J-Resistance curve testing of HY80 steel using SE(B) specimens and normalization method

The normalization method is adopted for standard and nonstandard specimens in this paper to develop J-R curves for HY80 steel directly from load versus load-line displacement records without use of automatic crack length measurement. The standard specimens usually contain high crack-tip constraints, while the nonstandard specimens involve low crack-tip constraints. To obtain J-R curves with different constraints, a series of single edge notched bend (SE(B)) specimens with different crack lengths for an HY80 steel are tested in accordance with ASTM standard E1820. The normalization method is then used for determining crack extension and J-R curves for these SE(B) specimens.To validate the normalization method, the J-R curves determined using the normalization method are compared with those obtained by the elastic unloading compliance method for the SE(B) specimens. The comparison shows that good agreements exist between the two methods, and the normalization method is a viable tool to be used to determine J-R curves of the HY80 steel for the standard as well as nonstandard SE(B) specimens. In the J-integral calculations, the resistance curve test method, the basic test method and the modified basic test method specified in ASTM E1820 are evaluated. The results indicate that the modified basic method can be equivalent to the resistance curve method.     

Estimation procedure of J-resistance curves for SE(T) fracture specimens using unloading compliance

This work provides an estimation procedure to determine J-resistance curves for pin-loaded and clamped SE(T) fracture specimens using the unloading compliance technique and the η-method. A summary of the methodology upon which J and crack extension are derived sets the necessary framework to determine crack resistance data from the measured load vs. displacement curves. The extensive plane-strain analyses enable numerical estimates of the nondimensional compliance, μ, and parameters η and γ for a wide range of specimen geometries and material properties characteristic of structural and pipeline steels. Laboratory testing of an API 5L X60 steel at room temperature using pin-loaded SE(T) specimens with side-grooves provide the load-displacement data needed to validate the estimation procedure for measuring the crack growth resistance curve for the material. The results presented here produce a representative set of solutions which lend further support to develop standard test procedures for constraint-designed SE(T) specimens applicable in measurements of crack growth resistance for pipelines.     

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.     

A hybrid approach to determine fracture resistance for mode I and mixed‐mode I and II fracture specimens

This paper proposes a hybrid approach to determine the fracture resistance for mode I and mixed‐mode I and II fracture specimens, combining both numerically computed and experimentally measured load (P) versus load‐line displacement (LLD or Δ) relationships for metallic fracture specimens. The hybrid approach predicates on the same principle as the conventional, multiple‐specimen experimental method in determining the energy release rate. The hybrid method computes the P–Δ curves from multiple finite element (FE) models, each with a different crack depth. The experimental procedure measures the P–Δ curve from a standard fracture specimen with a growing crack. The intersections between the experimental P–Δ curve and the numerical P–Δ curves from multiple FE models dictate the LLD levels to compute the strain energy (U) using the area under the numerical P–Δ curves. This method provides accurate estimates of the J resistance data for both SE(B) specimen under mode I loading and single‐edge notched specimens under mixed‐mode I and II loading.     

On the transfer of specimen J–R curve to piping components with throughwall circumferential flaw

Transferability of the specimen J–R/J–T curve to the component level is an important issue in the field of fracture mechanics. Towards this goal, fracture experiments have been carried out on single‐edge bend (SE(B)) and compact tension (CT) specimens and throughwall circumferentially cracked straight pipes/elbows of 200 mm nominal bore (NB) diameter. The pipe material is SA 333 Gr 6 steel (low strength and high toughness material) and specimens are machined from the pipes. Subsequently, elastic–plastic finite‐element analyses have been carried out on these cracked components/specimens in order to evaluate the stress triaxiality levels. It is found that the triaxial levels for these cracked components are similar. Hence, similar fracture behaviour is expected for these components. Consequently, one of the pipe J–R curves is used as a reference J–R curve to consider the crack growth in the analysis and the load deformation behaviour of other pipes/elbows is predicted. The load deformation behaviour of the piping components is also predicted using an extrapolated J–R curve from a specimen that exhibits the similar triaxiality level to that of the cracked components. The predicted results are in good agreement with the experiments.     

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.     

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.     

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.     

Micromechanical analysis of mechanical heterogeneity effect on the ductile tearing of weldments

The objective of this study is determination of the effect of mechanical heterogeneity on ductile crack initiation and propagation in weldments using micromechanical approach. Welded single-edge notched bend (SENB) specimens were experimentally and numerically analysed. Material properties of welded joint zones were estimated using a combined experimental and numerical procedure; strains on a smooth tensile specimen were determined using ARAMIS stereometric measuring system in order to obtain true stress – true strain curves. High-strength low-alloyed steel was used as base metal, in quenched and tempered condition. J–R curves and crack growth initiation values of fracture mechanics parameter were experimentally and numerically obtained for specimens with a pre-crack in the heat-affected zone (HAZ) and weld metal (WM). The complete Gurson model (CGM) was used in prediction of J–R curves and crack growth initiation. It is shown that the resistance to crack initiation and growth can be predicted using micromechanical analysis, and that the results are significantly affected by mechanical heterogeneity of the weldment.     

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.     

Dynamic J-R curves and tension-impact properties of AISI 308 stainless steel weld

In this paper, instrumented tension-impact (dynamic tensile) and instrumented Charpy impact test results for AISI 308 stainless steel welds at room temperature are reported. A few Charpy specimens precracked to a/W (crack length to width ratio) ratios of 0.42 to 0.59 were also tested. Dynamic yield strength obtained from tension-impact test agrees well with that from Charpy V-notch specimens. The strain rates obtained during the tension-impact test are compared with the various estimates of strain rates for V-notch and precracked Charpy specimens. A variation of the compliance changing rate method was necessary for determining the crack initiation point while crack growth was determined by power law key-curve procedure. J-R curves thus obtained from Charpy (precracked and V-notch) specimens are compared with those computed using handbook procedures using dynamic tensile results. Key words: Tension-impact testing, 308 stainless steel weld, Charpy V-notch, dynamic fracture toughness, dynamic yield strength, J-R curve, strain rate, key-curve.     

Size effects in tearing instability: An analysis based on energy dissipation rate

It is standard practice to use a G or J resistance curve (R-curve) to describe stable tearing. One important question is whether a J_R curve generated in a fully yielded specimen is the same as the G_R curve in a structure under small scale yielding. This paper argues that both the J_R and G_R curves are best viewed as derivatives of the energy dissipation rate D. Energy dissipation rate is not a material property, but various simple rules can be proposed to describe its likely variation with crack extension and with geometry. It is concluded that near size invariance of J_R curves is approached when D is high. As the tearing resistance reduces, cracks in structurally relevant configurations will begin to extend in contained yield. Differences between J_R and G_R curves may then cause problems. In general, the G_R curve has a shallower slope as instability approaches. If the whole J_R curve (from the small specimen) is very low, it is unlikely that a material would be accepted in a structure; but, if a material has a moderately high initiation toughness, J_0.2, combined with a low dJ_R/da (say less than 25 MPa) it becomes dangerous to rely on J_R curve theory to predict crack stability in the structure. An alternative approach using energy dissipation rate is explained.     

A node release approach to estimate J‐R curve for single‐edge‐notched tension specimen under reversed loading

This paper proposes a node release approach to estimate the fracture resistance curve, often known as the J‐R curve, for monotonic and cyclic fracture tests. The node release approach simulates the crack extension by releasing the constraints imposed on the node at the crack tip and estimates the J‐R curve by coupling the domain integral value with the corresponding crack extension. This proposed node release approach estimates closely the J‐R curve for SE(B) and SE(T) specimens subjected to monotonic loading. For SE(T) specimen under cyclic loading, this study implements the node release analysis in two approaches: (1) an equivalent monotonic analysis corresponding to the envelope of the cyclic load‐CMOD response and (2) a direct cyclic simulation. Both approaches lead to close estimations of the experimentally measured J‐R curve. The numerical analysis also confirms the path independence of the domain integral values in the direct cyclic simulation.     

Crack growth resistance behavior of a functionally graded material: computational studies

This paper describes crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) using a cohesive zone ahead of the crack front. The plasticity in the background (bulk) material follows J₂ flow theory with the flow properties determined by a volume fraction based, elastic-plastic model (extension of the original Tamura-Tomota-Ozawa model). A phenomenological, cohesive zone model with six material-dependent parameters (the cohesive energy densities and the peak cohesive tractions of the ceramic and metal phases, respectively, and two cohesive gradation parameters) describes the constitutive response of the cohesive zone. Crack growth occurs when the complete separation of the cohesive surfaces takes place. The crack growth resistance of the FGM is characterized by a rising J-integral with crack extension (averaged over the specimen thickness) computed using a domain integral (DI) formulation. The 3-D analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates solid elements with graded elastic and plastic properties and interface-cohesive elements coupled with the functionally graded cohesive zone model. The paper describes applications of the cohesive zone model and the DI method to compute the J resistance curves for both single-edge notch bend, SE(B), and single-edge notch tension, SE(T), specimens having properties of a TiB/Ti FGM. The numerical results show that the TiB/Ti FGM exhibits significant crack growth resistance behavior when the crack grows from the ceramic-rich region into the metal-rich region. Under these conditions, the J-integral is generally higher than the cohesive energy density at the crack tip even when the background material response remains linearly elastic, which contrasts with the case for homogeneous materials wherein the J-integral equals the cohesive energy density for a quasi-statically growing crack.     

Effect of fracture path on the toughness of weld metal

The crack propagation direction may affect weld metal fracture behavior. This fracture behavior has been investigated using two sets of single edge notched bend (SENB) specimens; one with a crack propagating in the welding direction (B×2B) and the other with a crack propagating from the top in the root direction (B×B) of a welded joint. Two different weld metals were used, one with low and one with high toughness values. For Weld Metal A, two specimen types have been used (B×B and B×2B) both with deep cracks. The weld metal A (with high toughness values) has reasonably uniform properties between weld root and cap. The resulting J-R curves show little effect of the specimen type, are ductile to the extent that the toughness exceeds the maximum J_max, value allowed by validity limits and testing is in the large –scale yielding regime. In the case of weld metal B (with low toughness values) with two specimen types (B×B and B×2B) the B×B specimen has shallow cracks while the B×2B specimen has deep cracks. Both resulting J-R curves show unstable behavior despite the fact that the types of specimen and their constraints are different. The analysis has shown that crack propagation direction is most influential for a weldment with low toughness in the small scale yielding regime, whereas its influence diminishes due to ductile tearing during stable crack growth and large scale yielding. The results have shown that these effects are different in both the crack initiation phase and during stable crack growth, indicating a dependence on weld metal toughness and the microstructure of the weld metal. It can be concluded that, if resistance curves during stable crack growth do not show differences in both notch orientations, the fracture toughness values of the whole weld metal can be treated as uniform.     

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.     

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.     

Crack resistance curves of GLARE laminates by elastic compliance

The objective of this work was to study the applicability of the elastic compliance technique for crack resistance curves evaluation of commercial GLARE laminates using small SE(B) and C(T) specimens. The experimental evaluation of R-curves of 25.0 mm wide SE(B) specimens of unidirectional GLARE 1 3/2 0.3 and 50.0 mm wide C(T) specimens of bidirectional GLARE 3 5/4 0.3 was performed. Fracture toughness was measured through a recently proposed experimental methodology based on standardized specimens and elastic-plastic methodologies (J-integral and CTOD δ₅), whereas crack growth was measured optically and estimated by elastic compliance. According to the results the elastic compliance technique seemed to be applicable to GLARE laminates, accurately predicting stable crack growth during the tests.     

J resistance behavior in functionally graded materials using cohesive zone and modified boundary layer models

This paper describes elastic–plastic crack growth resistance simulation in a ceramic/metal functionally graded material (FGM) under mode I loading conditions using cohesive zone and modified boundary layer (MBL) models. For this purpose, we first explore the applicability of two existing, phenomenological cohesive zone models for FGMs. Based on these investigations, we propose a new cohesive zone model. Then, we perform crack growth simulations for TiB/Ti FGM SE(B) and SE(T) specimens using the three cohesive zone models mentioned above. The crack growth resistance of the FGM is characterized by the J-integral. These results show that the two existing cohesive zone models overestimate the actual J value, whereas the model proposed in the present study closely captures the actual fracture and crack growth behaviors of the FGM. Finally, the cohesive zone models are employed in conjunction with the MBL model. The two existing cohesive zone models fail to produce the desired K–T stress field for the MBL model. On the other hand, the proposed cohesive zone model yields the desired K–T stress field for the MBL model, and thus yields J _R curves that match the ones obtained from the SE(B) and SE(T) specimens. These results verify the application of the MBL model to simulate crack growth resistance in FGMs.     

Fractal modeling of the J-R curve and the influence of the rugged crack growth on the stable elastic-plastic fracture mechanics

In this paper, fractal geometry is used to modify the Griffith-Irwin-Orowan classical energy balance. Crack fractal geometry is introduced in the elastic-plastic fracture mechanics by means of the Eshelby-Rice J-integral and the influence of the ruggedness of the crack surface on the quasistatic crack growth is evaluated. It is shown that the rising of the J-R curve correlates to the topological ruggedness dimension of the crack surface. Results from fracture experiments are shown to be very well fitted with the proposed model, which is shown to be a unifying approach for fractal models currently used in fracture mechanics.