending on the particular microstructure. The model proposed matches the experimental data well and can be applied to find an optimum steel microstructure for given brittle fracture design requirements.     

Flexible graphite as battery anode and current collector

In making graphite-based electrodes and current collectors, there is significant simplification if a flexible graphite process is used. The lithium intercalation capacity of Grafoil^®1 flexible graphite sheet and its powder was evaluated using electrochemical charge–discharge cycling in half-cell configuration (coin cell with Li anode and graphite cathode). The sheet form was used with and without a copper current collector. Excellent electrical conductivity of the monolithic material with very low interface resistance helps as current collector and electrode. The comparatively low capacity of Grafoil^® sheet is thought to be due to diffusion limitation of the structure, especially in the light of the very high capacity of its powder form. The highly irreversible capacity of the powdered material may be due to unfunctionalized graphitic structures or impurities present in the powder. Impedance response for the first intercalation–deintercalation was different than responses taken after several cycles. The presence of a second impedance arc suggests structural modification is taking place in the graphite anode, possibly through formation of a porous structure as a result of graphite expansion.     

On the mode III failure of a long submerged defect

This paper analyses the elastic-perfectly plastic failure of a long uniform submerged defect offset from the centre of a uniform block under Mode III loading by a uniform remote longitudinal shear. The analysis confirms that the shorter of the two uncracked ligaments is the first to go fully plastic or to fracture. Solutions are found for the ligament yield load, the crack tip opening displacement (CTOD) and stress intensity factor at each tip, and the mean elastic stress on the shorter ligament. The results are calculated numerically and presented graphically: analytical results are available in the limit of very small remaining ligaments.The results of the Mode III analysis provide insight into the elastic-plastic behaviour of similarly cracked plates in Mode I loading under tension, and more generally illustrate some of the interactions between ‘local’ and ‘global’ plasticity during defect assessment.     

Transferability of specimen J–R curve to straight pipes with throughwall circumferential flaws

The stress triaxiality is an important parameter in explaining the geometry dependence of J–R curves. By comparing the stress triaxiality across the ligament of a specimen and a cracked component, it is possible to assess whether the cracked component exhibits similar fracture behaviour to the specimen. In the present investigation, fracture experiments have been carried out on throughwall circumferentially cracked 8-in. diameter pipes under four point bending load and three point bend bar (TPBB) specimens machined from the same pipe. Subsequently, 3-D elastic–plastic finite element analyses have been carried out on cracked pipes and TPBB specimens to determine the stress triaxiality across the ligament. It is found that the stress triaxiality conditions across the ligament are similar for the specimen and the cracked pipes. Therefore, the specimen fracture parameters can be transferred to these cracked components. It is also verified from the experimental results that the specimen J–R curves also fall within the acceptable band of component J–R curves. These investigations emphasise the role of stress triaxiality in selecting the specimen type for transferring fracture parameters under large scale yielding.     

A re-assessment of J estimation procedures

Among the fascinations and frustrations of fracture mechanics are the continuing arguments between experts as to the best fracture-characterising parameters and the most accurate procedure for their estimation. To the layman these may appear to be academic irrelevancies but it is essential that the practising engineer is aware of all the tolerances appropriate to his work and the significance of any variations. This article re-examines previous test results for three-point SENB specimens in relation to recently published $\text{J-}\text{estimation}$ procedures. The new procedures are shown to give improved estimates of $\text{J-}\text{values}$ from records of load versus notch mouth opening displacement.     

Limit load and J estimates of a centre cracked plate with an asymmetric crack in a mismatched weld

The limit load and J estimates of a centre cracked plate with an asymmetric crack in the tensile properties mismatched weld were investigated. A limit load expression was derived on the basis of a simplified slip-line field. A good agreement between the predictions of the expression and finite element (FE) results was found for ratios of half-weld width to the crack ligament, H/l, of less than 0.5. The equivalent stress–strain relationship method (ESSRM) was used to predict elastic–plastic J values. Results from FE analyses show that the ESSRM is accurate for the crack with asymmetry in the mismatched weld provided an accurate theoretical or numerical value of the limit load of the same specimen is available. Defect assessment methods are discussed, and it is found that the failure assessment diagram (FAD) of an asymmetrically cracked mismatched weld can be constructed from the equivalent stress–strain relationship for the same mismatched geometry with a symmetric crack. The effect of an asymmetric crack on the FAD may then be covered by the limit load solution for the asymmetrically cracked mismatched weld.