Numerical investigation on J-integral testing of heterogeneous fracture toughness testing specimens: Part I – weld metal cracks

Based on extensive two‐dimensional (2D) finite element (FE) analyses, the present work provides the plastic η factor solutions for fracture toughness J‐integral testing of heterogeneous specimens with weldments. Solutions cover practically interesting ranges of strength mismatch and relative weld width, and are given for three typical geometries for toughness testing: a middle cracked tension (M(T)) specimen, single edge cracked bend (SE(B)) specimen and (C(T)) specimen. For mismatched M(T) specimens, both plane strain and plane stress conditions are considered, whereas for SE(B) and C(T) specimens, only the plane strain condition is considered. For all cases, only deep cracks are considered, and an idealized butt weld configuration is considered, where the weld metal strip has a rectangular cross section. Based on the present solutions for the strength mismatch effect on plastic η factors, a window is provided, within which the homogeneous J estimation procedure can be used for weldment toughness testing. The effect of the weld groove configuration on the plastic η factor is briefly discussed, concluding the need for further systematic analysis to provide guidance to practical toughness testing.     

Plastic eta factor and blunting line for characterization of fracture toughness of dissimilar metal weld

This paper addresses the fracture toughness evaluation procedure of different zones of dissimilar metal weld (DMW). Experiments have been conducted on compact tension specimens from DMW joint having initial notch in centre of weld and fusion boundaries. Plastic eta factors (η_p) and slope of blunting line (bl) for above specimens have been evaluated numerically. Experimental load, load line displacement, and crack growth data along with numerically evaluated η_p and bl have been used for calculation of fracture resistance curve and initiation fracture toughness, and finally, it has been compared with that evaluated as per ASTM E1820 and ESIS standard.     

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.     

Fracture toughness of high strength seamless pipe steel from SE(T) and SE(B) specimens evaluated by different standards

Recently released, BS 8571:2014 standard offers an alternative for the experimental determination of fracture toughness and resistance curves of metallic materials from SE(T) specimens. Similar in stress conditions and constraint to cracked tubes, specimens in SE(T) geometry should yield less conservative toughness values than conventional high‐constraint specimens, such as SE(B) geometry. However, the convention to determine the J‐integral fracture toughness proposed in the new BS standard is different from ASTM standards. In this work, SE(T) and SE(B) specimens of similar dimensions of a tough high‐strength seamless pipe steel were tested following the BS 8571:2014 and ASTM E1820‐16 standards, respectively. Because of the different standardized definitions, SE(T) specimens yield lower fracture toughness than SE(B) specimens, which could lead to more conservative results in structural integrity analysis. This investigation also suggests the introduction of the blunting line concept in the BS 8571:2014 standard in order to minimize this problem.     

Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens

Specimen size and geometry effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain an important technological impediment in industrial applications of fracture mechanics and in the on-going development of consensus fracture testing standards. This investigation employs 3-D nonllinear finite element analyses to conduct an extensive parametric evaluation of crack front stress triaxiality for deep notch SE(B) and C(T) specimens and shallow notch SE(B) specimens, with and without side grooves. Crack front conditions are characterized in terms of J-Q trajectories and the constraint model for cleavage fracture toughness proposed previously by Dodds and Anderson. An extension of the toughness scaling model suggested here combines a revised in-plane constraint correction with an explicit thickness correction derived from extreme value statistics. The 3-D analyses provide effective thicknesses for use in the statistical correction which reflect the interaction of material flow properties and specimen aspect ratios, a/W and W/B, on the varying levels of stress triaxiality over the crack front. The 3-D computational results imply that a significantly less strict size/deformation limit, relative to the limit indicated by previous plane-strain computations, is needed to maintain small-scale yielding conditions at fracture by a stress-controlled, cleavage mechanism in deep notch SE(B) and C(T) speciments. Moreover, the analyses indicate that side grooves (20 percent) should have essentially no net effect on measured toughness values of such specimens. Additional new results made available from the 3-D analyses also include revised -plastic factors for use in experimental studies to convert measured work quantities to thickness average and maximum (local) J-values over the crack front. To estimate CTOD values, new m-factors are included for use in the expression 131-1.     

Effects of weld strength mismatch on <Emphasis Type="Italic">J</Emphasis> and CTOD estimation procedure for SE(B) specimens

This work examines the effect of weld strength mismatch on fracture toughness measurements defined by J and CTOD fracture parameters using single edge notch bend (SE(B)) specimens. A central objective of the present study is to enlarge on previous developments of J and CTOD estimation procedures for welded bend specimens based upon plastic eta factors (η) and plastic rotational factors (r _p ). Very detailed non-linear finite element analyses for plane-strain models of standard SE(B) fracture specimens with a notch located at the center of square groove welds and in the heat affected zone provide the evolution of load with increased crack mouth opening displacement required for the estimation procedure. One key result emerging from the analyses is that levels of weld strength mismatch within the range ±20% mismatch do not affect significantly J and CTOD estimation expressions applicable to homogeneous materials, particularly for deeply cracked fracture specimens with relatively large weld grooves. The present study provides additional understanding on the effect of weld strength mismatch on J and CTOD toughness measurements while, at the same time, adding a fairly extensive body of results to determine parameters J and CTOD for different materials using bend specimens with varying geometries and mismatch levels.     

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens--Part I: Plane-strain analyses

This work presents a numerical investigation of crack-tip constraint for SE(T) specimens and axially surface cracked pipes using plane-strain, nonlinear computations. The primary objective is to gain some understanding of the potential applicability of constraint designed fracture specimens in defect assessments of pressurized pipelines and cylindrical vessels. The present study builds upon the J-Q approach using plane-strain solutions to characterize effects of constraint on cleavage fracture behavior for the analyzed fracture specimens and cracked pipes. Under increased loading, each cracked configuration follows a characteristic J-Q trajectory which enables comparison of the corresponding driving force curve in the present context. A key outcome of this investigation is that toughness data measured using SE(T) specimens appear more applicable for cleavage fracture predictions of pressurized pipelines and cylindrical vessels than standard, deep notch fracture specimens under bend loading. The results provide a strong support for use of constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.     

Evaluation of the two‐parameter fracture criterion for various crack configurations made of 7075‐T6 aluminium alloy using finite‐element fracture simulations

For many years, a two‐parameter fracture criterion (TPFC) has been used to correlate and predict failure loads on cracked metallic fracture specimens. The current study was conducted to evaluate the use of the TPFC on a high‐strength aluminium alloy, using elastic‐plastic finite‐element (FE) analyses with the critical crack‐tip‐opening angle (CTOA) fracture criterion. In 1966, Forman generated fracture data on middle‐crack tension, M(T), specimens made of thin‐sheet 7075‐T6 aluminium alloy, which is a quasi‐brittle material. The fracture data included a wide range of specimen half‐widths (w) ranging from 38 to 305 mm. A two‐dimensional FE analysis code (ZIP2D) with a “plane‐strain core” option was used to model the fracture process with a critical CTOA chosen to fit the M(T) test data. Fracture simulations were then conducted on other M(T), single‐edge‐crack tension, SE(T), and bend, SE(B), specimens over a wide range in widths (w = 19‐610 mm). No test data were available on the SE‐type specimens. The results supported the TPFC equation for net‐section stresses less than the material proportional limit. However, some discrepancies in the FE fracture simulations results were observed among the numerical analyses made on the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens for quasi‐brittle materials.     

Residual strength of unidirectional fibre-metal laminates based on JC toughness of C(T) and SE(B) specimens: comparison with M(T) test results

Fibre‐metal laminates (FMLs) are structural composites designed with the aim of producing very low fatigue crack‐propagation rate, damage‐tolerant and high‐strength materials, if compared to aeronautical Al alloys. Their application in aeronautical structures demands a deep knowledge of a wide set of mechanical properties and technological values, including both fracture toughness and residual strength. The residual strength of FMLs have been traditionally determined by using wide centre‐cracked tension panels M(T). The use of this geometry requires large quantities of material and heavy laboratory facilities. In this work, fracture toughness ( J_C) of some unidirectional FMLs laminates was measured using a recently proposed methodology for critical fracture toughness evaluation on compact tension C(T) and single‐edge bend SE(B) specimens. Additionally, residual strength values of wider M(T) specimens with different widths (W from 150 to 200 mm) and several crack to width ratios (2a/W) were experimentally obtained. Some experimental residual strength values of M(T) specimens (W from 150 to 400 mm and different 2a/W ratios) of Arall were also obtained from the bibliography. Based on J_C results from C(T) and SE(B) specimens, and either using or not using crack‐tip plasticity corrections, the residual strengths of the M(T) specimens were predicted and compared to the experimental ones. The results showed good agreement, especially when crack‐tip plasticity corrections were applied.     

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.     

Experimental J estimation equations for single-edge-cracked bars in four-point bend: homogeneous and bi-material specimens

The present paper provides the plastic η factor solutions for J testing of single-edge-cracked specimens in four-point bend (SE(PB)), based on limit (slip line field) and detailed finite element limit analyses. Both homogeneous specimens and bi-material specimens with interface cracks are considered. Moreover, two different η factor solutions are developed, one for J (or C^* in creep crack growth testing) estimation based on the load-load line displacement (LLD) records, η_p^VLL, and the other J estimation based on the load-crack mouth opening displacement (CMOD) records, η_p^CMOD.It is found that the use of load-LLD records can be recommended only for testing deeply cracked SE(PB) specimens. Moreover, depending on how the LLD is measured, a different value of η_p^VLL should be used. On the other hand, the use of load-CMOD records is recommended for all possible crack lengths. Moreover, the proposed η_p^CMOD solution can be used not only for a homogeneous specimen but also for any bi-material specimen with an interface crack.     

Application of the method of caustics to the centre-cracked diametral compression test specimen

Normalized Mode I stress intensity factors,N ₁(a/R), for symmetrical radial cracks in diametral compression test specimens were experimentally evaluated using disc specimens of polymethyl methacrylate and the method of caustics. The method of caustics was first employed with precracked three-point bend specimens to assess the optical constant for the test material. This material property and the diameters of the caustics as a function of the applied load at different relative crack lengths (a/R) yielded the non-dimensional stress intensity factors using equations presented by Theocaris. These experimental values agreed closely with the theoretical solutions reported in the literature. Disc specimens of a polycrystalline alumina were also tested in diametral compression at temperatures up to 1000° C and the measured fracture toughness values were compared to those measured with chevron-notched bend specimens. It is shown that the centre-cracked diametral compression specimens give very reproducible fracture toughness measurements, and the specimen and the test technique can be usefully employed to assess the fracture toughness of structural ceramics at both ambient and elevated temperatures.     

Limit load solution and loading behavior of C(T) fracture specimen

Deformations far from the crack tip and plastic collapse at limit load may control the fracture of specimens fabricated from highly ductile materials. To investigate the behavior of test specimen under plastic fracture, this paper derives solutions for the limit load of the C(T) specimen based on slip-line analysis. The modified Green's solution gives the most accurate results. Analysis of test data for many types of metal materials shows that, after some initial crack extension, the specimens reach the limit load. Yet, previous investigators analyzed the resistance to crack extension in these specimens with J-R curves. The large plastic deformations and unloading of the material in the wake of crack extension violate the basic assumptions of J-integral, thus invalidating the J-R analysis. It is, therefore, necessary to perform limit load analysis in the investigation of ductile crack extension.     

A method for dynamic fracture toughness determination using short beams

This paper deals with dynamic fracture toughness testing of small beam specimens. The need for testing such specimens is often dictated by the characteristic dimensions of the end product. We present a new methodology which combines experimentally determined loads and fracture time, together with a numerical model of the specimen. Calculations are kept to a minimum by virtue of the linearity of the problem. The evolution of the stress intensity factor (SIF) is obtained by convolving the applied load with the calculated specimen response to unit impulse force. The fracture toughness is defined as the value of the SIF at fracture time. The numerical model is first tested by comparing numerical and analytical solutions (Kishimoto et al., 1990) of the impact loaded beam. One point impact experiments were carried out on of commercial tungsten base heavy alloy specimens. The robustness of the method is demonstrated by comparing directly measured stress intensity factors with the results of the hybrid experimental-numerical calculation. The method is simple to implement, computationally inexpensive, and allows testing of large sample sizes, without restriction on the specimen geometry and type of loading.     

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens. Part II: 3-D effects on constraint

This study describes an extensive set of 3-D analyses conducted on conventional fracture specimens, including pin-loaded and clamped SE(T) specimens, and axially cracked pipes with varying crack configurations. The primary objective is to examine 3-D effects on the correlation of fracture behavior for the analyzed crack configurations using the J-Q methodology. An average measure of constraint over the crack front, as given by an average hydrostatic parameter, denoted Q_avg, is employed to replace the plane-strain measure of constraint, Q. Alternatively, a local measure of constraint evaluated at the mid-thickness region of the specimen, denoted Q_Z0, is also utilized. The analysis matrix considers 3-D numerical solutions for models of SE(T) fracture specimens with varying geometries (i.e., different crack depth to specimen width ratio, a/W, as well as different loading point distance, H) and test conditions (pin-loaded ends vs. clamped ends). The 3-D numerical models for the cracked pipes cover different crack depth to pipe wall thickness ratio, a/t, and a fixed crack depth to crack length ratio, a/c. The extensive 3-D numerical analyses presented here provide a representative set of solutions which provide further support for using constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.     

Failure mode of laser welds in lap‐shear specimens of high strength low alloy (HSLA) steel sheets

In this paper, the failure mode of laser welds in lap‐shear specimens of non‐galvanized SAE J2340 300Y high strength low alloy steel sheets under quasi‐static loading conditions is examined based on experimental observations and finite element analyses. Laser welded lap‐shear specimens with reduced cross sections were made. Optical micrographs of the cross sections of the welds in the specimens before and after tests are examined to understand the microstructure and failure mode of the welds. Micro‐hardness tests were also conducted to provide an assessment of the mechanical properties in the base metal, heat‐affected and fusion zones. The micrographs indicate that the weld failure appears to be initiated from the base metal near the boundary of the base metal and the heat‐affected zone at a distance away from the pre‐existing crack tip, and the specimens fail due to the necking/shear of the lower left load carrying sheets. Finite element analyses based on non‐homogenous multi‐zone material models were conducted to model the ductile necking/shear failure and to obtain the J integral solutions for the pre‐existing cracks. The results of the finite element analyses are used to explain the ductile failure initiation sites and the necking/shear of the lower left load carrying sheets. The J integral solutions obtained from the finite element analyses based on the 3‐zone finite element model indicate that the J integral for the pre‐existing cracks at the failure loads are low compared to the fracture toughness and the specimens should fail in a plastic collapse or necking/shear mode. The effects of the sheet thickness on the failure mode were then investigated for laser welds with a fixed ratio of the weld width to the thickness. For the given non‐homogenous material model, the J integral solutions appear to be scaled by the sheet thickness. With consideration of the plastic collapse failure mode and fracture initiation failure mode, a critical thickness can be obtained for the transition of the plastic collapse or necking/shear failure mode to the fracture initiation failure mode. Finally, the failure load is expressed as a function of the sheet thickness according to the governing equations based on the two failure modes. The results demonstrate that the failure mode of welds of thin sheets depends on the sheet thickness, ductility of the base metal and fracture toughness of the heat‐affected zone. Therefore, failure criteria based on either the plastic collapse failure mode or the fracture initiation failure mode should be used cautiously for welds of thin sheets.     

J and CTOD estimation formulas for C(T) fracture specimens including effects of weld strength overmatch

This work focuses on an evaluation procedure to determine the elastic?Cplastic J-integral and Crack Tip Opening Displacement (CTOD) fracture toughness based upon the ??-method for C(T) fracture specimens made of homogeneous and welded steels. The primary objective of this investigation is to enlarge on previous developments of J and CTOD estimation procedures for this crack configuration while, at the same time, addressing effects of strength mismatch on the plastic ??-factors. The present analyses enable the introduction of a larger set of factors ?? for a wide range of crack sizes (as measured by the a/W-ratio) and material properties, including different levels of weld strength mismatch, applicable to pipeline and pressure vessel steels. Very detailed non-linear finite element analyses for plane-strain and 3-D models of C(T) fracture specimens with centerline-cracked welds provide the evolution of load with increased load-line and crack mouth opening displacement required for the estimation procedure. Overall, the present study, when taken together with previous investigations, provides a fairly extensive body of results to determine parameters J and CTOD for different materials using C(T) specimens with varying overmatch conditions.     

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.     

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.     

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

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