Transferability of specimen J–R curve to straight pipe with circumferential surface flaw

Specimen J–R curve is extensively used for structural integrity of large components. It is well known that J–R curve heavily depends on constraint level ahead of crack tip in remaining ligament. In earlier work, it was demonstrated that J–R curve from Three Point Bending (TPB) specimen is transferable to straight pipe with circumferential through wall crack. In this paper, the transferability of J–R curve is investigated from TPB specimen to pipe with circumferential surface crack. A 16 in. diameter pipe with circumferential surface crack and TPB specimen machined from same piping material (SA333Gr6 Steel) are tested. Consequently, 3D finite element analysis (FEA) has been performed on surface cracked pipe and TPB specimen. Crack‐initiation load is also predicted for surface cracked pipe by FEA and compared with experimental result. J–R curve is calculated for the pipe using experimental data, that is, load, load line displacement and crack growth. J–R curve of pipe is compared with TPB specimen and it is found that the pipe is predicting much higher J–R curve than TPB. This difference of J–R curve is investigated by evaluating stress triaxiality in remaining ligament for both cases. Stress triaxiality is quantified using triaxiality factor (h) ahead of crack tip for pipe and TPB specimen. It is found that the TPB specimen has considerably higher constraint level than pipe with surface crack, which is well supported by trend of J–R curves for specimen and pipe. A study has also been carried out to investigate the effect of internal pressure on the stress triaxiality. It is found that there is negligible difference in stress triaxiality because of internal pressure. The stress triaxiality is re‐established as a qualitative parameter to assess the transferability of J–R curve from specimen to component.     

Establishing methodology to predict fracture behaviour of piping components by numerically predicting specimen fracture data using tensile specimen test

Using large deformation FEM analyses in SA333Gr.6 carbon steel material, the present study demonstrated the assessment of SZWc value that leads to J_SZWc and finally compares with the respective experimental results. It also includes numerical prediction of specimen J-R curve using Gurson-Tvergaard-Needleman parameters obtain from tensile specimen tests. Using numerically predicted results, the crack initiation and instability stages in circumferentially through-wall cracked elbows is finally predicted and compares with experimental results. The present study gives evidence that the non-linear FEM analysis supported with proper tensile test data can be helpful in assessing the safety of bend pipes with through-wall crack.     

J–R curves corrected by load-independent constraint parameter in ductile crack growth

The constraint effect on J–resistance curves of ductile crack growth is considered under the condition of two-parameter J–Q^* controlled crack growth, where Q^* is a modified parameter of Q in the J–Q theory. Both J and Q^* are used to characterize the J–R curves with J as the loading level and Q^* as a constraint parameter. It is shown that Q^* is independent of applied loading under large-scale yielding or fully plastic deformation, and so Q^* is a proper constraint parameter during crack growth. An approach to correct constraint effects on the J–R curve is developed, and a procedure of transferring the J–R curves determined from standard ASTM procedure to nonstandard specimens or real cracked structures is outlined.The test data of fracture toughness, J_IC, and tearing modulus, T_R, by Joyce and Link (Engng. Fract. Mech. 57(4) (1997) 431) for a single-edge notched bend specimen with various depth cracks are employed to demonstrate the efficiency of the present approach. The variation of J_IC and T_R with the constraint parameter Q^* is obtained, and then a constraint-corrected J–R curve is constructed for the test material of HY80 steel. Comparisons show that the predicted J–R curves can match well with the experimental data for both deep and shallow cracked specimens over a reasonably large amount of crack extension.Finally, the present approach is applied to predict the J–R curves of ductile crack growth for five conventional fracture specimens. The results show that the effect of specimen geometry on the J–R curves is generally much larger than the effect of specimen sizes, and larger specimens tend to have lower crack growth resistance curves.     

Elastic–plastic J and COD estimation schemes for 90° elbow with throughwall circumferential crack at intrados under in-plane opening moment

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic–plastic J-integral and crack opening displacement (COD)¹ for these piping components. Analytical estimation schemes to evaluate elastic–plastic J-integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, such schemes for elbow (or pipe bend), which is one of the important components for LBB analyses, is very meager. Recently, elastic–plastic J and COD estimation scheme has been developed for throughwall circumferentially cracked elbow subjected to closing bending moment. However, it is well known that the elbow deformation characteristics are distinctly different for closing and opening bending modes because the ovalisation patterns of elbow cross section are different under these two modes. Development of elastic–plastic J and COD estimation scheme for an elbow with throughwall circumferential crack at intrados subjected to opening bending moment forms the objective of the present paper. Experimental validation of proposed J-estimation scheme has been provided by comparing the crack initiation, unstable ductile tearing loads and crack extension at instability with the test data. The COD estimation scheme has been validated by comparing the COD of test data with the predictions of the proposed scheme.     

Analysis of the geometry dependence of fracture toughness at cracking initiation by comparison of circumferentially cracked round bars and SENB tests on Copper

In the first part of the paper, the use of circumferentially cracked round bars (CRB geometry) for characterizing fracture toughness of a ductile material, namely copper, is assessed experimentally through a comparison with the single edge notched bend (SENB) geometry. The J _R curve method with multiple-specimens was applied, but, as unstable cracking appeared very early in the CRB specimen, an engineering definition of fracture toughness was not pertinent. Unloaded specimens were analyzed metallographically to determine the CTOD at physical cracking initiation. The fracture toughness measured using the CRB geometry was 50% larger than using the SENB geometry. The second part of the paper aims at justifying this difference of fracture toughness at cracking initiation. Finite element simulations revealed a slightly higher constraint in the SENB specimens. The main difference between the two specimen geometries lies in a 50% larger extension of the finite strain zone with respect to the CTOD in the case of the SENB specimens. Based on the observation that, in the studied material, the critical CTOD is one order of magnitude larger than the void spacing, we conclude that the geometry dependence of the fracture toughness is caused by the difference in the finite strain zone extension rather than by a stress triaxiality effect.     

Elastic-plastic J and COD estimation schemes for throughwall circumferentially cracked elbow under in-plane closing moment

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic-plastic J-integral and crack opening displacement (COD)¹ for these piping components. Analytical estimation schemes to evaluate elastic-plastic J-integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, no such schemes are available for throughwall circumferentially cracked elbow (or pipe bend), an important component for LBB analysis. In this paper, simple J and COD estimation schemes are proposed for throughwall circumferentially cracked elbow subjected to closing bending moment. The ovalisation of elbow cross-section has a significant bearing on its fracture behavior. Therefore, unlike conventional deformation theory plasticity analysis, incremental flow theory is adopted considering both material and geometric non-linearities in the development of the proposed estimation schemes. Although it violates Ilyushin’s theorem, it has been shown that the resulting estimation schemes is still reasonably accurate for engineering purposes. Finally, experimental/numerical validation has been provided by comparing the J-integral and COD between numerical/test data and predictions of the proposed estimation schemes.     

Numerical prediction of notch bluntness effect on fracture resistance of SM490A carbon steel

The present work investigates the notch radius effect on fracture resistance using the finite element (FE) damage analysis based on the multiaxial fracture strain model. The damage model was determined from experimental data of notched bar tensile and fracture toughness test data using a sharp‐cracked compact tension specimen. Then, the FE damage analysis was applied to simulate fracture resistance tests of SM490A carbon steel specimens with different notch radii. Comparison of simulated results with experimental data showed good agreement. Further simulation was then performed to see effects of the specimen size, thickness, and side groove on J‐R curves for different notch radii. It was found that effects of the specimen size and thickness became more pronounced for the larger notch radius. Furthermore, it was found that without side groove, tearing modulus for notched specimens was similar to that for cracked specimens, regardless of the notch radius.     

Fracture behaviour of cracked carbon nanotube‐based polymer composites: Experiments and finite element simulations

This paper studies the fracture behaviour of cracked carbon nanotube (CNT)‐based polymer composites by a combined numerical–experimental approach. Tensile tests were conducted on single‐edge cracked plate specimens of CNT/polycarbonate composites at room temperature and liquid nitrogen temperature (77 K), and the critical loads for fracture instabilities were determined. Elastic–plastic finite element simulations of the tests were then performed to evaluate the J‐integrals corresponding to the experimentally determined critical loads. Scanning electron microscopy examinations were also made on the specimen fracture surfaces, and the fracture mechanisms of the CNT‐based composites were discussed.     

Ductile crack growth and constraint in pipelines subject to combined loadings

An important failure mode of offshore pipelines is ductile fracture of the pipe wall triggered by a hypothetical welding defect. In this study, pipelines having an external part-through semi-circumferential crack of various sizes, subject to combined internal pressure and inelastic bending are considered. This is done to assess the response of pipelines during both their installation and operational conditions. Detailed 3D nonlinear finite element (FE) models of pipelines are developed. A row of elements ahead of the initial crack front are modeled using a voided plasticity material model, which enables simulation of crack growth and the subsequent fracture failure mode (denoted by the critical curvature, κ_crit). After discussing the typical response characteristics of such pipelines, the FE model is used to parametrically investigate the influence of varying pipe and crack dimensions, and also the internal pressure levels, on κ_crit. In the second part of this paper, the crack tip constraint ahead of a growing crack in such pipes is evaluated and systematically compared to the crack tip constraint of both the traditionally used deeply cracked Single Edge Notch Bend (SENB) specimens and the constraint-matched Single Edge Notch Tensile (SENT) specimens. This is achieved by comparing the crack resistance curves (R-curves) along with stress triaxiality and equivalent plastic strain fields evaluated ahead of a growing crack of the three systems. The results present grounds for justification of usage of SENT specimens in fracture assessment of such pipes as an alternative to the traditional overly conservative SENB specimens.     

Mechanical heterogeneity and validity of J-dominance in welded joints

Fracture criterion of the J-integral finds wide application in the integrity evaluation of welded components, but there exist some confused problems such as the dependence of the fracture toughness on the strength mis-matching and specimen geometry which need to be clarified. It is rough and unsuitable to attribute the variation of J-integral fracture parameter simply to the effect of mechanical heterogeneity. In the present paper, a two-dimensional finite element method is employed to analyze the distribution and variation of crack tip field of welded joints with different strength mis-matching in four kinds of specimen geometry, and then the validity of J-dominance in welded joints is investigated. It is found that the crack tip field of mis-matched joint is different from that of either the weld metal or base metal of which the joint is composed, but it is situated between those of weld metal and base metal. Under the plane strain, there is obvious difference in stress triaxiality for different strength mis-matched joints. The validity of J-dominance in welded joint can not be obtained by comparing whether the stress triaxiality meets that required by the HRR solution because of the existence of mechanical inhomogeneity. By ascertaining if the stress triaxiality of welded joint near the crack tip is dependent of specimen geometry, the conclusion can be arrived at: for plane stress the validity of J-dominance is valid, whilst for plane strain the validity of J-dominance is lost. Based on the above, attempt has been made to point out that the influence of mechanical heterogeneity on the fracture toughness of weldment arises from the variation of constraint intensity-crack tip stress triaxiality. Compared with the effect of mechanical heterogeneity on the stress triaxiality, the losing of validity of J-dominance in mis-matched joint under plane strain may play a more critical role in the variation of J-integral fracture parameter of weldment.     

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens. Part II: 3-D effects on constraint

This study describes an extensive set of 3-D analyses conducted on conventional fracture specimens, including pin-loaded and clamped SE(T) specimens, and axially cracked pipes with varying crack configurations. The primary objective is to examine 3-D effects on the correlation of fracture behavior for the analyzed crack configurations using the J-Q methodology. An average measure of constraint over the crack front, as given by an average hydrostatic parameter, denoted Q_avg, is employed to replace the plane-strain measure of constraint, Q. Alternatively, a local measure of constraint evaluated at the mid-thickness region of the specimen, denoted Q_Z0, is also utilized. The analysis matrix considers 3-D numerical solutions for models of SE(T) fracture specimens with varying geometries (i.e., different crack depth to specimen width ratio, a/W, as well as different loading point distance, H) and test conditions (pin-loaded ends vs. clamped ends). The 3-D numerical models for the cracked pipes cover different crack depth to pipe wall thickness ratio, a/t, and a fixed crack depth to crack length ratio, a/c. The extensive 3-D numerical analyses presented here provide a representative set of solutions which provide further support for using constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.     

Finite element simulation of fracture behaviour for aged duplex stainless steels

In this paper, the local approach model developed by Gurson–Tvergaard has been applied to simulate both the crack initiation and the crack growth of aged duplex stainless steel. The parameters of the Gurson–Tvergaard model have been obtained, from axisymmetric notched specimen testing, as a function of the ageing time at 400°C, the ferrite content of the steel and the stress triaxiality. After that, to simulate the fracture of CT specimens, finite element (FE) calculations have been effected in order to obtain the stress triaxiality value at each point on the process zone ahead of the crack tip of these specimens. The adequate damage parameters concerning triaxiality are determined from the ones obtained at the notched specimens, in order to be used in FE simulations of fracture behaviour. With them, the corresponding J−Δa curves have been simulated as representative of both the crack initiation and crack propagation stages, and compared with experimental results in order to validate the methodology proposed.     

A fracture mechanics concept for the accelerated characterization of creep crack growth in PE-HD pipe grades

For the lifetime prediction of pressurized polyethylene (PE) pipes based on methods of the linear elastic fracture mechanics the knowledge of the crack resistance and the kinetics of creep crack growth (CCG) is essential. In the present work a rather brittle nonpipe material was used to develop a methodology for an accelerated measurement of crack kinetics in fatigue tests on cracked round bar (CRB) specimens at ambient temperatures of 23 °C. A material and specimen specific compliance calibration curve was generated to detect the crack kinetics with only one single CRB test. Based on an already proposed concept the kinetics at different R-ratios (minimum/maximum load) was measured and extrapolated to the case of CCG. To demonstrate the transferability of this concept to pipe materials a PE 80 pipe grade was used. Although the necessary testing time increased considerably the concept still has the potential to reduce the overall testing time for new pipe materials to be certified significantly. With the presented procedure a characterization of CCG in modern PE pipe grades at room temperature and without the use of stress cracking liquids is possible within a few months.     

A STUDY OF SPECIMEN SIZE ON J-R CURVE BEHAVIOUR

This paper presents results from an experimental programme to study size effects in J-R curves. Results are presented from unloading compliance R curve tests on different sized single edge notch bend specimens of nickel aluminium bronze and compared with previously published R curve data on a Ti3A1-2.5V titanium and an HY 100 steel alloy. The crack growth resistance was measured in terms of the standard fracture resistance J, J corrected for crack growth and the J modified parameter proposed by Ernst. It was observed that following a region of size independence small specimen J-R curves could fall either above or below the large specimen curve. It was found that although the limit to J controlled crack growth could be extended the limit is not unique but dependent on material type.     

An updated continuum damage model to investigate fracture process of structures in DBTT region

In the Ductile–Brittle Transition Temperature (DBTT) region, it is not realistic to take unique fracture stress or fracture strain as the fracture criterion to investigate the fracture properties. In this paper, an updated continuum damage model was proposed, in which the fracture energy density, a function of the stress triaxiality, temperature and strain rate in the transition region was taken as the critical damage factor. Uniaxial tension tests were carried out to get the basic material properties at different temperatures, to calibrate the fracture model constants and verify the validity of the damage model. The fracture behaviour of pipes with penetrating cracks under the internal pressure was experimentally investigated with the load–deflection curves and the crack propagation length captured from tests. The J–R curves were obtained from the testing results for different temperatures. Based on the Finite Element Analyses (FEA) with the proposed fracture criterion of the updated continuum damage model, the loading level of pipes with penetrating cracks were estimated and compared with the experimental results. Meanwhile the fracture processes of the pipeline structures in the transition region were reproduced. The experimental and numerical results agreed very well in present calculations. It has been shown that the fracture process in the transition region strongly depends on both the stress and strain states, and could be effectively predicted using the continuum damage model.     

Proposal of a new concept on creep fracture remnant life for a precracked specimen

Abstract

The creep life time of a smooth specimen can be predicted using existing laws for creep deformation and steady state creep rate. When crack growth behaviour is involved, it is necessary to construct a law of creep crack growth rate to predict creep fracture life. Creep fracture life can be measured by integrating the law of creep crack growth rate. One example is the creep crack growth rate, represented by the parameter Q*. In this study, we investigated the applicability of this prediction method to creep fracture remnant life for a cracked specimen. The Ω criterion is proposed to predict creep fracture remnant life for a smooth specimen for creep ductile materials. In this study, the correlation between Q*_L derived from the paremeters Q* and Ω is investigated. The correlation between Q_L* and Ω provided a unified theoretical prediction law of creep fracture remnant life for high-temperature creep-ductile materials in the range from smooth to precracked specimens.     

Modelling the softening within the fracture process zone associated with the fissuring mode of crack growth in Zr-2.5Nb CANDU pressure tube material

The fissuring mode of fracture in CANDU pressure tube material, and in particular Stage 1 crack growth (essentially flat J _R curve) as observed in some irradiated compact toughness specimens has been investigated. Models are presented of the fracture process zone associated with a crack that tunnels at the specimen mid-section, which extends preliminary work reported earlier. Various types of process zone behaviour are analysed, and based on an appropriate value for J _c, the J value associated with the cumulative mode of crack propagation in irradiated material, together with an estimate of the tensile stress at the leading edge of the process zone, the known failure mechanism (formation, growth and coalescence of voids) of the ligaments between the fissures is shown to be reasonably consistent with the experimental measurements of the fissure spacing and fissure length.     

DAMAGE MECHANICS APPROACH TO REMOVE THE CONSTRAINT DEPENDENCE OF ELASTIC–PLASTIC FRACTURE TOUGHNESS

It is now generally agreed that the applicability of a one-parameter J-based ductile fracture approach is limited to so-called high constraint crack geometries, and that the elastic-plastic fracture toughness J_1c, is not a material constant but strongly specimen geometry constraint-dependent. In this paper, the constraint effect on elastic-plastic fracture toughness is investigated by use of a continuum damage mechanics approach. Based on a new local damage theory for ductile fracture(proposed by the author) which has a clear physical meaning and can describe both deformation and constraint effects on ductile fracture, a relationship is described between the conventional elastic-plastic fracture toughness, J_1c, and crack tip constraint, characterized by crack tip stress triaxiality T. Then, a new parameter J_dc (and associated criterion, J_d=J_dc) for ductile fracture is proposed. Experiments show that toughness variation with specimen geometry constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper, and that the new parameter J_dc is a material constant independent of specimen geometry (constraint). This parameter can serve as a new parameter to differentiate the elastic-plastic fracture toughness of engineering materials, which provides a new approach for fracture assessments of structures. It is not necessary to determine which laboratory specimen matches the structural constraint; rather, any specimen geometry can be tested to measure the size-independent fracture toughness J_dc. The potential advantage is clear and the results are very encouraging.     

Constraint Loss under Dynamic Loading in Rate Independent Plastic Solids

The objectives of this paper are to examine the loss of crack tip constraint in dynamically loaded fracture specimens and to assess whether it can lead to enhancement in the fracture toughness at high loading rates which has been observed in several experimental studies. To this end, 2-D plane strain finite element analyses of single edge notched (tension) specimen and three point bend specimen subjected to time varying loads are performed. The material is assumed to obey the small strain J ₂ flow theory of plasticity with rate independent behaviour. The results demonstrate that a valid J–Q field exists under dynamic loading irrespective of the crack length and specimen geometry. Further, the constraint parameter Q becomes strongly negative at high loading rates, particularly in deeply cracked specimens. The variation of dynamic fracture toughness K _dc with stress intensity rate K for cleavage cracking is predicted using a simple critical stress criterion. It is found that inertia-driven constraint loss can substantially enhance K _dc for .     

A study of stable crack growth using experimental methods,finite elements and fractography

Systematic analysis of the in-plane constraint influence on J-resistance curves is presented. J_R curves were also recorded and analyzed beyond the limits of crack extension inside which the stress field can be assumed to be dominated by J-integral. Three steels and four types of specimen: SEN(B), SEN(T), CCT and DENT have been tested. Along with the J_R curves the fracture mechanisms have been analyzed with the help of scanning microscopy. The numerical, finite element analysis has been adopted to compute the Q-stresses, as a measure of the in-plane constraint prior to the onset of crack growth. The analysis of the stress field in front of the crack has been performed to check whether the state of stress prior to the crack growth can predetermine the way the crack will grow. It turns out that characteristic features in the J_R curves runs can be predicted qualitatively from the Q(a/W) and Q(J) curves. However, there is a good correlation between Q-stress and voids diameters on fractured surfaces. Several patterns in J_R curves runs have been observed for tested specimens; e.g. no influence of specimen thickness on J_R curves runs was observed for side-grooved specimens. Strong influence of specimen thickness on J_R curve shape was observed for non-side-grooved specimens. J_R curve run higher for thinner specimens unless they are dominated by plane stress. For bent specimens J_R curves run higher for shorter cracks but they run lower for specimens in tension.