A load–deformation formulation with fracture representation based on the J–R curve for tubular joints

This study presents a new fracture formulation to describe the ductile tearing and unstable fracture failure for circular hollow section (CHS) joints under monotonically increasing brace tension. The initiation of the ductile tearing occurs when the crack driving force in an assumed initial shallow crack reaches the material fracture toughness determined from a standard fracture toughness test. The joint behavior prior to the ductile crack initiation follows a previously proposed nonlinear formulation based on the latest strength equations recommended by the International Institute of Welding. The load–deformation characteristics beyond the crack initiation assume that the energy release rate and the amount of crack extension adhere to the experimentally measured J–R curve, prior to the unstable fracture failure. Unstable fracture, which leads to the total loss of the joint capacity, occurs when the crack driving force reaches the maximum fracture resistance determined from the J–R curve test. The proposed load–deformation representation for tubular joints, when implemented in the large-scale K-frame pushover analysis with a material fracture toughness test, predicts successfully the global frame response governed by the joint fracture failure, as observed in the frame test.     

Comparative studies of several methods to determine the dynamic fracture toughness of a nuclear pressure vessel steel A508 CL3 with Charpy-size specimen

In this investigation, five estimation methods have been adopted to estimate the dynamic fracture toughness of a nuclear pressure vessel steel A508 CL3 by using pre-cracked Charpy-size specimens on an instrumented impact test machine. Furthermore, the merits and the demerits of the five methods have also been compared. The experimental results indicate that the maximum load energy method based on the curve of load versus load-point displacement overestimates the dynamic fracture toughness J _Id , especially above room temperature. The method of compliance changing rate underestimates the dynamic fracture toughness. The method of measuring the critical stretch zone width (SZW _c ) at the crack tip by means of SEM fractography and then converting the SZW _c into J _Id has a relatively large error. In addition, it is expensive and difficult to measure the SZW _c . The method of energy revised at the maximum load may be considered a better single-specimen method for determining the dynamic fracture toughness. Furthermore, the results indicate that although the dynamic resistance curve method can exactly estimate the dynamic fracture toughness of the material, this method needs several specimens. Moreover, the test procedure is complicated. Thus, it is not suitable for nuclear reactor pressure vessel embrittlement surveillance.     

Effect of acid corrosion on crack propagation of concrete beams

The effect of acid corrosion on crack propagation of concrete beams was theoretically studied by the method of crack extension resistance curve. Based on this method, a calculation approach was proposed to determine fracture stress intensity factors in crack propagation of concrete beams. Loop iteration analysis was carried out to calculate maximum bearing capacity load, unstable crack toughness, resistance toughness curve, cohesive toughness curve and load–crack mouth opening displacement. Both bilinear and nonlinear softening traction–separation curves were adopted for each of these calculation parameters. The analysis results of each showed the effect of acid corrosion degrees. The influence of acid corrosion on fracture properties was discussed through the calculated results of cohesive toughness curves. These five kinds of simulated results were basically consistent, before the load attained the maximum value. However, with further crack propagation, cohesive toughness of nonlinear softening model was significantly larger than that of bilinear softening model, and the descending branch of P–CMOD curve by nonlinear law is higher than that by bilinear law. To validate the approach, tests of specimens under six different corrosion periods were experimentally studied, using three-point bending notched concrete beams soaked in sulphuric acid solution. The Double-K fracture parameters were investigated based on the test results, and load–crack mouth opening displacement curves for different acid conditions were obtained using synchronous sampling of a load sensor and clip-gauge. Numerical results by bilinear softening model showed a good correlation with the experimental ones.     

Numerical simulations to support the normalization data reduction technique

The normalization data reduction (NDR) technique is an analytical methodology for characterizing the upper shelf fracture toughness of steels in the ductile regime, both in terms of critical toughness (J_Ic) and resistance to ductile crack extension (J-R curve). It represents an alternative to the more commonly used multi-specimen or single-specimen (unloading compliance and potential drop) techniques.Finite element analyses of a growing crack are executed to evaluate the performance of the technique. This approach has the advantage to remove large uncertainties entailing experimental results. Results demonstrate the precision of the method.     

Evaluation of critical fracture energy parameter Gfr and assessment of its transferrability

Prediction of maximum load bearing capacity and crack growth for ductile materials using existing models like J-R curve approach has the problem of transferability and the use of micro-mechanical model (e.g. Gurson Tvergaard, and Needleman [Tvergaard V, Needleman A. Analysis of cup cone fracture in a round tensile bar. Acta Metall 1984;32:157-169]) are limited by the requirements of the huge computation time and large numbers of critical metallurgical parameters as input to analysis. Marie and Chapuliot [Marie S, Chapuliot S. Ductile tearing simulation based on local energy criterion. Fatigue Fract Engng Mater Struct 1998;21:215-227] of CEA, France, proposed a simple but convenient ductile crack growth model using critical fracture energy (G_fr) for crack growth and J_i for initiation, both of which are material parameters. They also proposed several schemes, namely, graphical and slope of modified plastic J-integral vs crack growth, J_M-pl − Δa methods for the evaluation of the value of G_fr from specimens as well as from components. In all these methods the role of non-crack displacement in the crack growth process was not considered. The necessary modifications due to non-crack displacement in the above methods to evaluate the values of G_fr was studied and published [Acharyya S, Dhar S, Chattopadhyay J. (2003). The effect of non-crack component on Critical fracture energy on ductile material. Int J Pressure Vessels Piping 2004;81:345-353] by the authors earlier. In this paper, the modified methods and formulation have been applied to evaluate the values of G_fr from experimental and FE simulated results for compact tensile (CT), three point bend (TPB) specimens and also from components like pipes and elbows. Then statistical estimation is done from these G_fr values to assess whether G_fr can be accepted as constant value material parameter. Finally, the mean value of G_fr obtained from statistical computation is used as material constant along with crack initiation toughness parameter (J_i)_SZW to consider crack growth for FE simulation of load vs load-line-displacement (LLD) and load vs crack growth curves for different specimens and components. Finite element simulated results are compared with the experimental results and good matching between the two for several components are found and maximum error in prediction of maximum load is found to be within 12%.     

Threshold toughness of polymers in the ductile to brittle transition region by different approaches

The fracture behavior of polymers in the ductile-to-brittle region is neither completely brittle nor entirely ductile. Besides, scatter in toughness results impairs the situation. Consequently, conventional methods based exclusively either on linear elastic fracture mechanics theory (LEFM) or on non-linear elastic fracture mechanics theory (NLEFM) are not suitable. It was demonstrated previously, that Weibull statistical method could be successfully used to determine the toughness threshold of polymers displaying ductile-to-brittle behavior. The present study compares the threshold toughness value determined by the statistical approach with other critical values calculated following other different suitable approaches: Low temperature plane strain fracture toughness, Plastic zone corrected fracture toughness, Stable and unstable propagation combined model, J extrapolated at zero stable propagation value, and Quasi J-R curve. The analysis was carried out on data points taken from fracture tests performed on polypropylene homopolymer, PPH, and on a blend of PPH and an elastomeric polyolefin, PPH/POes. The results of this analysis indicate that statistical, stable and unstable propagation combined model, and the J extrapolated at zero stable propagation value methods yield to very similar toughness threshold values being practically equivalent. In this case, threshold value was slightly smaller than the minimum J displayed by the experimental replicas, suggesting that it is an actual representative material toughness. Among these methodologies, the Statistical Method is applicable even if stable crack growth is difficult to determine. On the other hand, the methodologies based on LEFM tended to underestimate the fracture toughness, being very conservative while Quasi J-R curve method based on NLEFM overestimated the PPH/POes toughness value.     

High rate toughness of ductile polymers

Impact toughness of two highly ductile polymers: acrylonitrile-butadiene-styrene (ABS) terpolymer and polypropylene block copolymer (PPBC) - was evaluated using the essential work of fracture (EWF) - and a J-R resistance single specimen curve - S_pb techniques. The EWF has proved to be capable of determining toughness from the total fracture energy of several samples differing in initial ligament length and the linear regression of the data. On the other hand, the S_pb method, which is based on the load separation principle, is able of constructing J-R curves by inferring instantaneous crack growth length from the sole comparison between one sharp and one blunt-notched load-displacement traces. Results show that both methodologies can be used under impact conditions when evaluating ABS polymers. However, ABS impact fracture toughness value yielded by the EWF method, w_Ie, was larger than the J_0.2 value obtained from the S_pb method. This difference was imputed to the more progressive development of the necking zone in front of the crack tip under plane strain conditions. On the contrary, for very ductile fracture behavior like that demonstrated by PPBC in which J-controlled conditions were not achieved and hence J-R curves could not be built the EWF appeared as a valuable alternative to characterize impact toughness.     

Quantitative evaluation of the adhesion of metallic coatings using cylindrical substrate

This paper introduces an effective interfacial fracture toughness test based on interface fracture mechanics theory. This testing method uses a circumferentially notched tensile (CNT) specimen, which is ideally suited for determining the interfacial fracture resistance of coatings. Unlike other interfacial fracture tests, this test is simple to prepare, requires minimum test setup and is easy to model. An interfacial pre-crack was generated between a nickel coating and mild steel cylindrical substrate to evaluate adhesion strength. In situ acoustic and SEM analyses were used to determine the crack initiation or the critical load of failure. The critical energy release rate, critical stress intensity factors and phase angle were determined using the J integral which was determined by applying the critical load to the finite element model. A detailed finite element analysis was carried out to study the effect of different interface pre-crack positions and mode mixity on energy release rate for different notch angles and elastic modulus ratios. The cracking resistance of the interface was characterised by the notch angle of CNT specimens. The analysis showed an increase in interfacial fracture toughness as phase angle increases and was significant when the phase angle was large. The combined results of computational and experimental analysis showed that any defect or stress concentration at the interface could significantly weaken the adhesion of coating.     

Anwendung des instrumentierten Kerbschlagbiegeversuchs zur Abschätzung der Rissauffangzähigkeit

Application of Charpy V‐notch testing to estimate the crack‐arrest toughness Modern structural integrity assessment relies upon fracture mechanics, thus utilizing fracture mechanical parameters describing the material fracture resistance against crack initiation and crack propagation as well as the material crack‐arrest behaviour. However, crack‐arrest fracture toughness values are usually difficult and expensive to determine. In this paper correlations are proposed for estimating the nil‐ductility temperature (T_NDT) and the crack‐arrest fracture toughness (K_Ia) from a transition temperature, based on instrumented Charpy‐V crack‐arrest load information. The transition criteria used are the 4 kN crack‐arrest force and the mean crack‐arrest fracture toughness of 100 MPa√m according to the master curve approach. Correlations between transition temperatures, T(F_a = 4 kN), T(K_Ia), and T_NDT, which were proposed for various structural steels, work very well for the 18Ch2MFA material.     

Prediction of ductile fracture initiation using micromechanical analysis

In the paper ductile fracture initiation analysis of low-alloyed ferritic steel has been made by application of two micromechanical models: the Rice–Tracey void growth model and the Gurson–Tvergaard–Needleman (GTN) model. The aim of the study was to analyse transferability of micromechanical parameters determined on specimens without initial crack to pre-cracked specimens. A significant part of the research has been carried out through participation in the round robin project organised by the European Structural Integrity Society (ESIS). Tensile tests have been performed on cylindrical smooth specimens and CT specimens. Critical values of micromechanical parameters determined on smooth specimen for both applied models, have been used for prediction of the crack growth initiation in CT specimen. Modelling of the first phase of ductile fracture––void nucleation––has been carried out using quantitative metallographic analysis of non-metallic inclusion content in tested steel. For determination of critical values of model parameters corresponding to ductile fracture initiation a simple procedure has been applied based on a combination of experimental and numerical results. Evaluated J-integral values corresponding to onset of crack growth, J_i, are in good agreement with experimental result and both models have proved to be suitable for determination of the ductile fracture initiation in tested steel. The effect of FE size at a crack tip on J_i-value has been particularly analysed: it has been established that the calculation with FE size corresponding to the mean free path λ between inclusions in steel gives results that are in accordance with the experimental ones.     

Evaluating the linear normalization technique for deriving J-resistance curves

In this paper, results from the linear normalization (LN) technique of Reese and Schwalbe for deriving J‐crack resistance (J–R) curves have been compared, related to J–Δa (J‐integral–ductile crack growth) data points, to those obtained from traditional elastic compliance technique. Research results regarding a nuclear grade steel exhibiting a wide range of elastic–plastic fracture resistance agree quite well for both techniques until a certain level of toughness of the material. Below this critical level, LN produces inconsistent results for the sub‐sized compact tension specimens (0.4T C[T]). The evidence suggests that the loss of applicability of the LN technique can be determined on the basis of the η plastic factor (η_pl) for the best linear correlation achieved for ΔP_N–Δa (normalised load gradient–ductile crack growth) data.     

Essential work of fracture compared to fracture mechanics—towards a thickness independent plane stress toughness

The essential work of fracture (EWF) and the J-integral methods were applied in a study of the effect of the thickness on the cracking resistance of thin plates. The paper discusses two themes: (1) the relationships between the two methods or concepts is elucidated, and (2) a new, thickness independent plane stress toughness parameter is proposed. For that purpose, cracked aluminium 6082O thin plates of 1-6 mm thickness were tested in tension until final separation. The EWF, w_e, and the J-integral at cracking initiation, J_i, increase identically with thickness except at larger thickness for which the increase of J_i levels off. J_i reaches a maximum for 5-6 mm thickness whereas w_e keeps increasing linearly with thickness. This difference is related to the more progressive development of the necking zone in front of the crack tip when thickness increases: at large thickness, cracking initiates well before the neck has developed to its stationary value during propagation. A linear regression on the fracture toughness/thickness curve allows partitioning the two contributions of the work of fracture: the plastic work per unit area for crack tip necking and a plane stress work per unit area for material separation. The pertinence of this new measure of the pure plane stress cracking resistance is critically discussed based on a micromechanical model for ductile fracture. The micromechanical void growth model incorporates void shape effects, which is essential in the low stress triaxiality regime.     

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.     

Quantifying Tstress controlled constraint by the master curve transition temperature T0

Specimen size, crack depth and loading conditions may effect the materials fracture toughness. In order to safeguard against these geometry effects, fracture toughness testing standards prescribe the use of highly constrained deep cracked bend specimens having a sufficient size to guarantee conservative fracture toughness values. One of the more advanced testing standards, for brittle fracture, is the master curve standard ASTM E1921-97, which is based on technology developed at VTT Manufacturing Technology. When applied to a structure with low constraint geometry, the standard fracture toughness estimates may lead to strongly over-conservative estimate of structural performance. In some cases, this may lead to unnecessary repairs or even to an early “retirement” of the structure. In the case of brittle fracture, essentially three different methods to quantify constraint have been proposed, J small scale yielding correction, Q-parameter and the T_stress. Here, a relation between the T_stress and the master curve transition temperature T₀ is experimentally developed and verified. As a result, a new engineering tool to assess low constraint geometries with respect to brittle fracture has been obtained.     

Further developments in <Emphasis Type="Italic">J</Emphasis> evaluation procedure for growing cracks based on LLD and CMOD data

Laboratory testing of fracture specimens to measure resistance curves (J − Δa) have focused primarily on the unloading compliance method using a single specimen. Current estimation procedures (which form the basis of ASTM E1820 standard) employ load line displacement (LLD) records to measure fracture toughness resistance data incorporating a crack growth correction for J. An alternative method which potentially simplifies the test procedure involves the use of crack mouth opening displacement (CMOD) to determine both crack growth and J. However, while the J-correction for crack growth effects adopted by ASTM standard holds true for resistance curves measured using load line displacement (LLD) data, it becomes unsuitable for J-resistance measurements based upon the specimen response defined in terms of load-crack mouth opening displacement (CMOD). Consequently, direct application of the evaluation procedure for J derived from LLD records in laboratory measurements of resistance curves using CMOD data becomes questionable. This study provides further developments of the evaluation procedure for J in cracked bodies that experience ductile crack growth based upon the eta-method and CMOD data. The introduction of a constant relationship between the plastic components of LLD (Δ _p ) and CMOD (V _p ) drives the development of a convenient crack growth correction for J with increased loading when using laboratory measurements of P-CMOD data. The methodology broadens the applicability of current standards adopting the unloading compliance technique in laboratory measurements of fracture toughness resistance data (J resistance curves). The developed J evaluation formulation for growing cracks based on CMOD data provides a viable and simpler test technique to measure crack growth resistance data for ductile materials.     

Experimentally determined key curves for fracture specimens

Crack extension during fracture toughness tests of ferritic structural steels cannot be determined from measurements of unloading compliance or electric potential change when the specimen is dynamically tested. Measurements of crack extension in fracture toughness tests are also very difficult when the test temperature is high or the test environment is aggressive. To circumvent this limitation, researchers for years have been developing key curve and normalization function methods to estimate crack extension in standard elastic-plastic fracture toughness test geometries. In the key curve method (Ernst et al., 1979; Joyce et al., 1980) a load-displacement curve is measured for a so-called `source' specimen that is sub size or has a blunt notch so that the crack will not initiate during elastic-plastic loading. The load and displacement are then converted to normalized stress-strain units to obtain a key curve that can be used to predict crack extension in geometrically similar `target' specimens of same material loaded at similar loading rates and tested under similar environmental conditions. More recently Landes and coworkers (Herrera and Landes, 1990; Landes et al., 1991) proposed the normalization data reduction technique – Annex A15 of ASTM 1820 specification – that presents an alternative to the standard E1820 unloading compliance procedure. Although the normalization method works well in many cases, it has serious drawbacks: the load, displacement and crack length at the end of the test must be measured; the prescribed functional form that is fitted to the initial and final data may not be accurate for all materials; and the iterative method of inferring crack length from the combination of the data and the normalization function is complex. The compliance ratio (CR) method developed in this paper determines key curves for predicting crack extension as follows. First, a statically loaded source specimen with the unloading compliance procedure specified in ASTM 1820. Second, the so-called CR load-displacement curve is calculated for the source specimen, which is the load-displacement record that would have been obtained if the crack had not extended. Third, non-dimensionalizing the CR load by the maximum load and the displacement by the elastic displacement at the maximum load, P ^* _i/P _max and v _i/v _{el max} from the source specimen yields the adjusted key curve. Analysis of extensive data shows that the key curve is independent of notch type, initial crack length and temperature. But it is dependent on specimen size and steel type. Assuming that the key curves of the source and target specimens are one and the same, the compliance of the target specimens are calculated with a reverse application of the compliance ratio method, and the crack length is obtained using the equations in ASTM E1820. The CR Method is found to be much simpler than the normalization method described in the Annex A15 of ASTM 1820. With the compliance ratio method, Joyce et al. (2001) successfully predicted crack extension in dynamically loaded specimens using a key curve of a statically loaded specimen.     

A comparison of the geometry dependence of several nonlinear fracture toughness parameters

A number of fracture toughness tests on compact tension specimens have been performed for the purpose of comparing several nonlinear fracture toughness methods; including the nonlinear energy ($\text{G}\text{?}{}_{\mathrm{I}}$), J-integral ($\text{J}{}_{\mathrm{I}}$), COD ($\text{G}{}_{\mathrm{\delta }}$), and linear (–$\text{G}{}_{\mathrm{I}}$) approaches. The effect of variations in specimen thickness ($\text{B}$) and width ($\text{w}$) on the fracture toughness was examined for 7075-T651, 2124-T851, 2048-T35I, and 2048-T851 aluminum alloys, Ti-6Al-4V, and 4340 steel. Fracture toughness values were evaluated at both the initiation of stable crack growth and the onset of unstable fracture (peak load).It was found that the peak load toughness values are quite geometry sensitive at thicknesses below the requirement for plane strain fracture. At the initiation of stable crack growth, the toughness values are constant over a much larger range of specimen thickness. However, the nonlinearity of the load displacement curve is quite limited at this point and the associated fracture toughness is only 30–50% of the peak-load values.     

A modified damage potential to predict crack initiation: theory and experimental verification

Mesh dependency of cavity growth model due to Rice and Tracey has been overcome by integrating it over a process zone surrounding the crack tip. This integral represents a modified damage potential. The critical value of the integral for crack initiation in SA333Gr.6 material has been determined analysing a CT specimen and comparing the computed J with the experimentally measured J-initiation value. The critical value of the integral was then used to compute J-initiation in other fracture specimens having different crack-tip constraints. The critical value was also used to predict crack initiation loads in three 8 in. straight pipes and three 8 in. elbows having different measure of through-wall circumferential flaws. The computed values have been compared with the experimentally measured values. A close agreement between the computed crack initiation loads with the experimentally measured values justified the usefulness of the present modified damage potential.     

A mechanical model to predict elastic-plastic fracture toughness in high strength materials

A mechanical model of crack initiation and propagation, which is based on the actual mechanism of ductile fracture in high strength materials, is proposed. Assuming that a crack initiates when the equivalent stress at a distance ρ from the crack tip reaches a critical value $\text{}\text{?}$gsf, an equation for predicting fracture toughness J_IC is obtained. From comparison between the predicted values and the experimental results, it is found that the distance ρ corresponds to the spacing of micro-inclusions. The temperature dependence of fracture toughness J_IC estimated according to the derived equation is given in an Arrhenius form of equation and is nearly consistent with the experimental results.     

CTOD-R curve construction from surface displacement measurements

The construction of a fracture resistance δ–R (or J–R) curve requires the appropriate measurement of crack-tip opening displacement (CTOD) as a function of crack extension. This can be made by different procedures following ASTM E1820, BS7448 or other standards and procedures (e.g., GTP-02, ESIS-P2, etc.) for the measurement of fracture toughness. However, all of these procedures require standard specimens, displacement gauges, and calibration curves to get intrinsic material properties. This paper deals with some analysis and aspects related to the measurement of fracture toughness by observing the surface of the specimen. Tests were performed using three-dimensional surface displacement measurements to determine the fracture parameters and the crack extension values. These tests can be conducted without using a crack mouth opening displacement-CMOD or load-line displacement gauge, because CMOD can be calculated by using the displacement of the surface points. The presented method offers a significant advantage for fracture toughness testing in cases where a clip gauge is not easy to use, for example, on structural components. Simple analysis of stereo-metrical surface displacements gives a load vs. crack opening displacement curve. Results show that the initiation of stable crack propagation can be easy estimated as the point of the curve’s deviation. It is possible to determine the deviation point if the crack opening displacement measurements are close to crack tip in the plastic zone area. The resistance curve, CTOD-R, is developed by the local measurement of crack opening displacement (COD) in rigid body area of specimen. COD values are used for the recalculation with the CMOD parameter as a remote crack opening displacement, according to the ASTM standard.