The CODs of each analytical case are shown in Table 3. The plate length has the largest effect on the COD, and the minimum mesh size at the crack front is the second. However, the effects of the node pitch or the number of mesh in the thickness on the COD are very little. The effect of plate length increases with the crack length, and that effect is larger in the membrane stress case than the bending stress case. Compared with the plate length, the effect of the minimum mesh size at the crack front is very small. In order to evaluate the effect of the plate length, the analyses for two crack length cases (a/W=0.05, 0.8) which have the parameters H/W=0.5 to 3.0 were carried out. The CODs of these cases are shown in Table 4. When H/W is 2.0 or more, the COD hardly changes in all cases. From these results, it can be deduced that the plate whose H/W is 2.0 or more satisfies an infinite plate condition on the FEM analysis. Consequently, the conditions for specific analyses were decided as shown in Table 5.
compare closely to a single curve as shown in Figure 7. From this behaviour it is evident that an elastic-plastic value of COA could be obtained, for a mis-match case of a particular crack geometry and loading, by means of obtaining an elastic value of COA and then using an assessment diagram of the form shown in Figure 7. This is of course is only applicable to the material mis-match, geometry and loading cases investigated to date. If such a method can be shown to be universally applicable, this could lead the way for elastic-plastic values of crack opening area to be obtained for the same mis- match case of a particular crack geometry and loading, without carrying out any detailed finite element analysis. It is noted that the use of analytical expressions for the ratio of elastic-plastic to elastic centre crack opening displacement and hence, with an assumption on the crack shape, the COA has also been suggested by Kim and co-workers [e.g., Reference 4]
This paper describes the Leak-Before-Break (LBB) assessment procedure applicable to Japan Sodium cooled Fast Reactor (JSFR) pipes made of modified 9Cr-1Mo steel. For the sodium pipes of JSFR, the continuous leak monitoring will be adopted as an alternative to a volumetric test of the weld joints under conditions that satisfy LBB. Firstly, a LBB assessment flowchart eliminating uncertainty resulted from small scale leakage, such as self plugging phenomenon and influence of crack surface roughness on leak rate, was proposed. Secondly, a rational unstable fracture assessment technique, taking the compliance changing with crack extension into account, was also proposed. Thirdly, a Crack Opening Displacement (COD) assessment technique was developed, because COD assessment method applicable to JSFR pipes - thin wall and small work hardening material - had not been proposed yet. In addition, fracture toughness tests were performed using compact tension (CT) specimens to obtain the fracture toughness, J IC , and the crack growth resistance (J-R) curve at elevated temperature. Finally, by using the flowchart,
Abstract. Static experiments are performed to confirm the COD method that is the only method to measure the energy release rate of fast propagating cracks just after bifurcation. The crack opening displacement (COD) of the mother cracks of bifurcated cracks is measured in static condition by Moiré interferometry. Thin notches are used instead of cracks. The bifurcation angle is 13.5 degrees that is the same as the angle of bifurcation of fast propagating cracks in PMMA. The measured CODs are proportional to the square root of the distance from the nominal tip of the mother notch. Stress intensity factor of the bifurcated notch is obtained from the measured CODs through the formula of the COD of single cracks. The experimental results say that the stress intensity factor of a bifurcated crack has the same value as that of the single crack whose length is the same as that of the bifurcated crack. This is caused by the small bifurcation angle of 13.5 degrees. It is concluded that the COD method is correct to measure the energy release rate of rapidly bifurcating cracks.
Effect of Restraint of Pressure Induced Bending on LBB – In Test Case 1 (Table 1), the role of the restraint of pressure induced bending on the crack-opening displacements and associated leakage through-wall crack size for an LBB analysis was assessed. For this assessment, actual data from an LBB submittal for a surge line in a PWR was used. The exact location under consideration was the weld joint where the surge line joined to the pressurizer. For this comparative analysis, a baseline analysis was first conducted where the effect of restraint of pressure induced bending was not considered. Using the SQUIRT4 (Seepage Quantification of Upsets In Reactor Tubes) module in the Windows® version of SQUIRT (Windows Version 1.1), the leakage crack length and associated crack opening displacement were calculated. For the unrestrained condition, the leakage crack length was 204 mm (8.03 inches) and the associated COD was 0.549 mm (0.02163 inches). Next, the equations in Reference 2 were used to calculate the r cod values 2 for both the symmetric and asymmetric restraint cases. For both cases, the
The vibration behavior of an atomic force microscope [AFM] cantilever with a crack during the nanomachining process is studied. The cantilever is divided into two segments by the crack, and a rotational spring is used to simulate the crack. The two individual governing equations of transverse vibration for the cracked cantilever can be expressed. However, the corresponding boundary conditions are coupled because of the crack interaction.
results of the finite element analysis. The convergence test result is done based on the 50 kN concentrated static load at the mid span of the girder as shown in Fig. 6. It is observed from the convergence test that the optimum results are obtained in-between the elements 13600 and 16600. The difference of the displacement values within the element range 13600 to16600 is very diminutive. So, in the present study, the total number of element that is considered in each model of crack and un-crack girder for numerical analysis is around 14500 elements. Fig. 7 shows that the value of principal stress and vone-misses stress for the uncrack condition of the girder are same. However, the principal stresses at crack condition of the girder is higher than that of the vone-misses stress. The vone-misses stress is an equivalent stress of the principal stresses (σ 1, σ 2 and σ 3 ). It is
The newts were placed on a moistened tissue in a Plexiglas enclosure mounted on the experimental table of the X-ray setup. For the preliminary experiments performed at the University of Antwerp, we used a Tridoros-Optimatic 880 X-ray apparatus (Siemens, Erlangen, Germany); for the experiments at the University of Jena, a custom-build biplanar Neurostar setup (Siemens, Erlangen, Germany) was used. After acclimation, newts were fed maggots (29.8±5.1 mg, mean±s.d.) and in order to visualize the maggots in X-ray recordings, we glued small tantalum markers (diameter of 0.5 mm) to their cuticle. In total, 50 feeding events were recorded from which 106 processing cycles were extracted for statistical analyses described below (10, 21, 22, 24, 29 cycles for individuals 1 – 5, respectively). X-ray recordings were taken from the laterolateral and dorsoventral projections at 40 kV and 53 mA with a sampling frequency of 250 Hz. The dorsoventral recordings were performed to determine lateral movements of tongue and jaw systems during processing, but as no clear lateral movements were measured, they were excluded from further analyses. However, the dorsoventral image plane was used for the X-ROMM analyses (see below). Next, the resulting raw video recordings were filtered (e.g. gamma correction, contrast, sharpness) and the horizontal (x-axis) and vertical (y-axis) coordinates of previously defined landmarks (Fig. 1) were tracked frame by frame using SimiMotion software (SimiMotion Systems, Unterschleißheim, Germany). The 2D displacement of the landmarks was used to calculate the following movements: (1) jaw movements: angular displacement of the upper and lower jaw at the point ‘ occipital ’ ( jaw joint was not always visible in the X-ray movies so jaw displacement was measured at the point ‘ occipital ’ ) (Fig. 1A); (2) head rotation: angular displacement between the two linear slopes connecting (i) the points ‘ occipital ’ and ‘ snout tip ’ and (ii) the points ‘ first vertebra ’ and ‘ fifth vertebra ’ (Fig. 1B); (3) longitudinal tongue movement: horizontal (i.e. parallel to the linear slope connecting the points ‘ occipital ’ and ‘ snout tip ’ ) displacement of the tongue relative to the point ‘ occipital ’ ; (4) vertical tongue movement: vertical displacement of the tongue relative to the linear slope connecting the points ‘ occipital ’ and ‘ snout tip ’ ; (5) longitudinal transport of the prey: horizontal (i.e. parallel to the linear slope connecting the points ‘ occipital ’ and ‘ snout tip ’ ) displacement of the prey relative to the point ‘ occipital ’ ; (6) vertical movement of the prey: displacement of the point ‘ prey ’ relative to the linear slope connecting the points ‘ occipital ’ and ‘ snout tip ’ (Fig. 1C).
12 Read more
An interesting ﬁnding which emerged incidentally from this work is that in the multiscale (i.e. dual) models in which toughening occurred at two very di ﬀ erent scales (Figs. 4, 5 and 6a), only the macro scale contributed signi ﬁ cantly to the long-crack toughness. Microscopic features, whether barriers or ligaments, had a negligible e ﬀ ect on the strength of specimens with long initial cracks. The crucial role of the microscopic mechanism in those cases was to raise the performance of the short cracks and thus eﬀectively increase the plain-specimen strength of the material, which in both the ligament and barrier models was increased by about a factor of three compared to the strength of the macro material alone. This was of course due to the particular material constants chosen for these models. So for example the critical K value for the macro barrier was chosen to be larger than that for the micro barrier. However, if we had chosen to make the two critical K values equal, or make the micro one larger, then the macro toughening mechanism would have had no e ﬀ ect at all. Likewise if the macro mechanism were to give a relatively large strength as well as toughness, it will dominate for all crack lengths: this was seen in the ﬁnal combination studied (see Fig. 6b and Table 2). Given that L corresponds to the mid-point of the curve (as shown in Fig. 1a), the macro curve will always be shifted to higher length values than the micro one. The case of the model having micro barriers and macro ligaments (Fig. 6a) is also interesting for another reason. Here, when a long crack was present, the macro ligaments created a large process zone whilst the role of the micro barriers was eﬀectively to increase the material toughness parameter of the material between the ligaments from K m = 0.5 to 1.0. This doubling of the small-scale
12 Read more
Stress intensity factor (SIF) is successfully used to characterize the cracks in elastic materials and structures . It is also used to replace the concept of stress concentration factor leading to infinite stress especially when there is a sharp edge for example cracks. There are several other methods or techniques are used to investigate the defects and it can be found in . On the other hand, the basic crack configurations are also available in . However, the oblique or slanted cracks are rarely found in open literature [3-6]. In  present a closed form solution for the geometrical correction factors of slanted cracks in a plain stress plate. The closed form solution of SIFs comprised of three important parameters such as inclination angles, plate widths and crack lengths. They claimed that the results from such expression are well agreed with the analytical, numerical and experimental results.
The fracture toughness resistance (R) curve, such as the J-integral-resistance (J-R) or crack-tip opening displacement-resistance (CTOD-R) curve, is generally obtained from the small-scale fracture test specimens such as the single-edge notched three-point bend (SE(3PB) or SE(B)) and compact tension (C(T)) specimens. The test procedures for such specimens have been standardized in standards such as ASTM E1820-13 (ASTM, 2013), BS7448-4 (BSI, 1997) and ISO 12135 (ISO, 2002). Testing on the plane-sided (PS) SE(B) and C(T) specimens made of homogeneous materials generally leads to a curved crack front caused by the difference in the states of stress along the crack front (Shih et al., 1977; Anderson, 2005). The side-grooved (SG) specimens are used in the R-curve testing to achieve relatively straight crack fronts. Figure 6.1 schematically shows the configurations of a side groove in a typical SE(B) or C(T) specimen. As illustrated in the figure, one groove is machined into each lateral side of the specimen. The side groove has a depth (d sg ), a root radius (r sg ) and a machined angle ( sg ). The specimen has a gross thickness
244 Read more
The effect of large strength differences (mismatching) along the crack front in the thick ness direction may also play a role in low tough ness results. The highly overmatched repair weld metal (Re = 630 MPa) protects the crack tip por tion which samples the repair weld metal from applied deformation and hence forces the other part of the crack front neigbouring the low strength base metal (Re = 388 MPa) to accommodate the applied deformation. This asymmetric strength distribution along the crack front of the position 4a and 4b specimens can enhance the attainment of the critical stress for cleavage crack initiation at the ICCGHAZ region of the original SAW weld metal. Due to this negative effect of the over matching repair weld metal, the shallow cracked specimens (notch position 4b) also showed low CTOD results, despite their lower crack tip con straint (if one considers the crack depth only).
12 Read more
standard specimen dimensions and η = 2 for 3PB specimens and H is a power law function. In this study, this has been applied for cleavage fracture. The constants in the Key-Curve expression were obtained by fitting the load– displacement pairs between yield point and peak load preceding cleavage fracture and used to obtain crack arrest length. The results were validated by comparing with final crack length measured optically on unbroken specimens of 15% cold worked material aged for 650°C/5000h.
The strategy for increasing the number and modifying the location of the re- turn air inlets was to use three return air inlets and modify the location to an appropriate distance to the ventilation opening and fan as well as the areas prone to forming dead zones. Figure 6 indicates that some areas remain with low air velocity resulting dead zones. Figure 6(e) shows that the airflow was restricted by interior furnishings and thus could not fully move around the entire space after increasing and modifying the return air inlets. Nonetheless, the original short circuit was improved by changing the position of the return air inlets.
13 Read more
At this position in the r direction, the measurement points were determined directly below the crack surface (0.1 mm), at 2 mm, and at 4 mm in the d direction. The EBSD observation was conducted with 0.2 µm step size in the 87 µm square area for each measurement point. The inverse pole ﬁ gure (IPF) maps and the kernel average misorientation (KAM) maps are shown in Figs. 18 23. The KAM value represents the difference of crystal orientation which is calculated by the average misorientation between a point and its neighbors.
10 Read more
It has become apparent that 1) the presence of short-duration high-frequency signals (call them pulses) can be indicative of damage, 2) some types of damage result in the generation of a new high-frequency source mechanism in the structure, and 3) the response of a structure is consistent between trials when a similar source mechanism is applied at the same location. Information about repeating pulses present in the acceleration time series has potential use for damage detection. A schematic of the idea is illustrated in Figure 3.11. The basic idea is to compare pulses observed in the acceleration time series when the structure is in a potentially damaged state to pulses observed when the structure was known to be in an undamaged state. By comparing the pulses in these two situations, a change in this type of high-frequency dynamic behavior of the structure can be identified. The approximate location of the damage source can be determined from the arrival times and amplitudes of the pulses. These regions can be analyzed in the context of potential nearby sources of high- frequency excitation, including the possibility of damage. Pulses can be generated by various mechanisms related to damage, including acoustic emission generated by the propagation of a crack tip, elastic waves generated by mechanical impact of loose parts, or multi-modal traveling waves that can occur during the dynamic loading of flexible structural members such as the propagation of a flexural wave through a beam. Pulses can also be generated by environmental mechanisms, such as a car driving over a bump on a bridge, the collapse of a bookshelf during an earthquake, or an impact hammer. Hence, it is preferable to have a baseline recording to which possible damage features can be compared.
232 Read more
Cyclic de Mattia tests were performed using single specimens (testing machine 1) and multiple specimen (testing machine 2). The tests were stopped and the crack was identified and classified by visual observation. The results of these tests are shown in figure 6. A relatively high data scatter, in the range of a half decade was observed. To improve the quality and applicability of the de Mattia tests two novel methods are proposed. While method 1 uses the results of the full-field strain measurements, the crack growth kinetics is determined by an image data acquisition system in method 2.
A non-linear finite element analysis was performed using the WARP3D (Gullerud et al., 2001) code. The material was assumed to follow the Ramberg-Osgood relation. The constants used for the above relation are given in paragraph 5 above. Monotonic incremental in-plane closing load was applied as mentioned above. The load line displacement at the end of the extended straight pipe and the applied moment are used to generate the load-load line displacement curve. From this curve, the limit load is evaluated. The limit load mentioned herein is obtained by using the double slope of linear response method (twice elastic slope method). This is evaluated by drawing a line at a slope two times that of the elastic portion of the load-load line displacement curve, as shown in Fig. 3. The load with load-line displacement is plotted in a graph and the limit load was evaluated. Fig. 4 shows the variation of the load-line displacement with applied load for this elbow. From this graph, the limit load evaluated from the finite element results as per the twice-elastic slope method is 1452.03 KN. The limit load predicted experimentally gives 1463 KN. The result shows excellent agreement for the limit load with an error of 0.75%. Fig. 4 also shows the comparison of the load-line displacement with applied load for both experiment and the finite element prediction. It can be seen form the graph the load-line displacement of the finite element analysis agrees very well with the experimental results.
When a crack propagates in any material, a concentration of strain appears ahead of the crack tip, extending the FPZ. For plastic materials, the nonlinear zone is dominated mainly by plastic deformation until failure; however, for quasi-brittle materials such as concrete, only a small amount of plastic strain can be sustained before failure. As was mentioned previously, the nonlinear zone of concrete consists of a narrow band of damaged material with micro cracks and zones bridged by aggregates; therefore, LEFM is unsuitable for analysing the behaviour of concrete structures. The current state-of-the- art in fracture mechanics includes a wide variety of models to simulate concrete behaviour. The Dugdale and Barenblatt concept was used by Hillerborg (1976), who proposed the fictitious or cohesive crack model (FCM or CCM) for quasi-brittle materials such as concrete. In this model, it is assumed that prior to crack initiation, the material exhibits linear elastic behaviour. After crack initiation, stresses may be transmitted across the crack; hence, the crack is termed a “fictitious crack”. The crack-bridging stresses are taken to be a function of the crack opening, and are given by the stress-crack opening ( - w) relationship. In this model a narrow band of partially broken material is idealized as a crack, a line in two dimensions or a surface in three dimensions. The softening curve ( - w) is assumed to be a material property that is independent of structural geometry and size. The FCM assumes that the initial crack propagates when the principal tensile stress reaches the tensile strength of the material, f t . The -w curve can be completely
301 Read more
In this paper, load deformation diagrams such as load–crack length and load–CMOD curves, which might be of interesting to the design engineer, can be obtained using the abovementioned experimental procedure. Crack propagation of the 25 samples of pre-stressed concrete sleeper under 3-point-bending load is tested with the Replica test and image analysis. Sleepers are with initial crack lengths of 5 mm increasing to 45 mm (10 mm steps) and initial crack widths of 8 mm. Sleeper cracks are created in the notch and both sides of it, as shown in Figure 8. In this figure, crack propagation is almost symmetric in both sides of the notch [Rezaie and Farnam, 2015]. Therefore, both crack length and CMOD are only calculated in the notch itself and one side of it.
15 Read more