SIF Values Research Articles

A reverse identification of the friction coefficient operating within crack lips through a complete elastoplastic simulation of 3D fretting fatigue cracks

This study investigates the fretting fatigue cracking process for wires made of aluminum alloy through elastic and elastoplastic simulations of former tests where both crack arrest and crack growth until failure were observed. A three-dimensional finite element analysis (FEA), incorporating 3D cracks within the contact, is conducted to replicate the experiments in the conditions of these former results. The present study demonstrates that an elastic assumption fails to capture the threshold crack extension, which would result in systematically underestimated lengths for crack arrest. When considering elastoplastic behavior of the aluminum strands, instead of elastic behavior, the SIF values evolve consistently with experimental observations. By this way, it is now possible to carry out a sounded FEA so as to account for friction in the crack lips in the presence of plasticity. First, this model clarifies the role of friction in crack arrest. Secondly, a reverse analysis is proposed to assess the associated coefficient of friction between crack lips, yielding a value consistent with measurements obtained from gross slip fretting experiments.

Fields of residual stresses near open assemblage holes of aircraft wing panel

The results of fatigue tests of two geometrically identical and similar in design models of the lower wing panel of a commercial aircraft are were analyzed. The panels differed in the way of installing mounting bolts, which connect the skin and stringers. Cold expansion of holes drilled both in the skin and stringer has been performed for the first panel before joining. The second panel includes no additional treatment after drilling pilot holes and final reaming. Bolts are mounted with an interference fit varying from 1.3 to 2.1% and from 2.9 to 3.2% for the first and the second panel, respectively. Changes in the interference fit are the consequence of a scatter attributed to the presence of a tolerance zone for the diameters of both bolts and mounting holes. A two-step comparison of both technologies is based on the experimental study of residual stress fields. The first stage, being a subject of the present study, includes the analysis of residual stress fields, which arise after removing bolts and separation of skin from stringers. Hole drilling and gradual crack growth were used to determine the components of residual stresses. Deformation response is measured by electronic speckle-pattern interferometry. High quality interferograms, which provide a reliable resolution of the interference fringes of ultimate density over the hole edge or directly along the notch borders, have been obtained for both ways of local removing the material. The first point-wise method based on drilling a probe hole, provides a quantitative determination of the residual stress components, starting from 1.4 mm distance from the assemblage hole edge. The second technique implements the crack compliance method of subsequent lengthening of the notch, starting directly from the mounting hole edge. This approach provides for a quantitative analysis of residual stress fields, related to different bolt mounting technologies, proceeding from the comparison of SIF values. A high level of compressive residual stresses near open holes is characteristic for both types of panels. Both experimental approaches showed the benefits of joints, where bolts are mounted into cold-expanded (reinforced) holes. For this case, the estimation of the relaxation parameters of the principal component of residual stresses in the direction of the external load is presented.

Detecting drought stress occurrence using synergies between Sun induced fluorescence and vegetation surface temperature spatial records

Drought stress occurrence and recovery from drought can be detected using a single spatial set of simultaneous observations of SIF and canopy temperature records. Temporal and spatial responses to drought and heat stresses by plant stands of a drought-adapted diverse grassland ecosystem were studied using sun induced fluorescence (SIF,O2A and O2B bands) and further ecophysiological (canopy temperature (Tsurf), spatially modeled evapotranspiration, vegetation reflectance spectra) variables collected along spatial sampling grids while also utilizing eddy covariance measured carbon dioxide (net ecosystem exchange: NEE, gross primary production: GPP) and water flux (evapotranspiration: ET) data. The grids were of 0.5 and 5 ha spatial extents and contained 78 sampling points. Data were collected in four spatial sampling campaigns, two under drought (early summer) and another two during and after recovery (midsummer) at both spatial resolutions.Small values of spatial SIF_A averages (around 0.5 mW m−2 nm−1 sr−1) under strong early summer drought increased (to around 2 mW m−2 nm−1 sr−1) due recovery upon rain arrivals, showing high (R2: 0.8–0.88) positive temporal correlations to eddy covariance measured carbon (GPP, NEE) and water (ET) fluxes. Spatial averages of LAI, vegetation indices (NDVI, NIRv) and modeled ET followed similar temporal patterns.While SIF was depressed by drought, it showed higher values in high canopy temperature vegetation patches than in vegetation patches with lower Tsurf. The spatial pattern of higher SIF in higher Tsurf patches was persistent (2 weeks) under drought. The positive SIF_A-Tsurf spatial correlation turned into negative/not significant after recovery of the grassland from the drought, while hot summer weather persisted. It is proposed that, by using a single set of simultaneously measured spatial SIF and Tsurf data it is possible to infer whether the studied vegetation is under drought (and heat) stress while it could not be decided on the base of SIF data alone. Evaluation of the slope of the above relationship seems therefore beneficial before e.g. starting the (stress) classification procedure based on SIF.

A simple, robust novel Williams series-based FE-analytical hybrid technique for evaluation of SIFs and higher order coefficients

To evaluate crack-tip parameters, various hybrid methods (HMs) amalgamating experimental domain data with multi-parameter field-variable expressions have been extensively employed. On the other hand, simpler HMs leveraging boundary contour data and demonstrating the robustness of the HMs for input data errors have been scarcely reported. In this regard, the present work addresses these gaps by proposing and illustrating a novel HM coupling coarse-mesh FE boundary displacement data on the crack lips, but not limited to it, with Williams’s series. Additionally, the HM’s robustness for simulated Gaussian error distribution in the input data is demonstrated. Comparison of HM-computed SIF values with converged FE values shows rapid convergence after 2–3 terms in the series and a certain number of retrieving points. Histogram analyses quantifying the deviations of HM-computed SIFs in the sample set indicate error tolerance within a reasonable limit for the fracture modes. These observations demonstrate the efficacy of the HM; In addition, the HM yields higher-order coefficients — accuracy of which are corroborated by comparing reconstructed field variables in the vicinity of the crack-tip with converged FEA. On the other hand, robustness analyses demonstrate that ±1σ of the data is within about 10% of error for all the modes. Thus, the proposed simple and robust HM offers a potential practical approach for evaluation of SIFs and higher order coefficients.

An experimental analysis of crack terminating perpendicular to the bimaterial interface under varying mode mixities

SIFs for crack terminating perpendicular to the interface of a bimaterial subjected to varying mode mixities are evaluated with a novel bimaterial specimen using the experimental technique of photoelasticity. A simple form of multiparameter equation defining the stress field for the crack terminating at the interface at an arbitrary angle along with the details on interfacial SIF and combined SIF for a bimaterial problem are brought out. The stress field equation is incorporated in an in-house developed PSIF software as a separate problem module for the determination of crack tip stress field parameters using a non-linear least squares methodology. A compact bimaterial Brazilian disc specimen with crack in one of the material sides terminating perpendicular to the interface and at an arbitrary angle to the point of loading, is considered for the study. SIFs of two such specimens, a polymer–polymer pair, and a metal-polymer pair with two different bimaterial constants are determined. The normalized SIF values are evaluated as a function of crack orientation angles. The SIF values for the metal-polymer pair were found to be higher compared to the polymer–polymer interface. The peak values of SIFs are observed at a crack orientation angle of 30°. At orientation angles close to 0° and 90°, the SIF values were less pronounced.

Photoelastic analysis of crack terminating at an arbitrary angle to the bimaterial interface under four point bending

A bimaterial strip made of Aluminum-Epoxy pair with crack terminating at an arbitrary angle to the interface subjected to bending is studied using photoelasticity technique. When the crack terminates at an arbitrary angle to the interface, the stress singularity depends on the bimaterial elastic constants as well as the geometry of the crack. The shape of the photoelastic fringe patterns observed at the crack tip terminating at the interface varied based on the crack inclination angle. Complex crack tip stress field equation for crack terminating at an arbitrary angle to the interface along with an over deterministic non-linear least squares method incorporated in an in-house developed PSIF software is used for the evaluation of SIFs. The effect of the crack inclination angle on the SIF values is brought out. Mode-I and Mode-II SIFs, interfacial SIF, combined SIF, and phase angle are evaluated for the bimaterial pair considered. The corresponding normalized SIF values are calculated. It is observed that the SIF values increase with the crack inclination angle. Cracks at angles greater than 45° have significant SIF values, with highest SIF values occurring for 90° crack.

Monitoring of Drought Stress in Chinese Forests Based on Satellite Solar-Induced Chlorophyll Fluorescence and Multi-Source Remote Sensing Indices

Greenhouse gas emissions have largely changed the global climate, leading to an increase in the frequency and extent of droughts. Forests are essential natural resources, and they play an important role in maintaining ecological security. Effectively monitoring drought stress in forests can help promote sustainable forestry development. Solar-induced chlorophyll fluorescence is a spectral signal released by vegetation photosynthesis after light absorption. In this study, we used solar-induced chlorophyll fluorescence data (SIF), canopy fluorescence yield (SIFyield) data, vegetation indices (NDVI, EVI), leaf area index (LAI), and fraction of absorbed photosynthetically active radiation (fPAR) to study forest drought stress in the Yunnan, Fujian, Shaanxi, and Heilongjiang provinces in China, respectively. The temporal and spatial ranges of drought stress indicated by the Standardized Precipitation-Evapotranspiration Index (SPEI) values were used as a reference (SPEI ≤ −0.5 indicates the occurrence of drought). Firstly, the standardized anomalous values of SIF, SIFyield, NDVI, EVI, LAI, and fPAR were calculated. The temporal and spatial response abilities of each variable to drought stress were analyzed. Secondly, the correlation between each variable and the drought indicator SPEI was quantified. Finally, the validity and variability of SIF and other variables for drought monitoring were analyzed and verified with a random forest classification model. The results showed that on a temporal scale, SIFyield showed an earlier response to drought stress than other variables and the abnormal change of SIFyield was higher than other variables by 10% or more. Spatially, the range of drought areas indicated by SIFyield and SPEI had more coincident areas than other variables. The overall correlation between SIFyield and SPEI was also higher during the drought period, especially during late drought periods when other variables showed negative correlations. For SIFyield, the correlation coefficients of the Yunnan, Fujian, Shaanxi, and Heilongjiang provinces were 0.57, 0.43, 0.32, and 0.49, respectively. Additionally, the variable importance assessment using a random forest model also indicated that SIFyield is more sensitive to forest droughts. We concluded that SIFyield is an effective tool for monitoring forest drought stress in various regions of China and that it can provide a scientific basis for forest drought monitoring.

Numerical study of mechanical clamps crack arresting efficiency in temporary repair solutions for cracked marine pipelines

ABSTRACT In this study, a typical gas pipeline exposed to environmental conditions is modeled through the finite element method to investigate the fracture response of the cracked pipeline and compare various mechanical clamps crack arresting efficiency. Comparing numerical simulation results with those available analytical data reveals a good agreement. The results show that tight-fit sleeves practically arrest longitudinal cracks and stop their growth entirely, as SIF values for cracks with the inclination angle of more than 30° are entirely negative. Furthermore, it is understood that cracks with inclination angles of up to about 30° are critical to arrest. It is found that friction between the clamp and the outer surface of pipeline and also clamps’ contact length may not consider as important options for increasing the clamp efficiency, while they have insignificant effect on arresting longitudinal cracks with the inclination angle of more than 30°.

Numerical Simulation of 3-D Internal Crack Propagation in Rock under Semi-circle Bending

Semi-circle bending (SCB) test is an important test in the field of rock fracture. In order to investigate the propagation process of 3-D internal cracks under semi-circular bending, numerical simulations of SCB specimens were carried out based on the finite element method and adaptive mesh technique. The results show that the numerical simulation results of this method are in good agreement with the previous laboratory test. The symmetrical loading model belongs to the pure I loading where the value of KI is positively related to the bottom load span S/R. The asymmetric loading model belongs to mix-mode loading. With the increase of unilateral load span S2/R, there is a decline and then a rise of the value of SIF at the same point at the crack tip. The S2/R is an important factor affecting the mechanical properties of rock specimens. The crack propagation path was obtained based on the maximum tensile stress (MTS) criterion. In-plane propagation of the internal crack in the symmetrically loading model leads to failure of the specimen. Wing propagation of the internal crack in the asymmetrically loading model causes the specimen to fracture into two asymmetrical parts. Quantitative analysis of the internal crack propagation of the symmetrical loading model shows that the growth rate of the lower end of the crack is the largest, and the upper end of the crack is the smallest. The above results can provide a reference for the research on the propagation of 3-D internal cracks of SCB specimens.

Using High-Frequency PAR Measurements to Assess the Quality of the SIF Derived from Continuous Field Observations

Fluctuations in illumination are one of the major sources for SIF retrieval errors during temporal continuous field measurements. In this study, we propose a method for evaluating the quality of SIF based on simultaneous measurements of photosynthetically active radiation (PAR), which are acquired using a quantum sensor at a sampling frequency higher than that obtained using spectral measurements. The proposed method is based on the coefficient of variation (known as relative standard deviation) of the high-frequency PAR during a SIF measurement to determine the quality of the SIF value. To evaluate the method, spectral and PAR data of a healthy maize canopy were collected under various illumination conditions, including clear, cloudy, and rapidly fluctuating illumination. The SIF values were retrieved by 3FLD, SFM, and SVD. The results showed that SFM and 3FLD were sensitive to illumination stability. The determination coefficients (R2) between PAR and SIF extracted by SFM and 3FLD were higher than 0.8 on clear and cloudy days and only approximately 0.48 on the day with rapidly fluctuating illumination. By removing the unqualified data using the proposed method, the R2 values of SFM and 3FLD on the day of rapidly fluctuating illumination significantly increased to 0.72. SVD was insensitive to illumination stability. The R2 values of SVD on days with clear, cloudy, and rapidly fluctuating illumination were 0.73, 0.76, and 0.61, respectively. By removing the unqualified data, the R2 values of SVD were increased to 0.66 on the day with rapidly fluctuating illumination. The results indicated that the quality assessment method based on high-frequency PAR data can eliminate the incorrect SIFs due to unstable illumination. The method can be used to extract more accurate and reliable SIF datasets from long-term field observations for the study of the relationship between SIF and vegetation photosynthesis.

Effect of Fiber Orientation Angle on Stress Intensity Factor of Composite Plate Using Extended Finite Element Method (XFEM)

This paper presents the effect of fiber orientation angle on the stress intensity factor SIF for carbon epoxy composite plates with single-edge, center, and inclined cracks of varying lengths under tensile load. The stress intensity factor and shape factor were calculated individually for each case, with nine different fiber orientation angles computed using the extended finite element method XFEM concepts. It is found the stress intensity factor increases with increasing crack lengths while the shape factor decreases. In the case of single edge cracks, the SIF increases in the average value reached (173 %) for composite plates with different fiber orientation angles, while in the case of the center crack, the average value of SIF reaches (81 %). It was observed in this study that the increases in stress intensity factor and the decreases in the shape factor with different crack lengths were more stable in the composite plate with a fiber orientation angle of 75°. The higher values of SIF at an angle of 75° are because of the high probability of fiber slippage at 75° due to induced shear stresses in addition to the tensile stresses at the fiber-matrix interface. As a result, the crack tip has a high-stress intensity factor.

Effect of ultrasonic peening treatment on the fatigue behaviors of a magnesium alloy up to very high cycle regime

• Complete change of crack initiation site. • Quantitative evaluation of grain-boundary retarding effect. • Crack type affects the formation of FGA. Ultrasonic fatigue tests are performed on a magnesium alloy with and without ultrasonic peening treatment (UPT). Surface enhancement layer leads to the complete change of crack initiation sites. However, crack initiation mechanism keeps the same and results in a single-faceted morphology at crack initiation site. Microcracks initiate as Mode II crack within the original grain, but deflect to Mode I crack outside of the original cracked grain. A threshold SIF value is proposed to evaluate the retarding effect of grain boundary on microcrack propagation. Outside of the original cracked grain, Mode I crack propagation below the threshold ΔK σ-th is responsible for the formation of fine granular area (FGA, a nano-grain layer). Based on the Numerous Cyclic Pressing (NCP) model, it is proposed that crack type should be another necessary condition for the formation of FGA.

Experimental study on the interaction between two cracks by digital photoelasticity method: construction of the Williams series expansion

The multi-point Williams series expansions for the near-crack-tip fields in the vicinity of two interacting cracks in an isotropic linear elastic material are experimentally and numerically determined. The experimental method used to study the interaction of two cracks is the digital photoelasticity method which is applied for determination of coefficients of the higher-order terms of the Williams series expansion for a plate of finite width with two interacting cracks. The digital image processing tool for handling of the entire set of experimental data isochromatic fringes and isoclinic phase maps obtained from the photoelasticity experiments is developed and exploited. The digital image processing tool is relied on the classical Ramesh technique but enables to scan the experimental image in any direction and to analyse the image after any number of logical operations. The realized digital image analysis allows us to extract photoelastic data from the entire field isochromatic and isoclinic fringe patterns. In the digital image processing fringe analysis, the optical data contained in the transmission photoelastic isochromatic fringe patterns in the vicinity of the crack tips are converted into text file and then the points of isochromatic fringes with minimum light intensity are used for estimating linear elastic fracture mechanics parameters. The multi-parameter stress field description with the first fifteen terms is used. The mixed mode fracture parameters, especially stress intensity factors, T-stresses and higher-order coefficients of the Williams series expansion are obtained for specimen configurations like plates with two interacting cracks using 1) the classical over-deterministic method in the form based on the stress field and 2) the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for minimization of the objective function. It is demonstrated that the BFGS method has indisputable advantages over the classical over-deterministic method. The significance of higher-order terms in the Williams expansion is proved for the considered cracked specimen. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values, T-stresses and higher-order coefficients estimated using the proposed method are compared with finite element analysis (FEA) results, and are found to be in good agreement. This verifies the experimental analysis

Computational and experimental identification of coefficients of the Williams series expansion by considering higher order terms in the cracked specimens through digital image analysis

In the study, digital photoelasticity method is used for finding of the linear elastic fracture mechanics parameters for a plate of finite width with two inclined interacting cracks. The digital image processing tool for the whole set of experimental data namely isochromatic fringes and isoclinic phase maps obtained from the photoelasticity experiments is developed and exploited. The digital image processing tool is based on the well-known Ramesh technique but allows us to scan the image in any direction and to analyse the image after any number of logical operations. The performed digital image analysis allows us to extract photoelastic data from the whole field isochromatic and isoclinic fringe patterns. In the digital image processing fringe analysis, the optical data contained in the transmission photoelastic isochromatic fringe patterns near the crack tips were converted into text file and then the points of isochromatic fringes with minimum light intensity were used for evaluating fracture mechanics parameters. The multi-point stress field description is used. The mixed mode fracture parameters, especially stress intensity factors, T-stresses and higher-order coefficients of the Williams series expansion are obtained for specimen configurations like plates with two inclined interacting cracks using 1) the algorithm based on the classical over-deterministic method and 2) the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for minimization of the objective function. It is shown that the latter method has undeniable advantages over the classical over-deterministic method. The effects of higher-order terms in the Williams expansion were analysed for different the considered cracked specimen. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values, T-stresses and higher-order coefficients estimated using the proposed method are compared with finite element analysis (FEA) results, and are found to be in good agreement.

Mechanics of multilayered or functionally graded material pressed onto an imperfect rigid base with a circular opening by localized surface loading

Loaded materials constrained by imperfect boundary can be found in many engineering scenarios, including blanking process, contact pressure sensor and soil/rock foundation subjected to underground mining. This paper examines the surface loading problem of a multilayered or functionally graded material (FGM) resting on an imperfect rigid smooth base weakened by a circular opening. The surface loading is axisymmetric and coaxial with the circular opening. This mixed boundary value problem is analogous to a Mode-I penny-shaped crack in multilayered elastic medium. With the aid of the GKS-based method for N-layered elasticity, the problem is formulated as a system of dual integral equations and then reduced to a Fredholm integral equation of the second kind. Solutions of the SIF, COD and full elastic field are expressed in terms of the solution of the integral equation. Numerical results obtained from the present solutions are compared with the those from finite element method. Using the new solutions, numerical studies are also conducted for four examples, including a homogenous layer, a multilayered material, a material with FGM coating and an asphalt pavement structure with FGM properties. These numerical results demonstrate that (1) a small size of surface loading can result in high SIF value at the crack tip; (2) placing the hard layer as the top surface is most effective for reducing ground settlement; (3) the gradation in Poisson’s ratio can have non-negligible effect on the SIF for thin FGM coating; (4) effect of the circular opening to the ground settlement can be significant if its radius is comparable to the total thickness of the upper layers.

Land cover change alters seasonal photosynthetic activity and transpiration of Amazon forest and Cerrado

Tropical vegetation influences local, regional, and global climates, largely through its relationship with the atmosphere, including seasonal patterns of photosynthesis and transpiration. Removal and replacement of natural vegetation can alter both of these processes. In the Amazon, land use/land cover change (LULCC; e.g. deforestation) started decades ago and is expected to continue, with potentially strong effects on climate. However, long-term data on tropical photosynthetic activity and transpiration are scarce, limiting our ability to estimate large-scale effects of LULCC. Here, we use remote sensing data to analyze the impact of LULCC on seasonal patterns of photosynthetic activity and transpiration in the southern Amazon. This region, naturally dominated by forest and Cerrado, has seen high rates of LULCC. Within each of these two ecosystems, we compare estimates of photosynthetic activity (from GOME-2 and GOSIF solar induced fluorescence, SIF) and transpiration (from the Global Land Evaporation Amsterdam Model, GLEAM) in paired sites with high and low rates of LULCC. In forest-dominated regions, deforestation has reduced photosynthetic activity and transpiration, particularly during the dry season, and replaced dry season greening with dry season browning. The SIF datasets disagree on wet season responses; SIF increases with deforestation according to GOME-2, but decreases according to GOSIF. In Cerrado-dominated areas, LULCC has increased photosynthetic activity during the wet season. In both ecosystems, LULCC has resulted in a higher seasonal or annual range of photosynthetic activity levels. The observed effects are often stronger in regions with more extensive LULCC. We found large differences between the two SIF products in both forest- and Cerrado-dominated pixels, with GOME-2 consistently providing higher maximum SIF values. These discrepancies merit further consideration. This analysis broadly characterizes the effects of LULCC on photosynthetic activity and transpiration in this region, and can be used to validate model representations of these effects.

Study the effect of perforation type for plate with central crack on the stress intensity factor using the XFEM

n this study, loading was carried out for several types of perforated plates, such as circular, rhombic and rectangular holes, where the holes were arranged in two types, namely straight arrangement and alternating arrangement. The stress intensity factor and shape factor were calculated for each case, taking into account the diameter of the holes. So, it is found the SIF increases significantly when the plate is perforated, and the same applies to the shape factor, also increases. In the case of circular holes, the increases in the average value of (SIF) reached to (80.88 %) when the plate was perforated with alternated arranged of circular holes, while the straight arrangement of circular holes the increases of average values of SIF reach to (67.55 %). Either in the case of rhombus holes: the SIF values are increases to (51.07 %) when the plate was perforated with the alternated arrangement, while in the straight arrangement of holes the (SIF) increase to (35.43 %). It was observed through this study, the increases of stress intensity factor and the shape factor with different crack lengths were more stable in the plate that perforated with an alternated arrangement of holes than the straight arrangement. The higher values of stress intensity factor obtained when the plates were perforated with circular holes, due to the circular shape has more stiffness, so the Absorption of force will be small Compared with the rhombus and rectangular shape that will be less stiffness which the absorption of strength is greater.

Extended Meshfree Approach for Crack Statistical Analysis of Anisotropic Functionally Graded Brazilian Disc Subjected to Traction Load

An extended meshless method that relying upon Galerkin formulation is applied on the crack analysis of orthotropic functionally graded Brazilian disc. Weak form is involved to solve the governing equation in the numerical method. In addition, enrichment terms and sub-triangle techniques are applied to improve the accuracy of relevant results. This paper depicts the influence of variation in the crack stretch and non-homogeneity parameters on the values of stress intensity factors using a developed MATLAB program. In the isotropic case, it is clear that when the length of crack increases, SIF increases. Graduation in has more effect in increasing the values of SIF in corresponding increased crack length. The verification has been checked by changing the range of the J-integral domain and variation of the support domain.

Numerical Analysis of Mode I Fracture Toughness for Plain Concrete Beams

Fracture mechanics is based on the assumption that all engineering materials contain cracks from which failure starts. Structures have sizeable existing cracks that might or might not grow, depending on the load level. when a material has an existing crack, that lead to high stresses near the crack tip. Stress field type in the region of the crack tip can be defined of mode I, where two fracture surfaces are displaced perpendicular to each other in opposite direction where crack growth takes place. The crack tip stress and displacement field can be uniquely characterized by the stress intensity factor, SIF, It is neither the magnitude of stress nor strain, but it is a unique parameter that describes the effect of loading at the crack tip region and the resistance of the material. Stress intensity filed is valid for a small region around the crack tip. It depends on both the values of stress and crack size. In the present work, numerical models were designed to study the effect of specimen thickness, crack-depth ratios and concrete compressive strengths on the behavior of SIF for concrete beams. Nine beams were idealized with dimensions of 1500 mm length, 400 mm depth and different thickness 120, 250 and 400 mm. The crack-depth ratios were 0.1, 0.2 and 0.3 and the concrete compressive strengths were 25, 40 and 55 MPa. The results proved that there is a decrease in SIF with increase in specimen thickness. On the other hand; there is an increase in SIF values with increase in concrete compressive strength and crack-depth ratio.

The effect of crack length on SIF and elastic COD for elbow with circumferential through wall crack

Many damages due to flow-accelerated corrosion and cracking have been observed during recent in-service inspections of nuclear power plants. To determine the operability or repair for damaged pipes, an integrity evaluation related to the damaged piping system should be performed by using already proven code and standards. One of them, the ASME Code Case is most popularly used to integrity assessment in nuclear power plants. However, the recent version of CC N-513 still recommends the simplified method which means a damaged elbow is assumed as an equivalent straight pipe. In addition, to enhance the accuracy integrity assessment in elbow, several previous studies recommend that the SIF and elastic COD values for an elbow with relatively large crack could be predicted by an interpolation technique. However, those estimates for elbow with relatively large crack might be derived to inaccurate results for crack growth analysis, such as for the allowable crack size and life estimation. Therefore, in this paper, the effect of crack length (0.3≤θ1/π ≤ 0.5) on SIF and elastic COD for elbow is systematically investigated. Then, for large crack in elbow, accurate estimates for SIF and elastic COD, which are widely used to assess the integrity of elbows, are proposed. Those proposed solutions are expected to be the technical basis for revisions of CC N-513-4 through the validation.