It has been known that plasticity increases fracture toughness. The underlying mechanism is that yielding caused by plasticity eases stress concentration at the crack front. Consequently, fracture toughness increases and consists of elastic and plastic portions. In order to extract elastic fracture toughness from total fracture toughness, a failure assessment diagram was employed by Yang et al. (2016, 2017) and Li et al. (2017). The adopted failure assess- ment curve (Milne et al. 1988) is independent of both geometry and material properties and may be used for any structure. However, the derived elastic fracture toughness models may be overconservative, given that the curve was derived as a lower bound of the failure assessment diagrams obtained based on reference stress (SINTAP 1999). An alternative to the failure assessment diagram is the J -integral. Based on separation of elastic and plastic displacements, the J -integral can naturally be separated into elastic and plastic components (Zhu and Joyce 2012). When the applied load reaches its critical value, the elastic J -integral corresponds to elastic frac- ture toughness. Compared with the failure assessment diagram, the J -integral is more rigorous, allowing more accurate elastic fracture toughness models to be developed.
ABSTRACT: By postulating a defect at the tubesheet junctions in a steam generator, we utilize a local model and the J-integral method for the evaluation of fast fracture risks. To this end, a 3D finite element analysis is performed for a primary chamber model subjected to the service loads. Through-the-thickness opening stresses are obtained at the locations of the postulated defects, and exported into a 2D local model where a crack is modeled. Stress intensity factors are calculated via the J-integral formulation and compared with the fracture toughness of the material. Depending on the temperature range of the service loads, both brittle and ductile tearing failures are considered. To demonstrate the proposed methodology for fast fracture analysis, the French RCC-M code is adopted. From the present study, the proposed approach is deemed efficient yet conservative, thus making it suitable for the fast fracture analysis per the regulatory code requirements.
The growing use of steel in civil, mechanical and nuclear constructions is justified by the reduction of labor time and costs due to assembly simplicity. Almost all steel structures and components are manufactured using welding processes which can introduce some defects (cracks, for instance) on the structure or component. These defects must be evaluated and controlled within allowed levels indicated by the existing codes. Crack propagation resistance of welded joints, one of the major concerns, can be assessed through fracture toughness tests. On these cases, the region next to the melted zone, denominated heat affected zone, is more sensitive to crack initiation and growth, which means that the crack propagation resistance of this region is a critical parameter to be evaluated. On this work, the crack propagation resistance of the heat affected zone of USI-SAC-50 welded joints is experimentally evaluated on the longitudinal and transversal directions with respect to the weld bead, using the Charpy impact energy and the JIntegral.
with a/b<1.0. Increasing such area produced higher bar resistance to the loading applied and then reducing J- integral along the crack front. According to literature survey (Lei, 2008), there are no solution for h-function subjected to mode III loading currently. Therefore, no validation of the present results can be conducted and it is solely dependent on the validation using elastic results such as stress intensity factors as in Fig. 5. Limit load for torsion moment: Figure 8 and 9 show the normalized limit load under torsion moment, ξ t for
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.
reference stress method to evaluate J-integral under biaxial loading was then proposed based on the above limit moment solution. The applicability of the proposed method was validated through the comparison with elastic-plastic three-dimensional finite element analysis results. The proposed method could express the effect of the tensile/compressive load parallel to the crack on J-integral.
In this present study, surface crack in round bar subjected to combined loading is analyzed and discussed. Firstly, the present model is validated with the previous model using SIFs approach since limited solutions of J- integral are available. After, J-integral is calculated along the crack front for various types of crack geometries. Considering the first part of this paper, the analytical model is developed and the predicted values of J-integral are then compared.
and 11, the presented method results agree with FE analysis well, but, SC.ENG1 cannot predict the J- integral. In another case, the applied load is assumed to be three times greater than the moment, quantitatively, the assumption of sin will no longer be valid
In this paper, reference stress solutions for plates with semi-elliptical surface cracks were firstly reviewed, and the applicability of the solutions was examined through the comparison with finite element analysis results under uniaxial loading. Next, an extended reference stress method was newly developed to evaluate J-integral for cracked plates under biaxial loading. The predictive accuracy of the method was validated through the comparison with finite element analysis results under biaxial loading.
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
14 crack front showing the node locations and numbers. Node 1 is located at the far left crack edge and Node 25 is located at the far right crack edge when facing the crack opening. These node numbers are referred to in the results in Table 1, Table 2, Fig. 18 and Fig. 19. For each node along the crack front, the ΔJ was calculated at 5 contours encircling the crack front. This is illustrated in Fig. 15. The 5 contours at each node were averaged to give a single average value at each node along the crack front. This is believed to be accurate since the J-Integral is a path independent parameter, meaning that the value is the same, regardless of the path along which it is calculated. Within ABAQUS, numerical errors due to crack tip singularities mean that the values at each contour are not exactly equal, but any differences are very small and so average values are believed to be sufficiently accurate. Values of the cyclic J-Integral at each contour path at each load are shown in Table 3 for uniaxial tension and Table 4 for out of plane shear loading. It can be seen that the first contour is slightly different to the remaining 4 contours, which have close agreement. This demonstrates the differences that occur at the crack tip due to numerical errors are very minor and so the J-Integral can be assumed to be path independent.
The extended finite element method is capable of modelling mesh independent cracking, meaning that crack initiation and propagation can be modeled without prior definition. A propagating crack does not need to adhere to element boundaries unlike the traditional finite element method (FEM). This reduces the importance of mesh refinement in the region of the crack front. XFEM can model stationary or propagating cracks, however ABAQUS is currently only capable of determining crack parameters such as SIF and J-Integral for stationary cracks. This method is still in its infancy but it shows a great deal of potential. It provides a simple method of modeling complex crack geometries without the need for extensive mesh refinement which can be very computationally expensive both in implementation and analysis. This method is capable of calculating contour integrals such as the SIF and J- Integral, however, when a high level of geometrical detail is introduced, the accuracy of contour integration close to the crack tip is compromised. For this reason, XFEM will not be used as a technique for calculating contour integrals in this investigation and traditional FEM will be used instead.
The load–displacement curves approach (5) and ASTM standard methods (7-9) are selected in this study for the cyclic loading case, since the theoretical basis appears to be the best and permits easier processing of empirical data. Thus, the elastic–plastic cyclic J-integral is expressed as the summation of elastic and fully plastic solutions for various crack geometries and loading conditions which yield the following formula for estimating the total ΔJ value :
In this work, a subsurface crack near the surface is characterized to be 3 different models, including surface crack, subclad semi-elliptical crack, and embed elliptical crack. The fracture mechanics parameters are calculated by finite element method for the 3 models with same depth under a typical pressurized thermal shock transient. The J-integrals are compared to check which model is more reasonable. The results show that J-integral at the deepest point for surface crack model is greater than the subsurface crack models. At the same time, the SIF transferred from J-integral at the deepest point for surface crack model is about twice of the subsurface cracks. From the point of view of the work in FE model and calculation, a subclad model for the flaw can be used to evaluate the structure integrity of RPV under PTS.
The Grad procedure of CASTEM software allows the displacement gradients on the nodes to be extracted. To calculate the J-integral for circular contours Γ with varying dimensions, a C++ program is written using a form of the J-integral that is expressed in terms of the displacement gradients and material constants (equation 1). In Fig. 4, the J-plots versus to (r) are made.
For the SEN(B) specimens the parameter with the largest importance (in addition to a good global finite element mesh) was the selection of finite sliding contact implementation. This is preferable over the small sliding implementation since relative sliding of the surfaces in contact is larger than the size of the finite elements in the contact area. Friction is also important and can decrease the J-integral values of up to 20 % and η pl by up to 5.8 %. Contact mesh density has almost no effect on the J-integral values but tends to
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 part of the results obtained within the numerical bench- mark: ’Numerical Analyses of DMW Behaviour‘. Within the benchmark J-integral and η pl values were