The crack growth resistance of thin steel sheets under eccentric tension

The stable crack growth in thin steel sheets is the topic of this paper. The crack opening was observed using a videoextensometry system, allowing the crack extension determination. J_R-curve and δ_R-curve were established from obtained data. The ductile tearing properties of different thin sheets of steel were determined, including the impact of the specimen orientation, from test performed on compact tension specimens loaded under two conditions. The effect of the material, the rolling direction, and loading rate on the crack growth resistance of thin steel sheets was analyzed. In addition to the crack growth resistance, J-integral values for crack initiation were also estimated. The relation between J _i and J_0.2 was assessed using the basic mathematical and statistical methods. This relation was described by a linear regression model.     

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.     

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.     

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.     

R-curve behaviour of a structural steel

The ductile tearing behaviour-of BS4360 50D structural steel has been studied using two bending specimen geometries: square (W = B) cross section three point bend specimens with different initial fatigue crack length, ranging from a/W = 0.20 to about 0.75, and rectangular cross section (W = 2B) specimens with initial fatigue crack length a/W = 0.3.With the first set of specimens it was intended to investigate the possible dependence of the tearing behaviour on initial crack length. It was concluded that specimens with shorter values of initial crack length present higher resistance to ductile tearing. Two different methods of calculating the J-resistance curve, one based on the approximate equation J = 2A/(W?a)B and a more elaborate calculation procedure introduced by Garwood were used. The curves determined following the more accurate procedure were used to determine the value of the tearing modulus T, which is related to the occurrence of tearing instabilities in structures. It was found that T decreases slightly with increasing value of initial crack length.The tests using the wider specimen geometry were intended to examine the tearing behaviour over a larger amount of crack growth allowed by the wider geometry used. It was found that the resistance curves, using the COD concept, present a maximum after which the resistance begins to drop. This maximum value of the COD-resistance curve is higher than the conventional δ_max measured at max load. These tests were performed using the compliance technique of evaluating the crack length. Tests performed with 10% unloading presented slightly lower values of resistance than tests performed with complete unloading.It was found that the relationship J = mσ_flowδδ presents increasing values of m with crack growth. This is attributed to an increasing local yield stress, caused by the through thickness deformation.     

CHARACTERIZATION OF DUCTILE TEARING RESISTANCE BY ENERGY DISSIPATION RATE

The J integral, which is widely used in elastic-plastic fracture mechanics, is not the true driving force any more if the crack is propagating. This leads to some inconsistencies when ductile tearing resistance is characterized in terms of J, especially for large crack extensions. Instead, Turner has proposed the energy dissipation rate as a physically more meaningful quantity. His concept is discussed and more evidence is given that will provide a better understanding of ductile tearing. It is shown how this quantity can be determined by measuring the heat production ahead of a fast running crack, or calculated in a finite element analysis, or re-evaluated from J-R test records of bend and tensile specimens. The energy dissipation rate is decreasing with crack extension in gross plasticity and approaches a stationary state. From these relations, the shapes of the cumulative J-R curves can be derived for different specimen geometries.     

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.     

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.     

On the fitting and extrapolation of J-resistance data derived through the linear normalization technique

In this paper, an assessment is made regarding the effects of J–R curve fitting and extrapolation methods in two J‐integral criteria – namely crack initiation, J_i, and tearing instability, J₅₀– which were obtained through the linear normalization technique. Power‐law, logarithmic and linear fits were concurrently applied to J–Δa data derived from sub‐sized compact tensile specimens machined from a nuclear grade steel and tested at 300 °C. Research results show that the logarithmic J–R fit is the most conservative approach within a broad range of elastic–plastic fracture resistance, compared to the conventional power‐law fit. On the other hand, the linear fitting method provided the most non‐conservative J‐predictions. The values of J_i and J₅₀ have been successfully correlated with the net energy absorbed during Charpy impact testing of the materials.     

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.     

Fracture toughness evaluation for short glass fibre reinforced composites

Valid plane-stress fracture toughness evaluation of short fibre reinforced composites relies essentially on the successful separation of the energy absorbed in the localized crack-tip region out of the total energy absorbed by the cracked material body at large. Three different experimental techniques, all stemming from the energetic interpretation of theJ integral, are utilized and their relative merits in the characterization of fracture initiation in short glass fibre reinforced injection-moulded nylon 6.6 examined. Various theoretical aspects concerning these experimental methods are outlined. The rationale behind using a single-edge-notched tension type specimen for theJ _c test is presented. TheJ _c value obtained from the compliance calibration method and the quasistatic energy method agree closely and can be considered to be independent of pre-crack length and specimen geometry when the pre-crack length to specimen width ratio (a/w) is larger than 0.45. The extrapolation method fails nevertheless to yield a physically consistentJ _c value, possibly due to its questionable theoretical representation. As no constraint on boundary conditions is necessitated during the course of crack extension, the quasistatic energy is physically more appealing.     

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.     

CTOD‐R Curve Tests of API 5L X90 By SENT Specimen Using a Modified Normalization Method

A modified normalization method is presented for obtaining crack tip opening displacement (CTOD) resistance curves of single edge‐notched tension specimens. For the applied load mode, the normalization method should be based on force‐crack mouth opening displacement. A formula is proposed for C_LL(i), the core parameter used in the normalization calculation. The modified method is validated using the unloading compliance method. The study of specimen geometry shows that side‐groove depth and crack depth have significant impacts on the obtained CTOD resistance curves, and the shape of the crack front affects the determination accuracy of crack length.     

Quasi-static fracture toughness testing of a single CT specimen at two test conditions

Abstract

It is proposed that a single CT specimen can be used for determining J ₀.₂ at two testing conditions, provided it can be ensured that the crack tip plastic zones for the two tests do not interfere. This is achieved by extending the crack at the end of the first fracture test by fatigue cycling at ambient temperature to obtain the starting crack for the second test. This method has been validated by testing thermally aged CT specimens of modified 9Cr - 1Mo steel at 653 K and 803 K. The J-Δa values obtained by a multispecimen method at a specific temperature were on a single curve irrespective of whether the data were generated from the first test or second test on that sample. Also, the J-Δa curves obtained using a single specimen normalisation method from data on first and second tests were within the expected specimen to specimen variation.     

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.     

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.     

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.     

Specific aspects on crack advance during J-test method for structural materials at cryogenic temperatures

Cryogenic elastic plastic, J‐integral investigations on metallic materials often show negative crack extension values with respect to resistance curve J‐R. According to the present ASTM standard, the use of unloading compliance technique relies on the estimation procedure of the crack lengths during the unloading sequences of the test. The current standard, however, does not give any specific procedure for treating such negative data. To date, the applied procedure uses the shifting of the negative crack extension values either to the onset of the blunting line or to the offset of the resistance curve. The present paper represents a solution of the negative crack length problem on the basis of a mechanical evaluation procedure of the unloading slopes. The achieved progress using this evaluation technique is demonstrated on different materials such as cryogenic high toughness stainless steels, low carbon ferritic steel and aluminum alloys from the series of 7000 and 5000. In addition, this work deals with the crack tunnelling phenomenon, observed for high toughness materials, and shows the reduction of this crack extension appearance by using electro discharge machining (EDM) side groove technique. The differences between EDM processed side grooves and standard V‐notch machining have been investigated within these test series.     

Correction methods of an apparent negative crack growth phenomenon

It often occurs in J–R testing that some initial crack extension (a) data points have anomalous negative values. The reason for the apparent negative crack growth is due to the analysis method. The phenomenon as a possible source of error in determining J _IC or J–R curve from partial unloading compliance experiments may be eliminated by the compliance correction equation or the offset technique. In this study, new correction methods based on compliance correction and blunting behavior are proposed and verified by the measurement of the actual crack length and J _IC analysis.     

ELASTIC-PLASTIC FRACTURE MECHANICS FOR PRESSURE VESSEL DESIGN

The project has been concerned with the verification of the J-philosophy for initiation and growth of cracks on laboratory type specimens as well as on larger surface cracked plates. The analysis of the experiments involved extensive fully three-dimensional finite element calculations. It was found that the initiation events for the six surface cracked plates occurred at approximately the same J-value. A corresponding relation to the laboratory type specimen was less successful, mainly because of the short-comings of current methods for J_IC-evaluations. A somewhat puzzling feature of the surface crack experiments was that unstable crack growth occurred immediately after crack growth initiation in four out of six tests, while some amount of stable crack growth was evident in the remaining two and in all of the laboratory type specimens. An evaluation of the surface experiments by a type of R6-analysis was also performed. Using as K_cr the mean value from the surface crack experiments, it was found that the R6-method yielded conservative predictions.