The GE/EPRI[10] and Reference Stress Method (RSM)[11] offer simplified methods of approximating the **cyclic** **J**-**Integral**. However, due to the nature of these methods they exhibit considerable limitations and thus produce overly conservative results. The approximations that are made render these methods unable to assess detail along a 3D crack front. For example, the Reference Stress concept is based on the limit load analysis, and as such, the **J**-**Integral** variation is calculated with little consideration of the geometry of the specimen. This provides a greatly approximated value of the induced stress, thus reducing the accuracy of the calculation of the **J**-**Integral**. In addition, this method cannot provide three dimensional detail of a crack and so monitoring the crack front variation of the stress intensity factor and **J**-**Integral** is not possible. This introduces a major issue with this technique since any variation in crack parameters could be overlooked and hence fail to provide valuable information regarding crack initiation and thus, fatigue life. For this reason, these methods are not considered appropriate for complex 3D industrial applications.

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This paper investigates an approach for calculating the **cyclic** **J**-**Integral** through a new industrial application. A previously proposed method is investigated further with the extension of this technique through a new application of a practical 3D notched component containing a semi-elliptical surface crack. Current methods of calculating the **cyclic** **J**-**Integral** are identified and their limitations discussed. A modified monotonic loading concept is adapted to calculate the **cyclic** **J**-**integral** of this 3D Semi Elliptical Surface Crack under **cyclic** loading conditions. Both the finite element method (FEM) and the Extended Finite Element Method (XFEM) are discussed as possible methods of calculating the **cyclic** **J**-**Integral** in this investigation. Different loading conditions including uniaxial tension and out of plane shear are applied, and the relationships between the applied loads and the **cyclic** **J**-**integral** are established. In addition, the variations of the **cyclic** **J**-**integral** along the crack front are investigated. This allows the critical load that can be applied before crack propagation occurs to be determined as well as the identification of the critical crack direction once propagation does occur.

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Recently, the submodeling technique has often been used in the FE numerical analysis to study in detail an area of interest in a model. Herein, the area of interest is the region of high stress caused by the individual crack as shown in Fig.2b. The main idea of the submodeling technique is to perform a global-local transition. This approach gives an opportunity to make a local mesh refinement, since as the submodel region has a finer mesh, a submodel can provide an accurate, detailed solution. Besides better accuracy, another advantage is that one can avoid the other high stress fields caused by other stress risers, i.e., boundary conditions. In order to investigate the dependence of the **cyclic** **J**-**integral** results on the submodel size, five different submodel

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Recently, the submodeling technique has often been used in the FE numerical analysis to study in detail an area of interest in a model. Herein, the area of interest is the region of high stress caused by the individual crack as shown in Fig.2b. The main idea of the submodeling technique is to perform a global-local transition. This approach gives an opportunity to make a local mesh refinement, since as the submodel region has a finer mesh, a submodel can provide an accurate, detailed solution. Besides better accuracy, another advantage is that one can avoid the other high stress fields caused by other stress risers, i.e., boundary conditions. In order to investigate the dependence of the **cyclic** **J**-**integral** results on the submodel size, five different submodel size ratios are considered in this study, which are A sub1 /A Global =0.015, 0.05, 0.13, 0.24, 1.0.

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In this paper, 3D simulation of the fatigue crack growth process was performed in a simple riveted lap joint and the crack growth profiles were predicted. Then, the fracture mechanics- based life prediction of the riveted lap joint was considered using EIFS concept. Back extrapolation method was used for estimating EIFS by the aid of both **cyclic** stress intensity factor (ΔK) and **cyclic** **J** **integral** (ΔJ). Then, the results were compared.

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In the case of uncertainty or error in the material law, for instance when the measurements are made within the plastic zone, both direct and indirect techniques ex- perience issues. In the direct approach, measured strains are correct as they are derived from the displacement field but the calculated stresses would be erroneous. In the indirect-FE case, both strains and stresses in the FE regions are affected by the material law as they are determined from the displacement boundary conditions. However, they would be self-consistent with the im- posed material law and therefore would allow calcula- tion of a contour independent **J**-**integral** value. It is therefore important to correctly define the material law to obtain meaningful strain energy release rate values for indirect-FE calculation of the **J**-**integral**. Field fitting suffers the same problem, but with the additional draw- back that analytic solutions only exist for a limited number of material laws. The indirect-FE method dem- onstrated in this work can utilise any material law than can be described in the finite element simulation soft- ware Abaqus.

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This study presents two approached which are finite element and analytical methods. Due to lack of **J**- **integral** solution available especially in obtaining h- function for surface crack in round bars. Therefore, ANSYS finite element method is utilized. On the other hand, a mathematical model to predict **J**-**integral** for surface crack is developed which is based on the reference stress approach. According to the present results, it is found that **J**-**integral** along the crack front can be estimated for various types of cracks. However, the **J**-**integral** prediction is successfully conducted except for the elastic-dominated region.

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the 3D cases. By these experimental and numerical studies, the **J**-**integral** calculation confirms a presence of 3D effects surrounding the tip, as observed by out-of-plane displacement measurements, or numerical stress fields. For r<2 mm, the surface measurements are not sufficient to estimate the energy release rate G and consequently it is necessary to have a 3D measurement on the bulk of cracked specimen.

Material fracture toughness based on **J**-**integral** versus crack-extension relationship (**J**-R curve) is investigated with direct current potential drop (DCPD) technique and compared with results from elastic unloading compliance (EUC) or normalization technique. The test matrix covered four different materials, half inch thickness and one inch thickness compact tension (C(T))specimens, and temperatures ranging from 24 °C to 600 °C. The original **J**-R curves from DCPD yielded much smaller Jq value than EUC or normalization results due to the influence of plastic deformation on potential drop. To counter this effect, two new methods for adjusting DCPD data have been proposed. After adjustment, the average difference in Jq between DCPD and EUC or normalization results is only about 8% whereas the difference in tearing modulus is about 17%. The promising results prove the applicability of DCPD for **J**-R curve determination for C(T) specimens especially in extreme environments, such as elevated temperatures, where conventional EUC method faces considerable challenges.

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Using figure 8, which gives the relation between CMOD and the J-Integral, the predicted value of J for fracture initiation is given by 133 kJ/mL Table II shows [r]

At the moment there is no existing standard for the fracture resistance testing of multi-metallic com- ponents or specimens that are made up of different material sections joined together via a weld. Existing standards for fracture resistance testing like ASTM E1820-13 ASTM (2013), ISO 12135:2002 ISO (2002) and engineering procedures or schemes like DNV DNV (2006) for the estimation of **J**-**integral** values are intended for specimens made of homogeneous material only. Thus in early 2012 a group of 11 European or- ganisations started a R&D project MULTIMETAL MULTIMETAL (2012) with the aim of filling the above gaps. The objectives of the project are the development of a standard for fracture resistance testing of multi- metallic specimens and the development of harmonized procedures for dissimilar metal welds (DMWs) brittle and ductile integrity assessment. DMWs are typically present in safe-ends of LWRs primary circuits. The underlying aim of MULTIMETAL is to provide recommendations for a good practice approach for the integrity assessment of DMWs as part of overall integrity analyses and leak-before-break (LBB) proce- dures. The project was funded by the European Commission (EC) within its 7 th Framework Program and concluded in January 2015. This paper presents a sensitivity analysis of the influential modelling parame- ters for the SEN(B) and SEN(T) specimens containing various DMW material zones that were used within the numerical benchmark: ’Numerical Analyses of DMW Behaviour‘. Sensitivity to the **J**-**integral** and η pl

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DRAGOMIR, A Gr¨ uss type integral inequality for mappings of r-H¨ older’s type and applications for trapezoid formula, Tamkang J.. DRAGOMIR, Some integral inequalities of Gr¨ uss type, I[r]

As part of a strategy by the University of Southampton to further investigate the occuring soil pressures, Xu [2005] carried out radial controlled triaxial tests of granular material under **cyclic** loading. The applied strain and stress path used represented that typically experienced by an element of retained material behind an **integral** bridge abutment. This was the first time that the fundamental behaviour had been investigated in this way.

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Twenty-noded solid elements with 3 × 3 × 3 integration order are used to model the elbow. Because of symmetry, only one fourth of the elbow is modeled. There are total 528 elements and 3221 nodes for elbows with extrados crack. Spider web type mesh has been employed near the crack tip for mesh economy. Eight numbers of radial and circumferential divisions have been employed at the spider web with two elements across the thickness of elbow. A very small hole of radius 0.5% of crack length has been introduced at crack tip in the finite element model for faster convergence without much change of results. This was recommended by Kumar et al (1983). Figure 5 shows a typical finite element mesh. The same mesh pattern is used for all the cases. A mesh convergence study has been performed to check the adequacy of this mesh (Fig.6). Additionally, the reasonable path independence of **J**-**integral** also confirms the adequacy of the finite element mesh.

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The **J** -**integral** solution was derived to determine elastic fracture toughness for ductile metal plates with inclined surface cracks under biaxial loading. The derived elastic fracture toughness is a function of plate and crack geometry, strain-hardening coefficient, yield strength, fracture toughness, biaxiality ratio, and inclination angle. Parametric studies have shown that an increase in yield strength or relative crack depth, or a decrease in Mode-I fracture toughness, leads to greater relative elastic fracture toughness. It has also been shown that the effect of biaxiality ratio and inclina- tion angle on elastic fracture toughness is highly dependent on total fracture toughness values, which highlights the need for accurate experimental determination of total fracture toughness taking into account the effect of biaxial and mixed-mode loadings. It can be concluded that the developed elastic fracture toughness model en- ables engineers and asset managers to accurately predict fracture failure of ductile thin metal structures with inclined cracks under biaxial loading.

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Jiang, J., Liu, W., Wang, H.: Positive solutions for higher order nonlocal fractional diﬀerential equation with integral boundary conditions. Mao, J., Zhao, Z., Wang, C.: The exact itera[r]

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Partial transmit sequences is one of the best method to reduce the PAPR in OFDM. Therefore, the OFDM signal is divide into number of sub blocks and then phase rotated sub blocks are added to generate the candidate signals. In this paper we implemented **cyclic** shift sequence evolved in PTS method in this method how to reduce the PAPR in OFDM sequences by selecting good SV Set values by considering the autocorrelation functions.

Partial transmit sequences is one of the best method to reduce the PAPR in OFDM. Therefore the OFDM signal is divide into number of sub blocks and then phase rotated sub blocks are added to generate the candidate signals. In this paper we implemented **cyclic** shift sequence evolved in PTS method in this method how to reduce the PAPR in OFDM sequences by selecting good SV Set values by considering the autocorrelation functions.

The **J**-**integral** approach provides several advantages for the calculation of the stress intensity factor. For example, the approach does not necessarily require refining the mesh and using the singular type of elements around the crack tip. It also allows for an easy implementation in the numerical scheme especially in FEA and gives more accurate results than other approaches using the near-tip displacement/stress field. It is added that no quarter-point crack tip element is used in the local cracked model, as shown in Figure 4.

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Daud, J-Integral analysis of surface cracks in round bars under tension loadings, Applied Mechanics and Materials, 52-54 2011 37-42..[r]