The non-constant CTOD/CTOA in stable crack extension under plane-strain conditions

Contrary to the previous work that successfully applied the constant CTOD/CTOA fracture criteria to relatively thin structures, this paper demonstrates that the initial non-constant portion of the CTOD/CTOA plays an essential role in predicting fracture behavior under plane-strain conditions. Three- and two-dimensional finite element analyses indicate that a severe underestimation of the load would occur as the crack extends if a constant CTOD/CTOA criterion were used. However, the use of a simplified, bilinear CTOD/CTOA criterion to approximate its non-constant portion will closely duplicate the test data. Furthermore, using the experimental data from J-integral tests with various crack length to specimen width ratios (a/W), it is demonstrated that the critical CTOD/CTOA is crack tip constraint dependent. The initial high values of the CTOD/CTOA are in fact a natural consequence of crack growth process that is reflected by, and consistent with, the J-resistance (J-R) curve and its slope (tearing modulus).     

A SIMPLE TEST METHOD FOR ENERGY DISSIPATION RATE, CTOA AND THE STUDY OF SIZE AND TRANSFERABILITY EFFECTS FOR LARGE AMOUNTS OF DUCTILE CRACK GROWTH

Abstract— Simple extensions to the standard deep notch bend test procedure are suggested to allow the collection of data relevant to the energy dissipation rate, D , crack opening angle, COA, and J , all for arbitrarily large amounts of growth in extensive plasticity. The methods of analysis are detailed for real elastic-plastic behaviour of a high strength low-hardening type metal with a view to encouraging use on a wider range of materials. A proposal is made, and equations given, that the particular version of J used for an R -curve derived from the area under the loading diagram, should correspond to the value of the far-field integral, J _ff.
The relationship between the global measure of COA that emerges from D and the local crack tip opening angle, CTOA, as used in computational studies, is established. Transferability of CTOA data is examined in the light of effects of size and configuration. An explicit rule of the form CTOA √G = f (material and configuration) is proposed for the modelling of ductile growth in finite element studies. It is applied to a set of data in the literature, for the variation of CTOA with size in the deep notch bend test and for the configurations, bending, double edge and centre cracked tension.     

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.     

AN ENGINEERING FRACTURE PARAMETER FOR NON-J-CONTROLLED CRACK GROWTH

Abstract— An engineering fracture parameter (CTOA) is studied under non- J -controlled growth. Based on the asymptotic solution of the crack tip field and the concept of the ₁ integral, an analytical relation linking the crack tip opening angle (CTOA) and the ₁ integral is established. A numerical investigation of the process of crack growth is carried out by the finite element method. The whole field solution, fracture parameters and indeterminate parameters are determined by FE analysis. An experimental investigation on a ductile structural steel has also been conducted and the crack resistance curve (CTOA)_R is obtained. The numerical and experimental results validate the theoretical analysis and show that they are consistent. It can be concluded that CTOA is always constant during steady crack propagation.     

Crack tip opening angle measurement through a girth weld in an X100 steel pipeline section*

Crack tip opening angle (CTOA) is becoming one of the most accepted methods for characterizing fully plastic fracture. It provides a measure of the resistance to fracture for a material in cases where there is a large degree of stable‐tearing crack extension during the fracture process. Our current pipeline research uses the CTOA test as an alternative, or addition, to the CTOD (crack tip opening displacement) and the fracture energy characterization provided by the J‐integral approach. A test technique was developed for measurement of CTOA that uses a modified double cantilever beam (MDCB) specimen. A digital camera and image analysis software were used to record the progression of the crack tip and to estimate the CTOA. In this article, CTOA data on crack growth orientations perpendicular to pipeline girth welds are presented. The CTOA for X100 high strength bainitic gas pipeline steel is reported. Two different specimen gauge sections, 3 mm and 8 mm, were used and the effect of the specimen thickness on the CTOA is discussed. The results show a change in the CTOA as the crack grows into the heat affected zone (HAZ). A slight improvement in the fracture resistance is measured, and through the weld, a slight decrease in fracture resistance is observed.     

Use of J-integral as fracture parameter in simplified analysis of bonded joints

The simplified analytical approaches based on beam or plates theories are commonly used to solve the stress field in bonded laminates. However, to be correctly applied, these methods require an appropriate fracture criterion. In this paper, the use of J-integral as a fracture parameter in these simplified analytical approaches is discussed. After examining its path independence, the J-integral is calculated along two particular paths showing first that this integral is equal to the product of the strain energy at the end of the joint (i.e. at the debond tip) by its thickness. This relationship reveals the partitioning of the opening mode I and the shearing mode II. Secondly, the general expression of J as a function of the loading conditions is derived. It is shown that this parameter can be related to the strain energy release rate in the cases of small scale yielding conditions and for usual fracture mechanics specimens.     

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.     

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.     

Assessment of fatigue load spectrum from fracture surface topography

The possibility of deducing load spectrum parameters from fatigue failure surfaces is explored by applying innovative, three-dimensional topographic characterization and analysis techniques to failure surfaces in aluminum sheet. Precise, high-resolution elevation maps of fracture surfaces were obtained using confocal optics scanning laser microscopy. Elevation power spectral density curves resulting from a fast Fourier transform of the elevation data appear sensitive to stress intensity range and environment. A conjugate fracture surface matching procedure, FRASTA, can detect and may provide a way to quantify overloads.     

Crack tip parameters and elastic-plastic fracture of metals

By using optical displacement-measuring techniques we obtain the crack tip fields in terms of crack tip strain, crack opening angle (COA) and crack tip opening angle (CTOA). Thin plates with different crack configurations made of six elastic-plastic materials with strain hardening exponent ranging from 3 to are studied. We find that the COA resistance curve assumes certain characteristics common to all the materials. The experimental results indicate that the critical value of COA may be used as a fracture toughness parameter for these materials.

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Résumé En utilisant une technique de mesure optique des déplacements, on obtient les champs régnant à l'estrémité d'une entaille, qui s'experiment par la déformation d'extrémité d'entaille, l'angle d'ouverture de la crique (COA et l'angle d'ouverture de la pointe de la crique (CTOA). On étudie des feuillards présentant différentes configurations de fissures et réalisés en six matériaux élasto-plastiques dont les modules d'écrouissage s'échelonnent de 3 à l'infini.On trouve que la courbe de résistance COA suppose certaines caractéristiques communes à tous les matériaux. Les résultats expérimentaux indiquent que la valeur critique du COA peut être utilisée comme paramètre de ténacité à la rupture pour les matériaux étudiés.

     

Some contribution to process zone fracture mechanics

The mechanism of the ductile fracture is studied theoretically for the Al Alloy 7075-T6 specimens. A model for the interaction of a crack tip with a void nearby is analyzed by using the Modified Gurson's Model. Taking fracture criterion into consideration, the analysis of a crack propagation is carried out and besides the distribution of the equivalent plastic strain, the void volume fraction f and the localization are obtained. Microcracks nucleate on the ligament between crack and void, and grow and coalesce each other, and at last the main crack thus formed coalesces with the void and the coalescence of the crack and void is completed. And these phenomenon occurs in the localized region.The initiation of the microcrack of 7075 occurs at small J and the microcrack penetration between crack and void occurs at larger J, and the propagation does not occur smoothly. These results coincide with the results of the experiments by FRASTA (FRActure Surface Topographic Analysis) and Fractography.     

Microtopography for ductile fracture process characterization Part 2: application for CTOA analysis

The crack tip opening angle (CTOA) is seeing increased use to characterize fracture in so-called “low constraint” geometries, such as thin sheet aerospace structures and thin-walled pipes. With this increase in application comes a need to more fully understand and measure actual CTOA behavior. CTOA is a measure of the material response during ductile fracture, a “crack tip response function”. In some range of crack extension following growth initiation, a constant value of CTOA is often assumed. However, many questions concerning the use of CTOA as a material response-characterizing parameter remain. For example, when is CTOA truly constant? What three-dimensional effects may be involved (even in thin sheet material)? What are the effects of crack tunneling on general CTOA behavior? How do laboratory specimen measurements of CTOA compare to actual structural behavior?Measurements of CTOA on the outer surface of test specimens reveal little about three-dimensional effects in the specimen interior, and the actual measurements themselves are frequently difficult. The Idaho National Engineering and Environmental Laboratory (INEEL) use their microtopography system to collect data from the actual fracture surfaces following a test. Analyses of these data provide full three-dimensional CTOA distributions, at any amount of crack extension. The analysis is accomplished using only a single specimen and is performed entirely after the completion of a test. The resultant CTOA distributions allow development of full and effective understanding of CTOA behaviors. This paper presents underlying principles, various sources of measurement error and their corrections, and experimental and analytical verification of CTOA analysis with the microtopography method.     

Mixed-mode fracture load prediction in lead-free solder joints

Double cantilever beam (DCB) fracture specimens were made by joining copper bars with both continuous and discrete SAC305 solder layers of different lengths under standard surface mount (SMT) processing conditions. The specimens were then fractured under mode-I and various mixed-mode loading conditions. The loads corresponding to crack initiation in the continuous joints were used to calculate the critical strain energy release rate, J_ci, at the various mode ratios using elastic–plastic finite element analysis (FEA). It was found that the J_ci from the continuous joint DCBs provided a lower bound strength prediction for discrete 2 mm and 5 mm long joints at the various mode ratios. Additionally, these J_ci values calculated from FEA using the measured fracture loads agreed reasonably with J_ci estimated from measured crack opening displacements at crack initiation in both the continuous and discrete joints. Therefore, the critical strain energy release rate as a function of the mode ratio of loading is a promising fracture criterion that can be used to predict the strength of solder joints of arbitrary geometry subject to combined tensile and shear loads.     

Evaluation of the ISO <Emphasis Type="Italic">J</Emphasis> initiation procedure using the EURO fracture toughness data set

The multiple specimen J _0.2/BL initiation fracture toughness test procedure from the ISO standard, ISO 12135:2002, is evaluated using the EURO fracture toughness data set. This standard is also compared with the ASTM standard, ASTM E 1820, multiple specimen J _Ic procedure. The EURO round robin data set was generated to evaluate the transition fracture toughness methods for steels. However, many of the tests resulted in ductile fracture behavior giving final J versus ductile crack extension points. This is the information that is measured in a multiple specimen J initiation fracture toughness test. The data set has more than 300 individual points of J versus crack extension with four different specimen sizes. It may be the largest data set of that type produced for one material. Therefore, its use to determine J initiation values can provide an important evaluation of the standard procedures. The results showed that a J _0.2/BL value could be determined from the ISO standard for three of the four specimen sizes, the smallest size did not meet the specimen size requirement on J. The construction line slopes in this method are very steep compared with the ASTM construction line slopes. This resulted in low J initiation values, about a factor of two lower than the one from the ASTM method. Of the various criteria imposed to determine a valid J _0.2/BL value, the one limiting the maximum J value was the most questionable. It had an effect of eliminating small specimen data that was identical to acceptable large specimen data.     

The Use of Crack-Tip Opening Displacement for Testing of the Hydrogen Embrittlement of High-Strength Steels

Stress-corrosion cracks are, as a rule, brittle and often encountered under stresses much lower than the yield strength. For this reason, the methods of linear elastic fracture mechanics (LEFM) can be used for the investigation of stress-corrosion cracking (SCC). However, in some cases, these methods are inapplicable, and it is necessary to use the methods of so-called elastoplastic fracture mechanics (EPFM). In the EPFM approach, the J-integral is the most commonly used parameter for correlating crack initiation and propagation but the crack-tip opening displacement (CTOD) and crack-tip opening angle (CTOA) prove to be promising alternatives, especially for thin-sheet materials. Since both these parameters are connected with the crack geometry and, hence, reflect the level of strain at the crack tip, they appear to be useful correlation parameters for the cases of SCC, where the level of strain in the vicinity of the crack tip and, in particular, the strain rate, are the determining variables of the process. The hydrogen embrittlement of a higher-strength structural steel and welded joints of a C-Mn steel is assessed by using the CTOA and CTOD methodologies. In constant-extension-rate tests (CERT), fatigue precracked specimens were loaded with various low strain rates and electrolytically charged with hydrogen. It was discovered that hydrogen embrittlement significantly affects the crack-growth resistance curves (R-curves) thus generated and the opening angle for which the crack propagates into the material.__________Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 6, pp. 35–40, November–December, 2004.     

Reference Stress Approximations for J and COD of Circumferential Through-Wall Cracked Pipes

Reference stress approximations for the J integral and crack tip opening displacement (COD) for circumferential through-wall cracked pipes under tension and under bending are reported. The proposed J estimation equation is fully compatible with the existing reference stress based J estimation, currently embedded in the R6 assessment procedure, but involves a slightly different definition of the reference stress, using an optimised reference load instead of the limit load. This modification enhances the accuracy of the J estimation for circumferentially cracked pipes. Confidence in the proposed equation is gained from the significantly reduced hardening dependence of the plastic influence functions in the GE/EPRI method. The proposed COD estimation equation includes two further modifications. One is the use of a power-law fit to the plastic portion of the stress strain data, instead of the use of the actual stress strain data. In this context, a robust estimation equation for the strain hardening index is given. The other modification is to the plasticity correction term in contained yielding. A lower bound COD estimation equation is also given, similar to the R6 option 1 Jestimation curve, which is suitable when only limited tensile properties are available. The resulting estimation equations are simple to use. Comparisons with experimental pipe test data show that the proposed COD estimation equations provide overall good agreement, which gives confidence in applying them to Leak-before-Break (LBB) analyses.     

Formulation and implementation of a high-order 3-D domain integral method for the extraction of energy release rates

This article presents a three dimensional (3-D) formulation and implementation of a high-order domain integral method for the computation of energy release rate. The method is derived using surface and domain formulations of the J-integral and the weighted residual method. The J-integral along 3-D crack fronts is approximated by high-order Legendre polynomials. The proposed implementation is tailored for the Generalized/eXtended Finite Element Method and can handle discontinuities arbitrarily located within a finite element mesh. The domain integral calculations are based on the same integration elements used for the computation of the stiffness matrix. Discontinuities of the integrands across crack surfaces and across computational element boundaries are fully accounted for. The proposed method is able to deliver smooth approximations and to capture the boundary layer behavior of the J-integral using tetrahedral meshes. Numerical simulations of mode-I and mixed mode benchmark fracture mechanics examples verify expected convergence rates for the computed energy release rates. The results are also in good agreement with other numerical solutions available in the literature.     

Mode I–III Decomposition of the J‐integral from DIC Displacement Data

This paper presents the implementation of the decomposition method on digital image correlation (DIC) obtained displacement fields to obtain J‐integral results (J) and respective stress intensity factors (SIFs). DIC is increasingly used with the J‐integral approach in experimental mechanics to obtain J estimates from complex fracture processes. In this approach, the decomposition method is applied to DIC displacement fields for the first time. Here, displacement fields are separated before stresses and strains are computed, so that subsequent computation of separate J or SIF components may follow the classical full‐field J‐integral approach. The sensitivity of the decomposition method to experimental errors is investigated using synthetically generated errors imposed on crack tip displacement fields (Williams' series), from which improvements to the procedure are proposed. The method is experimentally tested on PMMA Arcan specimens under mode I, II, and III, and mixed‐mode I–III loading. Test results were compared to fracture toughness values obtained from ASTM tests and literature with close agreement.     

A crack propagation criterion based on ΔCTOD measured with 2D‐digital image correlation technique

The fatigue cracks growth rate of a forged HSLA steel (AISI 4130) was investigated using thin single edge notch tensile specimen to simulate the crack development on a diesel train crankshafts. The effect of load ratio, R, was investigated at room temperature. Fatigue fracture surfaces were examined by scanning electron microscopy. An approach based on the crack tip opening displacement range (ΔCTOD) was proposed as fatigue crack propagation criterion. ΔCTOD measurements were carried out using 2D‐digital image correlation techniques. J‐integral values were estimated using ΔCTOD. Under test conditions investigated, it was found that the use of ΔCTOD as a fatigue crack growth driving force parameter is relevant and could describe the crack propagation behaviour, under different load ratio R.     

An analytical expression for the J2‐integral of an interfacial crack in orthotropic bimaterials

This paper presents a new analytical expression relating the J₂‐integral and stress intensity factors (SIF) in an in‐plane traction‐free crack between two orthotropic elastic solids using the complex function method. The singular oscillatory near tip field of a bimaterial interfacial crack is usually characterized by a pair of SIFs. In linear elastic interfacial fracture mechanics, the majority of numerical and experimental methods rely on the analytical equations relating J_k‐integrals and SIFs. Although an analytical equation relating J₁‐integral or strain energy release rate and SIFs is available, a similar relation for J₂‐integral in debonded anisotropic solids is non‐existent. Using this new analytical expression, in conjunction with the values of J_k, the SIFs can be computed without the need for an auxiliary relation. An example with known analytical solutions for SIFs is presented to show the variation of the J₂‐integral near the crack tip of a bimaterial orthotropic plate. Different bimaterial combinations are considered, and the effect of material mismatch on J_k is demonstrated.