J-resistance Curve Research Articles

Estimation of the J-resistance curve for Cr2Ni2MoV steel using the modified load separation parameter S pb method

Based on load separation theory, the load separation parameter S pb method is an effective approach for estimating the J-resistance curve from records of load versus displacement directly, using one sharp cracked specimen and an additional reference blunt cracked specimen. However, the effect of the reference blunt cracked specimen on J-resistance determination was not explicitly considered in past work. In this paper, a modified load separation parameter S pb method was developed to eliminate this effect, and then a unique estimation of instantaneous crack length for one sharp cracked specimen could be obtained. Furthermore, a forced blunting calibration method was also adopted to determine the instantaneous crack length in the load inseparable region, referring to a normalization method. Experiments on steam turbine rotator steel Cr2Ni2MoV were carried out to estimate J-resistance curves using an unloading compliance method. By removing unload and reload data from load-displacement records, the J-resistance curve for the same sharp cracked specimen was estimated using the modified separation parameter S pb method. The results indicate that the modified S pb method completely eliminates the effect of the reference blunt cracked specimen on the instantaneous crack length determination of the sharp cracked specimen. However, different J-resistance curves in a small range of crack extension are present when different blunting coefficients are used in the blunting line equation. The J-resistance curve obtained from the modified S pb method agrees well with that obtained from the compliance method.

Investigation of fracture resistance of natural rubber/clay nanocomposites by J-testing

The present work is aimed at studying the fracture behavior of a series of vulcanized natural rubber/organoclay samples obtained by melt blending. A fracture mechanics approach based on J-testing was adopted to evaluate the material resistance to crack initiation and propagation from a J-resistance curve as experimentally obtained by a single specimen procedure. The basis of the method and the experimental procedure adopted are described. Further, the effect of the organoclay content within the elastomeric matrix on the fracture properties is analyzed. It is found that the capability of the organoclay to improve fracture resistance is rate dependent indicating the viscoelastic character of the fracture process in such filled systems.

A phenomenological form of the q2 parameter in the Gurson model

Continuum damage mechanics is applied to compute fracture J-initiation and the J-resistance (J-R) curve for SA333 Gr.6 carbon steel material. A parametric study is carried out to assess the effects of variation of Gurson material parameters on the J-R curve. A difficulty is experienced to obtain a set of Gurson parameters that can compute J-initiation as well as the entire J-R curve close to the measured values. It has been found that a phenomenological form of the q 2 parameter, used in the Gurson constitutive model, based on experimental observation helps to overcome this difficulty. The new form of q 2 has an exponential spatial variation near the crack tip and has two constants. These additional constants help analysts to compute the complete J-R curve (including J-initiation) close to experimental data. The same set of constants has also been found to be useful for other fracture specimens, materials and two piping components of a nuclear plant.

An Experimental Study of Fracture of LIGA Ni Micro-Electro-Mechanical Systems Thin Films

This article presents the results of an experimental study of fracture in LIGA Ni micro-electro-mechanical systems (MEMS) thin films. Microtesting techniques are developed for the study of the J-resistance curve (J-Δa) behavior in compact tension (CT) thin film specimens. In-situ measurements of crack-tip strain are presented together with in-situ and ex-situ microscopic images of crack-tip deformation and fracture mechanisms. Fractographic observation showed a mixture of inclined fracture planes (slant fracture) that are relatively featureless and normal fracture planes that exhibit dimples and microholes resulting from plastic deformation.

The jump-like crack growth model, the estimation of fracture energy and JR curve

In this paper the jump-like crack growth model for monotonic loading is applied to re-examine both the onset of crack growth and process of stable crack growth. In the former case the fracture energy associated with a new surface creation is estimated and the in-plane constraint influence on this quantity is examined using the J– A 2 approach. In the later case the formula to compute the J-resistance curve is re-examined and compared with the one known from the standards. In the analysis the plane strain model of a structural element made of elastic–plastic material is assumed.

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.

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.

Derivation of J-resistance curve for through wall cracked pipes from crack mouth opening displacement

In this paper, factors for calculating the J-resistance curve from the measured crack mouth opening displacement (CMOD) record are derived for circumferential through wall cracked straight pipes subjected to pure bending. Rigorous elastic plastic finite element analyses of around 125 circumferential through wall cracked straight pipes subjected to four point bending have been carried out to validate the proposed equations. The factors have also been validated with a few fracture experimental results on straight pipes. For these tests the J– R curve has been evaluated using the conventional as well as using the proposed factors along with the moment-CMOD record.

An Internal Conical Mandrel Technique for Fracture Toughness Measurements on Nuclear Fuel Cladding

Abstract An understanding of the limiting stress level for crack initiation and propagation in a fuel cladding material is a fundamental requirement for the development of water reactor clad materials. Conventional tests, in use to evaluate fracture properties, are of limited help, because they are adapted from ASTM standards designed for thick materials, which differ significantly from fuel cladding geometry (small diameter thin-walled tubing). The Internal Conical Mandrel (1CM) test described here is designed to simulate the effect of fuel pellet diametrical increase on a cladding with an existing axial throughwall crack. It consists in forcing a cone, having a tapered increase in diameter, inside the Zircaloy cladding with an initial axial crack. The aim of this work is to quantify the crack initiation and propagation criteria for fuel cladding material. The crack propagation is monitored by a video system for obtaining crack extension δa. A finite-element (FE) simulation of the ICM test is performed in order to derive J integrals. A node release technique is applied during the FE simulation for crack propagation and the J-resistance curves (J-δa) are generated. This paper presents the test methodology, the J computation validation, and results for cold-worked stress relieved Zircaloy-4 cladding at 20° and 300°C and also for Al 7050-T7651 aluminum alloy tubing at 20°C.

A Method of J Testing Based on Crack Opening Displacement for Circumferential Through-Wall Cracked Pipes under Combined Tension and Bending

Application of the leak-before-break concept to nuclear piping requires accurate fracture mechanics assessment on pipes with postulated circumferential through-wall crack subject to combined tension and bending. One important element is determination of relevant J-resistance curve for pipes under combined loading. This paper provides experimental J estimation method for the circumferential through-wall cracked pipe under combined tension and bending, based on the load-crack opening displacement (COD) record to estimate J-resistance curve. To give confidence in the proposed method, the J results from detailed elastic-plastic finite element (FE) analysis are also compared with estimated J based not only on proposed method but also on conventional method using load-load line displacement, which shows that estimated J based on the proposed method provides reliable J estimates regardless of analysis condition, on the other hand, the conventional method using the load-load line displacement record gives erroneous results for shallow cracks.

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).

Effect of Stress State on Mode II Stable Crack Extension

The effect of assumption of plane state of stress on the predictability of experimental results observed during the mode II stable crack growth (SCG) through 8 mm thick compact tension specimens (CTS) of a workhardening aluminum alloy (D16AT) has been studied. Experimental results include load-sliding displacement diagram, extent of SCG, crack front geometry and fracture surface fractographs. The experimental results show that the crack extends in its own plane, the fracture surface is flat, smooth and free of any shear lip. The crack front geometry, which is straight initially, remains mostly so throughout the SCG. Theoretical investigations have been done using an elastic-plastic finite element scheme and the COA/COD criterion as the criterion governing the growth. Finite element results, assuming plane stress and plane strain conditions separately, on the load-sliding displacement diagrams, J-resistance curve, plastic zones and variation of equivalent stress and strain along the crack-line ahead of the crack tip are also presented. The resistance curve is a straight-line and the magnitudes of equivalent stress and strain increases as the crack extension proceeds. In general, the predictions based on the assumption of plane state of stress are closer to the experimental results.

Prediction of Failure Behavior for Nuclear Piping Using Curved Wide-Plate Test

One important element of the Leak-Before-Break analysis of nuclear piping is how to determine relevant fracture toughness (or the J-resistance curve) for nonlinear fracture mechanics analysis. The practice to use fracture toughness from a standard C(T) specimen is known to often give conservative estimates of toughness. To improve the accuracy of predicting piping failure, this paper proposes a new method to determine fracture toughness using a nonstandard testing specimen, curved wide-plate in tension. To show validity of the proposed curved wide-plate test, the J-resistance curve from the full-scale pipe test is compared with that from the curved wide-plate test and that from C(T) specimen. It is shown that the J-resistance curve from the curved wide-plate tension test is similar to, but that from the C(T) specimen is lower than, the J-resistance curve from the full-scale pipe test. Further validation is performed by investigating crack-tip constraint conditions via detailed three-dimensional finite element analyses, which shows that the crack-tip constraint condition in the curved wide-plate tension specimen is indeed similar to that in the full-scale pipe under bending.

흰 광폭평판 시험을 이용한 원자력 배관의 파괴거동예측

One important element of the Leak-Before-Break analysis of nuclear piping is how to determine relevant fracture toughness (or the J-resistance curve) for nonlinear fracture mechanics analysis. The practice to use fracture toughness from a standard C(T) specimen is known to often give conservative estimates of toughness. To improve the accuracy, this paper proposes a new method to determine fracture toughness using a non-standard testing specimen, curved wide-plate in tension. To show validity of the proposed curved wide-plate test, the J-resistance curve from the full-scale pipe test is compared with that from the curved wide-plate test and that from the C(T) specimen. It is shown that the J-resistance curve form the curved wide-plate tension test is similar to, but that from the C(T) specimen is lower than, the J-resistance curve from the full-scale pipe test. Further validation is performed by investigating crack-tip constraint conditions via detailed 3-D FE analyses, which shows that the crack-tip constraint condition in the curved wide-plate tension specimen is indeed similar to that in the full-scale pipe under bending.

A study of stable crack growth using experimental methods, finite elements and fractography

Systematic analysis of the in-plane constraint influence on J-resistance curves is presented. J R curves were also recorded and analyzed beyond the limits of crack extension inside which the stress field can be assumed to be dominated by J-integral. Three steels and four types of specimen: SEN(B), SEN(T), CCT and DENT have been tested. Along with the J R curves the fracture mechanisms have been analyzed with the help of scanning microscopy. The numerical, finite element analysis has been adopted to compute the Q-stresses, as a measure of the in-plane constraint prior to the onset of crack growth. The analysis of the stress field in front of the crack has been performed to check whether the state of stress prior to the crack growth can predetermine the way the crack will grow. It turns out that characteristic features in the J R curves runs can be predicted qualitatively from the Q( a/ W) and Q( J) curves. However, there is a good correlation between Q-stress and voids diameters on fractured surfaces. Several patterns in J R curves runs have been observed for tested specimens; e.g. no influence of specimen thickness on J R curves runs was observed for side-grooved specimens. Strong influence of specimen thickness on J R curve shape was observed for non-side-grooved specimens. J R curve run higher for thinner specimens unless they are dominated by plane stress. For bent specimens J R curves run higher for shorter cracks but they run lower for specimens in tension.

Evaluation of interfacial crack growth in bimaterial metallic joints loaded by symmetric three-point bending

Bimetallic three-point bend specimens (TPB) were produced from explosive clad alloy aluminium LY12/pure aluminium Al by electron beam welding of homogeneous Al and homogeneous LY12 to the respective surfaces. Cracks were introduced at the interface in the specimens by milling and spark-erosion. Similar bimetallic specimens of explosive clad LY12/steel were also prepared. Finite element analyses were undertaken to evaluate the J-integral and the deformation ahead of the bimetallic interfacial crack tip field of the TPB specimens loaded normally. The calculations showed that, even for symmetric TPB loading of the specimens, a sharpening–blunting deformation existed on the profile of the interfacial crack tip for bimetals with a mismatch in mechanical properties. J-resistance curves for two kinds of bimetal interface were obtained from symmetric TPB tests. The results demonstrated that the resistance to crack propagation along the bimetallic interfaces was always lower than those of the respective counterpart metals.

연성재료의 균열진전에 따른 A2의 변화； 실험적 측정

A way to measure the second parameter Az of CT specimens is described. The displacement ??, which is measured continuously from visual images of the lateral surface during crack growth is used to calculate the A₂ as a function of craek growth. The crack length is measured by DCPD(Direct Current Potential Drop) method and the J-resistance curve is determined according to ASTM standard E1737 -96. To prove the validity of this method, three dimensional finite clement analyses were performed, and variation s of the displacements ??, and A₂ along the thickness were explored. As the result, it has been shown that the ??, measured from the visual images of the lateral surface and the corresponding A₂ can be regarded as the average through the thickness for 1T and 1/2T specimens of SA 106Gr.C steel.

The coupled effects of thickness and delamination on cracking resistance of X70 pipeline steel

The effects of thickness and delamination on the fracture toughness and stable crack growth behaviour of high-toughness pipeline steels were investigated experimentally by use of compact tension specimens with thicknesses of 3–15 mm cut from a 17 mm-thick wall pipe. Material resistance curves were generated based on the stress intensity factor (SIF) K and the J-integral. The critical SIF K c and the J-resistance curves are found to be independent of thickness as the delaminations near the crack tip within the material reduce the out-of-plane constraint in thicker specimens. Both fracture mechanism and mechanics analyses shown that the fracture behaviour of the steel is controlled by the strong-coupled effects of thickness and delaminations. With increasing thickness, the out-of-plane stress constraint increases and causes the inclusion separation, growth and coalescence to form delaminations of different sizes before the main crack initiates. The delaminations in turn, reduce the out-of-plane constraint and thus, the thickness effect upon fracture. The advantages and disadvantages of delaminations in a safety assessment of pipelines are also discussed based on three-dimensional fracture theory.

528 熱時効ステンレス鋳鋼管の弾塑性破壊評価について

Fracture toughness of stainless steel casting (duplex stainless steel) is reduced under the condition about 300℃ by the thermal aging. For the flaw evaluation on thermal aged duplex stainless steel pipes, Fracture Assessment Curve (FAC) of R6 Option2 method is calculated using the stress-strain curve and J-resistance curve of thermal aged duplex stainless steel. To evaluate the fracture load on thermal aged duplex stainless steel in simple method, corrective factor is prepared in order to convert limit load based on net section criteria to fracture load based on R6 method.

Finite element analyses of deformation around holes near a crack tip and their implications to the J‐resistance curve

The initiation phase of ductile crack growth is investigated in a detailed finite element analysis. The process is modelled by the growth and coalescence of a series of holes in front of a blunted crack tip, representing the growth of holes separated from large inclusions. The reductions of each ligament between neighbouring holes due to hole growth are calculated as well as crack‐tip opening displacements (CTOD). All the ligaments except the first and last show similar behaviour of reduction, with the reduction curves separated in an equal CTOD increment. The CTOD increment as a function of effective crack extension due to hole growth defines crack‐tip opening angle, a measure of crack‐growth resistance for a given condition. As the CTOD increment changes substantially due to crack extension in small‐scale yielding, crack initiation is defined at the point of deviation from the linear increment of CTOD against J for a stationary crack. The effective crack tip is defined at each hole with the ligament reduction of crack initiation. Therefore, the J‐resistance curve may be derived from the hole growth model, and hence the effects of specimen geometry, crack length and specimen size on the R‐curve are discussed. The calculations for a hole spacing 10 times of the initial hole diameter are in agreement with the experimental R‐curve of 2024‐T351 aluminium alloy.