J-integral Values Research Articles

용접부 중앙에 표면균열이 존재하는 인장 평판에 대한 강도 불일치 한계하중 해석 및 간략 J-적분 예측

In this work, the effect of strength mismatch on plastic limit loads is quantified for similar metal weld plates with cracks under tension load, via three-dimensional, small strain elastic-perfectly plastic finite element analyses. Relevant variables related to plate geometry and crack length are systematically varied, in addition to the weld width. An important finding is that mis-match limit loads can be uniquely quantified through strength mis-match ratio and one geometry-related parameter. Based on the proposed limit load solutions, reference stress based J-integral estimates is also investigated. When the reference stress is defined by the mis-match limit load, predicted J-integral values agree overall well with FE results.

PSEUDO-ELASTIC ANALYSIS OF ELASTIC–PLASTIC CRACK TIP FIELDS USING ELEMENT-FREE GALERKIN METHOD

A methodology for the characterization of asymptotic elastoplastic crack tip stress fields is presented by coupling the pseudo-elastic analysis with the element-free Galerkin method (EFGM). An iterative linear elastic analysis using EFGM is carried out for the determination of elastic–plastic crack tip stress fields by treating material parameters as spatial field variables. Effective material parameters are used to describe the constitutive behavior of the continuum and are defined by using the Hencky's total deformation theory of plasticity. The effective material parameters are updated in an iterative manner based on strain controlled projection method using experimental uniaxial tension test curve. The effectiveness of the method is illustrated by predicting the stress fields near the crack tip region of a square plate subjected to asymptotic linear elastic displacement field on the outer boundary of the plate. Different geometries subjected to mode-I and mode-II loadings are considered for the present study. The material model considered in these problems is Ramberg–Osgood model with different hardening exponent values. The predictions of the asymptotic elastic–plastic stress fields near the crack tip are compared with the results of nonlinear finite element analysis and also with the HRR singular stress fields and found to be in good agreement. J-integral values which characterize the amplitude of HRR stress field are also evaluated for the considered geometries and are found to close matching with the EPRI estimation scheme.

Interfacial Fracture Investigation of Low-k Packaging Using J-Integral Methodology

In order to resolve the issues of RC time delay and high power consumption, IC chips with Cu/low-k interconnects are developed to meet the foregoing requirements. However, there is a high potential that in doing so it may contribute to interfacial cracks occurring or propagating between the copper metal and the low-k dielectric material as a result of poor adhesion and lower fracture toughness, which results from the inherent mechanical imperfection of low-k materials. This fracturing problem is one of the most urgent issues for the thermomechanical reliability of Cu/low-k interconnects, and it needs to be resolved urgently. For this reason, we propose a prediction methodology of finite-element analysis (FEA) based on J-integral value estimation to investigate the interfacial fracture opportunity of low-k packages. However, the J-integral calculation is path dependent and so crucial in FEA for a crack on an interface between dissimilar materials. Therefore, various paths with an integral contour surrounding the crack tip are considered to avoid a misunderstanding of the cracking energy. All the analytic results indicate that a rectangular contour with a proper ratio of length/width, and multilayers of element close to the delaminating surfaces, is suggested for obtaining a stable J-integral value. On the other hand, the proposed methodology has been validated by a four-point bending test and compared with the relative experimental data of multi-low-k dielectric films. Moreover, under a reliable integral contour path that crack driving force predicted using the type of interfacial crack constructed by means of the element death technique, it shows good agreement with the simulated results of embedding actual crack.

Fracture mechanical evaluation of an in-vessel melt retention scenario

This paper presents methods to compute J-integral values for cracks in two- and three-dimensional thermo-mechanical loaded structures using the finite element code ANSYS. The developed methods are used to evaluate the behavior of a crack on the outside of an emergency cooled reactor pressure vessel (RPV) during a severe core melt down accident. It will be shown, that water cooling of the outer surface of a RPV during a core melt down accident can prevent vessel failure due to creep and ductile rupture. Further on, we present J-integral values for an assumed crack at the outside of the lower plenum of the RPV, at its most stressed location for an emergency cooling (thermal shock) scenario.

Assessment of the reference stress method for J-integral estimation of cracked riveted beams of an old wrought iron

This work deals with the application of the reference stress method to estimate the J-integral of cracked riveted beams of old puddle iron. The ductility of some of these materials makes it necessary to use elasto-plastic fracture criteria to assess damage tolerance. This requires a high computational effort, since it involves the determination of the J-integral in beams with plates and angles that interact by means of redundant forces dependent on crack size. The J-integral estimation method based on the reference stress could reduce this effort, provided it were shown to be valid for this type of beam. This work contributes to this end by comparing the J-integral values resultant from the reference stress method and a complete finite element modelling of a riveted beam consisting of two angles and a cracked plate made of actual puddle iron from a road bridge more than a century old but still in service. A number of samples removed from the bridge showed that this material failed in a ductile manner when it was fracture tested with fatigue precracked compact specimens, even at temperatures as low as −20 °C. The two types of J-integral values found are compared over the ranges of load and crack size explored.

J-integral determination in riveted beams of a structural old steel by estimation methods

This work deals with the application of the J-integral estimation method to cracked riveted beams of old puddle iron. The ductility of some of these materials makes it necessary to use elasto-plastic fracture criteria to assess damage tolerance. This requires a high computational effort because it involves the determination of the J-integral in beams with plates and angles that interact by means of redundant forces dependent on crack size. The J-integral estimation method proposed by the Electric Power Research Institute could reduce this effort provided it were shown to be valid for this type of beam. This work contributes to this end by comparing the J-integral values resultant from the estimation method and a complete finite element modelling of a riveted beam consisting of two angles and a cracked plate made of actual puddle iron from a road bridge more than a century old but still in service. A number of samples removed from the bridge showed that this material failed in a ductile manner when it was fracture tested with fatigue precracked compact specimens, even at temperatures as low as -20 °C. The two types of J-integral values found are in good agreement over the ranges of load and crack size explored.

The effect of undermatching on crack tip constraint in a welded structure of nodular irons

Abstract The main aim of this paper is to investigate the effect of yield strength mismatch of parent and weld metal on the fracture behavior of plain and heat-treated welded nodular cast iron. For this, experimental and theoretical studies were performed. Nickel electrode, which has lower yield strength value than that of the parent material, was used to join nodular cast iron by cold arc welding method. In experimental study, fracture toughness (J-integral) values were determined for various crack locations including base, weld metal and heat affected zone. In theoretical study, finite element analyses were performed for the same crack locations with different crack lengths. Stress triaxiality and equivalent plastic strain values were determined for all crack locations and various crack lengths. Finally, fracture toughness values of the base metal were determined as lower than those of the other regions including the weld metal and the heat affected zones. Stress triaxiality and equivalent plastic strain values used to clarify the effect of yield strength mismatch on the constraint around crack tip increased with growing crack length in annealed and under-matched models. In annealed models, stress triaxiality values became slightly lower but equivalent plastic strain values appeared higher than those of under-matched models.

Fatigue crack propagation analysis of surface cracks in pipe elbows

Piping elbows are one of the critical components of the cooling piping systems in power plants. This paper presents the details of fatigue crack propagation analysis based on code procedure and FEM and compares the results with experimental observations. The fatigue crack propagation was evaluated based on the inelastic range J integral, J s, which was obtained by applying the plastic correction factor (from RCC-MR code) to the elastic J-integral values obtained from the code as well as from the elastic finite element analysis. The fatigue crack propagation was also studied directly using the elastic–plastic J-integral value obtained from the finite element analysis. It was observed that the fatigue life calculated based on the modified J s-integral values was closer on the conservative side to the experimental results, than that from J-integral obtained directly from elastic–plastic finite element analysis.

Fracture behavior of overmatched ductile iron weldment

Abstract The fracture behavior of welded ductile iron is discussed by means of experimental and theoretical studies. Ferritic nodular cast irons were joined by cold arc welding in order to obtain over-matched weldment in which the yield strength of the weld metal is higher than that of the base metal. As a result of the welding process, various regions with different mechanical properties formed in the welded specimens. In the experimental part of the study, the mechanical properties of the different regions in the welded specimens were identified and J-Integral toughness values were determined by fracture toughness tests for different crack locations including the base metal, the heat affected zone and the weld metal. In the numerical part of the study, finite element analyses were conducted by fixing 3-D models precracked at different locations for different crack lengths. In these models, after stress – strain analysis, stress triaxiality and plastic deformation characteristics around the crack tip were determined for each crack location and different crack sizes. It was found that stress triaxiality values increase with growing crack length. Different regions with different strength levels in the weldment affect the extension of plastic deformation in the models. Hindrance to the extension of plastic deformation at the heat affected zone and diffusion line causes an extra increase in stress triaxiality at the crack tip.

Interaction of residual stress with mechanical loading in a ferritic steel

A well-defined residual stress field was introduced into modified single edge notched bend, SEN(B), specimens by the ‘in-plane compression’ procedure in order to investigate the interaction between residual stress and applied mechanical loading. Numerical predictions of the residual stress field arising from the in-plane compression procedure are given along with details of the numerical fracture modelling and experimental fracture test results made on A533B ferritic steel specimens in the lower transition region at −150 °C. Use was made of a recently developed finite element post-processor capable of determining path-independent J-integral values in the presence of residual stress fields. The paper compares the experimental results to predictions made using a probabilistic ‘global approach’ based on the conventional crack-tip parameters K and J and predictions made using a well-known structural integrity assessment code, R6 (Revision 4). It is shown that obtaining more accurate estimates of the crack driving force created by residual stresses leads to better correlation between experiments and predictions, and less conservatism in the assessment code.

Fracture toughness of glass microsphere-filled polypropylene and polypropylene/poly (ethylene terephthalate-co-isophthalate) blend-matrix composites

The fracture behaviour of glass microsphere-filled polypropylene/poly(ethylene terephthalate-co-isophthalate) blend-matrix composites was investigated in comparison with that of the glass microsphere-filled PP composites. Depending on the deformability displayed by the composite, it was carried out through the linear-elastic fracture mechanics or by applying the J-integral concept. The matrix ductility was regulated in the composite through the glass bead surface treatment applied with different silane-coupling agents, as well as with the addition of maleated PP as polymer compatibilizer. Whereas all the composites failed in a brittle manner at moderate impact speed, quasi-brittle fracture behaviour was only observed at low strain rate in composites having high and medium interfacial adhesion level. Results showed that composites containing both aminosilane-treated glass microspheres and maleated PP showed the highest values of fracture toughness. In composites with low adhesion level between matrix and glass beads, the critical J-integral value diminished due to the presence of PET.

Effect of the Welding Heat on Fracture Toughness and Fatigue Property in a T<sub>i</sub>-Alloy

Ti-alloy is widely used in engineering because it possesses excellent specific strength and corrosion resistance. The effect of welding process on J-integral value and fatigue crack growth (FCG) rate in a Ti-alloy is experimentally investigated in this paper. A series of test is performed with SENB specimens for J-integral test and CT specimens for the FCG rate test respectively. Base metal, welded joint and HAZ materials were used to make different test specimens. Results show that the J-integral values of welded joint and HAZ are obviously smaller than those of the base metal. And that the FCG rate value of welded joint is much higher than those of base metal and HAZ material. It means that welding process may lead to a great reduction in fracture toughness and the fatigue property for titanium alloy. Therefore, the inhomogeneity of the welded joint must be considered when assess welded structures.

Residual stresses and fracture mechanics analysis of a crack in welds of high strength steels

This study presented the characteristics of residual stresses in welds of high strength steels (POSTEN60, POSTEN80) whose tensile strengths were 600 MPa and 800 MPa, respectively. Three-dimensional thermal elastic–plastic analyses were conducted to investigate the characteristics of welding residual stresses in welds of high strength steels through the thermal and mechanical properties at high temperatures obtained from the elevated temperature tensile tests. A finite element analysis method which can calculate the J-integral for a crack in a residual stress field was developed to evaluate the J-integral for a centre crack when mechanical stresses were applied in conjunction with residual stresses. The results show that the volumetric changes associated with the austenite to martensite phase transformation during rapid cooling after welding of high strength steels significantly influence on the development of residual stresses in the weld fusion zone and heat-affected zone. For a centre crack in welds of high strength steels where only residual stresses are present, increased tensile strength of the steel, increased the J-integral values. The values of the J-integral for the case when mechanical stresses are applied in conjunction with residual stresses are larger than those for the case when only residual stresses are present.

The change of fracture toughness of martensitic steels after irradiation in SINQ target-3

Small bend specimens of martensitic steels T91, F82H and Optimax were irradiated in SINQ target-3 up to about 9 dpa in a temperature range of 100–250 °C. The single specimen method was used to determine the J-integral values. The specimens were tested in a temperature range from room temperature to 250 °C, mostly at irradiation temperatures. The results showed that the fracture toughness of the martensitic steels decreased with increasing irradiation dose. Specimens tested at the irradiation temperatures and 250 °C indicated that the fracture toughness of all three martensitic steels remained above 100 MPa m 1/2. One T91 specimen irradiated to 4.3 dpa tested at room temperature was totally brittle and broke in the elastic deformation region. The fracture toughness value was only about 28 MPa m 1/2, within the lower shelf of the fracture toughness. There was no obvious difference in the fracture toughness of the steels after irradiation.

An Experimental Study on Graze and Crack Growth Behavior of Polycarbonate

In this study, the J-Integral value was determined by using the caustics method. The diameter of the caustics is measured experimentally by using the CT specimens. The specimen used here is a polycarbonate specimen with different ligament lengths. The craze zone of the crack tip was determined using photoelasticity and the method of caustics. The correlation between the craze extension and the crack growth behavior is investigated by observing the craze patterns occuring in the vicinity of the crack tip.

Evaluation of the Fracture Characteristics with Thermal Aging on Dissimilar Welds in Reactor Coolant System

A dissimilar weld zone exists between the pipe and nozzle in a primary reactor cooling system (RCS). Thermal aging is observed in cast stainless steel, CF8M used in a pipe as the RCS is exposed for a long period of time to a reactor operating temperature between 290 and 330°C. No effect is observed in low-alloy steel. SA508 cl.3 is used in a nozzle. The artificially accelerated aging specimens are prepared to maintain for a temperature of 430°C for 300, 1800, and 3600hrs, respectively. Then, various mechanical tests such as hardness, tension, impact test, are performed in virgin and aged specimens in order to determine the existence of dissimilar weld zones. The specimens for elastic-plastic fracture toughness tests are prepared for one type, where a notch is created in the heat affected zone of CF8M. From the experiments, it was found that J-integral values decrease as age increases.

Spot-welded joints subjected to shear-tension loading. Part 2: Mixed-mode fracture parameters

Fracture parameters that can be used in the fatigue analysis of spot-welded joints subjected to shear-tension loading, with local restraints, are presented. Finite element analysis has been used to obtain stress intensities in the vicinity of three different types of fatigue crack which, from practical experience, are introduced into a spot-welded joint, i.e. assumed notch crack, through-thickness crack, and through-nugget crack. A combination of elastic-plastic finite element and linear elastic fracture mechanics finite element analysis has been used and the results are presented in the form of fatigue and fracture parameters (i.e. structure configuration factor, notch configuration factor, crack configuration factor, and J-integral value) for a wide range of specimen and crack geometric parameters. These parameters are chosen to be representative of typical practical situations and have been determined from evidence presented in the open literature. The extensive range of structure, notch, and crack configuration factors obtained from the finite element analyses are then used to obtain equivalent prediction equations using a statistical multiple non-linear regression model. The accuracy of this model is measured using a multiple coefficient of determination, R2, where 0 ≤ R2 ≤ 1. This coefficient is found to be greater than or equal to 0.98 for all cases considered in this study, demonstrating the quality of the model fit to the data. Predictive equations for stress intensity factors and J-integral values, which are based on the elastic stress concentration factor, are also developed. Some approximate equations for crack configuration factors have been published in the past, all based on analytical solutions. All equations were derived in terms of two sets of non-dimensional parameters (i.e. the bending stress-membrane stress ratio at the nugget and the geometric ratio). These equations have to be coupled with a shell-beam finite element analysis in order to predict bending and membrane stresses at the weld nugget. Therefore, the accuracy of the results depends on the accuracy of the shell-beam finite element models used. In the present study, all prediction equations are directly related to the geometric ratios, which provides a simple and independent calculation procedure. Discrepancies between the results from the present study and those from the literature are discussed.

Mixed-mode fracture analysis of aluminium repaired panels using composite patches

Three-dimensional analyses are conducted to study the fatigue crack growth of panels containing mixed-mode cracks, reinforced with composite patches. A procedure is developed to obtain the crack trajectories using dynamic mesh generation for repaired panels in both mode-I and mixed-mode conditions. It is shown that the fatigue crack growth life obtained using mid-plane fracture parameters of the repaired panels in mode-I condition are almost compatible with the experimental results, however, they are non-conservative in some cases. The calculated fatigue crack growth life using un-patched surface fracture parameters are too conservative. It is shown that in both mode-I and mixed-mode crack loading conditions the J-integral values at mid-plane of the cracked plates are reduced with increasing the patch thickness; however, they depend on the patch thickness at un-patched surface at the crack-tip. The crack propagation path may be changed by the amount of about 10% due to the various fibers orientations of the patch. It is also shown that the patch thickness has not a considerable effect on the crack propagation path. Furthermore, there are considerable differences between the life obtained using un-patched surface and mid-plane fracture parameters for various patches thicknesses and layers angles of the repaired panels. The optimum patch layer angle considering maximum fatigue crack growth life of the repaired panels with an inclined crack angel of 45° is also obtained. Finally, a simple formulation is presented to justify the trend of finite element results obtained for single-sided repaired panels with various patch thicknesses.

Specimen size effects in the cryogenic fracture toughness testing of Fe–12Cr–12Ni–10Mn–0.24N stainless steel

This paper examines the effects of test specimen size on the cryogenic fracture toughness properties of a nitrogen-strengthened austenitic stainless steel for superconducting magnet structures in fusion energy systems. Single-specimen J-integral tests were performed on CT (compact tension) specimens with and without side-grooves in liquid helium at 4 K. The aspect ratio (specimen width to thickness) and thickness were varied. A three-dimensional finite element analysis was also conducted to investigate the effects of specimen thickness and side-groove on the through thickness distributions of the J-integral values. The results of the finite element analysis are used to supplement the experimental data.

Elastic–plastic analysis of an elbow with a through-wall axial crack at crown under in-plane bending

Piping elbows under bending moment are vulnerable to cracking at crown. The structural integrity assessment requires knowledge of the J-integral. The J-integral values for axially through-wall cracked thick elbows under in-plane bending moment are not available in open literature. This paper presents the J-integral results for 90°, long radius elbows subjected to in-plane opening bending moment based on a large number of finite element analyses covering a wide range of standard geometries. The non-linear elastic–plastic finite element analyses were performed using WARP3D software. Both geometric and material non-linearity were considered in the study. The geometry considered were for R m/ t = 5, 6, 7.5, 9, 12, 15, 20 and 25 with crack angles of 9°, 18°, 27° and 36° and strain hardening exponent, ‘ n’ varied for 2, 3, 5, 7 and 10.