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.     

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.     

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.     

Effect of mechanical mismatching on the ductile-to-brittle transition curve of welded joints

The effect of mechanical mismatching (ratio between the yield strength of base and weld metal) on the toughness of welded joints at different temperatures was analysed and the ductile-to-brittle transition curves of these welded joints were experimentally obtained. The filler metal of the joints was always the same, varying the base metal and the width of the welded zone. Two base metals were selected, one with a higher strength than the filler metal (undermatched joint) and the other with a lower strength than the filler metal (overmatched joint). In addition, the joints were made using two different weld widths, 20 and 10 mm.The fracture behaviour of the joints were determined at different temperatures using SE(B) specimens provided with short cracks (a/W = 0.22). Besides, long crack specimens (a/W = 0.5) were also used for comparison. In the case of overmatched joints, the J-values for ductile crack growth are larger than for the undermatched joints. In addition, the ductile-to-brittle transition curve is displaced towards lower-temperatures and higher-toughness values and the toughness for cleavage fracture is also larger for overmatching than for undermatching. All these effects are more significant as the weld width decreases and have been explained in terms of constraint modifications.     

Constraint-modified J−R curves and its application to ductile crack growth

The concept of J-controlled crack growth is extended to J–A ₂ controlled crack growth using J as the loading level and A ₂ as the constraint parameter. It is shown that during crack extension, the parameter A ₂ is an appropriate constraint parameter due to its independence of applied loads under fully plastic conditions or large-scale yielding. A wide range of constraint level is considered using five different types of specimen geometry and loading configuration; namely, compact tension (CT), three-point bend (TPB), single edge-notched tension (SENT), double edge-notched tension (DENT) and centre-cracked panel (CCP). The upper shelf initiation toughness J _IC, tearing resistance T _R and J–R curves tested by Joyce and Link (1995) for A533B steels using the first four specimens are analysed. Through finite element analysis at the applied load of J _IC, the values of A ₂ for all specimens are determined. The framework and construction of constraint-modified J–R curves using A ₂ as the constraint parameter are developed and demonstrated. A procedure of transferring the J–R curves determined from standard ASTM procedure to non-standard specimens or practical cracked structures is outlined. Based on the test data, the constraint-modified J–R curves are presented for the test material of A533B steel. Comparison shows the experimental J–R curves can be reproduced or predicted accurately by the constraint-modified J–R curves for all specimens tested. Finally, the variation of J–R curves with the size of test specimens is produced. The results show that larger specimens tend to have lower crack growth resistance curves.     

Specimen Size Requirements for Two-parameter Fracture Toughness Testing

Using a single parameter fracture mechanics theory, a minimum specimen size requirement of min(a, b, B) >200J/σ₀ in tension and min(a, b, B) >25J/σ₀ in bending, where B is the thickness, b the remaining ligament and a is the crack length of the specimen, were derived [Shih and German (1981), International Journal of fracture 17, 27–43] which have provided the basis for modern fracture toughness testing procedures. Two-parameter fracture toughness testing including the constraint, on the other hand, is desirable since it offers a solution to the transferability issue. A size requirement for a valid two-parameter fracture toughness testing based on the J-A₂ three-term solution was determined as min(a, b, B) > 11J/σ₀ [Chao and Zhu (1998), International Journal of fracture 89, 285–307] in which the limiting case is bend specimens under large scale yielding (LSY). Recent work by Chao et al. (2004, International Journal of fracture, 27, 283–302) has shown that the J-A₂ dominance at a crack tip can be significantly enhanced for bending specimens under LSY if a modified J-A₂ solution is adopted. This current paper further studies the size of the J-A₂ dominant zone using the modified J-A₂ solution for deep bend specimens with hardening from low to high and loading from SSY to LSY using finite element analysis. Based on the results, a rather relaxed specimen size requirement min(a, b, B) >6J/σ₀ is developed and recommended for a valid two-parameter fracture toughness testing using the J-A₂ fracture criterion. Validity of the size requirement is demonstrated by using the experimental J-R curves from non-standard bending specimens for A285 steel.     

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.     

J–Q characterized stress fields of surface-cracked metallic liners – II. Composite overwrapped pressure vessels

Two-parameter J–Q elastic–plastic crack front fields are developed for surface-cracked metallic liners of composite overwrapped pressure vessels (COPV). Uniaxial tensile data from 6061-T6 aluminum coupon specimens for the metallic liner and anisotropic elastic material properties for the filament wound carbon fiber epoxy are used in three-dimensional finite element models. Modified boundary layer (MBL) finite element solutions are used to evaluate near tip dominance and parameterization limits. Semicircular surface cracks of varying depths inserted in the inner liner surface are investigated. J and Q crack front distributions, and the corresponding parameterization limits, and near tip triaxiality trends are obtained and the effects of elastic–plastic material discontinuity of the heterogeneous joint and the biaxiality of stresses are evaluated. J–Q predicted fields maintain accuracy for higher far-field loads and lower near tip deformations compared to the liner only models for angles near the free surface. However, for the critical crack growth region, Q does not maintain a radially independent measure of constraint for loads seen in a typical COPV; therefore, these fracture predictors may not be applicable. In the COPV, large-scale yielding marks a transition where triaxiality is higher as a function of constraint compared to the linear relationship common to homogeneous structures. Results from this study will facilitate the implementation of proof test logic and accurate fracture prediction of COPV liners with emphasis on geometric limits and fracture specimen applicability.     

Mismatch limit loads and approximate <Emphasis Type="Italic">J</Emphasis> estimates for tensile plates with constant-depth surface cracks in the center of welds

The present work provides mismatch limit loads and approximate J estimates for tensile plates with constant-depth, part-through surface cracks in the center of the weld metal. Based on systematic three-dimensional FE limit analyses, effects of strength mismatch related variables on limit loads are firstly quantified by the strength mismatch ratio and one geometry-related parameter. Mismatch limit loads for part-through surface cracks are then correlated to those for two-dimensional, through-wall crack problems. Based on the proposed limit load solutions, the applicability of the reference stress based J estimates is also investigated. When the reference stress is defined by the mismatch limit load, predicted J values agree overall well with FE results.     

The influence of weld strength mismatch on crack-tip constraint in single edge notch bend specimens

Previous work by Dodds and Anderson provides a framework to quantify finite size and crack depth effects on cleavage fracture toughness when failure occurs at deformation levels where J no longer uniquely describes the state of stresses and strains in the vicinity of the crack tip. Size effects on cleavage fracture are quantified by defining a value termed J _SSY: the J to which an infinite body must be loaded to achieve the same likelihood of cleavage fracture as in a finite body. In weld metal fracture toughness testing, mismatch between weld metal and baseplate strength can alter deformation patterns, which complicate size and crack depth effects on cleavage fracture toughness. This study demonstrates that there is virtually no effect of ±20 percent mismatch on J _SSYif the distance from the crack tip to the weld/plate interface (L _min) exceeds 5 mm. At higher levels of overmatch (50 to 100%), it is no longer possible to parameterize the departure of J _SSYfor a weldment from that for a homogeneous SE(B) based on L _min alone. Weld geometry significantly influences the accuracy with which J _SSYfor a welded SE(B) can be approximated by J _SSYfor a homogeneous specimen at these extreme overmatch levels.     

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.     

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.     

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.     

THE EFFECTS OF CRACK DEPTH ON THE J-INTEGRAL AND CTOD FRACTURE TOUGHNESS FOR WELDED BEND SPECIMENS

This work deals with the influence of crack depth on the fracture toughness at initiation of crack growth and the constraint factor in relationship between the J-integral and the crack tip opening displacement (CTOD). A series of tests were performed on high strength low alloyed HT80 steel welds, and the critical J-integral and CTOD were determined using the load versus load point displacement record from three-point bend specimens with 0.05 < a/W < 0.5. It was found that the fracture toughness for shallow cracks at the onset of crack growth was larger than that for deep cracks for the steel welds tested, but it is felt that there is no fixed relationship between these values in the welds tested. The constraint factor is also a function of crack depth, and values of the factor increase from 0.5 to 1.5 when a/W increases from about 0.05 to 0.5. The factors are not very sensitive to the crack tip materials (HAZ or weld metal) in the welds tested.     

A first report on fracture toughness ofbcc iron alloys as influenced by solutes: opposite effects of silicon and cobalt

The effect of solutes on resistance to fracture of body centred cubic iron single-phase solid-solution alloys has been investigated. TheJ-integral method has been used for the measurement of ductile fracture toughness. TheJ _IC values so determined quantitatively indicate the extent of degradation in fracture toughness due to the addition of hardening solute silicon. Cobalt addition results in alloy softening. The measuredJ _IC values clearly demonstrate the toughening effect of cobalt addition as a solute, which result renders the case of Fe-Co solid-solution alloys interesting.     

Fracture toughness behavior of weldments with mis-matched properties at elevated temperature

High temperature fracture toughness tests were performed on welded specimens of 1Cr-1Mo-14 V steel with different levels of mismatch between the base metal and the weld metal and the cracks lying along the fusion line. A wide range of fracture toughness values were obtained for weldments, as opposed to a unique value of J_IC and a unique J-R curve typically obtained for homogeneous materials. Detailed observations of the crack path within the weldments were made to understand the wide scatter in the fracture toughness behavior. The yield strength mismatch between the base metal and the weld metal was found to directly influence the stable crack path, and hence the fracture toughness behavior. The denomination of ‘apparent fracture toughness’ was used to describe the variability of the fracture toughness in the weld region due to microstructure and mechanical property gradients. The apparent fracture toughness exhibited a minima at a fixed distance from the fusion line for a specific weld. The relative position of the fatigue precrack with respect to the fusion line and the region of low fracture toughness was also shown to influence the measured fracture toughness behavior of the specimen. A frame-work is provided for representing the weld fracture toughness behavior and the associated variability due to microstructural gradients. This revised version was published online in August 2006 with corrections to the Cover Date.     

Single and multi-specimenR-curve methods forJ IC determination of toughened nylons

For characterization of the fracture resistance of materials used in the upper shelf toughness regime,J-R curves are widely considered the most promising candidates. However, there still remain problems concerning both the generation and measurement ofJ-R curves as material characterizing parameters and their application in ductile fracture analyses for failure prediction in polymeric materials. This paper reports the results of investigations conducted on two rubbertoughened nylons at room temperature. Two different methods ofJ-R curve determination are covered, namely multi-specimen and single specimen test methods. The resultingJ-R curves have also been evaluated to obtain values of the initiation toughness,J _IC, following the extrapolation and interpolation schemes prescribed by ASTM E813-81 and ASTM E813-87 test procedures, respectively. The results show that the multiple specimen unloading method and the single specimen partial unloading compliance method can be used to generate comparable crack growth resistanceJ-R curves of the toughened nylons. The value ofJ _IC for the crystalline rubber-toughened nylon was approximately twice the value obtained for the amorphous rubber-toughened nylon. The former material also exhibited a greater resistance to ductile crack growth.     

On the application of the damage work density as a new initiation criterion for ductile fracture

In this paper the ‘damage work’ proposed by Chaouadi et al. is used to formulate an energy crack initiation criterion to describe ductile crack initiation. The traditional assessment of structural integrity by the J-integral, a property of elastic-plastic fracture mechanics is compared. Two free-cutting and one structural steel are investigated. The measured values for the critical damage work density at initiation W_di are compared with values for copper and RPV steel. As the fracture mechanical approach is limited to sharp cracks in the material (high-constraint stress state) the present damage mechanics approach is regarded as important as a more general concept closer to reality. While old void growth models of damage mechanics cannot formulate a simple criterion for crack initiation the applied damage work reaches a constant value at initiation W_di which is independent of the stress state during the deformation process. We recommend W_di as a material property of toughness for testing and engineering purposes.     

A framework to correlate a/W ratio effects on elastic-plastic fracture toughness (J c )

Single edge-notched bend (SENB) specimens containing shallow cracks (a/W < 0.2) are commonly employed for fracture testing of ferritic materials in the lower-transition region where extensive plasticity (but no significant ductile crack growth) precedes unstable fracture. Critical J-values J _c ) for shallow crack specimens are significantly larger (factor of 2–3) than the J _c )-values for corresponding deep crack specimens at identical temperatures. The increase of fracture toughness arises from the loss of constraint that occurs when the gross plastic zones of bending impinge on the otherwise autonomous crack-tip plastic zones. Consequently, SENB specimens with small and large a/W ratios loaded to the same J-value have markedly different crack-tip stresses under large-scale plasticity. Detailed, plane-strain finite-element analyses and a local stress-based criterion for cleavage fracture are combined to establish specimen size requirements (deformation limits) for testing in the transition region which assure a single parameter characterization of the crack-tip stress field. Moreover, these analyses provide a framework to correlate J _c )-values with a/W ratio once the deformation limits are exceeded. The correlation procedure is shown to remove the geometry dependence of fracture toughness values for an A36 steel in the transition region across a/W ratios and to reduce the scatter of toughness values for nominally identical specimens.     

Role of nonlinear fracture mechanics in assessing fracture and crack growth in welds

An experimental study was conducted to assess the structural performance of repair welds in an ex-service 1Cr-1Mo-0.25V steam turbine casing material. Material from two weld techniques, one involving a post-weld heat-treatment that produced undermatched welds and the other involving a temper bead welding technique that produced overmatched welds were tested. Both welding techniques were implemented in two base metal conditions giving rise to four different welds and two different base metal conditions. The tests conducted included tensile tests, creep tests, fracture toughness tests, fatigue crack growth tests, creep crack growth tests, and creep-fatigue crack growth tests on the base metal, weld metal and the weldment region.The yield strength of the weld metal in the undermatched condition was approximately 10% lower than the base metal, while the weld metal in the overmatched condition had a yield strength that was 30% higher than the base metal at 565 °C. The creep deformation rates in the undermatched welds were 60 times faster than the base metal at a stress of 207 MPa. In the overmatched welds, the creep rates at 207 MPa were about 2.8 times faster in one case and 2.8 times slower in the other.The crack path in fracture toughness specimens followed the interface between the transition layer and the weaker of the weld metal and the base metal. The J-resistance curves for the weldments at 565 °C showed significant variability among duplicate samples from the same welds. This scatter was caused by the variability in the location of the precrack with respect to the fusion line and the location of the low fracture toughness region in the weldment. This behavior was explained using a novel approach for characterizing the fracture of welds. The creep-fatigue crack growth rates at equivalent (C_t)_avg values in undermatched welds was higher than the crack growth rates in the overmatched weld samples. In all cases under creep-fatigue, the crack appeared to grow in the weaker of the base metal and the weld metal. Recommendations for future work are provided to enhance the theoretical underpinnings of the nonlinear fracture mechanics frame-work to rigorously address fracture and crack growth in welds.